A Brief History of Time: From the Big Bang to Black Holes by Stephen Hawking (1988)

The whole history of science has been the gradual realisation that events do not happen in an arbitrary manner, but that they reflect a certain underlying order. (p.122)

This book was a publishing phenomenon when it was published in 1988. Nobody thought a book of abstruse musings about obscure theories of cosmology would sell, but it became a worldwide bestseller, selling more than 10 million copies in 20 years. It was on the London Sunday Times bestseller list for more than five years and was translated into 35 languages by 2001. So successful that Hawking went on to write seven more science books on his own, and co-author a further five.

Accessible As soon as you start reading you realise why. From the start is it written in a clear accessible way and you are soon won over to the frank, sensible, engaging tone of the author. He tells us he is going to explain things in the simplest way possible, with an absolute minimum of maths or equations (in fact, the book famously includes only one equation E = mc²).

Candour He repeatedly tells us that he’s going to explain things in the simplest possible way, and the atmosphere is lightened when Hawking – by common consent one of the great brains of our time – confesses that he has difficulty with this or that aspect of his chosen subject. (‘It is impossible to imagine a four-dimensional space. I personally find it hard enough to visualise three-dimensional space!’) We are not alone in finding it difficult!

Historical easing Also, like most of the cosmology books I’ve read, it takes a deeply historical view of the subject. He doesn’t drop you into the present state of knowledge with its many accompanying debates i.e. at the deep end. Instead he takes you back to the Greeks and slowly, slowly introduces us to their early ideas, showing why they thought what they thought, and how the ideas were slowly disproved or superseded.

A feel for scientific change So, without the reader being consciously aware of the fact, Hawking accustoms us to the basis of scientific enquiry, the fundamental idea that knowledge changes, and from two causes: from new objective observations, often the result of new technologies (like the invention of the telescope which enabled Galileo to make his observations) but more often from new ideas and theories being worked out, published and debated.

Hawking’s own contributions There’s also the non-trivial fact that, from the mid-1960s onwards, Hawking himself has made a steadily growing contribution to some of the fields he’s describing. At these points in the story, it ceases to be an objective history and turns into a first-person account of the problems as he saw them, and how he overcame them to develop new theories. It is quite exciting to look over his shoulder as he explains how and why he came up with the new ideas that made him famous. There are also hints that he might have trodden on a few people’s toes in the process, for those who like their science gossipy.

Thus it is that Hawking starts nice and slow with the ancient Greeks, with Aristotle and Ptolemy and diagrams showing the sun and other planets orbiting round the earth. Then we are introduced to Copernicus, who first suggested the planets orbit round the sun, and so on. With baby steps he takes you through the 19th century idea of the heat death of the universe, on to the discovery of the structure of the atom at the turn of the century, and then gently introduces you to Einstein’s special theory of relativity of 1905. (The special theory of relativity doesn’t take account of gravity, the general theory of relativity of 1915, does, take account of gravity).

Chapter 1 Our Picture of the Universe (pp.1-13)

Aristotle thinks earth is stationary. Calculates size of the earth. Ptolemy. Copernicus. In 1609 Galileo starts observing Jupiter using the recently invented telescope. Kepler suggests the planets move in ellipses not perfect circles. 1687 Isaac newton publishes Philosophiæ Naturalis Principia Mathematica (Mathematical Principles of Natural Philosophy) ‘probably the most important single work ever published in the physical sciences’, among many other things postulating a law of universal gravity. One implication of Newton’s theory is that the universe is vastly bigger than previously conceived.

In 1823 Heinrich Olbers posited his paradox which is, if the universe is infinite, the night sky out to be as bright as daylight because the light from infinite suns would reach us. Either it is not infinite or it has some kind of limit, possibly in time i.e. a beginning. The possible beginning or end of the universe were discussed by Immanuel Kant in his obscure work A Critique of Pure Reason  (1781). Various other figures debated variations on this theme until in 1929 Edwin Hubble made the landmark observation that, wherever you look, distant galaxies are moving away from us i.e. the universe is expanding. Working backwards from this observation led physicists to speculate that the universe was once infinitely small and infinitely dense, in a state known as a singularity, which must have exploded in an event known as the big bang.

He explains what a scientific theory is:

A theory is just a model of the universe, or a restricted part of it, and a set of rules that relate quantities in the model to observations that we make… A theory is a good theory if it satisfies two requirements: it must accurately describe a large class of observations on the basis of a model that contains only a few arbitrary elements, and it must make definite predictions about the results of future observations.

A theory is always provisional. The more evidence proving it, the stronger it gets. But it only takes one good negative observation to disprove a theory.

Today scientists describe the universe in terms of two basic partial theories – the general theory of relativity and quantum mechanics. They are the great intellectual achievements of the first half of this century.

But they are inconsistent with each other. One of the major endeavours of modern physics is to try and unite them in a quantum theory of gravity.

Chapter 2 Space and Time (pp.15-34)

Aristotle thought everything in the universe was naturally at rest. Newton disproved this with his first law – whenever a body is not acted on by any force it will keep on moving in a straight line at the same speed. Newton’s second law stats that, When a body is acted on by a force it will accelerate or change its speed at a rate that is proportional to the force. Newton’s law of gravity states that every particle attracts every other particle in the universe with a force which is directly proportional to the product of their masses and inversely proportional to the square of the distance between their centres. But like Aristotle, Newton believed all the events he described took place in a kind of big static arena named absolute space, and that time was an absolute constant. The speed of light was also realised to be a constant. In 1676 Danish astronomer Ole Christensen estimated the speed of light to be 140,000 miles per second. We now know it is 186,000 miles per second. In the 1860s James Clerk Maxwell unified the disparate theories which had been applied to magnetism and electricity.

In 1905 Einstein published his theory of relativity. It is derived not from observation but from Einstein working through in his head the consequences and shortcomings of the existing theories. Newton had posited a privileged observer, someone outside the universe who was watching it as if a play on a stage. From this privileged position a number of elements appeared constant, such as time.

Einstein imagines a universe in which there is no privileged outside point of view. We are all inside the universe and all moving. The theory threw up a number of consequences. One is that energy is equal to mass times the speed of light squared, or E = mc². Another is that nothing may travel faster than the speed of light. Another is that, as an object approaches the speed of light its mass increases. One of its most disruptive ideas is that time is relative. Different observes, travelling at different speeds, will see a beam of light travel take different times to travel a fixed distance. Since Einstein has made it axiomatic that the speed of light is fixed, and we know the distance travelled by the light is fixed, then time itself must appear different to different observers. Time is something that can change, like the other three dimensions. Thus time can be added to the existing three dimensions to create space-time.

The special theory of relativity was successful in explaining how the speed of light appears the same to all observers, and describing what happens to things when they move close to the speed of light. But it was inconsistent with Newton’s theory of gravity which says objects attract each other with a force related to the distance between them. If you move on of the objects the force exerted on the other object changes immediately. This cannot be if nothing can travel faster than the speed of light, as the special theory of relativity postulates. Einstein spent the ten or so years from 1905 onwards attempting to solve this difficulty. Finally, in 1915, he published the general theory of relativity.

The revolutionary basis of this theory is that space is not flat, a consistent  continuum or Newtonian stage within which events happen and forces interact in a sensible way. Space-time is curved or warped by the distribution of mass or energy within it, and gravity is a function of this curvature. Thus the earth is not orbiting around the sun in a circle, it is following a straight line in warped space.

The mass of the sun curves space-time in such a way that although the earth follows a straight line in four-dimensional pace-time, it appears to us to move along a circular orbit in three-dimensional space. (p.30)

In fact, at a planetary level Einstein’s maths is only slightly different from Newton’s but it predicts a slight difference in the orbit of Mercury which observations have gone on to prove. Also, the general theory predicts that light will bend, following a straight line but through space that is warped or curved by gravity. Thus the light from a distant star on the far side of the sun will bend as it passes close to the sun due to the curvature in space-time caused by the sun’s mass. And it was an expedition to West Africa in 1919 to observe an eclipse, which showed that light from distant stars did in fact bend slightly as it passed the sun, which helped confirm Einstein’s theory.

Newton’s laws of motion put an end to the idea of absolute position in space. The theory of relativity gets rid of absolute time.

Hence the thought experiment popularised by a thousand science fiction books that astronauts who set off in a space ship which gets anywhere near the speed of light will experience a time which is slower than the people they leave behind on earth.

In the theory of relativity there is no unique absolute time, but instead each individual has his own personal measure of time that depends on where he is and how he is moving. (p.33)

Obviously, since most of us are on planet earth, moving at more or less the same speed, everyone’s personal ‘times’ coincide. Anyway, the key central implication of Einstein’s general theory of relativity is this:

Before 1915, space and time were thought of as a fixed arena in which events took place, but which was not affected by what happened in it. This was true even of the special theory of relativity. Bodies moved, forces attracted and repelled, but time and space simply continued, unaffected. It was natural to think that space and time went on forever.

the situation, however, is quite different in the general theory of relativity. Space and time are now dynamic quantities. : when a body moves, or a force acts, it affects the curvature of space and time – and in turn the structure of space-time affects the way in which bodies move and forces act. Space and time not only affect but also are affected by everything that happens in the universe. (p.33)

This view of the universe as dynamic and interacting, by demolishing the old eternal static view, opened the door to a host of new ways of conceiving how the universe might have begun and might end.

Chapter 3 The Expanding Universe (pp.35-51)

Our modern picture of the universe dates to 1924 when American astronomer Edwin Hubble demonstrated that ours is not the only galaxy. We now know the universe is home to some hundred million galaxies, each containing some hundred thousand million stars. We live in a galaxy that is about one hundred thousand light-years across and is slowly rotating. Hubble set about cataloguing the movement of other galaxies and in 1929 published his results which showed that they are all moving away from us, and that, the further away a galaxy is, the faster it is moving.

The discovery that the universe is expanding was one of the great intellectual revolutions of the twentieth century. (p.39)

From Newton onwards there was a universal assumption that the universe was infinite and static. Even Einstein invented a force he called ‘the cosmological constant’ in order to counter the attractive power of gravity and preserve the model of a static universe. It was left to Russian physicist Alexander Friedmann to seriously calculate what the universe would look like if it was expanding.

In 1965 two technicians, Arno Penzias and Robert Wilson, working at Bell Telephone Laboratories discovered a continuous hum of background radiation coming from all parts of the sky. This echoed the theoretical work being done by two physicists, Bob Dicke and Jim Peebles, who were working on a suggestion made by George Gamow that the early universe would have been hot and dense. They posited that we should still be able to see the light from this earliest phase but that it would, because the redshifting, appear as radiation. Penzias and Wilson were awarded the Nobel Prize in 1987.

How can the universe be expanding? Imagine blowing up a balloon with dots (or little galaxies) drawn on it: they all move apart from each other and the further apart they are, the larger the distance becomes; but there is no centre to the balloon. Similarly the universe is expanding but not into anything. There is no outside. If you set out to travel to the edge you would find no edge but instead find yourself flying round the periphery and end up back where you began.

There are three possible states of a dynamic universe. Either 1. it will expand against the contracting force of gravity until the initial outward propulsive force is exhausted and gravity begins to win; it will stop expanding, and start to contract. Or 2. it is expanding so fast that the attractive, contracting force of gravity never wins, so the universe expands forever and matter never has time to clump together into stars and planets. Or 3. it is expanding at just the right speed to escape collapsing back in on itself, but but so fast as to make the creation of matter impossible. This is called the critical divide. Physicists now believe the universe is expanding at just around the value of the critical divide, though whether it is just under or just above (i.e. the universe will eventually cease expanding, or not) is not known.

Dark matter We can calculate the mass of all the stars and galaxies in the universe and it is a mystery that our total is only about a hundredth of the mass that must exist to explain the gravitational behaviour of stars and galaxies. In other words, there must a lot of ‘dark matter’ which we cannot currently detect in order for the universe to be shaped the way it is.

So we don’t know what the likely future of the universe is (endless expansion or eventual contraction) but all the Friedmann models do predict that the universe began in an infinitely dense, infinitely compact, infinitely hot state – the singularity.

Because mathematics cannot really handle infinite numbers, this means that the general theory of relativity… predicts that there is a point in the universe where the theory itself breaks down… In fact, all our theories of science are formulated on the assumption that space-time is smooth and nearly flat, so they break down at the big bang singularity, where the curvature of space-time is infinite. (p.46)

Opposition to the theory came from Hermann Bondi, Thomas Gold and Fred Hoyle who formulated the steady state theory of the universe i.e. it has always been and always will be. All that is needed to explain the slow expansion is the appearance of new particles to keep it filled up, but the rate is very low (about one new particle per cubic kilometre per year). They published it in 1948 and worked through all its implications for the next few decades, but it was killed off as a theory by the 1965 observations of the cosmic background radiation.

He then explains the process whereby he elected to do a PhD expanding Roger Penrose’s work on how a dying star would collapse under its own weight to a very small size. The collaboration resulted in a joint 1970 paper which proved that there must have been a big bang, provided only that the theory of general relativity is correct, and the universe contains as much matter as we observe.

If the universe really did start out as something unimaginably small then, from the 1970s onwards, physicists turned their investigations to what happens to matter at microscopic levels.

Chapter 4 The Uncertainty Principle (pp.53-61)

1900 German scientist Max Planck suggests that light, x-rays and other waves can only be emitted at an arbitrary wave, in packets he called quanta. He theorised that the higher the frequency of the wave, the more energy would be required. This would tend to restrict the emission of high frequency waves. In 1926 Werner Heisenberg expanded on these insights to produce his Uncertainty Principle. In order to locate a particle in order to measure its position and velocity you need to shine a light on it. One has to use at least one quantum of energy. However, exposing the particle to this quantum will disturb the velocity of the particle.

In other words, the more accurately you try to measure the position of the particle, the less accurately you can measure its speed, and vice versa. (p.55)

Heisenberg showed that the uncertainty in the position of the particle times the uncertainty in its velocity times the mass of the particle can never be smaller than a certain quantity, which is known as Planck’s constant. For the rest of the 1920s Heisenberg, Erwin Schrödinger and Paul Dirac reformulated mechanics into a new theory titled quantum mechanics. In this theory particles no longer have separate well-defined positions and velocities, instead they have a general quantum state which is a combination of position and velocity.

Quantum mechanics introduces an unavoidable element of unpredictability or randomness into science. (p.56)

Also, particles can no longer be relied on to be particles. As a result of Planck and Heisenberg’s insights, particles have to be thought of as sometimes behaving like waves, sometimes like particles. In 1913 Niels Bohr had suggested that electrons circle round a nucleus at certain fixed points, and that it takes energy to dislodge them from these optimum orbits. Quantum theory helped explain Bohr’s theory by conceptualising the circling electrons not as particles but as waves. If electrons are waves, as they circle the nucleus, their wave lengths would cancel each other out unless they are perfect numbers. The frequency of the waves have to be able to circle the nucleus in perfect integers. This defines the height of the orbits electrons can take.

Chapter 5 Elementary Particles and Forces of Nature (pp.63-79)

A chapter devoted to the story of how we’ve come to understand the world of sub-atomic particles. Starting (as usual) with Aristotle and then fast-forwarding through Galton, Einstein’s paper on Brownian motion, J.J. Thomson’s discovery of electrons, and, in 1911, Ernest Rutherford’s demonstration that atoms are made up of tiny positively charged nucleus around which a number of tiny positively charged particles, electrons, orbit. Rutherford thought the nuclei contained ‘protons’, which have a positive charge and balance out the negative charge of the electrons. In 1932 James Chadwick discovered the nucleus contains neutrons, same mass as the proton but no charge.

In 1965 quarks were discovered by Murray Gell-Mann. In fact scientists went on to discover six types, up, down, strange, charmed, bottom and top quarks. A proton or neutron is made up of three quarks.

He explains the quality of spin. Some particles have to be spin twice to return to their original appearance. They have spin 1/2. All the matter we can see in the universe has the spin 1/2. Particles of spin 0, 1, and 2 give rise to the forces between the particles.

Pauli’s exclusionary principle: two similar particles cannot exist in the same state, they cannot have the same position and the same velocity. The exclusionary principle is vital since it explains why the universe isn’t a big soup of primeval particles. The particles must be distinct and separate.

In 1928 Paul Dirac explained why the electron must rotate twice to return to its original position. He also predicted the existence of the positron to balance the electron. In 1932 the positron was discovered and Dirac was awarded a Nobel Prize.

Force carrying particles can be divided into four categories according to the strength of the force they carry and the particles with which they interact.

  1. Gravitational force, the weakest of the four forces by a long way.
  2. The electromagnetic force interacts with electrically charged particles like electrons and quarks.
  3. The weak nuclear force, responsible for radioactivity. In findings published in 1967 Abdus Salam and Steven Weinberg suggested that in addition to the photon there are three other spin-1 particles known collectively as massive vector bosons. Initially disbelieved, experiments proved them right and they collected the Nobel Prize in 1979. In 1983 the team at CERN proved the existence of the three particles, and the leaders of this team also won the Nobel Prize.
  4. The strong nuclear force holds quarks together in the proton and neutron, and holds the protons and neutrons together in the nucleus. This force is believed to be carried by another spin-1 particle, the gluon. They have a property named ‘confinement’ which is that you can’t have a quark of a single colour, the number of quarks bound together must cancel each other out.

The idea behind the search for a Grand Unified Theory is that, at high enough temperature, all the particles would behave in the same way, i.e. the laws governing the four forces would merge into one law.

Most of the matter on earth is made up of protons and neutrons, which are in turn made of quarks. Why is there this preponderance of quarks and not an equal number of anti-quarks?

Hawking introduces us to the notion that all the laws of physics obey three separate symmetries known as C, P and T. In 1956 two American physicists suggested that the weak force does not obey symmetry C. Hawking then goes on to explain more about the obedience or lack of obedience to the rules of symmetry of particles at very high temperatures, to explain why quarks and matter would outbalance anti-quarks and anti-matter at the big bang in a way which, frankly, I didn’t understand.

Chapter 6 Black Holes (pp.81-97)

In a sense, all the preceding has been just preparation, just a primer to help us understand the topic which Hawking spent the 1970s studying and which made his name – black holes.

The term black hole was coined by John Wheeler in 1969. Hawking explains the development of ideas about what happens when a star dies. When a star is burning, the radiation of energy in the forms of heat and light counteracts the gravity of its mass. When it runs out of fuel, gravity takes over and the star collapses in on itself. The young Indian physicist Subrahmanyan Chandrasekhar calculated that a cold star with a mass of more than one and a half times the mass of our sin would not be able to support itself against its own gravity and contract to become a ‘white dwarf’ with a radius of a few thousand miles and a density of hundreds of tones per square inch.

The Russian Lev Davidovich Landau speculated that the same sized star might end up in a different state. Chandrasekhar had used Pauli’s exclusionary principle as applied to electrons i.e. calculated the smallest densest state the mass could reach assuming no electron can be in the place of any other electron. Landau calculated on the basis of the exclusionary principle repulsion operative between neutrons and protons. Hence his model is known as the ‘neutron star’, which would have a radius of only ten miles or so and a density of hundreds of millions of tonnes per cubic inch.

(In an interesting aside Hawking tells us that physics was railroaded by the vast Manhattan Project to build an atomic bomb, and then to build a hydrogen bomb, throughout the 1940s and 50s. This tended to sideline large-scale physics about the universe. It was only the development of a) modern telescopes and b) computer power, that revived interest in astronomy.)

A black hole is what you get when the gravity of a collapsing star becomes so high that it prevents light from escaping its gravitational field. Hawking and Penrose showed that at the centre of a black hole must be a singularity of infinite density and space-time curvature.

In 1967 the study of black holes was revolutionised by Werner Israel. He showed that, according to general relativity, all non-rotating black holes must be very simple and perfectly symmetrical.

Hawking then explains several variations on this theory put forward by Roger Penrose, Roy Kerr, Brandon Carter who proved that a hole would have an axis of symmetry. Hawking himself confirmed this idea. In 1973 David Robinson proved that a black hole had to have ‘a Kerr solution’. In other words, no matter how they start out, all black holes end up looking the same, a belief summed up in the pithy phrase, ‘A black hole has no hair’.

What is striking about all this is that it was pure speculation, derived entirely from mathematical models without a shred of evidence from astronomy.

Black holes are one of only a fairly small number of cases in the history of science in which a theory was developed in great detail as a mathematical model before there was any evidence from observations that it was correct. (p.92)

Hawking then goes on to list the best evidence we have for black holes, which is surprisingly thin. Since they are by nature invisible black holes can only be deduced by their supposed affect on nearby stars or systems. Given that black holes were at the centre of Hawking’s career, and are the focus of these two chapters, it is striking that there is, even now, very little direct empirical evidence for their existence.

(Eerily, as I finished reading A Brief History of Time, the announcement was made on 10 April 2019 that the first ever image has been generated of a black hole –

Theory predicts that other stars which stray close to a black hole would have clouds of gas attracted towards it. As this matter falls into the black hole it will a) be stripped down to basic sub-atomic particles b) make the hole spin. Spinning would make the hole acquire a magnetic field. The magnetic field would shoot jets of particles out into space along the axis of rotation of the hole. These jets should be visible to our telescopes.

First ever image of a black hole, captured the Event Horizon Telescope (EHT). The hole is 40 billion km across, and 500 million trillion km away

Chapter 7 Black Holes Ain’t So Black (pp.99-113)

Black holes are not really black after all. They glow like a hot body, and the smaller they are, the hotter they glow. Again, Hawking shares with us the evolution of his thinking on this subject, for example how he was motivated in writing a 1971 paper about black holes and entropy at least partly in irritation against another researcher who he felt had misinterpreted his earlier results.

Anyway, it all resulted in his 1973 paper which showed that a black hole ought to emit particles and radiation as if it were a hot body with a temperature that depends only on the black hole’s mass.

The reasoning goes thus: quantum mechanics tells us that all of space is fizzing with particles and anti-particles popping into existence, cancelling each other out, and disappearing. At the border of the event horizon, particles and anti-particles will be popping into existence as everywhere else. But a proportion of the anti-particles in each pair will be sucked inside the event horizon, so that they cannot annihilate their partners, leaving the positive particles to ping off into space. Thus, black holes should emit a steady stream of radiation!

If black holes really are absorbing negative particles as described above, then their negative energy will result in negative mass, as per Einstein’s most famous equation, E = mc² which shows that the lower the energy, the lower the mass. In other words, if Hawking is correct about black holes emitting radiation, then black holes must be shrinking.

Gamma ray evidence suggests that there might be 300 black holes in every cubic light year of the universe. Hawking then goes on to estimate the odds of detecting a black hole a) in steady existence b) reaching its final state and blowing up. Alternatively we could look for flashes of light across the sky, since on entering the earth’s atmosphere gamma rays break up into pairs of electrons and positrons. No clear sightings have been made so far.

(Threaded throughout the chapter has been the notion that black holes might come in two types: one which resulted from the collapse of stars, as described above. And others which have been around since the start of the universe as a function of the irregularities of the big bang.)

Summary: Hawking ends this chapter by claiming that his ‘discovery’ that radiation can be emitted from black holes was ‘the first example of a prediction that depended in an essential way on both the great theories of this century, general relativity and quantum mechanics’. I.e. it is not only an interesting ‘discovery’ in its own right, but a pioneering example of synthesising the two theories.

Chapter 8 The Origin and Fate of the Universe (pp.115-141)

This is the longest chapter in the book and I found it the hardest to follow. I think this is because it is where he makes the big pitch for His Theory, for what’s come to be known as the Hartle-Hawking state. Let Wikipedia explain:

Hartle and Hawking suggest that if we could travel backwards in time towards the beginning of the Universe, we would note that quite near what might otherwise have been the beginning, time gives way to space such that at first there is only space and no time. Beginnings are entities that have to do with time; because time did not exist before the Big Bang, the concept of a beginning of the Universe is meaningless. According to the Hartle-Hawking proposal, the Universe has no origin as we would understand it: the Universe was a singularity in both space and time, pre-Big Bang. Thus, the Hartle–Hawking state Universe has no beginning, but it is not the steady state Universe of Hoyle; it simply has no initial boundaries in time or space. (Hartle-Hawking state Wikipedia article)

To get to this point Hawking begins by recapping the traditional view of the ‘hot big bang’, i.e. the almost instantaneous emergence of matter from a state of infinite mass, energy and density and temperature.

This is the view first put forward by Gamow and Alpher in 1948, which predicted there would still be very low-level background radiation left over from the bang – which was then proved with the discovery of the cosmic background radiation in 1965.

Hawking gives a picture of the complete cycle of the creation of the universe through the first generation of stars which go supernova blowing out into space the heavier particles which then go into second generation stars or clouds of gas and solidify into things like planet earth.

In a casual aside, he gives his version of the origin of life on earth:

The earth was initially very hot and without an atmosphere. In the course of time it cooled and acquired an atmosphere from the emission of gases from the rocks. This early atmosphere was not one in which we could have survived. It contained no oxygen, but a lot of other gases that are poisonous to us, such as hydrogen sulfide. There are, however, other primitive forms of life that can flourish under such conditions. It is thought that they developed in the oceans, possibly as a result of chance combinations of atoms into large structures, called macromolecules, which were capable of assembling other atoms in the ocean into similar structures. They would thus have reproduced themselves and multiplied. In some cases there would have been errors in the reproduction. Mostly these errors would have been such that the new macromolecule could not reproduce itself and eventually would have been destroyed. However, a few of the errors would have produced new macromolecules that were even better at reproducing themselves. They would have therefore had an advantage and would have tended to replace the original macromolecules. In this way a process of evolution was started that led to the development of more and more complicated, self-reproducing organisms. The first primitive forms of life consumed various materials, including hydrogen sulfide, and released oxygen. This gradually changed the atmosphere to the composition that it has today and allowed the development of higher forms of life such as fish, reptiles, mammals, and ultimately the human race. (p.121)

(It’s ironic that he discusses the issue so matter-of-factly, demonstrating that, for him at least, the matter is fairly cut and dried and not worth lingering over. Because, of course, for scientists who’ve devoted their lives to the origins-of-life question it is far from over. It’s a good example of the way that every specialist thinks that their specialism is the most important subject in the world, the subject that will finally answer the Great Questions of Life whereas a) most people have never heard about the issues b) wouldn’t understand them and c) don’t care.)

Hawking goes on to describe chaotic boundary conditions and describe the strong and the weak anthropic principles. He then explains the theory proposed by Alan Guth of inflation i.e. the universe, in the first milliseconds after the big bang, underwent a process of enormous hyper-growth, before calming down again to normal exponential expansion. Hawking describes it rather differently from Barrow and Davies. He emphasises that, to start with, in a state of hypertemperature and immense density, the four forces we know about and the spacetime dimensions were all fused into one. They would be in ‘symmetry’. Only as the early universe cooled would it have undergone a ‘phase transition’ and the symmetry between forces been broken.

