On Old Age by Cicero (44 BC)

‘Of what immense worth is it for the soul to be with itself, to live, as the phrase is, with itself, discharged from the service of lust, ambition, strife, enmities, desires of every kind!’
(On old age by Cicero)

Cicero wrote De senectute or ‘Of old age’ to disabuse people of their negative stereotypes about old age, to defend old age, to make it less feared. It’s a relatively short treatise by Cicero’s standards. It is dedicated to his good friend Titus Pomponius (who gave himself the nickname ‘Atticus’ because he loved Athens so much).

Cicero sets it, like De republica and De amitia, back in the time of Scipio Aemilianus, about 130 BC, and has the characters in the dialogue be Scipio, his friend Caius Laelius, and the stern moralist Cato the Elder, who lived a very long life (234 to 149 BC) and so was eminently qualified to talk about age.

In De senectute Cicero, like the defence lawyer he was, mounts a defence of the state of old age against its alleged disadvantages. He has Cato tell Scipio and Laelius how foolish general attitudes to old age are. The best way to live is to ‘follow and obey Nature, the surest guide, as if she were a god,’ (which my recent reading has taught me to see as pure Stoicism). Hence the Stoic insistence on Virtue:

CATO: “The best-fitting defensive armour of old age, Scipio and Laelius, consists in the knowledge and practice of the virtues, which, assiduously cultivated, after the varied experiences of a long life, are wonderfully fruitful, not only because they never take flight, not even at the last moment, — although this is a consideration of prime importance, — but because the consciousness of a well-spent life and a memory rich in good deeds afford supreme happiness.”

Those who criticise old age are often simply projecting their own vices and shortcomings onto an inevitable part of life.

About a quarter of the way into the text, after this fictional Cato has given us profiles and anecdotes about quite a few eminent Romans of his time, he gets round to tabulating the four main criticisms people make of old age.

“One, that it calls us away from the management of affairs; another, that it impairs bodily vigour; the third, that it deprives us to a great degree of sensual gratifications; the fourth, that it brings one to the verge of death.”

The essay consists of him examining and refuting each of these claims in turn:

1. Old age withdraws us from active pursuits

It’s true old age prevents activities which are appropriate for youth and strength of body. But there are many activities appropriate to maturity and statesmanship, and he gives a list of eminent Romans who played decisive roles at key moments of Roman history:

The old man does not do what the young men do; but he does greater and better things. Great things are accomplished, not by strength, or swiftness, or suppleness of body, but by counsel, influence, deliberate opinion, of which old age is not wont to be bereft, but, on the other hand, to possess them more abundantly…Unless these were the characteristics of seniors in age, our ancestors would not have called the supreme council the Senate.

The word senate derives from senex, the Latin for old man, implying that with age comes wisdom and decision.

If you see fit to read or hear the history of foreign nations, you will find that states have been undermined by young men, but maintained and restored by old men.

Rashness, indeed, belongs to youth; prudence, to age.

Indeed, the crowning glory of old age is authority.

Old age, especially when it has filled offices of high public trust, has so much authority, that for this alone it is worth all the pleasures of youth.

Old men are said to forget, but Cato insists this is only true among those who do not exercise their memory or were slow-minded to begin with. No, old men remember everything that they care about and:

Old men have their powers of mind unimpaired when they do not suspend their usual pursuits and their habits of industry.

Examples of men who excelled at their craft well into old age include Sophocles, Homer, Hesiod, Simonides, Stesichorus, Isocrates, Gorgias, Pythagoras and Democritus, Plato, Xenocrates, Zeno and Cleanthes and so on. Did these men not continue working at the top of their bent till the end of their lives?

Some say old age is repellent to the young, but it need not be so if is considered with respect to the wisdom age has to offer:

As wise old men are charmed with well-disposed youth, so do young men delight in the counsels of the old, by which they are led to the cultivation of the virtues.

And so another of the benefits of age is the respect of the young and he details the respect afforded successful elder statesmen, such as being saluted in the morning, grasped by the hand, received by the rising of those present, escorted to the Forum, escorted home, asked for advice.

What pleasures of body are to be compared with the prerogatives of authority?

2. Old age makes the body weaker

It is becoming to make use of what one has, and whatever you do, to do in proportion to your strength

But the eloquence that becomes one of advanced years is calm and gentle, and not infrequently a clear-headed old man commands special attention by the simple, quiet elegance of his style

You can at least help others by your counsel; and what is more pleasant than old age surrounded by young disciples? Must we not admit that old age has sufficient strength to teach young men, to educate them, to train them for the discharge of every duty? And what can be more worthy of renown than work like this?

If you know someone stronger than you, does that make them better than you? No, each of us has the strength appropriate to our bodies and exercise, so:

Provided one husbands one’s strength, and does not attempt to go beyond it, one will not be hindered in one’s work by any lack of the requisite strength.

Accept the course of nature.

Life has its fixed course, and nature one unvarying way; each age has assigned to it what best suits it, so that the fickleness of boyhood, the sanguine temper of youth, the soberness of riper years, and the maturity of old age, equally have something in harmony with nature.

But do what you can to remain fit.

Exercise and temperance, then, can preserve even in old age something of one’s pristine vigour.

Live a healthy life.

Old age, like disease, should be fought against. Care must be bestowed upon the health; moderate exercise must be taken; the food and drink should be sufficient to recruit the strength, and not in such excess as to become oppressive. Nor yet should the body alone be sustained in vigour, but much more the powers of mind; for these too, unless you pour oil into the lamp, are extinguished by old age. Indeed, while overexertion tends by fatigue to weigh down the body, exercise makes the mind elastic.

Cato lists the intimidating roster of activities he is undertaking in his 84th year, including:

  • he is writing a history
  • he is collecting memorials of older times
  • he is writing out the speeches he gave in all his law cases
  • he is treating of augural, pontifical, civil law
  • to exercise his mind he recalls every evening whatever he has said, heard or done during the day
  • he often appears in court on behalf of friends
  • he attends the senate and still has motions he wants to propose

These are the exercises of the mind; these, the race-ground of the intellect.

If you remain alert and active:

One who is always occupied in these studies and labours is unaware when age creeps upon him. Thus one grows old gradually and unconsciously,

3. Old age deprives us of almost all physical pleasures

This is a positive thing, considering that the lure of physical pleasure is one of the most harmful things to youth. He quotes a violent speech against pleasure by Archytas of Tarentum:

“There is no form of guilt, no atrocity of evil, to the accomplishment of which men are not driven by lust for pleasure. Debaucheries, adulteries, and all enormities of that kind have no other inducing cause than the allurements of pleasure.

“Still more, while neither Nature nor any god has bestowed upon man aught more noble than mind, nothing is so hostile as pleasure to this divine endowment and gift. Nor while lust bears sway can self-restraint find place, nor under the reign of pleasure can virtue have any foothold whatever.”

If reason is the greatest gift of the gods and the highest faculty of man, and if indulgence in physical pleasure overrides or extinguishes it, then thank God for old age if it means all these harmful forces leave you.