If the temperature fell below the phase transition temperature without symmetry being broken then the universe would have a surplus of energy and it is this which would have cause the super-propulsion of the inflationary stage. The inflation theory:

  • would allow for light to pass from one end of the (tiny) universe to the other and explains why all regions of the universe appear to have the same properties
  • explain why the rate of expansion of the universe is close to the critical rate required to make it expand for billions of years (and us to evolve)
  • would explain why there is so much matter in the universe

Hawking then gets involved in the narrative explaining how he and others pointed out flaws in Guth’s inflationary model, namely that the phase transition at the end of the inflation ended in ‘bubble’s which expanded to join up. But Hawking and others pointed out that the bubbles were expanding so fat they could never join up. In 1981 the Russian Andre Linde proposed that the bubble problem would be solved if  a) the symmetry broke slowly and b) the bubbles were so big that our region of the universe is all contained within a single bubble. Hawking disagreed, saying Linde’s bubbles would each have to be bigger than the universe for the maths to work out, and counter-proposing that the symmetry broke everywhere at the same time, resulting in the uniform universe we see today. Nonetheless Linde’s model became known as the ‘new inflationary model’, although Hawking considers it invalid.

[In these pages we get a strong whiff of cordite. Hawking is describing controversies and debates he has been closely involved in and therefore takes a strongly partisan view, bending over backwards to be fair to colleagues, but nonetheless sticking to his guns. In this chapter you get a strong feeling for what controversy and debate within this community must feel like.)

Hawking prefers the ‘chaotic inflationary model’ put forward by Linde in 1983, in which there is no phase transition or supercooling, but which relies on quantum fluctuations.

At this point he introduces four ideas which are each challenging and which, taken together, mark the most difficult and confusing part of the book.

First he says that, since Einstein’s laws of relativity break down at the moment of the singularity, we can only hope to understand the earliest moments of the universe in terms of quantum mechanics.

Second, he says he’s going to use a particular formulation of quantum mechanics, namely Richard Feynman’s idea of ‘a sum over histories’. I think this means that Feynman said that in quantum mechanics we can never know precisely which route a particle takes, the best we can do is work out all the possible routes and assign them probabilities, which can then be handled mathematically.

Third, he immediately points out that working with Feynman’s sum over histories approach requires the use of ‘imaginary’ time, which he then goes on to explain.

To avoid the technical difficulties with Feynman’s sum over histories, one must use imaginary time. (p.134)

And then he points out that, in order to use imaginary time, we must use Euclidean space-time instead of ‘real’ space-time.

All this happens on page 134 and was too much for me to understand. On page 135 he then adds in Einstein’s idea that the gravitational field us represented by curved space-time.

It is now that he pulls all these ideas together to assert that, whereas in the classical theory of gravity, which is based on real space-time there are only two ways the universe can behave – either it has existed infinitely or it had a beginning in a singularity at a finite point in time; in the quantum theory of gravity, which uses Euclidean space-time, in which the time direction is on the same footing as directions in space it is possible:

for space-time to be finite in extent and yet to have no singularities that formed a boundary or edge.

In Hawking’s theory the universe would be finite in duration but not have a boundary in time because time would merge with the other three dimensions, all of which cease to exist during and just after a singularity. Working backwards in time, the universe shrinks but it doesn’t shrink, as a cone does, to a single distinct point – instead it has a smooth round bottom with no distinct beginning.

The Hartle-Hawking no boundary Hartle and Hawking No-Boundary Proposal

The Hartle-Hawking no boundary Hartle and Hawking No-Boundary Proposal

Finally Hawking points out that this model of a no-boundary universe derived from a Feynman interpretation of quantum gravity does not give rise to all possible universes, but only to a specific family of universes.

One aspect of these histories of the universe in imaginary time is that none of them include singularities – which would seem to render redundant all the work Hawking had done on black holes in ‘real time’. He gets round this by saying that both models can be valid, but in order to demonstrate different things.

It is simply a matter of which is the more useful description. (p.139)

He winds up the discussion by stating that further calculations based on this model explain the two or three key facts about the universe which all theories must explain i.e. the fact that it is clumped into lumps of matter and not an even soup, the fact that it is expanding, and the fact that the background radiation is minutely uneven in some places suggesting very early irregularities. Tick, tick, tick – the no-boundary proposal is congruent with all of them.

It is a little mind-boggling, as you reach the end of this long and difficult chapter, to reflect that absolutely all of it is pure speculation without a shred of evidence to support it. It is just another elegant way of dealing with the problems thrown up by existing observations and by trying to integrate quantum mechanics with Einsteinian relativity. But whether it is ‘true’ or not, not only is unproveable but also is not really the point.

Chapter 9 The Arrow of Time (pp.143-153)

If Einstein’s theory of general relativity is correct and light always appears to have the same velocity to all observers, no matter what position they’re in or how fast they’re moving, THEN TIME MUST BE FLEXIBLE. Time is not a fixed constant. Every observer carries their own time with them.

Hawking points out that there are three arrows of time:

  • the thermodynamic arrow of time which obeys the Second Law of Thermodynamics namely that entropy, or disorder, increases – there are always many more disordered states than ordered ones
  • the psychological arrow of time which we all perceive
  • the cosmological arrow of time, namely the universe is expanding and not contracting

Briskly, he tells us that the psychological arrow of time is based on the thermodynamic one: entropy increases and our lives experience that and our minds record it. For example, human beings consume food – which is a highly ordered form of energy – and convert it into heat – which is a highly disordered form.

Hawking tells us that he originally thought that, if the universe reach a furthest extent and started to contract, disorder (entropy) would decrease, and everything in the universe would happen backwards. Until Don Page and Raymond Laflamme, in their different ways, proved otherwise.

Now he believes that the contraction would not occur until the universe had been almost completely thinned out and all the stars had died i.e. the universe had become an even soup of basic particles. THEN it would start to contract. And so his current thinking is that there would be little or no thermodynamic arrow of time (all thermodynamic processes having come to an end) and all of this would be happening in a universe in which human beings could not exist. We will never live to see the contraction phase of the universe. If there is a contraction phase.

Chapter 10: The Unification of Physics (pp.155-169)

The general theory of relativity and quantum mechanics both work well for their respective scales (stars and galaxies, sub-atomic particles) but cannot be made to mesh, despite fifty of more years of valiant attempts. Many of the attempts produce infinity in their results, so many infinities that a strategy has been developed called ‘renormalisation’ which gets rid of the infinities, although Hawking conceded is ‘rather dubious mathematically’.

Grand Unified Theories is the term applied to attempts to devise a theory (i.e. a set of mathematical formulae) which will take account of the four big forces we know about: electromagnetism, gravity, the strong nuclear force and the weak nuclear force.

In the mid-1970s some scientists came up with the idea of ‘supergravity’ which postulated a ‘superparticle’, and the other sub-atomic particles variations on the super-particle but with different spins. According to Hawking the calculations necessary to assess this theory would take so long nobody has ever done it.

So he moves onto string theory i.e. the universe isn’t made up of particles but of open or closed ‘strings’, which can join together in different ways to form different particles. However, the problem with string theory is that, because of the mathematical way they are expressed, they require more than four dimensions. A lot more. Hawking mentions anywhere from ten up to 26 dimensions. Where are all these dimensions? Well, strong theory advocates say they exist but are very very small, effectively wrapped up into sub-atomic balls, so that you or I never notice them.

Rather simplistically, Hawking lists the possibilities about a complete unified theory. Either:

  1. there really is a grand unified theory which we will someday discover
  2. there is no ultimate theory but only an infinite sequence of possibilities which will describe the universe with greater and greater, but finite accuracy
  3. there is no theory of the universe at all, and events will always seems to us to occur in a random way

This leads him to repeat the highfalutin’ rhetoric which all physicists drop into at these moments, about the destiny of mankind etc. Discovery of One Grand Unified Theory:

would bring to an end a long and glorious chapter in the history of humanity’s intellectual struggle to understand the universe. But it would also revolutionise the ordinary person’s understanding of the laws that govern the universe. (p.167)

I profoundly disagree with this view. I think it is boilerplate, which is a phrase defined as ‘used in the media to refer to hackneyed or unoriginal writing’.

Because this is not just the kind of phrasing physicists use when referring to the search for GUTs, it’s the same language biologists use when referring to the quest to understand how life derived from inorganic chemicals, it’s the same language the defenders of the large Hadron Collider use to justify spending billions of euros on the search for ever-smaller particles, it’s the language used by the guys who want funding for the Search for Extra-Terrestrial Intelligence), it’s the kind of language used by the scientists bidding for funding for the Human Genome Project.

Each of these, their defenders claim, is the ultimate most important science project, quest and odyssey ever,  and when they find the solution it will for once and all answer the Great Questions which have been tormenting mankind for millennia. Etc. Which is very like all the world’s religions claiming that their God is the only God. So a) there is a pretty obvious clash between all these scientific specialities which each claim to be on the brink of revealing the Great Secret.

But b) what reading this book and John Barrow’s Book of Universes convinces me is that i) we are very far indeed from coming even close to a unified theory of the universe and more importantly ii) if one is ever discovered, it won’t matter.

Imagine for a moment that a new iteration of string theory does manage to harmonise the equations of general relativity and quantum mechanics. How many people in the world are really going to be able to understand that? How many people now, currently, have a really complete grasp of Einsteinian relativity and Heisenbergian quantum uncertainty in their strictest, most mathematical forms? 10,000? 1000,000 earthlings?

If and when the final announcement is made who would notice, who would care, and why would they care? If the final conjunction is made by adapting string theory to 24 dimensions and renormalising all the infinities in order to achieve a multi-dimensional vision of space-time which incorporates both the curvature of gravity and the unpredictable behaviour of sub-atomic particles – would this really

revolutionise the ordinary person’s understanding of the laws that govern the universe?

Chapter 11 Conclusion (pp.171-175)

Recaps the book and asserts that his and James Hartle’s no-boundary model for the origin of the universe is the first to combine classic relativity with Heisenberg uncertainty. Ends with another rhetorical flourish of trumpets which I profoundly disagree with for the reasons given above.

If we do discover a complete theory, it should in time be understandable in broad principle by everyone, not just a few scientists. Then we shall all, philosophers, scientists, and just ordinary people, be able to take part in the discussion of the question of why it is that we and the universe exist. If we find the answer to that, it would be the ultimate triumph of human reason. (p.175)

Maybe I’m wrong, but I think this is a hopelessly naive view of human nature and culture. Einstein’s general theory has been around for 104 years, quantum mechanics for 90 years. Even highly educated people understand neither of them, and what Hawking calls ‘just ordinary people’ certainly don’t – and it doesn’t matter. 

Thoughts

Of course the subject matter is difficult to understand, but Hawking makes a very good fist of putting all the ideas into simple words and phrases, avoiding all formulae and equations, and the diagrams help a lot.

My understanding is that A Brief History of Time was the first popular science to put all these ideas before the public in a reasonably accessible way, and so opened the floodgates for countless other science writers, although hardly any of the ideas in it felt new to me since I happen to have just reread the physics books by Barrow and Davies which cover much the same ground and are more up to date.

But my biggest overall impression is how provisional so much of it seems. You struggle through the two challenging chapters about black holes – Hawking’s speciality – and then are casually told that all this debating and arguing over different theories and model-making had gone on before any black holes were ever observed by astronomers. In fact, even when Hawking died, in 2018, no black holes had been conclusively identified. It’s a big shame he didn’t live to see this famous photograph being published and confirmation of at least the existence of the entity he devoted so much time to theorising about.


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The Book of Universes by John D. Barrow (2011)

This book is twice as long and half as good as Barrow’s earlier primer, The Origin of the Universe.

In that short book Barrow focused on the key ideas of modern cosmology – introducing them to us in ascending order of complexity, and as simply as possible. He managed to make mind-boggling ideas and demanding physics very accessible.

This book – although it presumably has the merit of being more up to date (published in 2011 as against 1994) – is an expansion of the earlier one, an attempt to be much more comprehensive, but which, in the process, tends to make the whole subject more confusing.

The basic premise of both books is that, since Einstein’s theory of relativity was developed in the 1910s, cosmologists and astronomers and astrophysicists have:

  1. shown that the mathematical formulae in which Einstein’s theories are described need not be restricted to the universe as it has traditionally been conceived; in fact they can apply just as effectively to a wide variety of theoretical universes – and the professionals have, for the past hundred years, developed a bewildering array of possible universes to test Einstein’s insights to the limit
  2. made a series of discoveries about our actual universe, the most important of which is that a) it is expanding b) it probably originated in a big bang about 14 billion years ago, and c) in the first few milliseconds after the bang it probably underwent a period of super-accelerated expansion known as the ‘inflation’ which may, or may not, have introduced all kinds of irregularities into ‘our’ universe, and may even have created a multitude of other universes, of which ours is just one

If you combine a hundred years of theorising with a hundred years of observations, you come up with thousands of theories and models.

In The Origin of the Universe Barrow stuck to the core story, explaining just as much of each theory as is necessary to help the reader – if not understand – then at least grasp their significance. I can write the paragraphs above because of the clarity with which The Origin of the Universe explained it.

In The Book of Universes, on the other hand, Barrow’s aim is much more comprehensive and digressive. He is setting out to list and describe every single model and theory of the universe which has been created in the past century.

He introduces the description of each model with a thumbnail sketch of its inventor. This ought to help, but it doesn’t because the inventors generally turn out to be polymaths who also made major contributions to all kinds of other areas of science. Being told a list of Paul Dirac’s other major contributions to 20th century science is not a good way for preparing your mind to then try and understand his one intervention on universe-modelling (which turned, in any case, out to be impractical and lead nowhere).

Another drawback of the ‘comprehensive’ approach is that a lot of these models have been rejected or barely saw the light of day before being disproved or – more complicatedly – were initially disproved but contained aspects or insights which turned out to be useful forty years later, and were subsequently recycled into revised models. It gets a bit challenging to try and hold all this in your mind.

In The Origin of the Universe Barrow sticks to what you could call the canonical line of models, each of which represented the central line of speculation, even if some ended up being disproved (like Hoyle and Gold and Bondi’s model of the steady state universe). Given that all of this material is pretty mind-bending, and some of it can only be described in advanced mathematical formulae, less is definitely more. I found The Book of Universes simply had too many universes, explained too quickly, and lost amid a lot of biographical bumpf summarising people’s careers or who knew who or contributed to who’s theory. Too much information.

One last drawback of the comprehensive approach is that quite important points – which are given space to breathe and sink in in The Origin of the Universe are lost in the flood of facts in The Book of Universes.

I’m particularly thinking of Einstein’s notion of the cosmological constant which was not strictly necessary to his formulations of relativity, but which Einstein invented and put into them solely in order to counteract the force of gravity and ensure his equations reflected the commonly held view that the universe was in a permanent steady state.

This was a mistake and Einstein is often quoted as admitting it was the biggest mistake of his career. In 1965 scientists discovered the cosmic background radiation which proved that the universe began in an inconceivably intense explosion, that the universe was therefore expanding and that the explosive, outward-propelling force of this bang was enough to counteract the contracting force of the gravity of all the matter in the universe without any need for a hypothetical cosmological constant.

I understand this (if I do) because in The Origin of the Universe it is given prominence and carefully explained. By contrast, in The Book of Universes it was almost lost in the flood of information and it was only because I’d read the earlier book that I grasped its importance.

The Book of Universes

Barrow gives a brisk recap of cosmology from the Sumerians and Egyptians, through the ancient Greeks’ establishment of the system named after Ptolemy in which the earth is the centre of the solar system, on through the revisions of Copernicus and Galileo which placed the sun firmly at the centre of the solar system, on to the three laws of Isaac Newton which showed how the forces which govern the solar system (and more distant bodies) operate.

There is then a passage on the models of the universe generated by the growing understanding of heat and energy acquired by Victorian physicists, which led to one of the most powerful models of the universe, the ‘heat death’ model popularised by Lord Kelvin in the 1850s, in which, in the far future, the universe evolves to a state of complete homegeneity, where no region is hotter than any other and therefore there is no thermodynamic activity, no life, just a low buzzing noise everywhere.

But this is all happens in the first 50 pages and is just preliminary throat-clearing before Barrow gets to the weird and wonderful worlds envisioned by modern cosmology i.e. from Einstein onwards.

In some of these models the universe expands indefinitely, in others it will reach a peak expansion before contracting back towards a Big Crunch. Some models envision a static universe, in others it rotates like a top, while other models are totally chaotic without any rules or order.

Some universes are smooth and regular, others characterised by clumps and lumps. Some are shaken by cosmic tides, some oscillate. Some allow time travel into the past, while others threaten to allow an infinite number of things to happen in a finite period. Some end with another big bang, some don’t end at all. And in only a few of them do the conditions arise for intelligent life to evolve.

The Book of Universes then goes on, in 12 chapters, to discuss – by my count – getting on for a hundred types or models of hypothetical universes, as conceived and worked out by mathematicians, physicists, astrophysicists and cosmologists from Einstein’s time right up to the date of publication, 2011.

A list of names

Barrow namechecks and briefly explains the models of the universe developed by the following (I am undertaking this exercise partly to remind myself of everyone mentioned, partly to indicate to you the overwhelming number of names and ideas the reader is bombarded with):

  • Aristotle
  • Ptolemy
  • Copernicus
  • Giovanni Riccioli
  • Tycho Brahe
  • Isaac Newton
  • Thomas Wright (1771-86)
  • Immanuel Kant (1724-1804)
  • Pierre Laplace (1749-1827) devised what became the standard Victorian model of the universe
  • Alfred Russel Wallace (1823-1913) discussed the physical conditions of a universe necessary for life to evolve in it
  • Lord Kelvin (1824-1907) material falls into the central region of the universe and coalesce with other stars to maintain power output over immense periods
  • Rudolf Clausius (1822-88) coined the word ‘entropy’ in 1865 to describe the inevitable progress from ordered to disordered states
  • William Jevons (1835-82) believed the second law of thermodynamics implies that universe must have had a beginning
  • Pierre Duhem (1961-1916) Catholic physicist accepted the notion of entropy but denied that it implied the universe ever had a beginning
  • Samuel Tolver Preson (1844-1917) English engineer and physicist, suggested the universe is so vast that different ‘patches’ might experience different rates of entropy
  • Ludwig Boltzmann and Ernst Zermelo suggested the universe is infinite and is already in a state of thermal equilibrium, but just with random fluctuations away from uniformity, and our galaxy is one of those fluctuations
  • Albert Einstein (1879-1955) his discoveries were based on insights, not maths: thus he saw the problem with Newtonian physics is that it privileges an objective outside observer of all the events in the universe; one of Einstein’s insights was to abolish the idea of a privileged point of view and emphasise that everyone is involved in the universe’s dynamic interactions; thus gravity does not pass through a clear, fixed thing called space; gravity bends space.

The American physicist John Wheeler once encapsulated Einstein’s theory in two sentences:

Matter tells space how to curve. Space tells matter how to move. (quoted on page 52)

  • Marcel Grossmann provided the mathematical underpinning for Einstein’s insights
  • Willem de Sitter (1872-1934) inventor of, among other things, the de Sitter effect which represents the effect of the curvature of spacetime, as predicted by general relativity, on a vector carried along with an orbiting body – de Sitter’s universe gets bigger and bigger for ever but never had a zero point; but then de Sitter’s model contains no matter
  • Vesto Slipher (1875-1969) astronomer who discovered the red shifting of distant galaxies in 1912, the first ever empirical evidence for the expansion of the galaxy
  • Alexander Friedmann (1888-1925) Russian mathematician who produced purely mathematical solutions to Einstein’s equation, devising models where the universe started out of nothing and expanded a) fast enough to escape the gravity exerted by its own contents and so will expand forever or b) will eventually succumb to the gravity of its own contents, stop expanding and contract back towards a big crunch. He also speculated that this process (expansion and contraction) could happen an infinite number of times, creating a cyclic series of bangs, expansions and contractions, then another bang etc
A graphic of the oscillating or cyclic universe (from Discovery magazine)

A graphic of the oscillating or cyclic universe (from Discovery magazine)

  • Arthur Eddington (1882-1944) most distinguished astrophysicist of the 1920s
  • George Lemaître (1894-1966) first to combine an expanding universe interpretation of Einstein’s equations with the latest data about redshifting, and show that the universe of Einstein’s equations would be very sensitive to small changes – his model is close to Eddington’s so that it is often called the Eddington-Lemaître universe: it is expanding, curved and finite but doesn’t have a beginning
  • Edwin Hubble (1889-1953) provided solid evidence of the redshifting (moving away) of distant galaxies, a main plank in the whole theory of a big bang, inventor of Hubble’s Law:
    • Objects observed in deep space – extragalactic space, 10 megaparsecs (Mpc) or more – are found to have a redshift, interpreted as a relative velocity away from Earth
    • This Doppler shift-measured velocity of various galaxies receding from the Earth is approximately proportional to their distance from the Earth for galaxies up to a few hundred megaparsecs away
  • Richard Tolman (1881-1948) took Friedmann’s idea of an oscillating universe and showed that the increased entropy of each universe would accumulate, meaning that each successive ‘bounce’ would get bigger; he also investigated what ‘lumpy’ universes would look like where matter is not evenly spaced but clumped: some parts of the universe might reach a maximum and start contracting while others wouldn’t; some parts might have had a big bang origin, others might not have
  • Arthur Milne (1896-1950) showed that the tension between the outward exploding force posited by Einstein’s cosmological constant and the gravitational contraction could actually be described using just Newtonian mathematics: ‘Milne’s universe is the simplest possible universe with the assumption that the universe s uniform in space and isotropic’, a ‘rational’ and consistent geometry of space – Milne labelled the assumption of Einsteinian physics that the universe is the same in all places the Cosmological Principle
  • Edmund Fournier d’Albe (1868-1933) posited that the universe has a hierarchical structure from atoms to the solar system and beyond
  • Carl Charlier (1862-1934) introduced a mathematical description of a never-ending hierarchy of clusters
  • Karl Schwarzschild (1873-1916) suggested  that the geometry of the universe is not flat as Euclid had taught, but might be curved as in the non-Euclidean geometries developed by mathematicians Riemann, Gauss, Bolyai and Lobachevski in the early 19th century
  • Franz Selety (1893-1933) devised a model for an infinitely large hierarchical universe which contained an infinite mass of clustered stars filling the whole of space, yet with a zero average density and no special centre
  • Edward Kasner (1878-1955) a mathematician interested solely in finding mathematical solutions to Einstein’s equations, Kasner came up with a new idea, that the universe might expand at different rates in different directions, in some parts it might shrink, changing shape to look like a vast pancake
  • Paul Dirac (1902-84) developed a Large Number Hypothesis that the really large numbers which are taken as constants in Einstein’s and other astrophysics equations are linked at a deep undiscovered level, among other things abandoning the idea that gravity is a constant: soon disproved
  • Pascual Jordan (1902-80) suggested a slight variation of Einstein’s theory which accounted for a varying constant of gravitation as through it were a new source of energy and gravitation
  • Robert Dicke (1916-97) developed an alternative theory of gravitation
  • Nathan Rosen (1909-995) young assistant to Einstein in America with whom he authored a paper in 1936 describing a universe which expands but has the symmetry of a cylinder, a theory which predicted the universe would be washed over by gravitational waves
  • Ernst Straus (1922-83) another young assistant to Einstein with whom he developed a new model, an expanding universe like those of Friedman and Lemaître but which had spherical holes removed like the bubbles in an Aero, each hole with a mass at its centre equal to the matter which had been excavated to create the hole
  • Eugene Lifschitz (1915-85) in 1946 showed that very small differences in the uniformity of matter in the early universe would tend to increase, an explanation of how the clumpy universe we live in evolved from an almost but not quite uniform distribution of matter – as we have come to understand that something like this did happen, Lifshitz’s calculations have come to be seen as a landmark
  • Kurt Gödel (1906-1978) posited a rotating universe which didn’t expand and, in theory, permitted time travel!
  • Hermann Bondi, Thomas Gold and Fred Hoyle collaborated on the steady state theory of a universe which is growing but remains essentially the same, fed by the creation of new matter out of nothing
  • George Gamow (1904-68)
  • Ralph Alpher and Robert Herman in 1948 showed that the ratio of the matter density of the universe to the cube of the temperature of any heat radiation present from its hot beginning is constant if the expansion is uniform and isotropic – they calculated the current radiation temperature should be 5 degrees Kelvin – ‘one of the most momentous predictions ever made in science’
  • Abraham Taub (1911-99) made a study of all the universes that are the same everywhere in space but can expand at different rates in different directions
  • Charles Misner (b.1932) suggested ‘chaotic cosmology’ i.e. that no matter how chaotic the starting conditions, Einstein’s equations prove that any universe will inevitably become homogenous and isotropic – disproved by the smoothness of the background radiation. Misner then suggested the Mixmaster universe, the  most complicated interpretation of the Einstein equations in which the universe expands at different rates in different directions and the gravitational waves generated by one direction interferes with all the others, with infinite complexity
  • Hannes Alfvén devised a matter-antimatter cosmology
  • Alan Guth (b.1947) in 1981 proposed a theory of ‘inflation’, that milliseconds after the big bang the universe underwent a swift process of hyper-expansion: inflation answers at a stroke a number of technical problems prompted by conventional big bang theory; but had the unforeseen implication that, though our region is smooth, parts of the universe beyond our light horizon might have grown from other areas of inflated singularity and have completely different qualities
  • Andrei Linde (b.1948) extrapolated that the inflationary regions might create sub-regions in  which further inflation might take place, so that a potentially infinite series of new universes spawn new universes in an ‘endlessly bifurcating multiverse’. We happen to be living in one of these bubbles which has lasted long enough for the heavy elements and therefore life to develop; who knows what’s happening in the other bubbles?
  • Ted Harrison (1919-2007) British cosmologist speculated that super-intelligent life forms might be able to develop and control baby universe, guiding the process of inflation so as to promote the constants require for just the right speed of growth to allow stars, planets and life forms to evolve. Maybe they’ve done it already. Maybe we are the result of their experiments.
  • Nick Bostrom (b.1973) Swedish philosopher: if universes can be created and developed like this then they will proliferate until the odds are that we are living in a ‘created’ universe and, maybe, are ourselves simulations in a kind of multiverse computer simulation

Although the arrival of Einstein and his theory of relativity marks a decisive break with the tradition of Newtonian physics, and comes at page 47 of this 300-page book, it seemed to me the really decisive break comes on page 198 with the publication Alan Guth’s theory of inflation.

Up till the Guth breakthrough, astrophysicists and astronomers appear to have focused their energy on the universe we inhabit. There were theoretical digressions into fantasies about other worlds and alternative universes but they appear to have been personal foibles and everyone agreed they were diversions from the main story.

However, the idea of inflation, while it solved half a dozen problems caused by the idea of a big bang, seems to have spawned a literally fantastic series of theories and speculations.

Throughout the twentieth century, cosmologists grew used to studying the different types of universe that emerged from Einstein’s equations, but they expected that some special principle, or starting state, would pick out one that best described the actual universe. Now, unexpectedly, we find that there might be room for many, perhaps all, of these possible universes somewhere in the multiverse. (p.254)

This is a really massive shift and it is marked by a shift in the tone and approach of Barrow’s book. Up till this point it had jogged along at a brisk rate namechecking a steady stream of mathematicians, physicists and explaining how their successive models of the universe followed on from or varied from each other.

Now this procedure comes to a grinding halt while Barrow enters a realm of speculation. He discusses the notion that the universe we live in might be a fake, evolved from a long sequence of fakes, created and moulded by super-intelligences for their own purposes.

Each of us might be mannequins acting out experiments, observed by these super-intelligences. In which case what value would human life have? What would be the definition of free will?

Maybe the discrepancies we observe in some of the laws of the universe have been planted there as clues by higher intelligences? Or maybe, over vast periods of time, and countless iterations of new universes, the laws they first created for this universe where living intelligences could evolve have slipped, revealing the fact that the whole thing is a facade.

These super-intelligences would, of course, have computers and technology far in advance of ours etc. I felt like I had wandered into a prose version of The Matrix and, indeed, Barrow apologises for straying into areas normally associated with science fiction (p.241).

Imagine living in a universe where nothing is original. Everything is a fake. No ideas are ever new. There is no novelty, no originality. Nothing is ever done for the first time and nothing will ever be done for the last time… (p.244)

And so on. During this 15-page-long fantasy the handy sequence of physicists comes to an end as he introduces us to contemporary philosophers and ethicists who are paid to think about the problem of being a simulated being inside a simulated reality.

Take Robin Hanson (b.1959), a research associate at the Future of Humanity Institute of Oxford University who, apparently, advises us all that we ought to behave so as to prolong our existence in the simulation or, hopefully, ensure we get recreated in future iterations of the simulation.

Are these people mad? I felt like I’d been transported into an episode of The Outer Limits or was back with my schoolfriend Paul, lying in a summer field getting stoned and wondering whether dandelions were a form of alien life that were just biding their time till they could take over the world. Why not, man?

I suppose Barrow has to include this material, and explain the nature of the anthropic principle (p.250), and go on to a digression about the search for extra-terrestrial life (p.248), and discuss the ‘replication paradox’ (in an infinite universe there will be infinite copies of you and me in which we perform an infinite number of variations on our lives: what would happen if you came face to face with one of your ‘copies?? p.246) – because these are, in their way, theories – if very fantastical theories – about the nature of the universe and he his stated aim is to be completely comprehensive.

The anthropic principle Observations of the universe must be compatible with the conscious and intelligent life that observes it. The universe is the way it is, because it has to be the way it is in order for life forms like us to evolve enough to understand it.

Still, it was a relief when he returned from vague and diffuse philosophical speculation to the more solid territory of specific physical theories for the last forty or so pages of the book. But it was very noticeable that, as he came up to date, the theories were less and less attached to individuals: modern research is carried out by large groups. And he increasingly is describing the swirl of ideas in which cosmologists work, which often don’t have or need specific names attached. And this change is denoted, in the texture of the prose, by an increase in the passive voice, the voice in which science papers are written: ‘it was observed that…’, ‘it was expected that…’, and so on.

  • Edward Tryon (b.1940) American particle physicist speculated that the entire universe might be a virtual fluctuation from the quantum vacuum, governed by the Heisenberg Uncertainty Principle that limits our simultaneous knowledge of the position and momentum, or the time of occurrence and energy, of anything in Nature.
  • George Ellis (b.1939) created a catalogue of ‘topologies’ or shapes which the universe might have
  • Dmitri Sokolov and Victor Shvartsman in 1974 worked out what the practical results would be for astronomers if we lived in a strange shaped universe, for example a vast doughnut shape
  • Yakob Zeldovich and Andrei Starobinsky in 1984 further explored the likelihood of various types of ‘wraparound’ universes, predicting the fluctuations in the cosmic background radiation which might confirm such a shape
  • 1967 the Wheeler-De Witt equation – a first attempt to combine Einstein’s equations of general relativity with the Schrödinger equation that describes how the quantum wave function changes with space and time
  • the ‘no boundary’ proposal – in 1982 Stephen Hawking and James Hartle used ‘an elegant formulation of quantum  mechanics introduced by Richard Feynman to calculate the probability that the universe would be found to be in a particular state. What is interesting is that in this theory time is not important; time is a quality that emerges only when the universe is big enough for quantum effects to become negligible; the universe doesn’t technically have a beginning because the nearer you approach to it, time disappears, becoming part of four-dimensional space. This ‘no boundary’ state is the centrepiece of Hawking’s bestselling book A Brief History of Time (1988). According to Barrow, the Hartle-Hawking model was eventually shown to lead to a universe that was infinitely large and empty i.e. not our one.
The Hartle-Hawking no boundary Hartle and Hawking No-Boundary Proposal

The Hartle-Hawking no boundary Hartle and Hawking No-Boundary Proposal

  • In 1986 Barrow proposed a universe with a past but no beginning because all the paths through time and space would be very large closed loops
  • In 1997 Richard Gott and Li-Xin Li took the eternal inflationary universe postulated above and speculated that some of the branches loop back on themselves, giving birth to themselves
The self-creating universe of J.Richard Gott III and Li-Xin Li

The self-creating universe of J.Richard Gott III and Li-Xin Li

  • In 2001 Justin Khoury, Burt Ovrut, Paul Steinhardt and Neil Turok proposed a variation of the cyclic universe which incorporated strong theory and they called the ‘ekpyrotic’ universe, epkyrotic denoting the fiery flame into which each universe plunges only to be born again in a big bang. The new idea they introduced is that two three-dimensional universes may approach each other by moving through the additional dimensions posited by strong theory. When they collide they set off another big bang. These 3-D universes are called ‘braneworlds’, short for membrane, because they will be very thin
  • If a universe existing in a ‘bubble’ in another dimension ‘close’ to ours had ever impacted on our universe, some calculations indicate it would leave marks in the cosmic background radiation, a stripey effect.
  • In 1998 Andy Albrecht, João Maguijo and Barrow explored what might have happened if the speed of light, the most famous of cosmological constants, had in fact decreased in the first few milliseconds after the bang? There is now an entire suite of theories known as ‘Varying Speed of Light’ cosmologies.
  • Modern ‘String Theory’ only functions if it assumes quite a few more dimensions than the three we are used to. In fact some string theories require there to be more than one dimension of time. If there are really ten or 11 dimensions then, possibly, the ‘constants’ all physicists have taken for granted are only partial aspects of constants which exist in higher dimensions. Possibly, they might change, effectively undermining all of physics.
  • The Lambda-CDM model is a cosmological model in which the universe contains three major components: 1. a cosmological constant denoted by Lambda (Greek Λ) and associated with dark energy; 2. the postulated cold dark matter (abbreviated CDM); 3. ordinary matter. It is frequently referred to as the standard model of Big Bang cosmology because it is the simplest model that provides a reasonably good account of the following properties of the cosmos:
    • the existence and structure of the cosmic microwave background
    • the large-scale structure in the distribution of galaxies
    • the abundances of hydrogen (including deuterium), helium, and lithium
    • the accelerating expansion of the universe observed in the light from distant galaxies and supernovae

He ends with a summary of our existing knowledge, and indicates the deep puzzles which remain, not least the true nature of the ‘dark matter’ which is required to make sense of the expanding universe model. And he ends the whole book with a pithy soundbite. Speaking about the ongoing acceptance of models which posit a ‘multiverse’, in which all manner of other universes may be in existence, but beyond the horizon of where can see, he says:

Copernicus taught us that our planet was not at the centre of the universe. Now we may have to accept that even our universe is not at the centre of the Universe.


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The Origin of the Universe by John D. Barrow (1994)

In the beginning, the universe was an inferno of radiation, too hot for any atoms to survive. In the first few minutes, it cooled enough for the nuclei of the lighter elements to form. Only millions of years later would the cosmos be cool enough for whole atoms to appear, followed soon by simple molecules, and after billions of years by the complex sequence of events that saw the condensation of material into stars and galaxies. Then, with the appearance of stable planetary environments, the complicated products of biochemistry were nurtured, by processes we still do not understand. (The Origin of the Universe, p.xi)

In the late 1980s and into the 1990s science writing became fashionable and popular. A new generation of science writers poured forth a wave of books popularising all aspects of science. The ones I remember fell into two broad categories, evolution and astrophysics. Authors such as Stephen Jay Gould and Edward O. Wilson, Richard Dawkins and Steve Jones (evolution and genetics) and Paul Davies, John Gribbin, John Polkinghorne and, most famously of all, Stephen Hawking, (cosmology and astrophysics) not only wrote best-selling books but cropped up as guests on radio shows and even presented their own TV series.

Early in the 1990s the literary agent John Brockman created a series titled Science Masters in which he commissioned experts across a wide range of the sciences to write short, jargon-free and maths-light introductions to their fields.

This is astrophysicist John D. Barrow’s contribution to the series, a short, clear and mind-blowing introduction to current theory about how our universe began.

The Origin of the Universe

Billions It is now thought the universe is about 13.7 billion years old, the solar system is 4.57 billion years old and the earth is 4.54 billion years old. The oldest surface rocks anywhere on earth are in northwestern Canada near the Great Slave Lake, and are 4.03 billion years. The oldest fossilised bacteria date from 3.48 billion years ago.

Visible universe The visible universe is the part of the universe which light has had time to cross and reach us. If the universe is indeed 13.7 billion years old, and nothing can travel faster than the speed of light (299,792,458 metres per second) then there is, in effect, a ‘horizon’ to what we can see. We can only see the part of the universe which is about 13.7 billion years old. Whether there is any universe beyond our light horizon, and what it looks like, is something we can only speculate about.

Steady state Until the early 20th century philosophers and scientists thought the universe was fixed, static and stable. Even Einstein put into his theory of relativity a factor he named ‘the cosmological constant’, which wasn’t strictly needed, solely in order to make the universe appear static and so conform to contemporary thinking. The idea of this constant was to counteract the attractive force of gravity, in order to ensure his steady state version of the universe didn’t collapse into a big crunch.

Alexander Friedmann It was a young mathematician, Alexander Friedmann, who looked closely at Einstein’s formulae and showed that the cosmological constant was not necessary, not if the universe was expanding; in this case, no hypothetical repelling force would be needed, just the sheer speed of outward expansion. Einstein eventually conceded that including the constant in the formulae of relativity had been a major mistake.

Edwin Hubble In what Barrow calls ‘the greatest discovery of twentieth century science’, the American astronomer Edwin Hubble in the 1920s discovered that distant galaxies are moving away from us, and the further away they are, the faster they are moving, which became known as Hubble’s Law. He established this by noticing the ‘red-shifting’ of frequencies denoting detectable elements in these galaxies i.e. their light frequencies had been altered downwards, as light (and sound and all waves are) when something is moving away from the observer.

Critical divide An argument against the steady-state theory of the universe is that, over time, the gravity of all the objects in it would pull everything together and it would all collapse into one massive clump. Only an initial throwing out of material could counter-act the affect of all that gravity.

So how fast is the universe expanding? Imagine a rate, x. Below that speed, the effect of gravity will eventually overcome the outward acceleration, the universe will slow down, stop expanding and start to contract. Significantly above this speed, x, and the universe would continue flying apart in all directions so quickly that gas clouds, stars, galaxies and planets would never be formed.

As far as we know, the actual acceleration of the universe hovers just around this rate, x – just fast enough to prevent the universe from collapsing, but not too fast for it to be impossible for matter to form. Just the right speed to create the kind of universe we see around us. The name for this threshold is the critical divide.

Starstuff Stars are condensations of matter large enough to create at their centre nuclear reactions. These reactions burn hydrogen into helium for a long, sedate period, as our sun is doing. At the end of their lives stars undergo a crisis, an explosive period of rapid change during which helium is transformed into carbon nitrogen, oxygen, silicon, phosphorus and many of the other, heavier elements. When the ailing star finally explodes as a supernova these elements disperse into space and ultimately find their way into clouds of gas which condense as planets.

Thus every plant, animal and person alive on earth is made out of chemical elements forged in the unthinkable heat of dying stars – which is what Joni Mitchell meant when she sang, ‘We are stardust’.

Heat death A theory that the universe will continue expanding and matter become so attenuated that there are no heat or dynamic inequalities left to fuel thermal reactions i.e. matter ends up smoothly spread throughout space with no reactions happening anywhere. Thermodynamic equilibrium reached at a universal very low temperature. The idea was formulated by William Thomson, Lord Kelvin, in the 1850s who extrapolated from Victorian knowledge of mechanics and heat. 170 years later, updated versions of heat death remain a viable theory for the very long-term future of the universe.

Steady state The ‘steady state’ theory of the universe was developed by astrophysicists Thomas Gold, Hermann Bondi and Fred Hoyle in 1948. They theorised that. although the universe appeared to be expanding it had always existed, the expansion being caused by a steady rate of creation of new matter. This theory was disproved in the mid-1960s by the confirmation of background radiation

Background radiation theorised In the 1940s George Gamow and assistants Alpher and Herman theorised that, if the universe began in a hot dense state way back, there should be evidence, namely a constant layer of background radiation everywhere which, they calculated, would be 5 degrees above absolute zero.

Background radiation proved In the 1960s researchers at Bell Laboratories, calibrating a sensitive radio antenna, noticed a constant background interference to their efforts which seemed to be coming from every direction of the sky. A team from Princeton interpreted this as the expected background radiation and measured it at 2.5 degrees Kelvin. It is called ‘cosmic microwave background radiation’ and is one of the strong proofs for the Big Bang theory. The uniformity of the background radiation was confirmed by observations from NASA’s Cosmic Background Explorer satellite in the early 1990s.

Empty universe There is very little material in the universe. If all the stars and galaxies in the universe were smoothed out into a sea of atoms, there would only be about one atom per cubic meter of space.

Inflation This is a theory developed in 1979 by theoretical physicist Alan Guth – the idea is that the universe didn’t arise from a singularity which exploded and grew at a steady state but instead, in the first milliseconds, underwent a period of hyper-growth, which then calmed back down to ‘normal’ expansion.

The theory has been elaborated and generated numerous variants but is widely accepted because it explains many aspects of the universe we see today – from its large-scale structure to the way it explains how minute quantum fluctuations in this initial microscopic inflationary region, once magnified to cosmic size, became the seeds for the growth of structure in the Universe.

The inflation is currently thought to have taken place from 10−36 seconds after the conjectured Big Bang singularity to sometime between 10−33 or 10−32 seconds after.

Chaotic inflationary universe Proposed by Soviet physicist Andrei Linde in 1983, this is the idea that multiple distinct sections of the very early universe might have experienced inflation at different rates and so have produced a kind of cluster of universes, like bubbles in a bubble bath, except that these bubbles would have to be at least nine billion light years in size in order to produce stable stars. Possibly the conditions in each of the universes created by chaotic inflation could be quite different.

Eternal inflation A logical extension of chaotic inflation is that you not only have multiple regions which undergo inflation at the same time, but you might have sub-regions which undergo inflation at different times – possibly one after the other, in other words maybe there never was a beginning, but this process of successive creations and hyper-inflations has been going on forever and is still going on but beyond our light horizon (which, as mentioned above, only reaches to about 13.7 billion light years away).

Time Is time a fixed and static quality which creates a kind of theatre, an external frame of reference, in which the events of the universe take place, as in the Newtonian view? Or, as per Einstein, is time itself part of the universe, inseparable from the stuff of the universe and can be bent and distorted by forces in the universe? This is why Einstein used the expression ‘spacetime’?

The quantum universe Right back at the very beginning, at 10−43 seconds, the size of the visible universe was smaller than its quantum wavelength — so its entire contents would have been subject to the uncertainty which is the characteristic of quantum physics.

Time is affected by a quantum view of the big bang because, when the universe was still shrunk to a microscopic size, the quantum uncertainty which applied to it might be interpreted as meaning there was no time. That time only ‘crystallised’ out as a separate ‘dimension’ once the universe had expanded to a size where quantum uncertainty no longer dictated.

Some critics of the big bang theory ask, ‘What was there before the big bang?’ to which exponents conventionally reply that there was no ‘before’. Time as we experience it ceased to exist and became part of the initial hyper-energy field.

This quantum interpretation suggests that there in fact was no ‘big bang’ because there was literally no time when it happened.

Traditional visualisations of the big bang show an inverted cone, at the top is the big universe we live in and as you go back in time it narrows to a point – the starting point. Imagine, instead, something more like a round-bottomed sack: there’s a general expansion upwards and outwards but if you penetrate back to the bottom of the sack there is no ‘start’ point.

This theory was most fully worked out by Stephen Hawking and James Hartle.

The Hartle-Hawking no boundary Hartle and Hawking No-Boundary Proposal

Wormholes The book ends with speculations about the possibility that ‘wormholes’ existed in the first few milliseconds, tubes connecting otherwise distant parts of the exploding ball of universe. I understood the pictures of these but couldn’t understand the problems in the quantum theory of the origin which they set out to solve.

And the final section emphasises that everything cosmologists work on relates to the visible universe. It may be that the special conditions of the visible universe which we know about, are only one set of starting conditions which apply to other areas of the universe beyond our knowledge or to other universes. We will never know.

Thoughts

Barrow is an extremely clear and patient explainer. He avoids formulae. Between his prose and the many illustrations I understood most of what he was trying to say, though a number of concepts eluded me.

But the ultimate thing that comes over is his scepticism. Barrow summarises recent attempts to define laws governing the conditions prevailing at the start of the universe by, briefly describing the theories of James Hartle and Stephen Hawking, Alex Vilenkin, and Roger Penrose. But he does so only to go on to emphasise that they are all ‘highly speculative’. They are ‘ideas for ideas’ (p.135).

By the end of the book you get the idea that a very great deal of cosmology is either speculative, or highly speculative. But then half way through he says it’s a distinguishing characteristic of physicists that they can’t stop tinkering – with data, with theories, with ideas and speculations.

So beyond the facts and then the details of the theories he describes, it is insight into this quality in the discipline itself, this restless exploration of new ideas and speculations relating to some of the hardest-to-think-about areas of human knowledge, which is the final flavour the reader is left with.


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Alex’s Adventures In Numberland by Alex Bellos (2010)

Alexander Bellos (born in 1969) is a British writer and broadcaster. He is the author of books about Brazil and mathematics, as well as having a column in The Guardian newspaper. After adventures in Brazil (see his Wikipedia page) he returned to England in 2007 and wrote this, his first book. It spent four months in the Sunday Times bestseller list and led on to five more popular maths books.

It’s a hugely enjoyable read for three reasons:

  1. Bellos immediately establishes a candid, open, good bloke persona, sharing stories from his early job as a reporter on the Brighton Argus, telling some colourful anecdotes about his time in Brazil and then being surprisingly open about the way that, when he moved back to Britain, he had no idea what to do. The tone of the book is immediately modern, accessible and friendly.
  2. However this doesn’t mean he is verbose. The opposite. The book is packed with fascinating information. Every single paragraph, almost every sentence contains a fact or insight which makes you sit up and marvel. It is stufffed with good things.
  3. Lastly, although its central theme is mathematics, it approaches this through a wealth of information from the humanities. There is as much history and psychology and anthropology and cultural studies and philosophy as there is actual maths, and these are all subjects which the average humanities graduate can immediately relate to and assimilate.

Chapter Zero – A Head for Numbers

Alex meets Pierre Pica, a linguist who’s studied the Munduruku people of the Amazon and discovered they have little or no sense of numbers. They only have names for numbers up to five. Also, they cluster numbers together logarithmically i.e. the higher the number, the closer together they clustered them. Same thing is done by kindergarten children who only slowly learn that numbers are evenly spaced, in a linear way.

This may be because small children and the Munduruku don’t count so much as estimate using the ratios between numbers.

It may also be because above a certain number (five) Stone Age man needed to make quick estimates along the lines of, Are there more wild animals / members of the other gang, than us?

Another possibility is that distance appears to us to be logarithmic due to perspective: the first fifty yards we see in close detail, the next fifty yards not so detailed, beyond 100 yards looking smaller, and so on.

It appears that we have to be actively taught when young to overcome our logarithmic instincts, and to apply the rule that each successive whole number is an equal distance from its predecessor and successor i.e. the rational numbers lies along a straight line at regular intervals.

More proof that the logarithmic approach is the deep, hard-wired one is the way most of us revert to its perspective when considering big numbers. As John Allen Paulos laments, people make no end of fuss about discrepancies between 2 or 3 or 4 – but are often merrily oblivious to the difference between a million or a billion, let alone a trillion. For most of us these numbers are just ‘big’.

He goes on to describe experiments done on chimpanzees, monkeys and lions which appear to show that animals have the ability to estimate numbers. And then onto experiments with small babies which appear to show that as soon as they can focus on the outside world, babies can detect changes in number of objects.

And it appears that we also have a further number skill, that guesstimating things – the journey takes 30 or 40 minutes, there were twenty or thirty people at the party, you get a hundred, maybe hundred and fifty peas in a sack. When it comes to these figures almost all of us give rough estimates.

To summarise:

  • we are sensitive to small numbers, acutely so of 1, 2, 3, 4, less so of 5, 6, 7, 8, 9
  • left to our own devices we think logarithmically about larger numbers i.e lose the sense of distinction between them, clump them together
  • we have a good ability to guesstimate medium size numbers – 30, 40, 100

But it was only with the invention of notation, a way of writing numbers down, that we were able to create the linear system of counting (where every number is 1 larger than its predecessor, laid out in a straight line, at regular intervals).

And that this cultural invention enabled human beings to transcend our vague guesstimating abilities, and laid the basis for the systematic manipulation of the world which followed

Chapter One – The Counter Culture

The probable origins of counting lie in stock taking in the early agricultural revolution some 8,000 years ago.

We nowadays count using a number base 10 i.e. the decimal system. But other bases have their virtues, especially base 12. It has more factors i.e. is easier to divide: 12 can be divided neatly by 2, 3, 4 and 6. A quarter of 10 is 2.5 but of 12 is 3. A third of 10 is 3.333 but of 12 is 4. Striking that a version of the duodecimal system (pounds, shillings and pence) hung on in Britain till we finally went metric in the 1970s. There is even a Duodecimal Society of America which still actively campaigns for the superiority of a base 12 counting scheme.

Bellos describes a bewildering variety of other counting systems and bases. In 1716 King Charles XII of Sweden asked Emmanuel Swedenborg to devise a new counting system with a base of 64. The Arara in the Amazon count in pairs, the Renaissance author Luca Paccioli was just one of hundreds who have devised finger-based systems of counting – indeed, the widespread use of base 10 probably stems from the fact that we have ten fingers and toes.

He describes a complicated Chinese system where every part of the hand and fingers has a value which allows you to count up to nearly a billion – on one hand!

The Yupno system which attributes a different value for parts of the body up to its highest number, 33, represented by the penis.

Diagram showing numbers attributed to parts of the body by the Yupno tribe

Diagram showing numbers attributed to parts of the body by the Yupno tribe

There’s another point to make about his whole approach which comes out if we compare him with the popular maths books by John Allen Paulos which I’ve just read.

Paulos clearly sees the need to leaven his explanations of comparative probability and Arrow’s Theorem and so on with lighter material and so his strategy is to chuck into his text things which interest him: corny jokes, anecdotes about baseball, casual random digressions which occur to him in mid-flow. But al his examples clearly 1. emanate from Paulos’s own interests and hobby horses (especially baseball) and 2. they are tacked onto the subjects being discussed.

Bellos, also, has grasped that the general reader needs to be spoonfed maths via generous helpings of other, more easily digestible material. But Bellos’s choice of material arises naturally from the topic under discussion. The humour emerges naturally and easily from the subject matter instead of being tacked on in the form of bad jokes.

You feel yourself in the hands of a master storyteller who has all sorts of wonderful things to explain to you.

In fourth millennium BC, an early counting system was created by pressing a reed into soft clay. By 2700 BC the Sumerians were using cuneiform. And they had number symbols for 1, 10, 60 and 3,600 – a mix of decimal and sexagesimal systems.

Why the Sumerians grouped their numbers in 60s has been described as one of the greatest unresolved mysteries in the history of arithmetic. (p.58)

Measuring in 60s was inherited by the Babylonians, the Egyptians and the Greeks and is why we still measure hours in 60 minutes and the divisions of a circle by 360 degrees.

I didn’t know that after the French Revolution, when the National Convention introduced the decimal system of weights and measures, it also tried to decimalise time, introducing a new system whereby every day would be divided into ten hours, each of a hundred minutes, each divided into 100 seconds. Thus there were a very neat 10 x 100 x 100 = 100,000 seconds in a day. But it failed. An hour of 60 minutes turns out to be a deeply useful division of time, intuitively measurable, and a reasonable amount of time to spend on tasks. The reform was quietly dropped after six months, although revolutionary decimal clocks still exist.

Studies consistently show that Chinese children find it easier to count than European children. This may be because of our system of notation, or the structure of number names. Instead of eleven or twelve, Chinese, Japanese and Koreans say the equivalent of ten one, ten two. 21 and 22 become two ten one and two ten two. It has been shown that this makes it a lot simpler and more intuitive to do basic addition and subtraction.

Bellos goes on to describe the various systems of abacuses which have developed in different cultures, before explaining the phenomenal popularity of abacus counting, abacus clubs, and abacus championships in Japan which helps kids develop the ability to perform anzan, using the mental image of an abacus to help its practitioners to sums at phenomenal speed.

Chapter Two – Behold!

The mystical sense of the deep meaning of numbers, from Pythagoras with his vegetarian religious cult of numbers in 4th century BC Athens to Jerome Carter who advises leading rap stars about the numerological significance of their names.

Euclid and the elegant and pure way he deduced mathematical theorems from a handful of basic axioms.

A description of the basic Platonic shapes leads into the nature of tessalating tiles, and the Arab pioneering of abstract design. The complex designs of the Sierpinski carpet and the Menger sponge. And then the complex and sophisticated world of origami, which has its traditionalists, its pioneers and surprising applications to various fields of advanced science, introducing us to the American guru of modern origami, Robert Lang, and the Japanese rebel, Kazuo Haga, father of Haga’s Theorem.

Chapter Three – Something About Nothing

A bombardment of information about the counting systems of ancient Hindus, Buddhists, about number symbols in Sanskrit, Hebrew, Greek and Latin. How the concept of zero was slowly evolved in India and moved to the Muslim world with the result that the symbols we use nowadays are known as the Arabic numerals.

A digression into ‘a set of arithmetical tricks known as Vedic Mathematics ‘ devised by a young Indian swami at the start of the twentieth century, Bharati Krishna Tirthaji, based on a series of 16 aphorisms which he found in the ancient holy texts known as the Vedas.

Shankaracharya is a commonly used title of heads of monasteries called mathas in the Advaita Vedanta tradition. Tirthaji was the Shankaracharya of the monastery at Puri. Bellos goes to visit the current Shankaracharya who explains the closeness, in fact the identity, of mathematics and Hindu spirituality.