For pleasure thwarts good counsel, is the enemy of reason, and, if I may so speak, blindfolds the eyes of the mind, nor has it anything in common with virtue.

Plato called pleasure ‘the bait of evil’, and so:

It is not only no reproach to old age, but even its highest merit, that it does not severely feel the loss of bodily pleasures.

It is said that old men have less intensity of sensual enjoyment. So I believe; but there is no craving for it. You do not miss what you do not want.

Sophocles very aptly replied, when asked in his old age whether he indulged in sensual pleasure, “May the gods do better for me! I rejoice in my escape from a savage and ferocious tyrant.”

So one can feel grateful for it:

I am heartily thankful to my advanced years for increasing my appetency for conversation, and diminishing my craving for food and drink.

Speaking personally, I’m glad I’m middle aged. When I was a young man I felt I had a raging fire burning in my mind which could only be extinguished by intoxicants and inebriants, I hurtled round London feeling like I might explode at any moment. Now the fires of testosterone have banked right down and I am content to read literature and tend my garden, like the best of the ancients. It is an enormous relief not to be young any more.

it is to Solon’s honour that he says, in the verse which I just now quoted, that as he advanced in age he learned something every day, — a pleasure of the mind than which there can be none greater.

He then has a passage about the joys of what he calls agriculture, but is nearer to horticulture, with an extended description of the joy of growing grapes and watching the vines grow and spread.

What can I say of the planting, upspringing, and growth of vines? It is with insatiable delight that I thus make known to you the repose and enjoyment of my old age.

I know what he means. This year I have planted seven trees, set up 10 trellises and planted five climbers to grow up them, and sown wild flowers seed along 20 metres of border. There is no pleasure like the calm pleasure of planning, planting, watering and tending your own garden.

He introduces some further accusations against old men 1) that they are morose, uneasy, irritable and hard to please, 2) that they become avaricious with age.

But these are faults of character, not of age itself.

He defends (some) old men from being uneasy and irritable because this is, in fact, a justified response to the way they are sometimes treated – when they are scorned, despised, mocked. Who can blame old people from being grumpy about being badly treated and neglected.

Also, if you have a weaker body, sometimes undermined by chronic health problems, then any cause of vexation is felt more keenly. But such infirmities of temper should be corrected by good manners and liberal culture.

As to old men becoming greedy, he can’t understand it at all. With less of life to live, why bother devoting your energies to acquiring wealth you won’t have time to spend. Better to cultivate a calm but active mind.

4. Old age is liable to excessive solicitude and distress because death is so near

But one of the key achievements of wisdom is to overcome your fear of death and learn to despise it. There are, after all, only two scenarios: either the soul / mind ceases to exist at death (in which case there is nothing to worry about) or we pass to an immortal realm (which is highly desirable). Win-win, either way.

In fact, young people are more liable to fatal incidents than old people: young people commit suicide, are killed in car or motorbike crashes, in fights or murders and, in Cicero’s time, in battle, much more than old people.

Young people hope to live to a ripe old age. An old person should rejoice because he has achieved that wish.

Each one should be content with such time as it is allotted to him to live.

In order to give pleasure to the audience, the actor need not finish the play; he may win approval in whatever act he takes part in; nor need the wise man remain on the stage till the closing plaudit. A brief time is long enough to live well and honourably.

But if you live on, you have no more reason to mourn over your advancing years, than the farmers have, when the sweet days of spring are past, to lament the coming of summer and of autumn.

What can be more natural than to die old. It is those who die young who are the tragic waste. Dying old is part of the natural cycle of things.

Old men die as when a spent fire goes out of its own accord, without force employed to quench it…This ripeness of old age is to me so pleasant, that, in proportion as I draw near to death, I seem to see land, and after a long voyage to be on the point of entering the harbour.

And:

Because old age has no fixed term, one may fitly live in it so long as one can observe and discharge the duties of his station, and yet despise death.

Old age, fearless of death, may transcend youth in courage and in fortitude.

As to the actual pain of dying:

There may be, indeed, some painful sensation in dying, yet for only a little while, especially for the old; after death there is either desirable sensation or none at all.

It is possible to have had enough, to have lived well and done everything one wanted so as to reach a stage of being ready for death:

satiety of life, as it seems to me, creates satiety of pursuits of every kind. There are certain pursuits belonging to boyhood; do grownup young men therefore long for them? There are others appertaining to early youth; are they required in the sedate period of life which we call middle age? This, too, has its own pursuits, and they are not sought in old age. As the pursuits of earlier periods of life fall away, so in like manner do those of old age. When this period is reached, satiety of life brings a season ripe for death.

Cato ends by sharing his personal thoughts about the soul. He believes, with the Pythagoreans, that each human soul is a fragment of the Divine Mind forced, for a while, into the prison of an earthly habitation. Indivisible and immortal, human souls knew things before we were born (as per Plato).

The wise soul knows it will live on after death:

Since men of the highest wisdom die with perfect calmness, those who are the most foolish with extreme disquiet, can you doubt that the soul which sees more and farther perceives that it is going to a better state, while the soul of obtuser vision has no view beyond death?

Cato is looking forward to meeting the great men he knew in life, as well as legendary figures from earlier days. And so, after a lifetime of toil for his nation, Cato is ready to move on for a better place, the abode of bliss and the company of heroes:

I depart from life, as from an inn, not as from a home; for nature has given us here a lodging for a sojourn, not a place of habitation. O glorious day, when I shall go to that divine company and assembly of souls, and when I shall depart from this crowd and tumult!

Thoughts

Unlike Cicero’s treatise on friendship, which was impossibly high-minded and deformed by Cicero’s obsession with Stoic philosophy, his insistence on spelling out the belief in God which underlies his belief in a God-given Human Nature and therefore God-given Moral Laws – this essay is far less theoretical, and therefore a genuinely useful, insightful guide to how to age gracefully and well.

Once or twice he mentions the Stoic nostrum that virtue can fortify the mind against all vicissitudes, but the philosophy is tamped right down in favour of the many practical, real world examples of fellow Romans who Cato has known or whose grace and wisdom and ongoing energy in old age offer genuinely inspiring examples, both to him and to anybody who reads it.


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On the nature of the gods by Cicero – 2

‘It is the task of philosophy to dispel errors so that when we talk about the immortal gods we may say only what is worthy of them.’
(Gaius Aurelius Cotta, page 219, book III, On the nature of the gods)

On the nature of Cicero’s books

Cicero’s books are extremely argumentative. By which I mean that there are no descriptive or literary passages, only the briefest autobiographical passage at the start and then – bang! – straight into 150 pages of non-stop, unrelenting argumentation. Every paragraph is arguing a point, and he sometimes makes two or 3 points on a page. On the nature of the gods is only 150 or so pages long in the Penguin paperback edition but every page is crammed with a non-stop barrage of arguments, proofs and refutations.

The one really obvious attraction of these ancient texts is that they are accessible. By that I mean that the protagonists in a text like this use examples and ideas which are completely understandable by the man or woman in the street. Unlike modern philosophy there is a complete absence of: maths and maths-style logic (as found in analytical and logical philosophy); specialised technical terms; and, above all, the clutter and detritus of hundreds of other philosophical schools which have arisen over the past 2,000 years and left their semantic and conceptual wreckage strewn across the intellectual landscape.

Instead, the three protagonists in this dialogue about the nature of the gods almost entirely use ordinary language and everyday examples to make their points. For example when Velleius says that, if God only decided to make the universe, the sun and the moon and so on at some point into infinite time, does that mean that up till that moment he had been living in darkness like a pauper in a hovel? There is a lot more like this, a lot more crude sarcasm and taunting and ridiculing than you might expect in a ‘philosophical’ work.

(Actually, that’s not strictly true: from time to time the speakers use philosophical terms coined by the original Greek philosophers. Not many and not often, though.)

The result is twofold: although a lot of the arguments come across as wrong, superficial and bizarre, nonetheless it is easy to read and enjoyable to follow the flow of each speaker’s case. The editor, J.M. Ross, points out that the text is very uneven, with chunks missing, other bits arranged in what seem to be the wrong order, with the protagonists failing to address each other’s points or wandering off the subject altogether. But this makes it all the more entertaining, like listening to a tipsy polymath holding forth at a dinner party or at the bar. I think of the comic monologues of entertainers of my youth like Victor Borge or Peter Ustinov. The combination of serious points embellished with ridicule and exaggeration are frequently more reminiscent of a comic monologue than a work of ‘philosophy’.

It also gives the book a pleasing naivety. Coming to Cicero after trying to read Derrida or Habermas is like walking from an intense undergraduate seminar down the corridor into the creche where a load of toddlers are playing with lego.

Three speakers

As explained before, the text is conceived as presenting three speakers, each of whom is a star representative of the three main philosophical schools of Cicero’s day – Epicurean, Stoic, Academic. There were many other minor schools but as his book is focusing on the specific questions of a) whether there are gods and b) what they’re like and c) how we should behave regarding them, Cicero only needed three positions or attitudes. The three interlocutors are:

  • Gaius Velleius who represents the Epicurean point of view
  • Quintus Lucilius Balbus who propounds the Stoic point of view
  • Gaius Aurelius Cotta who represents the Academic point of view

The three positions can be summarised as:

  • atheist / Epicurean (no gods or, if gods, no intervention in human affairs)
  • providence / Stoic (gods exist and are identical with nature, with the visible universe and its laws)
  • sceptic (voicing objections to both the above to arrive at a ‘common sense’ view of the existence of the gods and the reverence due them)

In what follows I’m not going to give an exhaustive summary of all the points made by all the speakers, just the ones which came over to me as important or interesting or quirky.

Introduction

In the brief introduction Cicero makes a couple of points which will recur throughout the book:

Cicero takes it as axiomatic that there are gods. Only a fool or anarchist would be an atheist. Belief in the existence of the gods follows from two key axioms:

1. All of history and all of anthropology suggests that all humanity is naturally and innately inclined to believe in gods. And this universal predilection is taken as incontrovertible proof.

2. Religious belief and practice are the vital glue holding society together and underpinning all moral and social values, underpinning interpersonal ethics and the rule of law and justice.

When piety goes, religion and sanctity go with it. And when these are gone, there is anarchy and complete confusion in our way of life…If our reverence for the gods were lost, we should see the end of good faith, of human brotherhood, and even of justice itself, which is the keystone of all the virtues. (I.2)

So although all three speakers may at points touch on the logical possibility of there being no gods, none of them actually propounds this view. Possibly this was also because, although there was no actual law against atheism, nonetheless Greek thinkers who had propounded atheism had been vilified. Cotta gives the example of Protagoras of Abdera who wrote in a book that he was not able to say whether the gods existed or not, and was as a result banished from the city and his works burned in public. Cicero himself had been elected a member of the College of Augurs in 53 BC and so was responsible for performing various religious duties in public. As he has Cotta say:

I myself hold a religious office and I believe that public religious worship and ritual ought to be reverently observed. (p.94)

If his book had openly espoused atheism, presumably he would have been sacked from that job and maybe faced further sanctions. So hidden behind the civilised chat of our three protagonists lurks a coercive social threat. (The notion that it is ‘prudent’ to profess belief in the gods is repeated on pages 104, 120 and 193.)

1a. Gaius Velleius and the Epicurean view of the gods (pages 77 to 92)

Rubbishing the opposition

A good deal of Velleius’s discourse consists of stating, then rubbishing, Stoic and other Greek philosophical views.

Velleius kicks off by rubbishing Stoic-style notions that the universe was built by a master artificer, the view put forward by Plato in his dialogue Timaeus. Can anyone actually imagine that happening? What tools did he use, what levers and pulleys and scaffolding? How came earth and air and fire and water to obey his commands?

Plato makes the world a manufactured article but he contradicts himself by saying the universe was made but at other points saying it is eternal.

We know time is infinite, eternal. Therefore the universe was created some point into infinite time. It had a beginning. Why? Why create it just at that moment? What triggered this sudden decision? What prompted God to decorate the universe with pretty lights like ‘some Minister of Public Works’? Is it because the world was created for the benefit of the wise? Then surely, never was so much trouble gone to to please so few.

Also: if the universe had a beginning, it must also have an ending.

How can the universe be a conscious being?

He mocks people who say the universe is a great consciousness, one conscious and immortal being (i.e. Stoics). They have no idea what consciousness is. They are ‘stupid’. Plato says the universe must be a sphere because the sphere is ‘the perfect shape’. How childish. He also says it must be spinning. If this sphere is conscious and is spinning at high speed, doesn’t God get giddy? And if the universe is ‘conscious’ some parts of the world are freezing ice caps, some parts are burning desert. So doesn’t it follow that god is roasting on one place and freezing in another?

Listing and rubbishing all other philosophers

Velleius then gives a long list of Greek philosophers starting with Thales, devoting a paragraph to summarising their chief contribution and then dismissing it with a sentence, being: Thales, Anaximander, Anaximenes, Anaxagoras, Alcmeon, Pythagoras, Xenophanes, Parmenides, Empedocles, Protagoras, Democritus, Diogenes, Plato, Xenophon, Antisthenes, Speusippus, Aristotle, Xenocrates, Heraclides, Theophrastus, Strato, Zeno (father of Stoicism), Aristo, Cleanthes, Persaeus, Chrysippus, Diogenes of Babylon, and more.

In his introduction Ross describes this list as an irritating digression which the reader can skip but, on the contrary, I found it an enjoyable and informative overview. Above all it is a useful counter to Cicero’s structural claim that there are only 3 schools of philosophy. On the contrary, this list demonstrates the huge jungley undergrowth of Greek philosophical opinions.