Chapter Four – Life of Pi

An entire chapter about pi which turns out not only to be a fundamental aspect of calculating radiuses and diameters and volumes of circles and cubes, but also to have a long history of mathematicians vying with each other to work out its value to as many decimal places as possible (we currently know the value of pi to 2.7 trillion decimal places) and the surprising history of people who have set records reciting the value if pi.

Thus, in 2006, retired Japanese engineer Akira Haraguchi set a world record for reciting the value of pi to the first 100,000 decimal places from memory! It took 16 hours with five minute beaks every two hours to eat rice balls and drink some water.

There are several types or classes of numbers:

  • natural numbers – 1, 2, 3, 4, 5, 6, 7…
  • integers – all the natural numbers, but including the negative ones as well – …-3, -2, -1, 0, 1, 2, 3…
  • fractions
  • which are also called rational numbers
  • numbers which cannot be written as fractions are called irrational numbers
  • transcendent numbers – ‘a transcendental number is an irrational number that cannot be described by an equation with a finite number of terms’

The qualities of the heptagonal 50p coin and the related qualities of the Reuleux triangle.

Chapter Five – The x-factor

The origin of algebra (in Arab mathematicians).

Bellos makes the big historical point that for the Greeks (Pythagoras, Plato, Euclid) maths was geometric. They thought of maths as being about shapes – circles, triangles, squares and so on. These shapes had hidden properties which maths revealed, thus giving – the Pythagoreans thought – insight into the secret deeper values of the world.

It is only with the introduction of algebra in the 17th century (Bellos attributes its widespread adoption to Descartes’s Method in the 1640s) that it is possible to fly free of shapes into whole new worlds of abstract numbers and formulae.

Logarithms turn the difficult operation of multiplication into the simpler operation of addition. If X x Y = Z, then log X + log Y = log Z. They were invented by a Scottish laird John Napier, and publicised in a huge book of logarithmic tables published in 1614. Englishman Henry Briggs established logarithms to base 10 in 1628. In 1620 Englishman Edmund Gunter marked logarithms on a ruler. Later in the 1620s Englishman William Oughtred placed two logarithmic rulers next to each other to create the slide rule.

Three hundred years of dominance by the slide rule was brought to a screeching halt by the launch of the first pocket calculator in 1972.

Quadratic equations are equations with an x and an x², e.g. 3x² + 2x – 4 = 0. ‘Quadratics have become so crucial to the understanding of the world, that it is no exaggeration to say that they underpin modern science’ (p.200).

Chapter Six – Playtime

Number games. The origin of Sudoku, which is Japanese for ‘the number must appear only once’. There are some 5 billion ways for numbers to be arranged in a table of nine cells so that the sum of any row or column is the same.

There have, apparently, only been four international puzzle crazes with a mathematical slant – the tangram, the Fifteen puzzle, Rubik’s cube and Sudoku – and Bellos describes the origin and nature and solutions to all four. More than 300 million cubes have seen sold since Ernö Rubik came up with the idea in 1974. Bellos gives us the latest records set in the hyper-competitive sport of speedcubing: the current record of restoring a copletely scrambled cube to order (i.e. all the faces of one colour) is 7.08 seconds, a record held by Erik Akkersdijk, a 19-year-old Dutch student.

A visit to the annual Gathering for Gardner, honouring Martin Gardner, one of the greatest popularisers of mathematical games and puzzles who Bellos visits. The origin of the ambigram, and the computer game Tetris.

Chapter Seven – Secrets of Succession

The joy of sequences. Prime numbers.

The fundamental theorem of arithmetic – In number theory, the fundamental theorem of arithmetic, also called the unique factorization theorem or the unique-prime-factorization theorem, states that every integer greater than 1 either is a prime number itself or can be represented as the product of prime numbers.

The Goldbach conjecture – one of the oldest and best-known unsolved problems in number theory and all of mathematics. It states that, Every even integer greater than 2 can be expressed as the sum of two primes. The conjecture has been shown to hold for all integers less than 4 × 1018, but remains unproven despite considerable effort.

Neil Sloane’s idea of persistence – The number of steps it takes to get to a single digit by multiplying all the digits of the preceding number to obtain a second number, then multiplying all the digits of that number to get a third number, and so on until you get down to a single digit. 88 has a persistence of three.

88 → 8 x 8 = 64 → 6 x 4 = 24 → 2 x 4 = 8

John Horton Conway’s idea of the powertrain – For any number abcd its powertrain goes to abcd, in the case of numbers with an odd number of digits the final one has no power, abcde’s powertrain is abcde.

The Recamán sequence Subtract if you can, unless a) it would result in a negative number or b) the number is already in the sequence. The result is:

0, 1, 3, 6, 2, 7, 13, 20, 12, 21, 11….

Gijswijt’s sequence a self-describing sequence where each term counts the maximum number of repeated blocks of numbers in the sequence immediately preceding that term.

1, 1, 2, 1, 1, 2, 2, 2, 3, 1, 1, 2, 1, 1, 2, 2, 2, 3, 2, 1, …

Perfect number A perfect number is any number that is equal to the sum of its factors. Thus 6 – its factors (the numbers which divided into it) are 1, 2 and 3. Which also add up to (are the sum of) 6. The next perfect number is 28 because its factors – 1, 2, 4, 7, 14 – add up to 28. And so on.

Amicable numbers A number is amicable if the sum of the factors of the first number equals the second number, and if the sum of the factors of the second number equals the first. The factors of 220 are 1, 2, 4, 5, 10, 11, 20, 22, 44, 55 and 110. Added together these make 284. The factors of 284 are 1, 2, 4, 71 and 142. Added together they make 220!

Sociable numbers In 1918 Paul Poulet invented the term sociable numbers. ‘The members of aliquot cycles of length greater than 2 are often called sociable numbers. The smallest two such cycles have length 5 and 28’

Mersenne’s prime A prime number which can be written in the form 2n – 1 a prime number that is one less than a power of two. That is, it is a prime number of the form Mn = 2n − 1 for some integer n. The exponents n which give Mersenne primes are 2, 3, 5, 7, 13, 17, 19, 31, … and the resulting Mersenne primes are 3, 7, 31, 127, 8191, 131071, 524287, 2147483647, …

These and every other sequence ever created by humankind are documented on The On-Line Encyclopedia of Integer Sequences (OEIS), also cited simply as Sloane’s. This is an online database of integer sequences, created and maintained by Neil Sloane while a researcher at AT&T Labs.

Chapter Eight – Gold Finger

The golden section a number found by dividing a line into two parts so that the longer part divided by the smaller part is also equal to the whole length divided by the longer part.

Phi The number is often symbolized using phi, after the 21st letter of the Greek alphabet. In an equation form:

a/b = (a+b)/a = 1.6180339887498948420 …

As with pi (the ratio of the circumference of a circle to its diameter), the digits go on and on, theoretically into infinity. Phi is usually rounded off to 1.618.

The Fibonnaci sequence Each number in the sequence is the sum of the two numbers that precede it. So the sequence goes: 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, and so on. The mathematical equation describing it is Xn+2= Xn+1 + Xn.

as the basis of seeds in flowerheads, arrangement of leaves round a stem, design of nautilus shell and much more.

Chapter Nine – Chance Is A Fine Thing

A chapter about probability and gambling.

Impossibility has a value 0, certainty a value 1, everything else is in between. Probabilities can be expressed as fractions e.g. 1/6 chance of rolling a 6 on a die, or as percentages, 16.6%, or as decimals, 0.16…

The probability is something not happening is 1 minus the probability of that thing happening.

Probability was defined and given mathematical form in 17th century. One contribution was the questions the Chevalier de Méré asked the mathematical prodigy Blaise Pascal. Pascal corresponded with his friend, Pierre de Fermat, and they worked out the bases of probability theory.

Expected value is what you can expect to get out of a bet. Bellos takes us on a tour of the usual suspects – rolling dice, tossing coins, and roulette (invented in France).

Payback percentage if you bet £10 at craps, you can expect – over time – to receive an average of about £9.86 back. In other words craps has a payback percentage of 98.6 percent. European roulette has a payback percentage of 97.3 percent. American roulette, 94.7 percent. On other words, gambling is a fancy way of giving your money away. A miserly slot machine has a payback percentage of 85%. The National Lottery has a payback percentage of 50%.

The law of large numbers The more you play a game of chance, the more likely the results will approach the statistical probability. Toss a coin three times, you might get three heads. Toss a coin a thousand times, the chances are you will get very close the statistical probability of 50% heads.

The law of very large numbers With a large enough sample, outrageous coincidences become likely.

The gambler’s fallacy The mistaken belief that, if something happens more frequently than normal during a given period, it will happen less frequently in the future (or vice versa). In other words, that a random process becomes less random, and more predictable, the more it is repeated.

The birthday paradox The probability that, in a set of n randomly chosen people, some pair of them will have the same birthday. By the pigeonhole principle, the probability reaches 100% when the number of people reaches 367 (since there are only 366 possible birthdays, including February 29). However, 99.9% probability is reached with just 70 people, and 50% probability with 23 people. (These conclusions are based on the assumption that each day of the year (excluding February 29) is equally probable for a birthday.) In other words you only need a group of 23 people to have an evens chance that two of them share a birthday.

The drunkard’s walk

The difficulty of attaining true randomness and the human addiction to finding meaning in anything.

The distinction between playing strategy (best strategy to win a game) and betting strategy (best strategy to maximise your winnings), not always the same.

Chapter Ten – Situation Normal

Carl Friedrich Gauss, the bell curve, normal distribution aka Gaussian distribution. Normal or Gaurrian distribution results in a bell curve. Bellos describes the invention and refinement of the bell curve (he explains that ‘the long tail’ results from a mathematician who envisioned a thin bell curve as looking like two kangaroos facing each other with their long tails heading off in opposite directions). And why

Regression to the mean – if the outcome of an event is determined at least in part by random factors, then an extreme event will probably be followed by one that is less extreme. And recent devastating analyses which show how startlingly random sports achievements are, from leading baseball hitters to Simon Kuper and Stefan Szymanski’s analysis of the form of the England soccer team.

Chapter Eleven – The End of the Line

Two breakthroughs which paved the way for modern i.e. 20th century, maths: the invention of non-Euclidean geometry, specifically the concept of hyperbolic geometry. To picture this draw a triangle on a Pringle. it is recognisably a triangle but all its angles do not add up to 180°, therefore it defies, escapes, eludes all the rule of Euclidean geometry, which were designed for flat 2D surfaces.

Bellos introduces us to Daina Taimina, a maths prof at Cornell University, who invented a way of crocheting hyperbolic surfaces. The result looks curly, like curly kale or the surface of coral.

Anyway, the breakaway from flat 2-D Euclidean space led to theories about curved geometry, either convex like a sphere, or hyperbolic like the pringle. It was this notion of curved space, which paved the way for Einstein’s breakthrough ideas in the early 20th century.

The second big breakthrough was Georg Cantor’s discovery that you can have many different types of infinity. Until Cantor the mathematical tradition from the ancient Greeks to Galileo and Newton had fought shy of infinity which threatened to disrupt so many formulae.

Cantor’s breakthrough was to stop thinking about numbers, and instead think of sets. This is demonstrated through the paradoxes of Hilbert’s Hotel. You need to buckle your safety belt to understand it.

Thoughts

This is easily the best book about maths I’ve ever read. It gives you a panoramic history of the subject which starts with innumerate cavemen and takes us to the edge of Einstein’s great discoveries. But Bellos adds to it all kinds of levels and abilities.

He is engaging and candid and funny. He is fantastically authoritative, taking us gently into forests of daunting mathematical theory without placing a foot wrong. He’s a great explainer. He knows a good story when he sees one, and how to tell it engagingly. And in every chapter there is a ‘human angle’ as he describes his own personal meetings and interviews with many of the (living) key players in the world of contemporary maths, games and puzzles.

Like the Ian Stewart book but on a vastly bigger scale, Bellos makes you feel what it is like to be a mathematician, not just interested in nature’s patterns (the basis of Stewart’s book, Nature’s Numbers) but in the beauty of mathematical theories and discoveries for their own sakes. (This comes over very strongly in chapter seven with its description of some of the weirdest and wackiest number sequences dreamed up by the human mind.) I’ve often read scientists describing the beauty of mathematical theories, but Bellos’s book really helps you develop a feel for this kind of beauty.

For me, I think three broad conclusions emerged:

1. Most mathematicians are in it for the fun. Setting yourself, and solving, mathematical puzzles is obviously extremely rewarding. Maths includes the vast territory of puzzles and games, such as the Sudoku and so on he describes in chapter six. Obviously it has all sorts of real-world application in physics, engineering and so on, but Bellos’s book really brings over that a true understanding of maths begins in puzzles, games and patterns, and often remains there for a lifetime. Like everything else maths is no highly professionalised the property of tenured professors in universities; and yet even to this day – as throughout its history – contributions can be made by enthusiastic amateurs.

2. As he points out repeatedly, many insights which started out as the hobby horses of obsessives, or arcane breakthroughs on the borders of our understanding, and which have been airily dismissed by the professionals, often end up being useful, having applications no-one dreamed of. Either they help unravel aspects of the physical universe undreamed of when they were discovered, or have been useful to human artificers. Thus the development of random number sequences seemed utterly pointless in the 19th century, but now underlies much internet security.

On a profounder note, Bellos expresses the eerie, mystical sense many mathematicians have that it seems so strange, so pregnant with meaning, that so many of these arcane numbers end up explaining aspects of the world their inventors knew nothing of. Ian Stewart has an admirably pragmatic explanation for this: he speculates that nature uses everything it can find in order to build efficient life forms. Or, to be less teleological, over the past 3 and a half billion years, every combination of useful patterns has been tried out. Given this length of time, and the incalculable variety of life forms which have evolved on this planet, it would be strange if every number system conceivable by one of those life forms – humankind – had not been tried out at one time or another.

3. My third conclusion is that, despite John Allen Paulos’s and Bellos’s insistence, I do not live in a world ever-more bombarded by maths. I don’t gamble on anything, and I don’t follow sports – the two biggest popular areas where maths is important – and the third is the twin areas of surveys and opinion polls (55% of Americans believe in alien abductions etc etc) and the daily blizzard of reports (for example, I see in today’s paper that the ‘Number of primary school children at referral units soars’).

I register their existence but they don’t impact on me for the simple reason that I don’t believe any of them. In 1992 every opinion poll said John Major would lose the general election, but he won with a thumping majority. Since then I haven’t believed any poll about anything. For example almost all the opinion polls predicted a win for Remain in the Brexit vote. Why does any sane person believe opinion polls?

And ‘new and shocking’ reports come out at the rate of a dozen a day and, on closer examination, lots of them turn out to be recycled information, or much much more mundane releases of data sets from which journalists are paid to draw the most shocking and extreme conclusions. Some may be of fleeting interest but once you really grasp that the people reporting them to you are paid to exaggerate and horrify, you soon learn to ignore them.

If you reject or ignore these areas – sport, gambling and the news (made up of rehashed opinion polls, surveys and reports) – then unless you’re in a profession which actively requires the sophisticated manipulation of figures, I’d speculate that most of the rest of us barely come into contact with numbers from one day to the next.

I think that’s the answer to Paulos and Bellos when they are in their ‘why aren’t more people mathematically numerate?’ mode. It’s because maths is difficult, and counter-intuitive, and hard to understand and follow, it is a lot of work, it does make your head ache. Even trying to solve a simple binomial equation hurt my brain.

But I think the biggest reason that ‘we’ are so innumerate is simply that – beautiful, elegant, satisfying and thought-provoking though maths may be to the professionals – maths is more or less irrelevant to most of our day to day lives, most of the time.


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Human evolution

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Psychology

Tau Zero by Poul Anderson (1970)

One of the most dazzling, mind-boggling and genuinely gripping novels I’ve ever read.

The story is set in the future, after the customary nuclear war which happens in so many futurestories. The twist on this one is that, after the radiation died down, the world’s powers agreed under something referred to as ‘the Covenant’ to put Sweden in charge, handing over all nuclear devices to a country big enough to manage them and keep the peace, but small enough not to have any global ambitions of her own.

Thus liberated from war, humanity – again, as in so many of these optimistic futurestories from the 1950s and 60s – has focused its efforts on space exploration using the handy new ‘ion drive’ which has been discovered, along with something called ‘Bussard engines’, helped along by elaborate ‘scoopfield webs’ to create ‘magnetohydrodynamic fields’.

Reaction mass entered the fire chamber. Thermonuclear generators energised the furious electric arcs that stripped those atoms down to ions; the magnetic fields that separated positive and negative particles; the forces that focused them into beams; the pulses that lashed them to ever higher velocities as they sped down the rings of the thrust tubes, until they emerged scarcely less fast than light itself.

The idea is that the webs are extended ‘nets’ a kilometre or so wide, which drag in all the hydrogen atoms which exist in low density in space, charging and channeling them towards the ‘drive’ which strips them to ions and thrusts them fiercely out the back of the ship – hence driving it forward.

Several voyages of exploration have already been undertaken to the nearest star systems in space ships which use these drives to travel near the speed of light, and fast-moving ‘probes’ have been sent to all the nearest star systems.

One of these probes reached the star system Centauri and now, acting on its information, a large spaceship, the Leonora Christine, is taking off on a journey to see if the third planet orbiting round Centauri really is habitable, as the probe suggests, and could be settled by ‘man’.

Einstein’s theory of relativity suggests that as any object approaches the speed of light, its experience of time slows down. The plan is for the Leonora Christine to accelerate for a couple of years towards near light speed, travel at that speed for a year, then slow down for a couple of years.

Five years there, whereupon they will either a) stay if the planet is habitable b) return, if it is not. Due to this time dilation effect those on the expedition will only age twelve years or so, while 43 or more years will pass back on earth (p.49).

(Time dilation is a key feature of Joe Haldeman’s novel, The Forever War, in which the protagonist keeps returning from tours of duty off-world to discover major changes in terrestrial society have taken place in his absence: it is, therefore, a form of one-way time travel.)

The Leonora Christine carries no fewer than fifty passengers, a cross-section of scientists, engineers, biologists and so on. Unlike any other spaceship I’ve read of it is large enough to house a gym, a theatre, a canteen and a swimming pool!

Two strands

Tau Zero is made up of two very different types of discourse. It is (apparently) a classic of ‘hard’ sci fi because not three pages go by without Anderson explaining in daunting technical detail the process workings of the ion drive, or the scoopnets, explaining the ratio of hydrogen atoms in space, or how the theory of relativity works, and so on. Not only are there sizeable chunks of uncompromising scientific information every few pages, but understanding them is key to the plot and narrative.

Starlike burned the hydrogen fusion, aft of the Bussard module that focused the electromagnetism which contained it. A titanic gas-laser effect aimed photons themselves in a beam whose reaction pushed the ship forward – and which would have vaporised any solid body it struck. The process was not 100 percent efficient. But most of the stray energy went to ionise the hydrogen which escaped nuclear combustion. These protons and electrons, together with the fusion products, were also hurled backward by the force fields, a gale of plasma adding its own increment of momentum. (p.40)

But at the same time, or regularly interspersed with the tech passages, are the passages describing the ‘human interest’ side of the journey, which is full of clichés and stereotypes, a kind of Peyton Place in space. To be more specific, the book was first published in instalments in 1967 and it has a very 1960s mindset. Anderson projects idealistic 1960s talk about ‘free love’ into a future in which adults have no moral qualms about ‘sleeping around’.

Before they leave, the novel opens with a pair of characters in a garden in Stockholm walking and having dinner and then the woman, Ingrid Lindgren, proposes to the man, Charles Reymont, that they become a couple. During all the adventures that follow, there is a continual exchanging of partners among the 25 men and 25 women on board, with little passages set aside for flirtations and guytalk about the girls or womentalk about the boys.

When a partnership ends one of the couple moves out, the other moves in with a room-mate of the same sex for a period, or immediately moves in with their new partner. It’s like wife-swapping in space. In a key moment of the plot, the ship’s resident astronomer, a short ugly anti-social and smelly man, becomes so depressed that he can no longer function. At which point Ingrid tactfully gets rid of the concerned captain and officers and… sleeps with him. So sex is deployed ‘tactically’ as a form of therapy.

Sex

He admired the sight of her. Unclad, she could never be called boyish. The curves of her breasts and flank were subtler than ordinary, but they were integral with the rest of her – not stuccoed on, as with too many women – and when she moved, they flowed. So did the light along her skin which had the hue of the hills around San Francisco Bay in their summer, and the light in her hair, which had the smell of every summer day that ever was on earth. (p.62)

Feminism

From a feminist perspective, it is striking how the 25 women aboard the ship are a) all scientists and experts in their fields b) are not passive sex objects, but very active in deciding who they want to partner with and why. One of the two strong characters in the narrative is a woman, Ingred Lindgren.

Characters

  • Captain Lars Telander
  • Ingrid Lindgren, steely disciplined first officer
  • Charles Reymont, takes over command when the ship hits crisis
  • Boris Fedoroff, Chief Engineer
  • Norbert Williams, American chemist
  • Chi-Yuen Ai-Ling, Planetologist
  • Emma Glassgold, molecular biologist
  • Jane Sadler, Canadian bio-technician
  • Machinist Johann Freiwald
  • Astronomer Elof Nilsson
  • Navigation Officer, Auguste Boudreau
  • Biosystems Chief Pereira
  • Margarita Jimenes
  • Iwamoto Tetsuo
  • Hussein Sadek
  • Yeshu ben-Zvi
  • Mohandas Chidambaran
  • Phra Takh
  • Kato M’Botu

Thus the ship’s progress proceeds smoothly, while the crew discuss decorating the canteen and common rooms, paint murals and have numerous affairs. Five years is a long time to pass in a confined ship. And meanwhile the effects of travelling ever closer to light speed create unusual effects and, to be honest, I was wondering what all the fuss was about this book.

When Leonora Christine attained a substantial fraction of light speed, its optical effects became clear to the unaided sight. Her velocity and that of the rays from a star added vectorially; the result was aberration. Except for whatever lay dead aft or ahead, the apparent position changed. Constellations grew lopsided, grew grotesque, and melted, as their members crawled across the dark. More and more, the stars thinned out behind the ship and crowded before her. (p.45)

Tau

Anderson gives us a couple of pages introducing the tau equation. This defines the ‘interdependence of space, time, matter, and energy’, If v is the velocity of the spaceship, and c the velocity of light, then tau equals the square root of 1 minus v² divided by c². In other words the closer the ship’s velocity, v, gets to the speed of light, c (186,00 miles per second), then v² divided by c² gets closer and closer to 1; therefore 1 minus something which is getting closer to 1 gets closer and closer to 0; and the square root of that number similarly approaches closer and closer to zero.

Or to put it another way, the closer tau gets to zero the faster the ship is flying, the greater its mass, and the slower the people inside it experience time, relative to the rest of the ‘static’ universe.

The plot kicks in

So the narrative trundles amiably along for the first 60 or so pages, interspersing passages of dauntingly technical exposition with the petty jealousies, love affairs and squabbles of the human characters, until…

The ship passes through an unanticipated gas cloud, just solid enough to possibly destroy her, at the very least do damage – due to the enormous speed she’s now flying at which effects her mass.

Captain Telander listens to his experts feverishly calculating what impact will mean but ultimately they have to batten down the hatches, make themselves secure and hope for the best, impact happening on page 75 of this 190-page long book.

In the event the ship survives but the technicians quickly discover that impact has knocked out the decelerating engines. Now, much worse, the technicians explain to the captain and the lead officers, First Officer Lindgren and the man responsible for crew discipline, Reymont, the terrible catch-22 they’re stuck in.

In order to investigate what’s happened to the decellerator engines, the technicians would have to go to the rear of the ship and investigate manually. Unfortunately, they would be vaporised in nano-seconds by the super-powerful ion drive if they got anywhere near it. Therefore, no-one can investigate what’s wrong with the decelerator engine until the accelerator engine is turned off.

But here’s the catch: the ship is travelling so close to the speed of light that, if they turned the accelerator engines off, the crew would all be killed in moments. Why? Because the ship is constantly being bombarded by hydrogen atoms found in small amounts throughout space. At the moment the accelerator engines and scoopfield webs are directing these atoms away from the ship and down into the ion drive. The ion drive protects the ship. The moment it is turned off, these hydrogen atoms will suddenly be bombarding the ship’s hull and, because of the speed it is going at, the effect will be to split the hydrogen atoms releasing gamma rays. The gamma rays will penetrate the hull and fry all the humans inside in moments.

Thus they cannot stop. They are doomed to continue accelerating forever or until they all die.

It is at this point that the way Anderson has introduced us to quite a few named characters, and shown them bickering, explaining abstruse theory, getting drunk and getting laid begins to show its benefits. Because the rest of the novel consists of a series of revelations about the logical implications of their plight and, if these were just explained in tech speak they would be pretty flat and dull: the drama, the grip of the novel derives from the way the matrix of characters he’s developed respond to each new revelation: getting drunk, feeling suicidal, determined to tough it out, relationships fall apart, new relationships are formed. In and of themselves these human interest passages are hardly Tolstoy, but they are vital for the novel’s success because they dramatise each new twist in the story and, as the characters discuss the implications, the time spent reading their dialogue and thoughts helps the reader, also, to process and assimilate the story’s mind-blowing logic.

A series of unfortunate incidents

Basically what happens is there is a series of four or five further revelations which confirm the astronauts in their plight, but expand it beyond their, or our, wildest imaginings.

At first the captain and engineer come up with a plan of sorts. They know, or suspect, that between galaxies the density of hydrogen atoms in the ether falls off. If they can motor beyond our galaxy they can find a place where the hydrogen density of space is so minute that they can afford to turn off the ion drive and repair the decelerator.

This is discussed in detail, with dialogue working through both the technical aspects and also the emotional consequences. Many of the crew had anticipated returning to earth to be reunited with at least some members of their family. Now that has gone for good. As has the original plan of exploring an earth-style planet.

And so we are given some mind-blowing descriptions of the ship deliberately accelerating in order to pass right through the galaxy and beyond. But unfortunately, the scientists then discover that the space between galaxies is not thin enough to protect them. Also there is another catch-22. In order to travel out of the galaxy they have had to increase speed. But now they are flying everso close to the speed of light, the risk posed by turning off the ion drive and exposing themselves to the stray hydrogen atoms in space has become greater. The faster they go in order to find space thin enough to stop in, the thinner that space has to become.

The astronomers now come to the conclusion that space is still to full of hydrogen atoms in the sectors which contain clusters of galaxies. They decide to increase the ship’s velocity even more in order not just to leave our galaxy, but to get clear of our entire family of galaxies. This they calculate, will take another year or so at present velocities.

Thus it is that the book moves forward by presenting a new problem, the scientists suggest a solution which involves travelling faster and further, the crew is told and slowly gets used to the idea, as do we, via various conversations and attitudes and emotional responses. But when that goal is attained, it turns out there is another problem, and so the tension and the narrative drive of the book is relentlessly ratcheted up.

And of course, the further they travel and the closer to light speed, the more the tau effect predicts that time slows down for them, or, to put it another way, time speeds up for the rest of the universe. Early on in the post-disaster section, the crew assemble to celebrate the fact that a hundred years have passed back on earth: everyone they knew is dead. It is a sombre assembly with heavy drinking, casual sex, melancholy thoughts.

But by the time we get to the bit where they have flown clear of the galaxy only to be disappointed to find that inter-galactic space is too full of hydrogen for them to stop, by this stage they realise that thousands of years have passed back on earth.

By the time they fly free of the entire cluster of galaxies, they know that tens of thousands of years have passed. And eventually, as their tau approaches closer and closer to zero, they realise that millions of years have passed (one million is passed n page 136).

For when they do eventually fly beyond our entire family of galaxies they encounter another problem which is discovering that empty space is now too dispersed to allow them to decelerate. Even if they turn off the ion drive and fix the decelerating engine, there isn’t enough matter in truly empty space for the engine to latch on to and use as fuel to slow them (p.147).

Thus they decide to continue onwards, letting their acceleration, and mass, increase until they find a part of space with just the right conditions.

The accessible mass of the whole galactic clan that was her goal proved inadequate to brake her velocity. Therefore she did not try. Instead, she used what she swallowed to drive forward all the faster. She traversed the domain of this second clan – with no attempt at manual control, simply spearing through a number of its member galaxies – in two days. On the far side, again into hollow space, she fell free. The stretch to the next attainable clan was on the order of another hundred million light-years. She made the passage in about a week. (p.151)

On they fly at incomprehensible speed, while various human interest stories unfurl between the ship’s crew, until they (and the reader) reach the blasé condition of feeling the ship’s hull rattle and hum for a few moments and a character will say, ‘There goes another galaxy’.

Now if this was a J.G. Ballard novel, they’d all have gone mad and started eating each other by now. Anderson’s take on human psychology is much more bland and optimistic. Some of the crew get a bit depressed, but nothing some casual sex, or a project to redecorate the canteen can’t fix.

The main ‘human’ part of the narrative describes the way the ship’s ‘constable’, Charles Reymont who we met back on the opening pages, takes effective control from the captain. Initially this is basic psychology, Charles realising it will help discipline best if the captain becomes an aloof figure beyond criticism or reproach while he, Charles, imposes discipline, structure and purpose – allotting the crew tasks and missions to perform to maintain their morale, and letting them hate or resent him for it if they will. But over time the captain really does lose the ability to decide anything and Charles becomes the ship’s dictator. This is complicated by the fact that he discovers the woman who had suggested they become a couple, Ingrid, in someone else’s bed though she swears she was only doing it for therapeutic purposes. They split up and Charles pairs off with the Chinese planetologist, Chi-Yuen Ai-Ling, leading to a number of sexy descriptions of her naked body. But Ingrid continues to hold a torch for him and he for her. That’s the spine of the ‘human interest’ part of the novel.

Hundreds of millions of years have passed and indeed, in the last 40 pages or so a character lets slips that it must be over a billion years since they left earth.

it’s at this stage that the book becomes truly visionary. For, after some delay and conferring with colleagues, the astronomer comes to the captain and Reymont and Lindgren to announce that… the universe itself is changing. The galaxies they are flying through no longer contain fit young stars. Increasingly what they’re seeing through their astronomical instruments (not the naked eye) is that the galaxies are made of low intensity red dwarfs.

The universe is running down.

So many billion years have passed – one character estimates one hundred billion years (p.170) that they have travelled far into ‘the future’ and are witnessing the end of the universe. The stars are going out and the actual space of the universe is contracting.

Anderson’s vision is based on the theory that the universe began in a big bang, has and will expand for billions of years but will eventually reach a stage where the initial blast of energy from the bang is so dispersed that it is countered by the cumulative gravity of all the matter in the universe – which will stop it expanding and make it slowly and then with ever-increasing speed, hurtle towards a ‘Big Crunch’ when all the matter in the universe returns to the primal singularity.

Face with this haunting, terrifying fact, the scientists again make calculations and act on a hunch. They guess that the singularity won’t actually become a minute particle but will be shrouded in ‘en enormous hydrogen envelope’ (p.175), the simplest chemical, and calculate that the ship will be flying so fast that it will survive the Big Crunch and live on to witness the creation of the next universe.

‘The outer part of that envelope may not be too hot or radiant or dense for us. Space will be small enough, though, that we can circle around and around the monobloc as a kind of satellite. When it blows up and space starts to expand again, we’ll spiral out ourselves.’ (Reymont, p.175)

And this is what happens. Anderson gives a mind bogging description of the ship reaching such an infinitesimal value of tau that it flies right through the Big Crunch and out into the new universe which explodes outwards (pp.181-3).

Indeed it is travelling so fast, and time outside is moving so fast, that they can chose how many billions of years into the history of the new universe they want to stop (p.184). A quick calculation suggests that it took about 10 billion years for a plenty like earth to come into being and establish the conditions for life to evolve, and so they calculate their deceleration to take place that far into the future of this new universe.

Epilogue

And this is what they do, and the last few pages cut to Reymont and Ingrid, the lovers we met in the opening pages falling dreamily in love, now lying under a tree on a planet which has an earth-like atmosphere but blue vegetation, three moons and all sorts of weird fauna and flora, as they plan their lives together (pp.188-190)

We left plausibility behind a long time ago. Instead the book turns into an absolutely gripping rollercoaster of a ride, one of the most genuinely mind-blowing and gripping stories I’ve ever read. What a trip!


Style

the foregoing summary may give the impression the story is told in language as clear as an instruction manual, but this would be wrong.

Putting the plot to one side, one of the most striking features of Tau Zero is its prose style – an odd and ungainly variant of standard English which makes you pause on every page.

Leonora Christine was nearing the third year of her journey, or the tenth year as the stars counted time, when grief came upon her. (p.63)

Anderson was born in America (in 1926) but his mother took him as a boy to live in Denmark where she’d originally come from, until the outbreak of war forced them to return. For this or the general fact of growing up in an immigrant Scandinavian family, Anderson’s English is oddly stilted and phrased. It often sounds like it’s been translated from a Norse saga.

She gave him cheerful greeting as he entered. (p.52)

They would live out their lives, and belike their children and grandchildren too (p.53)

He stood moveless (p.58)

Nor would he have stopped to dress, had he been abed. (p.64)

Telander must perforce smile a bit as he went out the door. (p.69)

Fedoroff spoke. His words fell contemptuous. (p.80)

He clapped the navigator’s back in friendly wise. (p.159)

She rested elbow on head, forehead on hand. (p.161)

Every pages has sentences containing odd kinks away from natural English. As a small example it’s typified by the way Anderson refers throughout the story not to the ship’s ‘crew’, but to its folk. Another consistent quirk is the way people don’t experience emotions or psychological states, these, in the form of abstract nouns, come over them.

Soberness had come upon her. (p.100)

Dismay sprang forth on Williams. (p.105)

Anger still upbore the biologist. (p.106)

Dismay shivered in her. (p.116)

Hardness fell from him. (p.125)

Weight grabbed at Reymont. (.167)

Sometimes he achieves a kind of incongruous poetry by accident.

Footsteps thudded in the mumble of energies. (p.70)

Ingrid Lindgren regarded him for a time that shivered. (p.71)

The ship jeered at him in her tone of distant lightnings. (p.84)

Sometimes it makes the already challenging technical explanations just that little bit more impenetrable.

Then again, maybe this slightly alien English helps to create a sense of mild dislocation which is not inappropriate for a science fiction story, especially one which takes us right to the edge of the universe and then beyond!


Related links

Other science fiction reviews

1888 Looking Backward 2000-1887 by Edward Bellamy – Julian West wakes up in the year 2000 to discover a peaceful revolution has ushered in a society of state planning, equality and contentment
1890 News from Nowhere by William Morris – waking from a long sleep, William Guest is shown round a London transformed into villages of contented craftsmen

1895 The Time Machine by H.G. Wells – the unnamed inventor and time traveller tells his dinner party guests the story of his adventure among the Eloi and the Morlocks in the year 802,701
1896 The Island of Doctor Moreau by H.G. Wells – Edward Prendick is stranded on a remote island where he discovers the ‘owner’, Dr Gustave Moreau, is experimentally creating human-animal hybrids
1897 The Invisible Man by H.G. Wells – an embittered young scientist, Griffin, makes himself invisible, starting with comic capers in a Sussex village, and ending with demented murders
1898 The War of the Worlds – the Martians invade earth
1899 When The Sleeper Wakes/The Sleeper Wakes by H.G. Wells – Graham awakes in the year 2100 to find himself at the centre of a revolution to overthrow the repressive society of the future
1899 A Story of the Days To Come by H.G. Wells – set in the same future London as The Sleeper Wakes, Denton and Elizabeth defy her wealthy family in order to marry, fall into poverty, and experience life as serfs in the Underground city run by the sinister Labour Corps

1901 The First Men in the Moon by H.G. Wells – Mr Bedford and Mr Cavor use the invention of ‘Cavorite’ to fly to the moon and discover the underground civilisation of the Selenites
1904 The Food of the Gods and How It Came to Earth by H.G. Wells – scientists invent a compound which makes plants, animals and humans grow to giant size, prompting giant humans to rebel against the ‘little people’
1905 With the Night Mail by Rudyard Kipling – it is 2000 and the narrator accompanies a GPO airship across the Atlantic
1906 In the Days of the Comet by H.G. Wells – a comet passes through earth’s atmosphere and brings about ‘the Great Change’, inaugurating an era of wisdom and fairness, as told by narrator Willie Leadford
1908 The War in the Air by H.G. Wells – Bert Smallways, a bicycle-repairman from Kent, gets caught up in the outbreak of the war in the air which brings Western civilisation to an end
1909 The Machine Stops by E.M. Foster – people of the future live in underground cells regulated by ‘the Machine’ until one of them rebels

1912 The Lost World by Sir Arthur Conan Doyle – Professor Challenger leads an expedition to a plateau in the Amazon rainforest where prehistoric animals still exist
1912 As Easy as ABC by Rudyard Kipling – set in 2065 in a world characterised by isolation and privacy, forces from the ABC are sent to suppress an outbreak of ‘crowdism’
1913 The Horror of the Heights by Arthur Conan Doyle – airman Captain Joyce-Armstrong flies higher than anyone before him and discovers the upper atmosphere is inhabited by vast jellyfish-like monsters
1914 The World Set Free by H.G. Wells – A history of the future in which the devastation of an atomic war leads to the creation of a World Government, told via a number of characters who are central to the change
1918 The Land That Time Forgot by Edgar Rice Burroughs – a trilogy of pulp novellas in which all-American heroes battle ape-men and dinosaurs on a lost island in the Antarctic

1921 We by Evgeny Zamyatin – like everyone else in the dystopian future of OneState, D-503 lives life according to the Table of Hours, until I-330 wakens him to the truth
1925 Heart of a Dog by Mikhail Bulgakov – a Moscow scientist transplants the testicles and pituitary gland of a dead tramp into the body of a stray dog, with disastrous consequences
1927 The Maracot Deep by Arthur Conan Doyle – a scientist, engineer and a hero are trying out a new bathysphere when the wire snaps and they hurtle to the bottom of the sea, there to discover…

1930 Last and First Men by Olaf Stapledon – mind-boggling ‘history’ of the future of mankind over the next two billion years
1938 Out of the Silent Planet by C.S. Lewis – baddies Devine and Weston kidnap Ransom and take him in their spherical spaceship to Malacandra aka Mars,

1943 Perelandra (Voyage to Venus) by C.S. Lewis – Ransom is sent to Perelandra aka Venus, to prevent a second temptation by the Devil and the fall of the planet’s new young inhabitants
1945 That Hideous Strength: A Modern Fairy-Tale for Grown-ups by C.S. Lewis– Ransom assembles a motley crew to combat the rise of an evil corporation which is seeking to overthrow mankind
1949 Nineteen Eighty-Four by George Orwell – after a nuclear war, inhabitants of ruined London are divided into the sheep-like ‘proles’ and members of the Party who are kept under unremitting surveillance

1950 I, Robot by Isaac Asimov – nine short stories about ‘positronic’ robots, which chart their rise from dumb playmates to controllers of humanity’s destiny
1950 The Martian Chronicles – 13 short stories with 13 linking passages loosely describing mankind’s colonisation of Mars, featuring strange, dreamlike encounters with Martians
1951 Foundation by Isaac Asimov – the first five stories telling the rise of the Foundation created by psychohistorian Hari Seldon to preserve civilisation during the collapse of the Galactic Empire
1951 The Illustrated Man – eighteen short stories which use the future, Mars and Venus as settings for what are essentially earth-bound tales of fantasy and horror
1952 Foundation and Empire by Isaac Asimov – two long stories which continue the future history of the Foundation set up by psychohistorian Hari Seldon as it faces attack by an Imperial general, and then the menace of the mysterious mutant known only as ‘the Mule’
1953 Second Foundation by Isaac Asimov – concluding part of the ‘trilogy’ describing the attempt to preserve civilisation after the collapse of the Galactic Empire
1953 Earthman, Come Home by James Blish – the adventures of New York City, a self-contained space city which wanders the galaxy 2,000 years hence powered by spindizzy technology
1953 Fahrenheit 451 by Ray Bradbury – a masterpiece, a terrifying anticipation of a future when books are banned and professional firemen are paid to track down stashes of forbidden books and burn them
1953 Childhood’s End by Arthur C. Clarke a thrilling narrative involving the ‘Overlords’ who arrive from space to supervise mankind’s transition to the next stage in its evolution
1954 The Caves of Steel by Isaac Asimov – set 3,000 years in the future when humans have separated into ‘Spacers’ who have colonised 50 other planets, and the overpopulated earth whose inhabitants live in enclosed cities or ‘caves of steel’, and introducing detective Elijah Baley to solve a murder mystery
1956 The Naked Sun by Isaac Asimov – 3,000 years in the future detective Elijah Baley returns, with his robot sidekick, R. Daneel Olivaw, to solve a murder mystery on the remote planet of Solaria
1956 They Shall Have Stars by James Blish – explains the invention – in the near future – of the anti-death drugs and the spindizzy technology which allow the human race to colonise the galaxy
1957 The Black Cloud by Fred Hoyle – a vast cloud of gas heads into the solar system, blocking out heat and light from the sun with cataclysmic consequences on Earth, until a small band of maverick astronomers discovers that the cloud contains intelligence and can be communicated with
1959 The Triumph of Time by James Blish – concluding story of Blish’s Okie tetralogy in which Amalfi and his friends are present at the end of the universe

1961 A Fall of Moondust by Arthur C. Clarke a pleasure tourbus on the moon is sucked down into a sink of moondust, sparking a race against time to rescue the trapped crew and passengers
1962 A Life For The Stars by James Blish – third in the Okie series about cities which can fly through space, focusing on the coming of age of kidnapped earther, young Crispin DeFord, aboard New York
1962 The Man in the High Castle by Philip K. Dick In an alternative future America lost the Second World War and has been partitioned between Japan and Nazi Germany. The narrative follows a motley crew of characters including a dealer in antique Americana, a German spy who warns a Japanese official about a looming surprise German attack, and a woman determined to track down the reclusive author of a hit book which describes an alternative future in which America won the Second World War
1963 Planet of the Apes by Pierre Boulle French journalist Ulysse Mérou accompanies Professor Antelle on a two-year space flight to the star Betelgeuse, where they land on an earth-like plane to discover that humans and apes have evolved here, but the apes are the intelligent, technology-controlling species while the humans are mute beasts
1968 2001: A Space Odyssey a panoramic narrative which starts with aliens stimulating evolution among the first ape-men and ends with a spaceman being transformed into galactic consciousness
1968 Do Androids Dream of Electric Sheep? by Philip K. Dick In 1992 androids are almost indistinguishable from humans except by trained bounty hunters like Rick Deckard who is paid to track down and ‘retire’ escaped andys
1969 Ubik by Philip K. Dick In 1992 the world is threatened by mutants with psionic powers who are combated by ‘inertials’. The novel focuses on the weird alternative world experienced by a group of inertials after a catastrophe on the moon

1970 Tau Zero by Poul Anderson – spaceship Leonora Christine leaves earth with a crew of fifty to discover if humans can colonise any of the planets orbiting the star Beta Virginis, but when its deceleration engines are damaged, the crew realise they need to exit the galaxy altogether in order to find space with low enough radiation to fix the engines, and then a series of unfortunate events mean they find themselves forced to accelerate faster and faster, effectively travelling through time as well as space until they witness the end of the entire universe
1971 Mutant 59: The Plastic Eater by Kit Pedler and Gerry Davis – a genetically engineered bacterium starts eating the world’s plastic
1973 Rendezvous With Rama by Arthur C. Clarke – in 2031 a 50-kilometre long object of alien origin enters the solar system, so the crew of the spaceship Endeavour are sent to explore it
1974 Flow My Tears, The Policeman Said by Philip K. Dick – America after the Second World War has become an authoritarian state. The story concerns popular TV host Jason Taverner who is plunged into an alternative version of this world in which he is no longer a rich entertainer but down on the streets among the ‘ordinaries’ and on the run from the police. Why? And how can he get back to his storyline?
1974 The Forever War by Joe Haldeman The story of William Mandella who is recruited into special forces fighting the Taurans, a hostile species who attack Earth outposts, successive tours of duty requiring interstellar journeys during which centuries pass on Earth, so that each of his return visits to the home planet show us society’s massive transformations over the course of the thousand years the war lasts.

1981 The Golden Age of Science Fiction edited by Kingsley Amis – 17 classic sci-fi stories from what Amis considers the Golden Era of the genre, namely the 1950s
1982 2010: Odyssey Two by Arthur C. Clarke – Heywood Floyd joins a Russian spaceship on a two-year journey to Jupiter to a) reclaim the abandoned Discovery and b) investigate the monolith on Japetus
1984 Neuromancer by William Gibson – burnt-out cyberspace cowboy Case is lured by ex-hooker Molly into a mission led by ex-army colonel Armitage to penetrate the secretive corporation, Tessier-Ashpool at the bidding of the vast and powerful artificial intelligence, Wintermute
1986 Burning Chrome by William Gibson – ten short stories, three or four set in Gibson’s ‘Sprawl’ universe, the others ranging across sci-fi possibilities, from a kind of horror story to one about a failing Russian space station
1986 Count Zero by William Gibson
1987 2061: Odyssey Three by Arthur C. Clarke – Spaceship Galaxy is hijacked and forced to land on Europa, moon of the former Jupiter, in a ‘thriller’ notable for Clarke’s descriptions of the bizarre landscapes of Halley’s Comet and Europa
1988 Mona Lisa Overdrive by William Gibson – third of Gibson’s ‘Sprawl’ trilogy in which street-kid Mona is sold by her pimp to crooks who give her plastic surgery to make her look like global simstim star Angie Marshall who they plan to kidnap but is herself on a quest to find her missing boyfriend, Bobby Newmark, one-time Count Zero, while the daughter of a Japanese ganster who’s sent her to London for safekeeping is abducted by Molly Millions, a lead character in Neuromancer

1990 The Difference Engine by William Gibson and Bruce Sterling – in an alternative history Charles Babbage’s early computer, instead of being left as a paper theory, was actually built, drastically changing British society, so that by 1855 it is led by a party of industrialists and scientists who use databases and secret police to keep the population under control

2010: Odyssey Two by Arthur C. Clarke (1982)

This is a direct sequel to 2001: A Space Odyssey and nothing like as good. In the original book the best parts were: the vivid imagining of life among primitive man-apes, the hair-raising mental collapse of the computer HAL 9000 aboard the spaceship, and then the extraordinary vision of Bowman hurtling through the star gate and being transformed into a cosmic consciousness.

The weakest part was the middle which described the mundane, chatty, boring bureaucrats and scientists who held interminable meetings to discuss the mysterious monolith which had been discovered on the moon, and the practical physics of orbits and apogees and escape velocities attached to the journey of spaceship Discovery.

Well, 2010: Odyssey Two, for the first half or so, is an extension of precisely those mundane, boring parts of the first book. It’s nearly 100 pages longer than the original novel, and cast in 55 chapters, themselves divided into seven parts.

1. Leonov

Clarke’s protagonists always have sensible home lives. We met Dr Heywood Floyd, retired space expert, when he flew via a space station to the moon to explore the artifact in 2001.

Now we meet him again. Floyd has remarried a much younger woman, has a two-year-old son, and lives in an idyllic house by the Indian Ocean which appears to have a kind of dock into which swim tame dolphins to ‘talk’ to them.

Floyd is informed that an expedition is being prepared to go rendezvous with the Discovery, the spaceship HAL 900 went mental on, and from which David Bowman undertook his last journey through the alien star gate.

The catch is that this new expedition is being mounted by the Russians. In this version of the future (2010) Russia is still a communist country, but less paranoid than in the 1980s, and Russians and Americans are co-operating, at least in space.

So, in typical Clarke fashion, we learn a lot, an awful lot about the technical spec of the spaceship Cosmonaut Alexei Leonov (including the typically Clarkean fact, given us in the extended preface, that Clarke was a friend of the real Alexei Leonov, an actual Russian cosmonaut. Clarke gives the impression of knowing everyone who was anyone in space exploration of his day).

Characteristically, Clarke gives us some of this information in the form of extended official memos which he ‘quotes’ – typical of his fondness for bureaucracy, meetings and the ways of large organisations which, to be fair, he was himself very familiar with, having run several (e.g. chair of the British Interplanetary Society 1946–47 and 1951–53).

The Leonov has a crew of seven Russians and we get lengthy profiles of all of them, starting with captain Tatiana Orlova (women have figured prominently in the crews of Clarke’s previous novels, though this is the first woman captain), plus a couple of westerners – the big, bear-like Walter Curnow, systems specialist, and the small, slight and intense computer specialist, Dr Sivasubramanian Chandrasegarampillai, known more familiarly as Dr Chandra.

The Leonov will be using the new (fictional) ‘Sakharov Drive’, which uses a pulsed thermonuclear reaction to heat and expel almost any propellant (p.49). All space-based science fiction has to invent new ‘drives’ since, using our current rocket technology, we would never be able to get anywhere in human lifetimes.

Even using the made-up Sakharov Drive, it will take two years to get to Saturn, so Floyd and Curnow and the Sri Lankan will be put into hibernation / a cryogenic state. As you can imagine, this is carefully and realistically described.

2. Tsien

Clarke gives a powerful but factually based account of what it must be like to wake from a cryogenic sleep. This is followed by vivid descriptions of seeing Jupiter from close up (based, as the preface tells us, on the pictures relayed by the 1979 Voyager flybys of Jupiter).

But to the crew’s astonishment they see another spaceship crossing Jupiter’s vast outline and realise that the ‘space station’ they and everyone else knew the Chinese were building in earth’s orbit – was in fact a space ship.

Here it is. It has matched and even beaten their speed. Since the Chinese ship refuses to reply to messages, the scientists aboard Leonov do some calculations and realise it is going to use the gravity of Jupiter to give it the ‘slingshot’ effect (which Clarke fully explained in Rendezvous with Rama and fully explains here) in order to land on Europa, one of Jupiter’s moons!

Our guys speculate that the Tsien (they’ve found out that’s the Chinese ship’s name) will refuel from the ice/water which covers most of Europa’s surface and use that as propellant fuel to travel on towards Europa – water being a perfect propellant for their version of the Sakharov Drive.

Having figured all this out during intense discussions with the rest of the Russian crew, Floyd retired for asleep, but is woken because they’ve received a Mayday from the Tsien.

It is a Dr Chang broadcasting from his spacesuit radio. He is asking for Floyd by name because – of course – they met at some astronomy conference in China a few years ago. And he proceeds to tell an astonishing tale that there is life on Europa.

The Chinese landed and immediately began drilling down into the frozen ice of one of the many ‘canals’ that criss-cross Europa, but arc lights they were using to illuminate their activities awoke some kind of seaweed monsters which rose to the surface, broke through the ice, and slowly crawled various ‘arms’ towards the spaceship, clambered up it and crushed it killing everyone inside

At which point Dr Chang managed to turn off all the floodlights and the thing, already freezing out in the open, began to withdraw back to the canal whence it came. Chang forlornly broadcasts his message (he is broadcasting on his weak personal spacesuit radio and cannot receive a reply from the Leonov) before Europa disappears round the other side of Jupiter and radio contact is cut off.

3. Discovery

Clarke gives an encyclopedia description of the various moons of Jupiter before describing with scientific accuracy how the Leonov itself descends into the outer atmosphere of the planet in order to benefit from the slingshot effect which they will use to slow down their velocity so that they can rendezvous with the floating empty hulk of Discovery and investigate the anomaly which Bowman identified on one of its moon, Japetus.

When they finally arrive in the same orbit as the Discovery they find it is spinning on its axis (as a reaction to the circular motion of the central centrifuge part of the ship). All this, all the problems of getting aboard the empty Discovery, slowing its spin, docking the Leonov to it, clearing out the stale air (and rotten food) and activating all the life support systems, are described with typically Clarkean thoroughness and plausibility.

The focus switches to Dr Chandra who now undertakes the long process of reactivating HAL 9000. Unsurprisingly, HAL has no memory of the antenna unit malfunctioning, which was the pretext for making Frank Poole go for a spacewalk – and then murdering him in the first book. He has no memory of that happening, or of anything that followed, of Dave Bowman managing to re-enter the ship and then disabling the computer’s ‘higher’ mental functions, before taking a pod out on his last, ill-fated mission to explore the two-kilometer-high monolith sticking up from the surface of Japetus

Floyd, the central focus of the narrative, remains deeply suspicious of HAL and watches Dr Chandra’s efforts with a sceptical eye.

(Clarke takes the opportunity to remind us of everything that happened on the first mission, including a second slightly clearer explanation of why the computer had a breakdown: It was caused by the conflict between the priorities its human programmers gave HAL. On the one hand it was ordered to be utterly candid, open and helpful to the astronauts. On the other hand, the higher-ups who commissioned the flight, decided that its real goal, to investigate the anomaly on Japetus, should be kept secret from Poole and Bowman. So HAL knew the real nature of the mission, was told he should be utterly honest with the astronauts, but was also told to lie to them. This led to a slow deterioration in his functioning until he developed the (psychotic) idea that if he removed the humans from the equation, he would be able to proceed with the mission in peace.)

4. Lagrange

With Discovery reclaimed and HAL 9000 now operative, the crew manoeuvre the two ships into an orbit close to Japetus and proceed to investigate the enormous artefact using the full range of scientific methods (which Clarke explains in careful detail).

If I haven’t mentioned it, the mundane, down to earth feel of the text is emphasised by two elements: 1. the jokey camaraderie among the crew, the seven Russians, two Yanks and one Sri Lankan, along with Clarke’s very sensible descriptions of changing relationships and slight frictions among them. None of this is ever mysterious. Even in their relationships and emotions people are always, to Clarke, understandable.