Rubbishing Aristotle

Velleius castigates Aristotle for holding at least three separate views: in one place attributing divinity to mind only, in another saying the entire universe is God, in another setting God above the universe with the power to order all its motions; in yet another claiming the fiery ether is God, so how does that square with the entire universe being God? And if heaven is a God where do the gods reside? Anyway, how could the heavens, in their endless fast revolutions around the earth, maintain consciousness worthy of a god? And if God is bodiless how can he be in motion?

See what I mean by argumentative? In just one paragraph Velleius rubbishes 9 theological propositions of Aristotle. So this list of silly philosophers also feeds into Cicero’s Academic scepticism by demonstrating what a range of absurd and contradictory opinions have been held by such ‘clever’ people. Velleius calls them ‘the fantasies of lunatics’, no better than the fictions of the poets and the wonders of the magicians.

Velleius’s exposition of Epicurus (pages 87 to 92)

Epicurus thought the gods must exist because nature has imprinted an idea of them in the minds of all mankind. This is one of the fundamental axioms of human thought without which there can be no knowledge, rational thought or argument. It is the basis of a firm and continuing consensus.

The same nature which imprints this idea also imprints the notion that they are blessed and immortal. If this is so, the gods must be free from care, anxiety and other human emotions, and must cause no care or anxiety in others i.e. mortals.

The logical consequence of this is that a) the gods deserve reverence as everything which is excellent deserves reverence, but b) we need not fear the gods because blessed and immortal beings have no motive to cause anxiety and fear in others (p.89). This is the core aim of Epicureanism – to banish anxiety, fear, worry and care from its followers.

The gods have human form

Evidence for this includes:

  1. The universal conviction of all humanity i.e. nature has implanted this idea in all human minds.
  2. Because the divine nature is perfect, it must be clothed in the most perfect form and what form is more perfect and beautiful than the human body?
  3. Reason cannot dwell in any other form but the human form.

He gives a good example of the poor, biased and sometimes absurd arguments used throughout the book when he claims that: everyone agrees that the gods are happy, and no happiness is possible without virtue, and there is no virtue without reason, and reason is associated only with the human form: therefore, the gods must have human form. Cotta picks up on this sentence to point out that the final link – that reason is only associated with the human form – does not follow but is willed (p.104 and p.114).

BUT individual human bodies are fallible, vulnerable, age and die. Not so immortal bodies. Therefore the gods have the shape of human bodies but not actual human flesh and blood.

The gods are blissfully detached

Happiness is a state of rest. The gods do not strive and work. They have attained stasis, contemplating their own holiness and wisdom (which sounds very Buddhist). Therefore they have no involvement whatsoever in the world of men, which would involve them in anxiety and endeavour.

A being which is blessed and immortal is itself without cares and brings no cares to others. (p.104)

The universe was created by natural causes

Rather than created by some God, the universe came into being quite naturally by the clash of the infinite number of atoms falling infinitely through infinite space, banging into each other, congealing and constellating. No need for any God labouring away with levers and pulleys.

Thus there is no overseeing God, no God involved in creating the universe, it and everything in it have developed by natural processes. Thus there is no reason to be afraid of a curious god poking and prying into our lives, ‘a busybody god’.

Velleius’s conclusion

Epicurus has saved us from all such fears and set us free, so that we have no terror of the gods, whom we know neither devise any mischief for themselves nor seek to bring it upon others. And so with reverence and awe we worship them in their divine perfection. (p.92)

1b. Cotta’s refutation of Velleius (pages 93 to 120)

Cotta the sceptic is ‘one of those who can more easily see why something is false than true’. Cicero, rather unfairly, gives more space to Cotta’s demolition of Velleius than to the former’s main exposition. Cotta calls Velleius’s Epicurean views ‘irresponsible and ridiculous’.

1. Velleius’s main argument for the existence of the gods is that ‘all mankind’ believes in them. Well, how does he know the opinion of all mankind? There may be any number of wild and primitive peoples who don’t believe in gods, how can he know? Also, there is a record of known philosophers in Greece who have been out-and-out atheists; it doesn’t take many instances to disprove a claim to universality.

2. Cotta comes down hard on Velleius’s theory of atoms endlessly falling in infinite space, whose collisions eventually give rise to matter and the universe. Cotta denies the existence of atoms but says that, even if they existed, the notion that from sheer chance they have created the universe and all the order and regularity and life forms which we observe is ridiculous (p.114). The entire cock and bull theory is a working backwards from the necessary core of Epicureanism i.e. the non-intervention of the gods.

More fatally, if everything is made of atoms then the gods are made of atoms too and can be dissolved as easily as they came into being. If they had a beginning they must have an end: so how can they avoid anxiety about death and dissolution? (p.115)

3. Cotta ridicules Epicurus for saying that the gods must have a human body, as that is the highest form of perfection, and yet it is not actually a body because that is subject to decay – so they have something like a body but not subject to decay. Velleius criticised all other philosophers for their absurdities; Cotta calls Epicurus’s ideas ‘fanciful dreams’.

The notion that the gods must have human form is the product of:

  • superstitious minds who created phantom images of the gods because it was easy
  • poets and painters who need to work with something tangible, and therefore promoted the idea of gods having bodily form
  • humanity’s bias or prejudice towards thinking itself fabulous and the highest of all possible life forms; it is a form of narcissism; anthropomorphism (“the attribution of human traits, emotions, or intentions to non-human entities. It is considered to be an innate tendency of human psychology.”)

Are the gods different as human beings are different, one from another? In which case, how can they be perfect? Surely there is only one model of perfection and all gods ought to embody it?

Anyway, it’s not true to say that all cultures envision the gods in human form: the Egyptians envision gods as animals (dog, crocodile, jackal, cat), as do many other cultures.

Similarly, is there a fixed number of gods with fixed identities? Because a) all cultures appear to have their own gods and b) many gods who are recognisably the same (king of the gods, queen of the gods, god of war, god of love) seem to have multiple names.

‘Do you really think that a god looks like me or like you? The fact is, you have no idea.’ (p.103)

Epicurus appears to say that there is no causal link between humans looking like gods and gods having human form, that both are just accidents of the infinite interaction of an infinite number of atoms in infinite space. This is a ridiculous assertion.

If the gods are so powerful why do they need bodies at all? Why do they need hands or feet or limbs let alone the complex internal organs? If they have godly powers they have no need of all these clumsy encumbrances. If they have bodies the gods would have to walk and climb and bend and stoop. they would have to eat and drink and pee and defecate. If they have the usual organs of generation they would have sex, with all the indignity that implies.

If the gods are vastly superior to us in mind and reason why shouldn’t they be similarly superior to us in body, inhabiting bodies whose shape and powers we can’t even conceive of?

Cotta ridicules the notion of the gods’ detachment. Even idle children get up to games. No human can rest idle indefinitely. What is the point of having the body he insists they have, if they don’t use them?

All creatures, all living things, have a sphere of operation within which they live and are active. Where is the gods’ sphere? To what objects do they use their mind and intelligence. If they know everything their minds are, in a sense, empty, because unexercised.