And this is backed up by 2. the periodic taped messages which Floyd makes to his wife, Caroline, and little boy, Chris, back on earth, filling in homely little details about the mission, and longing to be back at their house by the sea. As he had realised when he accepted the mission, going into suspended animation for two years, during which he would only age a few weeks, means that Caroline will catch him up, that their ages will become closer, and he hopes they will, too.

Floyd and one of the Russians, Vasili Orlov, are floating in zero gravity near an observation window from which they can see the artefact, when Orlov notices something come flying out of it at immense speed, and zoom off in the direction of earth.

5. Child of the stars

It is Dave Bowman. Clarke reprises the most mind-blowing part of the first book, which is the way Bowman was transported through the star gate to a remote part of the galaxy, where his mind was stripped down, recorded and his consciousness transferred from his physical body into some form of light-based life which can materialise anywhere in the universe. Now he wants to return to earth and so that was him whizzing past which Orlov saw.

And the book recaps the abrupt worrying conclusion of the first book which is that, just as Bowman arrives, a nuclear war appears to commence, with both sides shooting nuclear missiles at each other – which Bowman has achieved such galactic powers that he simply explodes them all in the air.

In this version of the story there is only one nuclear warhead and he explodes it in passing, as an afterthought, as he fleets through the stratosphere. Earth authorities of course notice this detonation, and various reports of an unidentified flying object which they (and Clarke) treat with the usual scepticism.

There then follow some sequences which are strange because of their… thumping banality. We are taken into an old memory of Bowman’s dating from when he was a boy and he and his brother went diving in a local pond, and his brother drowned. A few years later he started going out with his dead brother’s girlfriend, Betty (like Frank Spenser’s wife, Betty). Now Bowman uses his godlike powers to… infiltrate America’s names and address database, then to appear on Betty’s TV, where the spirit of Bowman easily enough manipulates the cathode ray tube and… I couldn’t believe I read this but… Bowman projects onto his old flame’s TV screen, pornographic images!!!

The divorce between mind and body was still far from complete, and not even the most complaisant of the cable networks would have transmitted the blatantly sexual images that were forming there now. (p.172)

Which Betty watches with enjoyment, some a bit shocked, and then turns away with ‘regret for lost delights’. What? Did I just read that? Did David Bowman, the first man to travel through the star gate and be transformed into a cosmic consciousness, return all the way to earth in order to… show his old girlfriend pornography?? The mind boggles.

Then he zooms all over earth visiting sights like the Grand Canyon, Mecca, ancient temples, till he finds himself in Olduvai Gorge which, it is implied, was the location where the artifact first appeared to man-apes three million years ago (as so vividly described in 2001). He appears to his mother in her care home. He uses his telekinetic powers to comb her hair.

This is all an incredible letdown after the end of 2001, which climaxed with the cosmic spirit of Bowman looking down on planet earth, wondering what to do next. This gave the original book a tremendously pregnant ending because we,the readers, were free to project anything we could imagine on to his next steps.

To learn that what Dave did next turns out to be go sightseeing, show porn to his old girlfriend, and comb his mum’s hair, well the phrase anti-climax isn’t strong enough to convey the sense of crushing disappointment.

Then Dave zooms off back onto the solar system and undertakes a tour of the moons of Jupiter, described in Clarkean detail, although with extra information about the (entirely fictional) forms of life to be found on Europa, including the type we saw destroy the Chinese space craft.

Bowman’s spirit has, by this stage, realised that he is being used as a probe, an investigator, for some vast overmind which he can only vaguely sense. He penetrates to the heart of each of the moons and then – in a bravura display of imagination and description on Clarke’s part – down to the very core of Jupiter and something, somewhere, is monitoring it all.

There is a simple case to be made that these passages – Clarke’s super-vivid imaginings of what Jupiter and its moons are like, the colour, taste, texture, feel and overwhelming sight of them – are by far the most powerful parts of the book.

Then Bowman is told to contact the beings in the spaceship. Having no body he puzzles how to do this – then uses HAL’s circuits. As usual it happens to Dr Floyd, most things happen to Dr Floyd.

Bowman projects text onto HAL’s computer screen. It is a simple message. They must leave Europa’s orbit within the next 15 days or be destroyed.

When Floyd tells Captain Tatiana, she doesn’t believe him, she thinks he must have been tired and hallucinating, or some other reason.

Then the vast anomaly sited on Japetus which they came all this way to observe (and from which they have got such disappointing results) disappears. Just… vanishes! That clinches the discussion. They will leave.

Victor the engineer comes up with a plan. To use the fuel/rockets/engines of Discovery as a sort of booster stage to propel Leonov back to earth.

6. Devourer of worlds

Clarke gives a characteristically detailed account of how they bind the Discovery to the Leonov in order to benefit from its booster rockets and then deliberately descend closer to Jupiter, swing round it to pick up extra momentum, and then fire the booster rockets to break free and set off back to earth. However:

  1. There are worries that HAL might protest. That he might object to them abandoning the mission he is programmed with i.e. investigation of the anomaly. And indeed, right at the critical moment before he is scheduled to fire Discovery’s rockets, HAL questions Dr Chandra about what they’re doing and suggests they abort the detonation. It is a tense moment but, in the event, HAL obeys instructions.– The cumulative effect of reading 2001 and this novel is never to trust ‘intelligent’ computers.
  2. As they swing closer towards Jupiter before firing away, they all notice a black circle on the face of the planet which appears to be growing. Once they re-emerge from the other side of Jupiter, they are astonished to see hundreds, nay thousands of the black monoliths swarming across the surface. Could it be that they are eating Jupiter’s atmosphere and… reproducing? Why?

7. Lucifer Rising

Then, in the last 25 pages, it all happens. Bowman’s spirit enters Discovery, merges with HAL and tells him to send a message to earth.

ALL THESE WORLDS ARE YOURS – EXCEPT EUROPA.
ATTEMPT NO LANDINGS THERE

Then (as usual) it is Dr Floyd who sees the next development. In the observation lounge of Leonov, he watches in awe as Jupiter explodes!

The millions of monoliths have absorbed its hydrogen and somehow created a steadily heavier and heavier core, until the planet explodes and becomes a star.

Clarke gives a couple of pages of explanation of how this could happen in terms of the physics. And then a highly fantastical explanation of why. They – the alien minds behind the whole story – have travelled far and wide across the universe interfering wherever they see signs of possible life. They intervened on earth three million years ago to set humanity on course to intelligent evolution.

Now, using Bowman’s mind as a probe, they have discovered the potentiality for intelligent life on Europa, one of the moons of Jupiter. So they blow Jupiter up, turning it into a sun which orbits ‘our’ sun, but primarily so that it will become a sun for Europa. It will thaw out Europa’s deep icy seas and prompt evolution there, to create intelligent life.

Epilogue

The narrative cuts to a short epilogue dated 20,001, in which we learn that the Europans have indeed been warmed by this new sun which has melted its frozen ice-bound oceans allowing them to evolve into intelligent life, which has developed all kinds of theories about the planet it exists on, the other moons and its ‘sun’.

Standing sentinel over their ‘planet’ is a large version of the monoliths, at the border between the fixed daylight and fixed night-time which Europa experiences, warding off the occasional probes sent from earth, ensuring the inhabitants of Europa become one of the two intelligent life forms in the solar system.

The narrative ends on a gee whizz sci-fi cliff hanger. In the long run, will only one of these intelligent life forms triumph and control the solar system, and which will it be? Tune back in a million years to find out.

Lucifer

Hang on, did Clarke just write that the aliens turn the planet Jupiter into a star orbiting round the sun, in effect a sun to the many moons which circle it? What!

And did he just write that this Jupiter-sun – christened by earthlings ‘Lucifer’ from that word’s original meaning of ‘light-bringer’ – that Lucifer put an end to night on earth!!!!

Because when half the world is facing away from the sun, it is facing outwards towards the new sun out at the edge of the solar system?

Hang on – forget all the trivial details of the plot – did Clarke just write that night on earth has been abolished? There is no more night on earth?

Wow. Isn’t that the stuff of nightmares? Not to mention the extinction of God knows how many nocturnal species? What inconceivable psychological damage that would wreak on the human race.


Clichés

When a write says ‘in the words of the old cliché…’, or ‘to quote the hoary old saying’ or ‘in the well-worn words of tradition’ – the mere fact that they’re flagging up that they’re using clichés and tired old forms of words doesn’t get them off the hook. They are still using them. It is still a tired use of language (and thought).

  • Who had once called the eyes ‘windows on the soul’? (p.216)
  • Floyd could not help smiling at that old Space Age cliché, ‘If all goes well’ (p.216)
  • ‘Well, you know the old saying: Once is an accident; twice is a coincidence; three times is a conspiracy!’ (p.221)

Same with the frequent use of quotes, they tie down and retard the narrative, by pegging it to the already-known, to the mundane.

  • ‘Let me remind you of Haldane’s famous remark: ‘The Universe is not only stranger than we imagine – but stranger than we can imagine.’ (p.219)
  • ‘Sasha has dug up a good phrases: “The Ghost in the Machine”.’ (p.223)
  • ‘What did Einstein call that sort of thing? A “thought experiment”.’ (p.228)

It’s a mark of second rate, genre fiction – thrillers, sci-fi and so on – that the writer uneasily realises they are writing schlock and so, to try to deflect the accusation has one of his own characters mention it. But it doesn’t work. It still draws the reader’s attention to the fact:

  • ‘Baby sitting a psychotic computer!’ muttered Curnow. ‘I feel like I’m in a Grade-B science-fiction videodrama.’ (p.238)

And once I’d noticed this tendency to domesticate even the wildest events by cloaking them in tired cliches and hoary old quotes, I also noticed Clarke’s habit of liking good old, solid old, old-fashioned x, y or z. The phrase epitomises the hearty, bluff, sensible tone which typifies Clarke’s fiction:

  • Well, one could always fall back on a few kilometres of good old-fashioned string. (p.225)
  • ‘Do you know what Zagadka [the name the Russians gave the artefact] really is? A good old Swiss Army knife!’ (p.266)

All these usages take things away from the zone of the marvellous and unknowable and bring them back into the orbit of the totally known, familiar and friendly.

It typifies the dynamic of Clarke’s fiction which is to make everything homely. Thus the characters are always giving weird extra-terrestrial objects homely nicknames to tame and domesticate them. This was particularly noticeable in Rendezvous With Rama where the astronauts exploring this alien ship called the groups of buildings ‘cities’ and then named them London, New York etc.

In this novel they domesticate the enormous two-kilometre-high monolith on Japetus by nicknaming it Big Brother.

There is often a heavy thump to Clarke’s depictions of people, who largely come over as clichés and caricatures. His description of the moons of Jupiter or the astrophysics of perihelion are always rock solid and convincing. His characterisation of big bearish Curnow or small but authoritative Captain Tatiana or reserved and ascetic Indian Dr Chandra – taste like cardboard.


Related links

Arthur C. Clarke reviews

  • Childhood’s End (1953) a thrilling narrative involving the ‘Overlords’ who arrive from space to supervise mankind’s transition to the next stage in its evolution
  • A Fall of Moondust (1961) a pleasure tourbus on the moon is sucked down into a sink of moondust, sparking a race against time to rescue the trapped crew and passengers
  • 2001: A Space Odyssey (1968) a panoramic narrative which starts with aliens stimulating evolution among the first ape-men and ends with a spaceman being transformed into galactic consciousness
  • Rendezvous with Rama (1973) a 50-kilometre-long object of alien origin enters the solar system so the crew of the spaceship Endeavour are sent to explore it
  • 2010: Odyssey Two (1982) Heywood Floyd joins a Russian spaceship on a two-year journey to Jupiter to a) reclaim the abandoned Discovery and b) investigate the enormous monolith on Japetus

Other science fiction reviews

1888 Looking Backward 2000-1887 by Edward Bellamy – Julian West wakes up in the year 2000 to discover a peaceful revolution has ushered in a society of state planning, equality and contentment
1890 News from Nowhere by William Morris – waking from a long sleep, William Guest is shown round a London transformed into villages of contented craftsmen

1895 The Time Machine by H.G. Wells – the unnamed inventor and time traveller tells his dinner party guests the story of his adventure among the Eloi and the Morlocks in the year 802,701
1896 The Island of Doctor Moreau by H.G. Wells – Edward Prendick is stranded on a remote island where he discovers the ‘owner’, Dr Gustave Moreau, is experimentally creating human-animal hybrids
1897 The Invisible Man by H.G. Wells – an embittered young scientist, Griffin, makes himself invisible, starting with comic capers in a Sussex village, and ending with demented murders
1898 The War of the Worlds – the Martians invade earth
1899 When The Sleeper Wakes/The Sleeper Wakes by H.G. Wells – Graham awakes in the year 2100 to find himself at the centre of a revolution to overthrow the repressive society of the future
1899 A Story of the Days To Come by H.G. Wells – set in the same future London as The Sleeper Wakes, Denton and Elizabeth defy her wealthy family in order to marry, fall into poverty, and experience life as serfs in the Underground city run by the sinister Labour Corps

1901 The First Men in the Moon by H.G. Wells – Mr Bedford and Mr Cavor use the invention of ‘Cavorite’ to fly to the moon and discover the underground civilisation of the Selenites
1904 The Food of the Gods and How It Came to Earth by H.G. Wells – scientists invent a compound which makes plants, animals and humans grow to giant size, prompting giant humans to rebel against the ‘little people’
1905 With the Night Mail by Rudyard Kipling – it is 2000 and the narrator accompanies a GPO airship across the Atlantic
1906 In the Days of the Comet by H.G. Wells – a comet passes through earth’s atmosphere and brings about ‘the Great Change’, inaugurating an era of wisdom and fairness, as told by narrator Willie Leadford
1908 The War in the Air by H.G. Wells – Bert Smallways, a bicycle-repairman from Kent, gets caught up in the outbreak of the war in the air which brings Western civilisation to an end
1909 The Machine Stops by E.M. Foster – people of the future live in underground cells regulated by ‘the Machine’ until one of them rebels

1912 The Lost World by Sir Arthur Conan Doyle – Professor Challenger leads an expedition to a plateau in the Amazon rainforest where prehistoric animals still exist
1912 As Easy as ABC by Rudyard Kipling – set in 2065 in a world characterised by isolation and privacy, forces from the ABC are sent to suppress an outbreak of ‘crowdism’
1913 The Horror of the Heights by Arthur Conan Doyle – airman Captain Joyce-Armstrong flies higher than anyone before him and discovers the upper atmosphere is inhabited by vast jellyfish-like monsters
1914 The World Set Free by H.G. Wells – A history of the future in which the devastation of an atomic war leads to the creation of a World Government, told via a number of characters who are central to the change
1918 The Land That Time Forgot by Edgar Rice Burroughs – a trilogy of pulp novellas in which all-American heroes battle ape-men and dinosaurs on a lost island in the Antarctic

1921 We by Evgeny Zamyatin – like everyone else in the dystopian future of OneState, D-503 lives life according to the Table of Hours, until I-330 wakens him to the truth
1925 Heart of a Dog by Mikhail Bulgakov – a Moscow scientist transplants the testicles and pituitary gland of a dead tramp into the body of a stray dog, with disastrous consequences
1927 The Maracot Deep by Arthur Conan Doyle – a scientist, engineer and a hero are trying out a new bathysphere when the wire snaps and they hurtle to the bottom of the sea, there to discover…

1930 Last and First Men by Olaf Stapledon – mind-boggling ‘history’ of the future of mankind over the next two billion years
1938 Out of the Silent Planet by C.S. Lewis – baddies Devine and Weston kidnap Ransom and take him in their spherical spaceship to Malacandra aka Mars,

1943 Perelandra (Voyage to Venus) by C.S. Lewis – Ransom is sent to Perelandra aka Venus, to prevent a second temptation by the Devil and the fall of the planet’s new young inhabitants
1945 That Hideous Strength: A Modern Fairy-Tale for Grown-ups by C.S. Lewis– Ransom assembles a motley crew to combat the rise of an evil corporation which is seeking to overthrow mankind
1949 Nineteen Eighty-Four by George Orwell – after a nuclear war, inhabitants of ruined London are divided into the sheep-like ‘proles’ and members of the Party who are kept under unremitting surveillance

1950 I, Robot by Isaac Asimov – nine short stories about ‘positronic’ robots, which chart their rise from dumb playmates to controllers of humanity’s destiny
1950 The Martian Chronicles – 13 short stories with 13 linking passages loosely describing mankind’s colonisation of Mars, featuring strange, dreamlike encounters with Martians
1951 Foundation by Isaac Asimov – the first five stories telling the rise of the Foundation created by psychohistorian Hari Seldon to preserve civilisation during the collapse of the Galactic Empire
1951 The Illustrated Man – eighteen short stories which use the future, Mars and Venus as settings for what are essentially earth-bound tales of fantasy and horror
1952 Foundation and Empire by Isaac Asimov – two long stories which continue the future history of the Foundation set up by psychohistorian Hari Seldon as it faces attack by an Imperial general, and then the menace of the mysterious mutant known only as ‘the Mule’
1953 Second Foundation by Isaac Asimov – concluding part of the ‘trilogy’ describing the attempt to preserve civilisation after the collapse of the Galactic Empire
1953 Earthman, Come Home by James Blish – the adventures of New York City, a self-contained space city which wanders the galaxy 2,000 years hence powered by spindizzy technology
1953 Fahrenheit 451 by Ray Bradbury – a masterpiece, a terrifying anticipation of a future when books are banned and professional firemen are paid to track down stashes of forbidden books and burn them
1953 Childhood’s End by Arthur C. Clarke – a thrilling tale of the Overlords who arrive from space to supervise mankind’s transition to the next stage in its evolution
1954 The Caves of Steel by Isaac Asimov – set 3,000 years in the future when humans have separated into ‘Spacers’ who have colonised 50 other planets, and the overpopulated earth whose inhabitants live in enclosed cities or ‘caves of steel’, and introducing detective Elijah Baley to solve a murder mystery
1956 The Naked Sun by Isaac Asimov – 3,000 years in the future detective Elijah Baley returns, with his robot sidekick, R. Daneel Olivaw, to solve a murder mystery on the remote planet of Solaria
1956 They Shall Have Stars by James Blish – explains the invention – in the near future – of the anti-death drugs and the spindizzy technology which allow the human race to colonise the galaxy
1959 The Triumph of Time by James Blish – concluding story of Blish’s Okie tetralogy in which Amalfi and his friends are present at the end of the universe

1961 A Fall of Moondust by Arthur C. Clarke – a pleasure tourbus on the moon is sucked down into a sink of quicksand-like moondust, sparking a race against time to rescue the trapped crew and passengers
1962 A Life For The Stars by James Blish – third in the Okie series about cities which can fly through space, focusing on the coming of age of kidnapped earther, young Crispin DeFord, aboard New York
1962 The Man in the High Castle by Philip K. Dick In an alternative future America lost the Second World War and has been partitioned between Japan and Nazi Germany. The narrative follows a motley crew of characters including a dealer in antique Americana, a German spy who warns a Japanese official about a looming surprise German attack, and a woman determined to track down the reclusive author of a hit book which describes an alternative future in which America won the Second World War
1968 2001: A Space Odyssey by Arthur C. Clarke – panoramic narrative which starts with aliens stimulating evolution among the first ape-men and ends with a spaceman transformed into galactic consciousness
1968 Do Androids Dream of Electric Sheep? by Philip K. Dick In 1992 androids are almost indistinguishable from humans except by trained bounty hunters like Rick Deckard who is paid to track down and ‘retire’ escaped andys
1969 Ubik by Philip K. Dick In 1992 the world is threatened by mutants with psionic powers who are combated by ‘inertials’. The novel focuses on the weird alternative world experienced by a group of inertials after a catastrophe on the moon

1971 Mutant 59: The Plastic Eater by Kit Pedler and Gerry Davis – a genetically engineered bacterium starts eating the world’s plastic
1973 Rendezvous With Rama by Arthur C. Clarke – in 2031 a 50-kilometre long object of alien origin enters the solar system, so the crew of the spaceship Endeavour are sent to explore it
1974 Flow My Tears, The Policeman Said by Philip K. Dick – America after the Second World War is a police state but the story is about popular TV host Jason Taverner who is plunged into an alternative version of this world where he is no longer a rich entertainer but down on the streets among the ‘ordinaries’ and on the run from the police. Why? And how can he get back to his storyline?

1981 The Golden Age of Science Fiction edited by Kingsley Amis – 17 classic sci-fi stories from what Amis considers the Golden Era of the genre, namely the 1950s

2001: A Space Odyssey by Arthur C. Clarke (1968)

Origins

It all started with a short story Clarke wrote for a BBC competition in 1948 when he was just 21, and titled The Sentinel. It was eventually published in 1951 under the title Sentinel of Eternity.

13 years later, after completing Dr. Strangelove in 1964, American movie director Stanley Kubrick turned his thoughts to making a film with a science fiction subject. Someone suggested Clarke as a source and collaborator, and when they met, later in 1964, they got on well and formed a good working relationship.

Neither of them could have predicted that it would take them four long years of brainstorming, viewing and reading hundreds of sci-fi movies and stories, and then honing and refining the narrative, to develop the screenplay which became the film 2001: A Space Odyssey, released in 1968 and one of the most influential movies of all time.

The original plan had been to develop the story as a novel first, then turn it into a screenplay, then into the film, but the process ended up being more complex than that. The novel ended up being written mostly by Clarke, while Kubrick’s screenplay departed from it in significant ways.

The most obvious difference is that the book is full of Clarke’s sensible, down-to-earth, practical explanations of all or most of the science involved. It explains things. From the kick-start given to human evolution by the mysterious monolith through to Bowman’s journey through the Star Gate, Clarke explains and contextualises.

This is all in stark contrast with the film which Kubrick made as cryptic as possible by reducing dialogue to an absolute minimum, and eliminating all explanation. Kubrick is quoted as saying that the film was ‘basically a visual, nonverbal experience’, something which a novel, by definition, can not be.

The novel

The novel is divided into 47 short snappy chapters, themselves grouped into six sections.

1. Primeval Night

The basic storyline is reasonably clear. A million years ago an alien artefact appears on earth, materialising in Africa, in the territory of a small group of proto-human man-apes. Clarke describes their wretched condition in the hot parched Africa of the time, permanently bordering on starvation, watered only by a muddy streamlet, dying of malnutrition and weakness or of old age at 30, completely at the mercy of predators like a local leopard.

The object – 15 feet high and a yard wide – appears from nowhere. When the ape-men lumber past it on the way to their foraging ground, it becomes active and literally puts ideas into their heads. It takes possession of members of the group in turn and forces them to tie knots in grass, to touch their fingers together, to perform basic physical IQ tests. Then, crucially, it patiently shows them how to use stones and the bones of dead animals as tools.

The result is that they a) kill and eat a wild pig, the first meat ever eaten by the ape-men b) surround and kill the leopard that’s been menacing the tribe c) use these skills to bludgeon the leader of ‘the Others’, a smaller weaker tribe on the other side of the stream. In other words, the alien artefact has intervened decisively in the course of evolution to set man on his course to becoming a planet-wide animal killer and tool maker.

In the kind of fast-forward review section which books can do and movies can’t, Clarke then skates over the hundreds of thousands of years of evolution which follow, during which human’s teeth became smaller, their snouts less prominent, giving them the ability to make more precise sounds through their vocal cords – the beginnings of speech – how ice ages swept over the world killing most human species but leaving the survivors tougher, more flexible, more intelligent, and then the discovery of fire, of cooking, a widening of diet and survival strategies. And then to the recent past, to the Stone, Iron and Bronze ages, and sweeping right past the present to the near future and the age of space travel.

Compare and contrast the movie where all this is conveyed by the famous cut from a bone thrown into the air by an ape-man which is half way through its parabola when it turns into a space ship in orbit round earth. Prose describes, film dazzles.

2. T.M.A.-1

It is 2001. Humanity has built space stations in orbit around the earth, and a sizeable base on the moon. Dr Heywood Floyd, retired astrophysicist, is taking the journey from the American launch base in Florida, to dock with the orbiting space station, and then on to the moon base.

Clarke in his thorough, some might say pedantic, way, leaves no aspect of the trip undescribed and unexplained. How the rocket launcher works, how to prepare for blast-off, how the space station maintains a sort of gravity by rotating slowly, the precise workings of its space toilets (yes), the transfer to the shuttle down to the moon: Clarke loses no opportunity to mansplain every element of the journey, including some favourite facts familiar from the other stories I’ve read: the difference between weight and mass; how centrifugal spin creates increased gravity the further you are from the axis of spin; ‘the moon’s strangely close horizon’ (p.74); how damaging an alien artifact would be the work of a ‘barbarian’ (a thought repeated several times in Rama).

Two other features emerge. Clarke’s protagonists are always men, and they are almost always married men, keen to keep in touch with their wives, using videophones. In other words they’re not valiant young bucks as per space operas. It’s another element in the practical, level-headed approach of Clarke’s worldview.

Secondly, Clarke is a great one for meetingsChildhood’s End‘s middle sections rotate around the Secretary General of the United Nations who has a busy schedule of meetings, from his weekly conference with the Overlords to his meetings with the head of the Freedom league, and his discussion of issues arising with his number two.

A Fall of Moondust features hurried conferences between the top officials on the moon. The narrative of Rendezvous with Rama is punctuated all the way through by meetings of the committee made up of with representatives from the inhabited planets, who discuss the issues arising but also get on each other’s nerves, bicker and argue, grandstand, storm out and so on. His fondness for the set meeting, with a secretary taking notes and a chairman struggling to bring everyone into line, is another of the features which makes Clarke’s narratives seem so reassuringly mundane and rooted in reality.

Same here. Floyd is flying to the moon to take part in a top secret, high-level meeting of moon officials. He opens the meeting by conveying the President’s greetings and thanks (as people so often do in sci-fi thrillers like this).

In brief: a routine survey of the moon has turned up a magnetic anomaly in the huge crater named Tycho. (The anomaly has been prosaically named Tycho Magnetic Anomaly One – hence the section title T.M.A.-1.) When the surveyors dug down they revealed an object, perfectly smooth and perfectly black, eleven foot high, five foot wide and one and a quarter foot deep. Elementary geology has shown that the object was buried there three million years ago.

After a briefing with the moon team Floyd goes out by lunar tractor to the excavation site where digging has now fully revealed the artifact. Floyd and some others go down into the excavation and walk round the strange object which seems to absorb light. The sun is rising (the moon turns on its axis once in fourteen days) and as its light falls onto the artifact – for probably the first time in millions of years – Floyd and the others are almost deafened by five intense burst of screeching sound which cut through their radio communications.