Velleius had said that the gods are happy because they have achieved the height of virtue. But virtue doesn’t mean anything unless it is tested in action i.e. someone has a choice of actions and decisions and acts accordingly. But Epicurus’s gods do not act in any way. Therefore they do not exercise virtue. Therefore they cannot be happy. Humans exercise decision and judgement all the time, therefore are more able to behave virtuously, therefore humans must be happier than the gods (p.115).

Epicurus derives all happiness, ultimately, from bodily pleasure (hence his reputation). Yet the gods have no bodies in the flesh and blood human sense and so cannot experience pleasure in the Epicurean sense and so cannot by happy (p.116).

Cotta attacks the Innate Theory i.e. that the notion of the gods is a universal aspect of human nature so must be true. Because plenty of other ideas and notions seem to be universal. Are they also true? And our minds can conceive and imagine all manner of things and situations. Are they all true, too?

Epicureanism undermines reverence for the gods

What reverence is due to beings who have never done anything and will never do anything? What reverence do we owe beings who have never done anything for us and never will? Piety is a bond but what bond can there be for beings who never interact? Why should we thank the gods if they have never done anything for us?

This undermining of any reason for humans to reverence or worship the gods in effect destroys religion.

One of the noblest qualities of people is their love and affection for others. Epicurus’s gods have no interest in anyone or anything else at all, but sit perfectly passively uninvolved with anything contemplating their own sterile ‘happiness’. This is to take away the ‘graciousness’ which is the highest attribute of humanity.

Compare and contrast with the doctrine of the Stoics that we should love all good and honest people as ourselves. Epicurean detachment teaches a terrible ethical lesson. A true human friendship is free and selfless. The love and selflessness of the gods ought to be that much superior to human love, yet Epicurus strips his gods of all fine feelings.

Cotta concludes by saying the whole tendency of Epicurus’s thought is atheist, he just tacked on his incoherent ‘defence’ of his very peculiar conception of the gods ‘in order to avoid the odour of atheism’. He was merely paying lip service to the gods that he had actually destroyed (p.120).

Summary of Velleius

Having read it twice I can see how Velleius’s points of view, with all their distortions of fact, the weird atomic theory and the, in the end, weird view of gods who are utterly detached from the world – I can see how these are all the tortured consequences of a reasonable premise and intention which was to free human beings from fear and anxiety.

As a philosophy it appeals to those who seek an oriental-style detachment from involvement in the trials and tribulations of life and instead seek detachment and calm.

Its weak spots are its implausible atomic theory about the creation of not one but infinite universes; and its bloodless vision of gods which are supposedly made in human form and yet utterly lifeless, like beautiful shop window mannequins.

2. Balbus’s presentation of the Stoic view of the gods (pages 123 to 190)

Balbus says he can divide Stoic views into 4 areas. The Stoics:

  • teach that divine beings exist
  • explain their nature
  • describe their government of the world
  • show how they care for mankind

The Argument from Design

If Velleius rested his case on the universal innate conviction of the gods’ existence, Balbus bases his on the Argument from Design. Look up at the sky and survey the beauty of the heavens. What more proof do you need that god exists? You might as well doubt the existence of the sun. Both god and the sun are as obvious to our senses. (It was to refute this age-old argument that Richard Dawkins wrote his long argumentative book The Blind Watchmaker.)

As ancient superstitions are sloughed off, true religion is growing more popular with every day. Balbus bases this assertion on:

  • the intervention of the gods in human history, especially at key moments of Roman history
  • predictions and prophecies
  • the special level of piety of the ancient Romans (like everyone in antiquity, Balbus thinks things, in this case religious piety, have declined in his day)

The proof of prophecies and soothsaying is that they have accurately predicted the future. Plenty of evidence from Rome’s history. So who can doubt the gods exist if they send messages?

‘Beings who do not exist can send us no messages. But the gods do have their prophets and messengers. So how can we deny they exist.’ (p.128)

The state prospers only under the guidance of men of religious faith.

In fact Balbus then echoes Velleius’s nostrum: The existence of gods is inscribed on the human mind from birth (p.128). Thus there is no debate about the existence of gods, only about their nature.

Cleanthes speaks of 4 influences which have formed men’s images of gods:

  1. the power and evidence and proof of divination and prophecy
  2. the blessings of a temperate climate and fertile soil
  3. the awe inspired by natural phenomena such as storms, hailstorms, blizzards, floods, plagues, earthquakes etc
  4. the regularity of the motion of the heavenly bodies. Movements so vast and purposive and regular must be guided and controlled by a divine intelligence. He lists the motion of the sun and moon and stars and the tides and oceans and says none of this would work unless it were powered by a divine and omnipotent spirit. These are all variations on the Argument from Design (p.129).

Only an arrogant fool would think there is nothing in the universe smarter than him. Therefore there must be something greater than Man. And that something must be God.

There is nothing more beautiful or perfect in the world than Reason or mind or intellect. The universe is perfect. Therefore the universe must be possessed of reason i.e. be rational. All natural laws, the passage of the seasons etc etc all these bespeak ‘the planning of a divine and omnipresent spirit’ (p.131).

The universe and God are one. He cites arguments formulated by Zeno of Citium, founder of Stoicism.

If a being is without consciousness then every part of it must be without consciousness. But some parts of the universe are conscious beings, therefore the entire universe as a whole must be a conscious being. Therefore the universe is a living intelligence.

The universe must be a rational being and the nature which permeates all things must be endowed with reason in its highest form. So God and the world of Nature must be one and all the life of the world must be contained within the being of God. As the universe is surely superior to any other being, then it must be endowed with reason. ‘The universe was endowed with wisdom from eternity and is itself divine.’ (p.137).

There is no quality higher than goodness and nothing more perfect than the universe. Therefore goodness must be a characteristic of the universe. (p.138)

[Pages 141 to 145 consist of a sluggish digression on astronomy i.e. the movements of the planets and stars.]

He then argues that the sun must be a conscious rational being, and so are all the stars, as proved by the regularity of their motions. The stars move of their own free will and motivated by their own intelligence – what other force could move them so efficiently?

I cannot understand this regularity in the stars, his harmony of time and motion in their various orbits through all eternity, except as the expression of reason, mind and purpose in the planets themselves, which we must therefore reckon in the number of the gods. (p.145)

At which point he makes the leap that the fact that the gods exist is so obvious that anyone who disagreed must be mad (p.141). Anyone who looks up and observes the beautiful order and regularity of the movement of the stars and doesn’t feel the power of God must be out of his mind (p.145, repetition of p.124).

As we have an innate idea in our minds that God must be a living God and supreme above all else in the world, there seems to me nothing more consonant with this idea than to recognise the whole universe, than which there can be nothing more sublime, as being the living God. (p.141)

The gods just exist because there must be some supreme being which is superior to all else. 

Another reason is that, although all men acknowledge the existence of the gods, to give them human form is to assign them limitations and imperfections. This, also, is an argument for equating God with the entire universe.