Millions of miles away in space, deep space monitors, orbiters round Mars, a probe launched to Pluto – all record and measure an unusual burst of energy streaking across the solar system… Cut to:

3. Between Planets

David Bowman is captain of the spaceship Discovery. It was built to transport two live passengers (himself and Frank Poole) and three others in suspended animation, to Jupiter. But two years into the project the TMA-1 discovery was made and plans were changed. Now the ship is intending to use the gravity of Jupiter as a sling to propel it on towards Saturn. When they enter Saturn’s orbit the three sleeping crew members (nicknamed ‘hibernauts’) will be woken and the full team of five will have 100 days to study the super-massive gas giant, before all the crew re-enter hibernation, and wait to be picked up by Discovery II, still under construction.

Clarke is characteristically thorough in describing just about every aspect of deep space travel you could imagine, the weightlessness, the scientific reality of hibernation, the food, what the earth looks like seen from several million miles away. He gives an hour by hour rundown of Bowman and Poole’s 24-hour schedule, which is every bit as boring as the thing itself. He describes in minute astronomical detail the experience of flying through the asteroid belt and on among the moons of Jupiter, watching the sun ‘set’ behind it and other strange and haunting astronomical phenomena which no one has seen.

Then there’s a sequence in which he imagines the pictures sent back by a probe which Bowman and Poole send down into Jupiter’s atmosphere: fantastic but completely plausible imaginings. After reporting what they see from the ship, and the images relayed by the probe, the couple have done with Jupiter and set their faces to Saturn, some three months and four hundred million miles away.

The awesomeness doesn’t come from the special effects and canny use of classical music, as per the movie, but from straightforward statement of the scientific and technical facts – such as that they are now 700 million miles from earth (p.131), travelling at a speed of over one hundred thousand miles an hour (p.114).

4. Abyss

All activities on the Discovery are run or monitored by the ship’s onboard computer, HAL 9000, ‘the brain and nervous system of the ship’ (p.97). HAL stands for Heuristically programmed ALgorithmic computer. It is the most advanced form of the self-teaching neural network which, Clarke predicts, will have been discovered in the 1980s.

HAL has a nervous breakdown. He predicts the failure of the unit which keeps the radio antenna pointed at earth. Poole goes out in one of the nine-foot space pods, anchors to the side of the ship, then does a short space walk in a space suit, unbolts the failing unit and replaces it.

But back inside the ship the automatic testing devices find nothing wrong with the unit. When a puzzled Bowman and Poole report all this back to earth, Mission Control come back with the possibility that the HAL 9000 unit might have made a mistake.

Poole and Bowman ponder the terrifying possibility that the computer which is running the whole mission might be failing. Mission Control send a further message saying the two HAL 9000 units they are using to replicate all aspects of the mission back home both now recommend disconnecting the HAL computer aboard the Discovery. Earth is just in the middle of starting to give details about how to disconnect HAL when the radio antenna unit really does fail and contact with earth is broken. Coincidence? Bear in mind that HAL has been monitoring all of these conversations…

After discussing the possibility that HAL was right all along about the unit and that they are being paranoid  about him, Poole goes out for another space walk and repair. He’s in the middle of installing the new unit when he sees something out the corner of his eye, looks up and sees the pod suddenly shooting straight at him. With no time to take evasive action Poole is crushed by the ten-ton pod, his space suit ruptured, he is dead in seconds. Through an observation window Bowman sees first the pod and then Bowman’s body fly past and away from the ship.

Bowman confronts Hal, who calmly regrets that there has been accident. Mission orders demand that Bowman now revive one of the three hibernators since there must always be two people active on the ship. HAL argues with Bowman, saying this won’t be necessary, by which stage Bowman realises there is something seriously wrong. He threatens to disconnect HAL at which point the computer abruptly relents. Bowman makes his way to the three hibernator pods and has just started to revive the next in line of command, Whitehead when… HAL opens both doors of the ship’s airlock and all the air starts to flood out into space. In the seconds before the ship becomes a vacuum, Bowman manages to make it to an emergency alcove, seal himself in, jets it up with oxygen and climb into the spacesuit kept there for just such emergencies.

Having calmed down from the shock, Bowman secures his suit then climbs out, makes his way through the empty, freezing, lifeless ship to the sealed room where HAL’s circuits are stored and powered and… systematically removes all the ‘higher’ functions which permit HAL to ‘think’, leaving only the circuits which control the ship’s core functions. HAL asks him not to and, exactly as in the film, reverts to his ‘childhood’, his earliest learning session, finally singing the song ‘Daisy, Daisy, give me your answer do.’

Hours later Bowman makes a journey in the remaining pod to fix the radio antenna, then returns, closes the airlock doors and slowly restores atmosphere to the ship. Then contacts earth. And it is only now that Dr Floyd, summoned by Mission Control, tells him the true reason for the mission. Tells him about the artifact in Tycho crater. Tells him that it emitted some form of energy which all our monitors indicate was targeted at Saturn, specifically at one of its many moon, Japetus. That is what the Discovery has been sent to investigate.

And it is only in the book that Clarke is able to tell us why HAL went mad. It was the conflict between a) the demand to be at all times totally honest, open and supportive of his human crew and b) the command to keep the true purpose of the mission secret, which led HAL to have a nervous breakdown, and decide to remove one half of the conflict i.e. the human passengers, which would allow him to complete the second half, the mission to Saturn, in perfect peace of ‘mind’.

5. The Moons of Saturn

So now Bowman properly understands the mission, goes about fixing the Discovery, is in constant contact with earth and Clarke gives us an interesting chapter pondering the meaning of the sentinel and what it could have been saying. Was it a warning to its makers, or a message to invade? Where was the message sent? To beings which had evolved on or near Saturn (impossible, according to all the astrophysicists)? Or to somewhere beyond the solar system itself? In which case how could anything have travelled that far, if Einstein is correct and nothing can travel faster than light?

These last two chapters have vastly more factual information in than the movie. What the movie does without any dialogue, with stunning images and eerie music, Clarke does with his clear authoritative factual explanations. He gives us detailed descriptions of the rings of Saturn from close up, along with meticulously calculated information about perihelions and aphelions and the challenges of getting into orbit around Saturn.

But amid all this factuality is the stunning imaginative notion that the moon of Saturn, Japetus, bears on its surface a vast white eye shape at the centre of which stands an enormous copy of the TMA artifact, a huge jet black monolith maybe a mile high.

Which leads into a chapter describing the race which placed it there, which had evolved enough to develop planet travel, then space travel, then moved their minds into artificial machines and then into lattices of light which could spread across space and so, finally, into what humans would call spirit, free from time and space, at one with the universe.

It is this enormous artifact which Bowman now radios Mission Control he is about to go down to in the pod and explore.

6. Through the Star Gate

In the movie this section becomes a non-verbal experience of amazing visual effects. A book can’t do that. It has to describe and, being Clarke, can’t help also explaining, at length, what is going on.

Thus the book is much clearer and more comprehensible about what happens in this final section. Bowman guides his pod down towards the enormous artifact and is planning to land on its broad ‘top’ when, abruptly it turns from being an object sticking out towards him into a gate or cave or tunnel leading directly through the moon it’s situated on. He has just time to make one last comment to Mission Control before the pod is sucked through into the star gate and his adventure begins.

He travels along some faster-than-light portal, watching space bend around him and time slow down to a halt. He emerges into a place where the stars are more static and, looking back, sees a planet with a flat face pockmarked by black holes like the one he’s just come through, and what, when he looks closely, seems to be the wreck of a metal spaceship. He realises this must be a kind of terminal for spaceships between voyages, then the pod slowly is sucked back into one of the holes.

More faster than light travelling, then he emerges into a completely unknown configuration of stars, red dwarfs, sun clusters, the pod slows to a halt and comes to rest in… a hotel room.

Terrified, Bowman makes all the necessary checks, discovers it has earth gravity and atmosphere, gets out of the pod, takes off his spacesuit, has a shower and shave, dresses in one of the suits of clothes provided in a wardrobe, checks out the food in the fridge, or in tins or boxes of cereal.

But he discovers that the books on the coffee table have no insides, the food inside the containers is all the same blue sludge. When he lies on the bed flicking through the channels on the TV he stumbles across a soap opera which is set in this very same hotel room he is lying in. Suddenly he understands. The sentinel, after being unearthed, monitored all radio and TV signals from earth and signalled them to the Japetus relay station and on here – wherever ‘here’ is – and used them as a basis to create a ‘friendly’ environment for their human visitor.

Bowman falls asleep on the bed and while he sleeps goes back in time, recapitulating his whole life. And part of him is aware that all the information of his entire life is being stripped from his mind and transferred to a lattice of light, the same mechanism which Clarke explained earlier in the novel, was the invention of the race which created the sentinel. Back, back, back his life reels until – in a miraculous moment – the room contains a baby, which opens its mouth to utter its first cry.

The crystal monolith appears, white lights flashing and fleering within its surface, as we saw them do when it first taught the man-apes how to use tools and eat meat, all those hundreds of thousands of years ago.

Now it is probing and instructing the consciousness of Bowman, guiding him towards the next phase. The monolith disappears. The being that was Bowman understands, understands its meaning, understands how to travel through space far faster than the primitive star gate he came here by. All he needs is to focus his ‘mind’ and he is there.

For a moment he is terrified by the immensity of space and the infinity of the future, but then realises he is not alone, becomes aware of some force supporting and sustaining him, the guiders.

Using thought alone he becomes present back in the solar system he came from. Looking down he becomes aware of alarm bells ringing and flotillas of intercontinental missiles hurtling across continents to destroy each other. He has arrived just as a nuclear war was beginning. Preferring an uncluttered sky, he abolishes all the missiles with his will.

Then he waited, marshalling his thoughts and brooding over his still untested powers. For though he was master of the world, he was not quite sure what to do next.

But he would think of something.

And those are the final sentences of the book.

Thoughts

Like Childhood’s End the book proceeds from fairly understandable beginnings to a mind-boggling, universe-wide ending, carrying the reader step by step through what feels almost – if you let it take control of your imagination – like a religious experience.

Eliot Fremont-Smith reviewing the book in the New York Times, commented that it was ‘a fantasy by a master who is as deft at generating accelerating, almost painful suspense as he is knowledgeable and accurate (and fascinating) about the technical and human details of space flight and exploration.’

That strikes me as being a perfect summation of Clarke’s appeal – the combination of strict technical accuracy, with surprisingly effective levels of suspense and revelation.

His concern for imagining the impact of tiny details reminds me of H.G. Wells. In the Asimov and Blish stories I’ve been reading, if there’s a detail or the protagonist notices something, it will almost certainly turn out to be important to the plot. Clarke is the direct opposite. Like Wells his stories are full of little details whose sole purpose is to give the narrative a terrific sense of verisimilitude.

To pick one from hundreds, I was struck by the way that Dr Floyd finds wearing a spacesuit on the surface of the moon reassuring. Why? Because its extra weight and stiffness counter the one sixth gravity of the moon, and so subconsciously remind him of the gravity on earth. Knowing that fact, and then deploying it in order to describe the slight but detectable impact it has on one of his characters’ moods,strikes me as typical Clarke.

Hundreds of other tiny but careful thinkings-though of the situations which his characters find themselves in, bring them home and make them real.

And as to suspense, Clarke is a great fan of the simple but straightforward technique of ending chapters with a threat of disaster. E.g. after his first space walk Poole returns to the ship confident that he has fixed the problem.

In this, however, he was sadly mistaken. (p.140)

Although this is pretty cheesy, it still works. He is a master of suspense. The three other novels I’ve read by him are all thrilling, and even though I’ve seen the movie umpteen times and so totally know the plot, reading Clarke’s book I was still scared when HAL started malfunctioning, and found Bowman’s struggle to disconnect him thrilling and moving.

As to the final section, when Bowman travels through the star gate and is transformed into a new form of life, of celestial consciousness, if you surrender to the story the experience is quite mind-boggling.

It also explains a lot – and makes much more comprehensible – what is left to implication and special effects in the movie.

Forlorn predictions

Clarke expects that by 2001:

  • there will be a permanent colony on the moon, where couples will be having and bringing up children destined never to visit the earth
  • there will also be a colony on Mars
  • there will be a ‘plasma drive’ which allows for super-fast spaceship travel to other planets

I predict there will never be a colony on the moon, let alone Mars, and no ‘plasma drive’.

On the plus side, Clarke predicts that by 2001 there will be a catastrophic six billion people on earth, which will result in starvation, and food preservation policies even in the rich West. In the event there were some 6.2 billion people alive in 2001, but although there were the usual areas of famine in the world, there wasn’t the really widespread food shortages Clarke predicted.

The future has turned out to be much more human, mundane, troubled and earth-bound than Clarke and his generation expected.

Trailer

Credit

All references are to the 2011 reprint of the 1998 Orbit paperback edition of 2001: A Space Odyssey by Arthur C. Clarke, first published by Hutchinson in 1968.


Related links

Arthur C. Clarke reviews

  • Childhood’s End (1953) a thrilling narrative involving the ‘Overlords’ who arrive from space to supervise mankind’s transition to the next stage in its evolution
  • A Fall of Moondust (1961) a pleasure tourbus on the moon is sucked down into a sink of moondust, sparking a race against time to rescue the trapped crew and passengers
  • 2001: A Space Odyssey (1968) a panoramic narrative which starts with aliens stimulating evolution among the first ape-men and ends with a spaceman being transformed into galactic consciousness
  • Rendezvous With Rama (1973) it is 2031 and when an alien object, a cylinder 15 k wide by 50 k long, enters the solar system, and Commander Norton and the crew of Endeavour are sent to explore it

Other science fiction reviews

1888 Looking Backward 2000-1887 by Edward Bellamy – Julian West wakes up in the year 2000 to discover a peaceful revolution has ushered in a society of state planning, equality and contentment
1890 News from Nowhere by William Morris – waking from a long sleep, William Guest is shown round a London transformed into villages of contented craftsmen

1895 The Time Machine by H.G. Wells – the unnamed inventor and time traveller tells his dinner party guests the story of his adventure among the Eloi and the Morlocks in the year 802,701
1896 The Island of Doctor Moreau by H.G. Wells – Edward Prendick is stranded on a remote island where he discovers the ‘owner’, Dr Gustave Moreau, is experimentally creating human-animal hybrids
1897 The Invisible Man by H.G. Wells – an embittered young scientist, Griffin, makes himself invisible, starting with comic capers in a Sussex village, and ending with demented murders
1898 The War of the Worlds – the Martians invade earth
1899 When The Sleeper Wakes/The Sleeper Wakes by H.G. Wells – Graham awakes in the year 2100 to find himself at the centre of a revolution to overthrow the repressive society of the future
1899 A Story of the Days To Come by H.G. Wells – set in the same London of the future described in the Sleeper Wakes, Denton and Elizabeth fall in love, then descend into poverty, and experience life as serfs in the Underground city run by the sinister Labour Corps

1901 The First Men in the Moon by H.G. Wells – Mr Bedford and Mr Cavor use the invention of ‘Cavorite’ to fly to the moon and discover the underground civilisation of the Selenites
1904 The Food of the Gods and How It Came to Earth by H.G. Wells – two scientists invent a compound which makes plants, animals and humans grow to giant size, leading to a giants’ rebellion against the ‘little people’
1905 With the Night Mail by Rudyard Kipling – it is 2000 and the narrator accompanies a GPO airship across the Atlantic
1906 In the Days of the Comet by H.G. Wells – a passing comet trails gasses through earth’s atmosphere which bring about ‘the Great Change’, inaugurating an era of wisdom and fairness, as told by narrator Willie Leadford
1908 The War in the Air by H.G. Wells – Bert Smallways, a bicycle-repairman from Bun Hill in Kent, manages by accident to be an eye-witness to the outbreak of the war in the air which brings Western civilisation to an end
1909 The Machine Stops by E.M. Foster – people of the future live in underground cells regulated by ‘the Machine’ until one of them rebels

1912 The Lost World by Sir Arthur Conan Doyle – Professor Challenger leads an expedition to a plateau in the Amazon rainforest where prehistoric animals still exist
1912 As Easy as ABC by Rudyard Kipling – set in 2065 in a world characterised by isolation and privacy, forces from the ABC are sent to suppress an outbreak of ‘crowdism’
1913 The Horror of the Heights by Arthur Conan Doyle – airman Captain Joyce-Armstrong flies higher than anyone before him and discovers the upper atmosphere is inhabited by vast jellyfish-like monsters
1914 The World Set Free by H.G. Wells – A history of the future in which the devastation of an atomic war leads to the creation of a World Government, told via a number of characters who are central to the change
1918 The Land That Time Forgot by Edgar Rice Burroughs – a trilogy of pulp novellas in which all-American heroes battle ape-men and dinosaurs on a lost island in the Antarctic

1921 We by Evgeny Zamyatin – like everyone else in the dystopian future of OneState, D-503 lives life according to the Table of Hours, until I-330 wakens him to the truth
1925 Heart of a Dog by Mikhail Bulgakov – a Moscow scientist transplants the testicles and pituitary gland of a dead tramp into the body of a stray dog, with disastrous consequences
1927 The Maracot Deep by Arthur Conan Doyle – a scientist, engineer and a hero are trying out a new bathysphere when the wire snaps and they hurtle to the bottom of the sea, there to discover…

1930 Last and First Men by Olaf Stapledon – mind-boggling ‘history’ of the future of mankind over the next two billion years
1932 Brave New World by Aldous Huxley
1938 Out of the Silent Planet by C.S. Lewis – baddies Devine and Weston kidnap Ransom and take him in their spherical spaceship to Malacandra aka Mars,

1943 Perelandra (Voyage to Venus) by C.S. Lewis – Ransom is sent to Perelandra aka Venus, to prevent a second temptation by the Devil and the fall of the planet’s new young inhabitants
1945 That Hideous Strength: A Modern Fairy-Tale for Grown-ups by C.S. Lewis– Ransom assembles a motley crew to combat the rise of an evil corporation which is seeking to overthrow mankind
1949 Nineteen Eighty-Four by George Orwell – after a nuclear war, inhabitants of ruined London are divided into the sheep-like ‘proles’ and members of the Party who are kept under unremitting surveillance

1950 I, Robot by Isaac Asimov – nine short stories about ‘positronic’ robots, which chart their rise from dumb playmates to controllers of humanity’s destiny
1950 The Martian Chronicles – 13 short stories with 13 linking passages loosely describing mankind’s colonisation of Mars, featuring strange, dreamlike encounters with Martians
1951 Foundation by Isaac Asimov – the first five stories telling the rise of the Foundation created by psychohistorian Hari Seldon to preserve civilisation during the collapse of the Galactic Empire
1951 The Illustrated Man – eighteen short stories which use the future, Mars and Venus as settings for what are essentially earth-bound tales of fantasy and horror
1952 Foundation and Empire by Isaac Asimov – two long stories which continue the future history of the Foundation set up by psychohistorian Hari Seldon as it faces down attack by an Imperial general, and then the menace of the mysterious mutant known only as ‘the Mule’
1953 Second Foundation by Isaac Asimov – concluding part of the ‘trilogy’ describing the attempt to preserve civilisation after the collapse of the Galactic Empire
1953 Earthman, Come Home by James Blish – the adventures of New York City, a self-contained space city which wanders the galaxy 2,000 years hence powered by spindizzy technology
1953 Fahrenheit 451 by Ray Bradbury – a masterpiece, a terrifying anticipation of a future when books are banned and professional firemen are paid to track down stashes of forbidden books and burn them
1953 Childhood’s End by Arthur C. Clarke – a thrilling tale of the Overlords who arrive from space to supervise mankind’s transition to the next stage in its evolution
1954 The Caves of Steel by Isaac Asimov – set 3,000 years in the future when humans have separated into ‘Spacers’ who have colonised 50 other planets, and the overpopulated earth whose inhabitants live in enclosed cities or ‘caves of steel’, and introducing detective Elijah Baley to solve a murder mystery
1956 The Naked Sun by Isaac Asimov – 3,000 years in the future detective Elijah Baley returns, with his robot sidekick, R. Daneel Olivaw, to solve a murder mystery on the remote planet of Solaria
1956 They Shall Have Stars by James Blish – explains the invention – in the near future – of the anti-death drugs and the spindizzy technology which allow the human race to colonise the galaxy
1959 The Triumph of Time by James Blish – concluding story of Blish’s Okie tetralogy in which Amalfi and his friends are present at the end of the universe

1962 A Life For The Stars by James Blish – third in the Okie series about cities which can fly through space, focusing on the coming of age of kidnapped earther, young Crispin DeFord, aboard New York

1971 Mutant 59: The Plastic Eater by Kit Pedler and Gerry Davis – a genetically engineered bacterium starts eating the world’s plastic

1980 Russian Hide and Seek by Kingsley Amis – in an England of the future which has been invaded and conquered by the Russians, a hopeless attempt to overthrow the occupiers is easily crushed
1981 The Golden Age of Science Fiction edited by Kingsley Amis – 17 classic sci-fi stories from what Amis considers the Golden Era of the genre, namely the 1950s

Atomic by Jim Baggott (2009)

This is a brilliantly panoramic, thrilling and terrifying book.

The subtitle of this book is ‘The First War of Physics and the Secret History of the Atom Bomb 1939-49‘ and it delivers exactly what it says on the tin. At nearly 500 pages Atomic is a very thorough account of its subject – the race to develop a workable atomic bomb between the main warring nations of World War Two, America, Britain, France, Germany, Italy, Russia –  with the additional assets of a 22-page timeline, a 20-page list of key characters, 18 pages of notes and sources and a 6-page bibliography.

A cast of thousands

The need for a list of key characters is an indication of one of the main learnings from the book: it took a lot of people to convert theoretical physics into battlefield nuclear weapons. Every aspect of it came from theories and speculations published in numerous journals, and then from experiments devised by scores of teams of scientists working around the industrialised world, publishing results, meeting at conferences or informally, comparing and discussing and debating and trying again.

Having just read The Perfect Theory by Pedro Ferreira, a ‘biography’ of the theory of relativity, I had gotten used to the enormous number of teams and groups and institutes and university faculties involved in science – or this area of science – each containing numerous individual scientists, who collaborated and competed to devise, work through and test new theories relating to Einstein’s famous theory.

Baggott’s tale gives the same sense of a cast of hundreds of scientists – it feels like we are introduced to two or three new characters on every page, which can make it quite difficult to keep up. But whereas progress on the theory of relativity took place at a leisurely pace over the past 100 years, the opposite is true of the development of The Bomb.

This was kick-started when a research paper showing that nuclear fission of uranium might be possible was published in 1939, just as the world was on the brink of war (hence the start date for this book). From that point the story progresses at an increasing pace, dominated by a Great Fear – fear that the Nazis would develop The Bomb first and use it without any scruples to devastate Europe.

The first three parts of the book follow the way the two warring parties – the Allies and the Nazis – assembled their teams from civilian physicists, mathematicians and chemists at various institutions, bringing them together into teams which were assembled and worked with increasing franticness, as the Second World War became deeper and darker.

If the you thought the blizzard of names of theoretical and experimental physicists, mathematicians, chemists and so on in the first part was a bit confusing, this is as nothing compared to the tsunami of names of Army administrators, security chiefs, civil servants, bureaucrats and politicians who are roped in to create and administer the facilities which were established to research and build, first a nuclear reactor, then a nuclear bomb.

Baggott unfolds the story with a kind of unflinching factual pace which is extremely gripping. Each chapter is divided into sections, often only a page long, which explain contemporaneous events at research bases in Chicago, out in the desert at Los Alamos, in Britain, in German research centres, and among Stalin’s harassed scientific community. Each one of these narratives is fascinating, but intercutting them like this creates an almost filming effect of cutting from one exciting scene to another. Baggott’s prose is spare and effective, almost like good thriller writing.

The nuclear spies

And indeed the book strays into actual thriller territory because interwoven with the gripping accounts of the British, Russian, German and American scientists, and their respective military and political masters, is the story of the nuclear spies. I read Paul Simpson’s A Brief History of The Spy a few months ago and it gives good accounts of the activities of Soviet spies Klaus Fuchs, David Greengrass, Theodore Hall, as well as the Rosenbergs. But the story of their spying and the huge amounts of top secret information they handed over to the Russians is so much more intense and exciting when it is situated in the broader story of the nail-biting scientific, chemical, logistical and political races to build The Bomb.

German failure

As everyone knows, the Nazis were not able to construct a functioning bomb before they were militarily defeated in May 1945. But it wasn’t for want of trying, and the main impression from the book was the sense of vicarious horror from the thought of what they’d done if they had made a breakthrough in the final desperate months of spring 1945. London wouldn’t be here. I wouldn’t be here.

Baggott’s account of the German bomb is fascinating in numerous ways. Basically, once the leadership were told it wouldn’t be ready in the next few years, they didn’t make it a priority. Baggott follows the end of the war with a chapter on hos most of the German nuclear scientists were flown to England and interned in a farm outside Cambridge which was bugged. Their conversations were recorded in which they were at first smugly confident that they were being detained because they were so far in advance of the Allies. Thus they were all shocked when they heard the Allies had dropped an atom bomb on Japan in August 1945. At which point they began to develop a new line, one much promoted by German historians since, which is that they could have developed a bomb if they’d wanted to, but had morals and principles and so did all they could to undermine, stall and sabotage the Nazi attempt to build an A bomb.

They were in fact ‘good Germans’ who always hated the Nazis. Baggott treats this claim with the contempt it deserves.

Summary of the science

The neutron was discovered in 1932, giving a clearer picture of what atoms are made of i.e. a nucleus with at least one proton (with a positive electric charge) balancing at least one electron (with a negative charge) in orbit around it. Heavier elements have more than one neutron and electron (always the same number) as well as an increasing number of neutrons which give weight but have no electric charge. Hence the periodic table lists the elements in order of heaviness, starting with hydrogen with one proton and going all the way to organesson, with its 118 protons. Ernest Lawrence in California invented the cyclotron, a device for smashing sub-atomic particles into nuclei to see what happened. In 1934 Enrico Fermi’s team in Italy set out to bombard the nuclei of every known element with neutrons, starting with hydrogen (1) and going through the entire periodic table.

The assumption was that, by bombarding elements with neutrons they would dislodge one or two protons in each nucleus and ‘shift’ the element down the periodic table by one or two places. When the team came to bombard one of the heaviest elements, uranium, they were amazed to discover that the process seemed to produce barium, about half the weight of uranium. The bombardment process seemed to blast uranium nuclei in half. Physics theory, influenced by Einstein, suggested that a) this breakdown would result in the release of energy b) some of the neutrons within the uranium nucleus would not be required by the barium atoms and would themselves shoot out to hit other uranium nuclei, and so on.

  • The process would create a chain reaction.
  • Although the collapse of each individual atom would release a minuscule amount of energy, the number of atoms in such a dense element suggested a theoretically amazing release of energy. If every nucleus of uranium in a 1 kilogram lump was split in half, it would release the same energy as 22,000 tons of TNT explosive.

Otto Frisch, an Austrian Jewish physicist who had fled to Niels Bohr’s lab in Copenhagen after the Nazis came to power, heard about all this from his long-time collaborator, and aunt, Lise Meitner, who was with the German team replicating Fermi’s results. He told Bohr about the discovery. Frisch named it nuclear fission.