Balbus argues that the gods don’t of course have the form of humans with all the frailties and limitations that implies. The traditional names of the gods embody qualities of the universe which are gifts to humankind and which we ought to worship (p.147).

[Pages 147 to 151 consist of a digression on the etymology of the names of the gods.]

On the providence of the gods

Balbus then sets out to prove that the world is governed by the wisdom and foresight of the gods.

My belief is that the universe and everything in it has been created by the providence of the gods and is governed by their providence through all eternity. (p.154)

Stoics like him give three reasons:

  1. if you grant the existence of gods, you must grant their providence
  2. all things are ordered by a sentient natural power impelling them towards their own perfection
  3. the wonders of the earth and sky (Argument from Design)

1. All men acknowledge that the gods exist. If they exist, they must be active. What kind of activity could be better than the government of the world. Therefore the world is governed by the wisdom of the gods (p.154). There is nothing greater or more wonderful than the universe. Therefore it must be governed by the wisdom and foresight of the gods (p.156).

2. Nature is a principle of reason which pursues its own methodical course. His explanation of nature/God is based on the ancients’ belief that the world was made of four elements (earth, air, water, fire) and theories about reason and mind, all of which are twaddle, so it’s difficult to follow in its complexity something you know is rubbish. A central problem is the interchangeability of the words universe’ and ‘nature’ throughout this book.

  • Nature is the power which rules the universe.

There follows an extended passage (pages 161 to 177) describing the wonders of the stars and the planets and the sun and then of geography (seas and rivers and forests and deserts) and then a lot of ‘wonders’ of the natural world, every one of which Balbus recruits as evidence for his simple-minded insistence that every single one proves the universe is controlled by an intelligent and caring providence.

From all this evidence we must conclude that everything in the world is marvellously ordered by divine providence and wisdom for the safety and protection of us all. (p.177)

Wrong. The ludicrously naive self-centredness of this view becomes apparent when he goes on to ask for whom all this wonder was laid on? Well, obviously not for the lifeless rocks or even for mindless animals. Obviously for those with mind and reason, ta-dah! Us humans!

We can therefore well believe that the earth and everything in it was created for the gods and for mankind. (p.177)

Balbus then goes on to consider the ‘perfection’ of the design of man, how perfect the human mouth is for drinking, how perfect the lungs for drawing in air, the stomach for digesting food and so on, the gift of speech, the wonder of the human hand (pages 178 to 184). Balbus attributes all this to:

the wise and careful providence of nature, which shows the great and gracious benefits the gods have bestowed upon mankind. (p.180)

Everything in the world which we enjoy was made and ordered for our sake. (p.185)

I attribute it to evolution. Balbus’s anthropocentric narcissism leaps out when he claims that ‘every human sense far surpasses the sense of beast’ (p.182) which is plumb wrong, as we now know that all human senses are far excelled by any number of other animals.

To sum up: man has been given all manner of gifts in the design of the universe, the beauty of the world, the provision of plants and animals to rear and eat, in the wonderfully apt design of his own body and, above all, in the gift of reason so we can understand it all. Contemplating all this must lead to awareness of a guiding and kindly providence working throughout the universe and in our favour, and from this stems Religion and a sense of the virtues, of the good life which is living in harmony with the universe, in loving-kindness and generosity to our fellow men.

Summary of Balbus

Although every factual claim he makes about the universe, the solar system and the natural world are howlingly wrong, I can see the aim of Balbus’s Stoic philosophy. It is for those who appreciate the beauty of the night skies and the wonders of the natural world and believe that they indicate some natural law or harmony and that, in order to live well, in order to live wisely and virtuously, we humans should acknowledge these gifts and try and bring our way of living into harmony with the natural world. A not unreasonable ambition.

Its weak spot is Stoics odd insistence on the importance of ‘prophesy’ as a strong proof of providence. Both Epicureans and Academics were quick to ridicule this and it’s hard to see why it is needed in their system and couldn’t be quietly dropped.

3. Cotta puts the academic view (pages 193 to 235)

Cotta introduces himself as a member of the College of Augurs and a priest. He will never abandon the views he has inherited from his Roman forebears about worship of the gods. He doesn’t require a load of fancy arguments to prove the existence of the gods: the traditional belief of their Roman ancestors was enough. As a rational man, he simply wants to question the arguments of the other two more closely in order to base his own belief on a sound foundation.

Remember that a substantial portion of Cotta’s book is missing, and it feels like it. Anyway, he says he will not refute Balbus’s argument in its entirety but ask him about specific aspects. He attacks Balbus’s stories about ‘prophecy’ and ‘omens’ as superstitious hearsay.

Then he attacks one of the central arguments of both Velleius and Balbus, that the gods exist because the notion of immortal gods is innate in human nature. Not so, says Cotta. Just because a large number of people believe something to be true does not make it true.

More importantly, for me, Cotta refutes most of the arguments Balbus put forward to prove that the universe, the sun and the moon and the stars are all gods. No, says Cotta. Just because something behaves with mechanical regularity and is beautiful to look at (like the stars) doesn’t mean it is either conscious or immortal (p.202).

One flaw in his argument is to assume that anything bigger than man must be Perfect and Immortal, such as the movement of tides, and rivers and the seasons and the stars. not at all. They might just be part of the mechanical rhythm of the universe. The parts of nature move in consonance but this does not require a guiding intelligence.

Nature persists and coheres by its own power without any help from the gods. (p.204)

Just because something is bigger than man doesn’t make it a god. Otherwise all mountains would be gods. Every hill, every bluff, every tree would be a god.

Cotta’s critique of Balbus is less effective than his attack on Velleius. This seems to be because he is actually missing a lot of Balbus’s point. He says that all things made up of the elements will eventually decompose and die but this isn’t as effective an attack on Balbus as on Velleius. He says the so-called gods experience no evil so cannot judge between good and evil so cannot really enact virtue. How can we respect a god who doesn’t exercise reason or moral qualities?

Then he moves on to attack the way many humans, either legendary or historical figures, have, allegedly been translated into gods. This didn’t strike me as central to Balbus’s argument. What both of them seem to be missing is the centrality of prophecy to Stoic beliefs and the enormous problems thrown up by trying to reconcile God’s Preknowledge of the future and human free will (without which there can be no morality), a topic which was to bedevil Christian theology for 2,000 years.

Instead he wastes his time on the secondary argument of which of the actual Roman gods who have temples devoted to them Balbus includes in his pantheon, and which he excludes, and why. As he rattles off an enormous list of gods major and minor and then nymphs and satyrs and demi-gods and so on, it dawned on me he is missing a major distinction to be made between religion as theology and religion as practice. I’m betting most people are attached to their religions as traditions and practices which bind together families and communities. Cotta’s attack on the pantheon of the gods makes it clear just how futile it is trying to come up with a coherent intellectual underpinning for the super-diverse world of actual religious practice. Religious practices just are.

This reductio ad absurdem list of gods goes on for some time (pages 208 to 219), with Cotta asking Balbus whether he allows the rainbow to be a god or clouds and so on, ridiculing the idea that qualities such as Faith or Courage or objects of desire such as Victory and Honour can be gods.

Lacuna in the text.

He spends so much time on it because, apparently, many Stoic writers have devoted a lot of time to giving philosophical rationales for all these gods. But, says Cotta, this is all superstitious twaddle.

Lacuna in the text.

Balbus had assumed all through his speech that Reason is the highest attribute imaginable. So Cotta sets out to destroy this view by quoting an extensive number of examples where people have used their reason for evil i.e. have acted rationally in order to achieve wicked ends.

If the divine mind willed the good of men, when it endowed them with reason, then it willed only the good of those whom it also endowed with the power to use their reason well, whom we see to be very few indeed, if any. (p.222)

Maybe it would have been better if the gods had never given man reason at all. Maybe philosophy does more to lead students astray into immoral or unnatural beliefs and activities than improve them.

The problem of pain

Then Cotta moves on to a version of the perennial ‘problem of pain’, asking why the gods gave men the power of ‘reason’ instead of the ability to act virtuously? Instead, monsters have thrived and honest men met violent ends. If the gods do look upon our world they apparently make no distinction between good and bad men.

There can be no divine guidance of human affairs if the gods make no distinction between good and evil. (p.230)

And:

The prosperity and good fortune of the wicked absolutely disprove the power of the gods. (p.232)

Why don’t the gods intervene on the side of good while letting evil prosper? It’s the central question which has plagued the Abrahamic religions with their notion of an all-powerful all-loving god down to the present day, crystallised by the central catastrophe of the twentieth century: if there is an all-powerful, all-loving God why did he allow the Holocaust?

Abrupt ending

Right at the last minute on the last page Cotta re-emphasises that he doesn’t say this to argue against the gods but to submit men’s arguments to strict scrutiny and show how difficult the issue is. This feels very much like a last-minute cop-out designed to avert accusations of atheism which most of the rest of the document strongly endorses.

The host, Lucilius, is made to say that he would take up arms to defend their venerable religious traditions and temples and so on, and Cotta repeats that he agrees and will join him and has been merely working through the arguments not denying religion. Perish the thought!

It’s worth quoting the final sentence for two reasons. It purportedly gives the view of Cicero who has been a silent witness throughout the previous 3 books, never saying a word.

The conversation ended here, and we parted. Velleius judged that the arguments of Cotta were truest; but those of Balbus seemed to me to have the greater probability.

It has puzzled commentators that Cicero came down on the side of Balbus rather than sympathising with his fellow Academician, Cotta. It rather suggests that the debate was never between three points of view, but between two major points of view both of which were then critiqued by Cotta, with the result that onlookers (such as Cicero) only had a choice of two.

Lastly, its abruptness has convinced most commentators that the work was never finished properly and would probably have been revised and polished if Cicero had lived long enough.


Related links

Roman reviews

The Journey To The East by Hermann Hesse (1932)

A slender novella, 88 pages in the Picador paperback version, The Journey To The East is a first-person narrative told by a former member of the secretive ‘League’ of poets, writers and seekers who, in their different ways, all undertook journeys to the East in ‘the troubled, confused, yet so fruitful period following the Great War’ (p.5).

What sets it apart, at least to begin with, is that it is nothing like a sensible factual account of a straightforward ‘journey’ such as you might read by traditional travel writers like Robert Byron or Peter Fleming.

Instead it is more like a fairy story, in which the ‘travellers’ encounter legendary figures and mythical beasts, pass through fictional lands from fables and fairy tales, and travel not only in space, but in time – back into the past, penetrating ‘into the heroic and the magical’ (p.7).

One day, when I was still quite a new member, someone suddenly mentioned that the giant Agramant was a guest in our leaders’ tent, and was trying to persuade them to make their way across Africa in order to liberate some League members from Moorish captivity. Another time we saw the Goblin, the pitch-maker, the comforter, and we presumed that we should make our way towards the Blue Pot.

The giant Agramant, the Goblin. It is fairy land.

Despite these imaginative frills, though, the League feels like a Christian monastic order – casual phrases continually remind the reader that Hesse had an intensely pious Christian upbringing, against which he rebelled but whose stern moral seriousness he kept for the rest of his life.

Thus newcomers to the League are ‘novitiates’, must take an ‘oath’ to renounce the world and its temptations, must wear a ring proclaiming their membership of the order. The journey is referred to as a ‘pilgrimage’ and the travellers as ‘pilgrims’. The leader of the narrator’s group talks freely about ‘grace’ and ‘repentance’, both utterly Christian concepts.

But at the same time it is a phantasmagoria of all the cultural greats through the ages:

Our League was in no way an off-shoot of the post-war years, but that it had extended throughout the whole of world history, sometimes, to be sure, under the surface, but in an unbroken line, that even certain phases of the World War were nothing else but stages in the history of our League; further, that Zoroaster, Lao Tse, Plato, Xenophon, Pythagoras, Albertus Magnus, Don Quixote, Tristram Shandy, Novalis and Baudelaire were co-founders and brothers of our League.

This is a kind of greatest hits of world culture. And the way the ‘pilgrims’ travel is both a physical path or itinerary, very much in the style of medieval pilgrims –

And as we moved on, so had once pilgrims, emperors and crusaders moved on to liberate the Saviour’s grave, or to study Arabian magic; Spanish knights had traveled this way, as well as German scholars, Irish monks and French poets.

But also an imaginative one, as they travel through realms of magic and myth, experiencing not only all times, but the real and the imaginary on the same terms.

The core of the experience, the thing which, looking back, the narrator realises brought him the greatest happiness, was:

The freedom to experience everything imaginable simultaneously, to exchange outward and inward easily, to move Time and Space about like scenes in a theatre.

When you reflect on this, it sounds increasingly like the adventures of someone in their library – with the leisure time to roam freely over time and space, and between factual and imaginative literature.

The plot

The first-person narrator is ‘a violinist and story-teller’ who joined the League with the aim of travelling to the East to meet the princess Fatima and, if possible, to win her love (we learn that all League members have quirky or idiosyncratic goals, one wants to see the coffin of Mohammed, another to learn the Tao).

But the oddest thing about the story is that… they don’t travel to the East. About a third of the way through the text, the narrator tells us that at an early point of the journey, while they were still in Europe, at a place called Morbio Inferiore, a municipality in Switzerland, one of his team’s most loyal servants, Leo, goes missing, so the entire squad sets out to find him, searching up hill and dale.

Not only do they never find him, but his group begins to squabble amongst itself, loses focus. Somehow the journey was abandoned and he never made it to the East. Now, we learn, the narrator is struggling to set it all down in a written account, in a bid to revive the heady joy of those young days.

Now the narrative cuts to ‘the present’, some ten years after the journey. The narrator tells us it is a long time since he was active in the League, he doesn’t know whether it exists any more, he’s not sure it ever existed and these things ever happened to him.