In early 1939 papers were published in a German science journal and Nature, while Bohr himself travelled to a conference in America. In the spring of that year fission research groups sprang up around the scientific world. In America Bohr realised anomalies in the experimental results were caused by the fact that uranium comes in two isotopes, U-235 and U-238. The numbers derive from the total number of neutrons and protons in an atom: U-238 has 92 protons and 146 neutrons; U-235 has three fewer neutrons. Slowly evidence emerged that it is the U-235 which breaks down. But it is much rarer than the stable U-238 and difficult to extract and purify. In March 1939 a French team summarised the evidence for nuclear chain reactions in a paper in Nature, specifying the number of particles released by disintegrated nuclei.

All the physicists involved realised that the massive release of energy implied by the experiments could theoretically be used to create an explosive device vastly more powerful than anything then existing. And so did the press. Newspaper articles began appearing about a ‘superbomb’. In April the head of physics at the German Reich Research Council assembled a group devoted to fission research, named the Uranverein, calling for the ban of all uranium exports, and for it to be stockpiled. British MP Winston Churchill asked a friend, Oxford physicist Frederick Lindemann, to prepare a report on the feasibility of a fission bomb. Soviet scientists replicated the results of their western colleagues but didn’t bring the issue to the attention of the authorities – yet. Three Hungarian physicists who were exiles from the Nazis in America grasped the military importance of the discoveries. They approached Einstein and persuaded him to write a warning letter to President Roosevelt, which was written in August 1939 though not delivered to the president until October. Meanwhile the Germans invaded Poland on 1 September and war in Europe began. At this point the Nazis approached the leading theoretical physicist in Germany, Werner Heisenberg, and he agreed to head the Uranverein, leading German research into an atomic bomb until the end of the war.

And so the race to build the first atomic bomb began! The major challenges were to:

  • isolate enough of the unstable isotope U-235 to sustain a chain reaction
  • to kick start the chain reaction somehow, not with the elaborate apparatus available in a lab, but with something which could be packed inside a contain (a bomb) and then triggered somehow
  • a material which could ‘damp’ the process enough so that it could be controlled in experimental conditions

From the start there was debate over the damping material, with the two strongest contenders being graphite – but it turned out to be difficult to get graphite which was pure enough – or ‘heavy water’, water produced with a heavier isotope of hydrogen, deuterium. Only one chemical plant in all of Europe produced heavy water, a fertiliser factory in Norway. The Germans invaded Norway in April 1940 and a spin-off was the ability to commandeer regular supplies from this factory. That is why the factory, and its shipments of heavy water, were targeted for the commando raid and then air raids dramatised in the war movie, The Heroes of Telemark. (Baggott gives a thorough and gripping account of the true, more complex, more terrifying story of the raids.)

Learnings

I never realised that:

  • In the end the Americans built the bomb because they were the only ones with enough resources. Although Hitler and Stalin were briefed about the potential, their scientists told them it would be three or four years before a workable bomb could be made and they both had more pressing concerns. The British had the know-how but not the money or resources. There is a kind of historical inevitability to America being the first to build a bomb.
  • But I never realised there were quite so many communist sympathisers in American society and that so many of them slipped across the line into passing information and/or secrets to the Soviets. The Manhattan Project was riddled with Soviet spies.
  • And I never knew that J. Robert Oppenheimer, the man put in charge of the facilities at Los Alamos and therefore widely known as the ‘father’ of the atom bomb, was himself was such a dubious character, from the security point of view. Well-known for his left-wing sympathies, attending meetings and donating money to crypto-communist causes, he was good friends with communist party members and was approached at least once by Soviet agents to pass on information about the bomb project. No wonder elements in the Army and the FBI wanted him banned from the very project which he was in fact running.

Hiroshima

The first three parts of the book follow in considerable detail the story from the crucial discoveries on the eve of the war, and then interweaves developments in Britain, America and the USSR up until the detonation of the two A-bombs over Hiroshima and Nagasaki on August 6 and 9, 1945.

  • I was shocked all over again to read the idea that, on the eve of the first so-called Trinity test, the scientists weren’t completely confident that the chain reaction might not spread to the nitrogen in the atmosphere and set the air on fire.
  • I was dazzled by the casual way military planners came up with a short list of cities to hit with the bombs. The historic and (by all accounts) picturesque city of Kyoto was on the list but it was decided it would be a cultural crime to incinerate it. Also US Secretary of War Henry Stimson had gone there on his honeymoon, so it was removed from the list. Thus, in this new age, were the fates, the lives and agonising deaths, of hundreds of thousands of civilians decided.
  • I never knew they only did one test – the Trinity test – before Hiroshima. So little preparation and knowledge.

The justification for the use of the bomb has caused argument from that day to this. Some have argued that the Japanese were on the verge of surrendering, though the evidence presented in Baggott’s account militates against this interpretation. My own view is based on two axioms: 1. the limits of human reason 2. a moral theory of complementarity.

Limits of reason When I was a young man I was very influenced by the existentialism of Jean-Paul Sartre and Albert Camus. Life is absurd and the absurdity is caused by the ludicrous mismatch between human claims and hopes of Reason and Justice and Freedom and all these other high-sounding words – and the chaotic shambles which people have made of the world, starting with the inability of most people to begin to live their own lives according to Reason and Logic.

People smoke too much, drink too much, eat too much, marry the wrong person, drive cars too fast, take the wrong jobs, make the wrong decisions, jump off bridges, declare war. We in the UK have just voted for Brexit and Donald Trump is about to become US President. Rational? The bigger picture is that we are destroying the earth through our pollution and wastefulness, and global warming may end up destroying our current civilisation.

Given all these obvious facts about human beings, I don’t see how anyone can accuse us of being rational and logical.

But in part this is because we evolved to live in small packs or groups or tribes, and to deal with fairly simple situations in small groups. Ever since the Neolithic revolution and the birth of agriculture led to stratified and much larger societies and set us on the path to ‘civilisation’, we have increasingly found ourselves in complex situations where there is no one obviously ‘correct’ choice or path; where the notion of a binary choice between Good and Evil breaks down. Most of the decisions I’ve taken personally and professionally aren’t covered by so-called ‘morality’ or ‘moral philosophy’, they present themselves – and I make the decisions – based purely on practical outcomes.

Complementarity Early in his account Baggott explains Niels Bohr’s insight into quantum physics, the way of ‘seeing’ fundamental particles which changed the way educated people think about ‘reality’ and won him a Nobel Prize.

In the 1920s it became clear that electrons, one of the handful of sub-atomic particles, behave like waves and like particles at the same time. In Newton’s world a thing is a thing, self-identical and consistent. In quantum physics this fixed attitude has to be abandoned because ‘reality’ just doesn’t seem to be like that. Eventually, the researchers arrived a notion of complementarity i.e. that we just have to accept that electrons could be particles and waves at the same time depending on how you chose to measure them. (I understand other elements of quantum theory also prove that particles can be in two places at the same time). Conceivably, there are other ways of measuring them which we don’t know about yet. Possibly the incompatible behaviour can be reconciled at some ‘deeper’ level of theory and understanding but, despite nearly a century of trying, nobody has come up with a grand unifying theory which does that.

Meanwhile we have to work with reality in contradictory bits and fragments, according to different theories which fit, or seem to fit, to explain, the particular phenomena under investigation: Newtonian mechanics for most ordinary scale phenomena; Einstein’s relativity at the extremes of scale, black holes and gravity where Newton’s theory breaks down; and quantum theory to explain the perplexing nature of sub-atomic ‘reality’.

In the same way I’d like to suggest that everyday human morality is itself limited in its application. In extreme situations it frays and breaks. Common or garden morality suggests there is one ‘reality’ in which readily identifiable ideas of Good and Bad always and everywhere apply. But delve only a little deeper – consider the decisions you actually have to make, in your real life – and you quickly realise that there are many situations and decisions you have to make about situations which aren’t simple, where none of the alternatives are black and white, where you have to feel your way to a solution often based in gut instinct.

A major part of the problem may be that you are trying to reconcile not two points of view within one system, but two or more incompatible ways of looking at the world – just like the three worldviews of theoretical physics.

The Hiroshima decision

Thus – with one part of my mind I am appalled off the scale by the thought of a hideous, searing, radioactive death appearing in the middle of your city for no reason without any warning, vaporising half the population and burning the other half to shreds, men, women and little children, the old and babies, all indiscriminately evaporated or burned alive. I am at one with John Hersey’s terrifying account, I am with CND, I am against this anti-human abomination.

But with another part of the calculating predatory brain I can assess the arguments which President Truman had to weigh up. Using the A-bomb would:

  1. End a war which had dragged on too long.
  2. Save scores of thousands of American lives, an argument bolstered as evidence mounted that the Japanese were mobilising for a fanatical defence to the death of their home islands. I didn’;t know that the invasion of the southern island of Japan was scheduled for December 1945 and the invasion of the main island and advance on Tokyo was provisionally set to start in march 1946. Given that it took the Allies a year to advance from Normandy to Berlin, this suggests a scenario where the war could have dragged on well into 1947, with the awesome destruction of the entire Japanese infrastructure through firebombing and house to house fighting as well, of course, of vast casualties, Japanese and American.
  3. As the US commander of strategic air operations against Japan, General Curtis LeMay pointed out, America had been waging a devastating campaign of firebombing against Japanese cities for months. According to one calculation some two-and-a-half million Japanese had been killed in these air attacks to date. He couldn’t see why people got so upset about the atom bombs.

Again, I was amazed at the intransigence of the Japanese military. Baggott reports the cabinet meetings attended by the Japanese Prime Minister, Foreign Minister and the heads of the Army and Navy, where the latter refused to surrender even after the second bomb was dropped on Nagasaki. In fact, when the Emperor finally overruled his generals and issued an order to surrender, the generals promptly launched a military coup and tried to confiscate the Emperor’s recorded message ordering the surrender before it could be broadcast. An indication of the fanaticism American troops would have faced if a traditional invasion had gone ahead.

The Cold War

And the other reason for using the bombs was to prepare for after the war, specifically to tell the Soviet Union who was boss. Roosevelt had asked Stalin to join the war on Japan and this he did in August, making a request to invade the north island (the Russians being notoriously less concerned about their own troop losses than the Allies). the book is fascinating on how Stalin ordered an invasion then three days later backed off, leaving all Japan to America. But this kind of brinkmanship and uneasiness which had appeared at Yalta became more and more the dominant issue of world politics once the war was won, and once the USSR began to put in place mini-me repressive communist regimes across Eastern Europe.

Baggott follows the story through the Berlin Airlift of 1949 and the outbreak of the Korean War (June 1950), while he describes the ‘second physics war’ i.e. the Russian push to build an atomic reactor and then a bomb to rival America’s. In this the Russians were hugely helped by the Allied spies who, ironically, now Soviet brutality was a bit more obvious to the world, began to have second thoughts. In fact Klaus Fuchs, the most important conduit of atomic secrets to the Russians, eventually confessed his role.

Baggott’s account in fact goes up to the Cuban Missile Crisis of October 1962 and it is so grippingly, thrillingly written I wished it had gone right up to the fall of the Soviet Union. Maybe he’ll write a sequel which covers the Cold War. Then again, most of the scientific innovation had been achieved and the basic principles established; now it was a question of engineering, of improving designs and outcomes. Of building bigger and better bombs and more and more of them.

The last section contains a running thread about the attempts by some of the scientists and politicians to prevent nuclear proliferation, and explains in detail why they came to nothing. The reason was the unavoidable new superpower rivalry between America and Russia, the geopolitical dynamic of mutually assured destruction which dominated the world for the next 45 years (until the fall of the USSR).

A new era in human history was inaugurated in which ‘traditional’ morality was drained of meaning. Or to put it another way (as I’ve suggested above) in which the traditional morality which just about makes sense in large complex societies, reached its limits, frayed and broke.

The nuclear era exposed the limitations of not only human morality but of human reason itself, showing that incompatible systems of values could apply to the same phenomena, in which nuclear truths could be good and evil, vital and obscene, at the same time. An era in which all attempts at rational thought about weapons of mass destruction seemed to lead only to inescapable paradox and absurdity.


Credit

Atomic: The First War of Physics and the Secret History of the Atom Bomb 1939-49 by Jim Baggott was published in 2009 by Icon Books. All quotes and references are to the 2015 Icon Books paperback edition.

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The Perfect Theory by Pedro G. Ferreira (2014)

On page three of this book, astrophysicist Pedro G. Ferreira explains that part of what enthralled him as a student studying the theory of relativity was the personalities and people behind the ideas.

I felt that I had entered a completely new universe of ideas populated by the most fascinating characters. (p.xiii)

This is the approach he takes in the 14 chapters and 250 pages of this book which skip lightly over the technicalities of the theory in order to give us an account of the drama behind the discovery of the theory. Ferreira describes relativity’s slow acceptance and spread among the community of theoretical physicists, many of whom went on to unravel unexpected consequences from his equations which Einstein hadn’t anticipated (and often fiercely opposed). He shows how the theory was eclipsed in the middle years of the century by the more fashionable theory of quantum physics, then underwent a resurgence from the 1960s onwards, until Ferreira brings the story right up to date with predictions that we are trembling on the brink of major new, relativity-inspired, discoveries.

This book isn’t about the theory of relativity so much as the story of how it was devised, received, tested, studied and expanded, and by whom. It is ‘the biography of general relativity’ (p.xv).

Thus the narrative eschews maths and scientific formulae to focus on a narrative with plenty of human colour and characters. For example, early explanations of the theory are dovetailed with accounts of Einstein’s opposition to the Great War and the political attitudes of Sir Arthur Eddington, his chief promoter in Britain, who was a Quaker. A typically vivid and grabby opening sentence of a new section reads:

While Einstein was working on his theory of general relativity, Alexander Friedmann was bombing Austria. (p.31)

Some reviews I’ve read say that – following Stephen Hawking’s example in his A Brief History of Time (1988) – there isn’t a single equation in the book, but that isn’t quite true; there’s one on page 72:

2 + 2 = 4

is the only equation in the book – which I suspect is a joke. For the most part the ideas are explained through the kind of fairly simple-to-describe thought experiments (Gedankenexperimenten) which led Einstein to his insights in the first place – simple except that they are taking place against an impossibly sophisticated background of astrophysical knowledge, maths theories, weird geometry and complex equations.

Timeline

In 1905 Albert Einstein wrote a number of short papers based on thought experiments he had been carrying out in his free time at his undemanding day job working in the Berne Patent Office. The key ones aimed to integrate Newtonian mechanics with James Clerk Maxwell’s force of electromagnetism. His breakthrough was ‘seeing’ that space and time are not fixed entities but can, under certain circumstances, bend and curve. (It is fascinating to learn that Einstein’s insights came through thought experiments, thinking through certain, fairly simple, scenarios and working through the consequences – only then trying to find the mathematical formulas which would express essentially mental concepts. Only years later was any of it subjected to experimental proof.)

The book gives a powerful sense of the rivalry and jostling between different specialisms. It’s interesting to learn that pure mathematicians often looked down on physicists; they thought physicists too ready to bodge together solutions, whereas mathematicians always strive for elegance and beauty in the equations. Physicists, for their part, suspect the mathematicians of coming up with evermore exotic and sometimes bizarre formulas, which bear little or no relation to the ‘reality’ which physicists have to work with.

So the short or ‘special’ theory of relativity – focusing on mechanics and electromagnetism – was complete by around 1907. But Einstein was acutely aware that it didn’t integrate gravity into his model of the universe. It would take Einstein another ten years to integrate gravity into his theory which, as a result, is known as the general theory of relativity.

Ferreira explains how he was helped by his friend, the mathematician Marcel Grossman, who introduced him to the realm of non-Euclidean mathematics devised by Bernhard Riemann. This is typical of how the book proceeds: by showing us the importance of personal contacts, exchanges, dialogue between scientists in different specialities.

For example, Ferreira explains that the ‘Hilbert program’ was the attempt by David Hilbert to give an unshakable theoretical foundation to all mathematics. Einstein visited Hilbert at the university of Göttingen in 1915, because his general theory still lacked complete mathematical provenance. He had intuited a way to integrate gravity into his special theory – but didn’t have the maths to prove it. Eventually, by the end of 1915, in a process Ferreira describes as Einstein dropping some of his ‘intuitions’ in order to ‘follow the maths’, Einstein completed his general theory of relativity, expressed as a set of equations which became known as the ‘Einstein field equations’.

In fact the field equations were ‘a mess’. A set of ten equations of ten functions of the geometry of space and time, all nonlinearly tangled and intertwined, so that solving any one function by itself was impossible. The theory argued that what we perceive as gravity is nothing more than objects moving in the geometry of spacetime. Massive objects affect the geometry, curving space and time.

Almost before he had published the theory (in an elegantly compact three-page paper) other physicists, mathematicians, astronomers and scientists had begun to take the equations and work through their implications, sometimes with results which Einstein himself strongly disapproved of. One of the most interesting themes in the book is the way that Einstein himself resisted the implications of his own theory.

For example, Einstein assumed, on the classical model, that matter was spread evenly through the universe; but mathematicians pointed out that, if so, Einstein’s equations suggested that at some point the universe would start to evolve i.e. large clumps of matter would be attracted to each other; nothing would stay still; potentially, the entire universe could end up collapsing in on itself. Einstein bent over backwards to exclude this ‘evolving universe’ scenario from his theory by introducing a ‘cosmological constant’ into it, a notional force which pushed back against gravity’s tendency to collapse everything: between the attraction of gravity and the repellent force of the ‘cosmological constant’, the universe is held in stasis. Or so he claimed.

Ferreira explains how the Dutch astronomer Willem de Sitter was sympathetic to Einstein’s (gratuitous) cosmological constant and worked through the equations, initially to support Einstein’s theory, but in so doing discovered that the universe could be supported by the constant alone – but it would contain very little matter, very little of the stars and planets which we seem to see. Einstein admired the maths but abhorred the resulting picture of a relatively empty universe.

In fact this was just the beginning of Einstein’s theory running away from him. The Russian astronomer and mathematician Alexander Friedmann worked through the field equations to prove that the perfectly static universe Einstein wanted to preserve – and had introduced his ‘cosmological constant’ to save – was in fact only one out of many possible scenarios suggested by the field equations – in all the others, the universe had to evolve.

Friedmann explained his findings in his 1922 paper, ‘On the Curvature of Space’, which effectively did away with the need for a cosmological constant. His work and that of the Belgian priest, Georges Lemaître, working separately, strongly suggested that the universe was in fact evolving and changing. They provided the theoretical underpinning for what astronomers had observed and named the ‘de Sitter effect’, namely the observation, made with growing frequency in the 1920s, that the furthest stars and nebulae from earth were undergoing the deepest ‘red shift’ i.e. the light emanating from them was shifted down the spectrum towards red, because they were moving away from us. Even though Einstein himself disapproved of the idea, his theory and the observations it inspired both showed us that the universe is expanding.

If so – does that mean that the universe must have had a definite beginning? When? How? And could the theory shed light on what were just beginning to be known as ‘dwarf stars’? What about the bizarre new concept of ‘black holes’ (originally developed by the German astronomer Karl Schwarzchild, who sent his results to Einstein in 1916, but died later that year)?

What Einstein called ‘the relativity circus’ was well underway – and the rest of the book continues to introduce us to the leading figures of 20th century physics, astrophysics, cosmology and mathematics, giving pen portraits of their personalities and motivations and describing the meetings, discussions, conferences, seminars, experiments, arguments and debates in which the full implications of Einstein’s theory were worked out, argued over, rejected, revived and generally played with for the past 100 years.

We are introduced:

  • To Subrahmanyan Chandrasekhar who proposed a sophisticated solution to the problem of white dwarfs and how stars die – which was rejected out of hand by Eddington and Einstein.
  • To the Soviet physicist Lev Davidovich Landau who proposed that stars shine and burn as a result of the radioactive fission of tremendously dense neutrons at their core (before he was arrested for anti-Stalin activities in 1938).
  • To J. Robert Oppenheimer who read Landau’s paper and used its insights to prove Schwarzchild’s wartime idea that stars collapse into such a dense mass that gravity itself cannot escape, and therefore a bizarre barrier is created around the star from which light, energy, radiation or gravity can emerge – the ‘event horizon’ of a ‘black hole’.

These are the main lines of research and investigation which Ferreira outlines in the first quarter or so of the book up to the start of World War Two. At this point, of course, many leading physicists and mathematicians of all nationalities were roped into the massive research projects run in America and Germany into designing a bomb which could harness the energy of nuclear fusion. This had been thoroughly investigated in theory and in observations of distant galactic phenomena – but never created on earth. Not until August 1945, that is, when the two atom bombs dropped on Japan killed about 200,000 people.

Learnings

Some of the several fascinating things to learn from this mesmerising account are:

  • How often Einstein was wrong and wrong-headed, obstinately refusing to believe the universe evolved and changed, refusing to believe (therefore) that it had an origin in some ‘big bang’, and his refusal to accept the calculations which proved the possibility of black holes.
  • That although a great genius may devise a profound theory, in the world of science he doesn’t ‘own’ it – there is literally no limit to the number of other scientists who can probe and poke and work through and analyse and falsify it – and that the strangeness and weirdness of general relativity made it more liable than most theories to produce unexpected and counter-intuitive results, in the hands of its many epigones.
  • That after early successes, namely:
    • predicting the movement of the planets more accurately than Newton’s classical mechanical theory
    • showing that light really is bent by gravity when this phenomenon was observed and measured during a solar eclipse in 1919
    • inspiring the discovery that the universe is expanding
  • the theory of relativity was increasingly thought of as a generator of bizarre mathematical exotica which had little or no relevance to the real world. We learn that ambitious physicists from the 1930s onwards preferred to choose careers in the other great theoretical breakthrough of the 20th century, quantum physics. Quantum could be tested, experimented with and promised many more practical breakthroughs.

Almost everyone’s attention was elsewhere now, enthralled by the triumph of quantum physics. Most of the talented young physicists were focusing their efforts on pushing the quantum theory further, looking for more spectacular discoveries and applications. Einstein’s general theory of relativity, with all its odd predictions and exotic results, had been elbowed out of the way and sentenced to a trek in the wilderness. (p.65)

  • And so that Einstein, now safely ensconced in the rarefied atmosphere of the Institute for Advanced Studies in Princeton, New Jersey, dedicated the last thirty years of his life (he died in 1955) to an ultimately fruitless quest for a ‘Grand Unified Theory’ which would combine all aspects of physics into one set of equations. He was, in the 1940s and 50s, an increasingly marginal figure – yesterday’s man – while the world hurried on without him. He died before the great revival of his theory in the 1960s which the second part of Ferreira’s book chronicles.

Visualisation

Again and again Ferreira shows how the researchers proceeded – or summarises the differences between their approaches and results – in terms of how they visualised the problem. Thus Schwarzchild’s vision of a relativistic universe described a spacetime that was perfectly symmetric about one point; whereas 40 years later, in 1963, New Zealander Roy Kerr modeled a solution for a spacetime that was symmetric about a line (p.121). A different way of visualising and conceiving the problem, which led to a completely different set of equations, and completely different consequences.

Other scientists take an insight like this, a new vision with accompanying new mathematics, and themselves subject it to further experimental modeling. The Soviet physicists Isaak Khalatnikov and Evgeny Lifshitz took Oppenheimer and Snyder’s 1930s model of a star collapsing – which assumed the shape of the star to be a perfect sphere – and modeled what happened if the star-matter was rough and unequal, like the surface of the earth. In this model, different bits collapsed at different rates, creating a churning of space time and never achieving the perfect collapse into a singularity modeled by Schwarzchild 60 years earlier or by Kerr more recently. This Soviet model was itself disproved by Roger Penrose, who had spent years devising his own diagrams and maths to model spacetime, and submitted a paper in 1965 which proved that ‘the issue of the final state’ always ended in singularities (pp.123-125).

And that is how the field progresses, via new ways of seeing and modeling. One revealing anecdote is how, at a conference in the 1990s on the newly hot topic of ‘dark matter’, one presenter put up a slide listing over one hundred different models for how dark matter exists, is created and works (p.192), all theoretical, derived from different sets of equations or observations, all awaiting proof.

It is not only the complexity of the subject matter which makes this such a daunting field of knowledge – it is the sheer number and variety of theories, ancient and modern, which its practitioners are called on to understand and sift and evaluate and which – as the first half makes plain – even the giants in the field, Einstein and Eddington, could get completely wrong.

The 1960s and since

In Ferreira’s account the 1960s saw a great revival of the theory of general relativity to explain the host of new astronomical phenomena which were being discovered and named – joining black holes and dwarf stars were pulsars, quasars and so on – as well as new theoretical micro-particles, like the Higgs boson. Kip Thorne called the 60s and 70s the Golden Age of Relativity, when the theory provided elegant solutions to problems about black holes, dark energy and dark matter, singularities and the Big Bang.

Over the past forty years or so new theories have arisen which take and transcend general relativity, including string theory (which rose to prominence in the 1980s but has since fallen into unpopularity) and supersymmetry (which invokes up to six extra dimensions in its quest for a total theory), loop quantum theory (where reality is comprised of minute loops of quantum gravity which bind together like chainmail), spin networks (frameworks like a children’s climbing frame, devised by Roger Penrose), Modified Newtonian Dynamics (or MOND) or a new theory to rival Einstein’s named the Tensor-Vector-Scalar theory of gravity (TeVeS).

When Ferreira and colleagues undertook a review of theories of quantum mechanics they discovered there are scores of them, ‘a rich bestiary of gravitational theories’ (p.221).

The great ambition is to incorporate quantum gravity into general relativity in order to produce a grand unified theory of everything. Although clever people bet this would happen before the end of the 20th century, it didn’t. 17 years later, we seem as far away as ever.

Thirty years after Stephen Hawking predicted the end of physics and then unleashed his black hole information paradox on an unsuspecting world, there isn’t an agreed-upon theory of quantum gravity, let alone a complete unified theory of all the fundamental forces. (p.205)

Ferreira draws together various developments in theory at the sub-atomic level to conclude that we may be on the brink of moving beyond Einstein’s vision of a curving spacetime: the real stuff of the universe is, depending on various theories, a bubbling foam of intertwining strings or structures or membranes or loops – but certainly not continuous. Newtonian mechanics still work fine at the gross level of our senses; it is only at extremes that Einstein’s theories need to be evoked. Now Ferreira wonders if it’s time to do the same to Einstein’s theories; to go beyond them at the new extremes of physical reality which are being discovered.

Notes

The deliberate non-technicality of the text is compensated by 18 pages of excellent notes, which give a chatty overview of each of the chapter topics before recommending up-to-the-minute websites for further reading, including the websites and even Facebook groups for specific projects and experiments. And there is also a detailed bibliography of books and articles.

All in all this is an immensely useful overview of the ideas and debates in this field.


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