And now the narrator tells us that the episode of missing Leo has given him writer’s block, he doesn’t know how to tell the episode correctly, and can’t manage to get the story past it.

And in an abrupt and surprising switch, the narrative stops being about any journey to the East whatsoever.

Now, surprisingly, the scene cuts back to the narrator’s home town and becomes spectacularly more realistic and mundane. To address his problem of writer’s block, the narrator goes to meet a friend of his who’s a newspaper editor, named Lukas, and who wrote a successful book of war memoirs.

Discussion of the war memoirs gives rise to a consideration of how difficult it is to describe any human experience, at how you need to create eras or characters or plots to even begin to get it down.

Even further than this, how some experiences are so intense or evanescent, that you can’t even be sure you had them. In which case, how do you describe them? Lukas replies that he wrote his book about the war because he simply had to, whether it was any good or not was secondary, the writing itself was vital therapy, which helped him control ‘the nothingness, chaos and suicide’ which would otherwise have overwhelmed him (p.46)

So. This is less a book about a journey anywhere, and a lot more a book about the difficulty of writing a book. Ah.

When the narrator tells Lukas how, in writing his account of the journey to the East, he’s got blocked on this episode of the missing servant, Leo, Lukas promptly looks Leo up in the telephone directory and finds there is a Andreas Leo living at 69a Seilergraben. Maybe it’s the same guy, he says – as if we’re in a 1930s detective novel and not the imaginative phantasmagoria we started out in. ‘Go and see him,’ the editor suggests.

So the narrator does, and finds 69a Seilergraben to be an apartment in an anonymous building in a quiet street. The narrator knocks on the door, questions the neighbours, hangs around, and goes back on successive days. Finally he sees this Leo exit his apartment block and walk quietly to the park where he sits on a bench and eats dried fruit from a tin.

This is not at all the mystical imaginative phantasmagoria I was promised on the back of the book, is it? This is staggeringly mundane.

The narrator approaches Leo, and tries to remind him of their time back in the League and on the great journey East which, the text confirms, happened some 10 years earlier. But Leo is calmly dismissive and walks off, leaving the narrator standing alone in the park as dusk falls, in the rain.

Now he is rejected like this, we learn the narrator is prone to depression, in fact to despair and thoughts of suicide.

I had experienced similar hours in the past. During such periods of despair it seemed to me as if I, a lost pilgrim, had reached the extreme edge of the world, and there was nothing left for me to do but to satisfy my last desire: to let myself fall from the edge of the world into the void — to death. In the course of time this despair returned many times; the compelling suicidal impulse…

In other words, he shows the same bouncing from one to extreme to the other that characterised the Steppenwolf and his moods of suicidal despair. And very like the author himself, a glance at whose biography reveals attempts at suicide, prolonged psychotherapy, and a spell in a mental sanatorium.

The narrator gets home and sits down, still damp from the rain and writes a long letter to Leo, then falls asleep. When he wakes up Leo, is sitting in his living room. Leo reveals he is still a member of the League and says he will take the narrator to see the current President. Leo leads him through the streets of the quiet town by a circuitous route, stopping at various inconsequential locations including a church, to an anonymous building, which is large and labyrinthine on the inside (reminding me of the labyrinthine buildings Franz Kafka’s protagonists stumble through).

The narrator is led into an enormous room full of shelves lined with books which turn out to be the archive the League. Leo suddenly starts singing and, as in movie special effects, the archive recedes into the distance and in the foreground appears a large judgement chamber.

A jury assembles and a ‘Speaker’, who acts like a judge. It has turned into a sort of court-room, which makes the comparison with Kafka feel overwhelming – a confused little man dragged to judgement before a huge, imposing court which he doesn’t understand. The essence of the Kafkaesque.

For the first time the narrator is named as ‘H.H.’. H.H.? So a barely veiled reference to the author himself which, yet again, could barely be more like the Kafka who named his two most famous protagonists K. and Joseph K. with his own initial.

The ‘Speaker’ refers to H.H. as ‘the self-accused’ and asks him:

‘Is your name H.H.? Did you join in the march through Upper Swabia, and in the festival at Bremgarten? Did you desert your colours shortly after Morbio Inferiore? Did you confess that you wanted to write a story of the Journey to the East? Did you consider yourself hampered by your vow of silence about the League’s secrets?’
I answered question after question with ‘Yes’…

So I was expecting H.H. to get hammered, but, surprisingly, he is now given permission to go right ahead and write a full account of the League and all its laws.

He is handed a copy of the manuscript of the Journey he had been working on and which had got bogged down at that moment when Leo left the group. But now, when he rereads it, he feels it is bodged, clumsy, inaccurate and – further – as he tries to amend it, he watches the letters change shape, become patterns and pictures, illegible, the entire manuscript changes form in front of his eyes.

Rather improbably, the Speaker gives him free run of the immense archive to research his book, which leads to a passage where H.H. rummages through the archives to find records about his friends and then himself, but finds the records written in strange languages and arcane scripts. Slowly he realises there isn’t enough time in the world to go through this immense and probably infinite library.

From all sides the unending spaciousness of the archive chamber confronted me eerily. A new thought, a new pain shot threw me like a flash of lightning. I, in my simplicity, wanted to write the story of the League, I, who could not decipher or understand one-thousandth part of those millions of scripts, books, pictures and references in the archives! Humbled, unspeakably foolish, unspeakably ridiculous, not understanding myself, feeling extremely small, I saw myself standing in the midst of this thing with which I had been allowed to play a little in order to make me realize what the League was and what I was myself.

the court magically re-assembles, with the Speaker presiding. Now we learn that this little episode was a further step in H.H.’s trial, to show him how vain and presumptuous his aim of writing a history of the league was. The Speaker asks if he is ready for the verdict on him, and whether he wants it delivered by the Speaker or the President himself.

In a surreal development, the grand figure who emerges from the bloom of the archive hall turns out to be none other than… Leo! The Leo he had followed into the party, who is himself the Leo who was his group’s servant on the Journey and now he comes to think about it, was the same President who initiated him into the League and gave him his ring.

H.H. is covered in shame and confusion. To think that he could write a history of the League. To think that he had imagined the League had ended or had never existed. Now Leo recounts H.H.s sins against the League. Forgetting about its existence. Losing his League ring. Even their long walk through the town had been a test because H.H. should have gone into the church and worshipped, as is fitting, instead of standing outside locked in his impatient egotism. It is his egotism which made him deny the League and sink into a world plagued with depression and despair.

Again, as in so many of Hesse’s books, which you imagine will be about Eastern philosophy, the most eloquent passages are about misery and despair. Leo tells the jury how H.H.s loss of faith in the League led him down into the pit, and delivers some puzzling lines:

‘The defendant did not know until this hour, or could not really believe, that his apostasy and aberration were a test. For a long time he did not give in. He endured it for many years, knowing nothing about the League, remaining alone, and seeing everything in which he believed in ruins. Finally, he could no longer hide and contain himself. His suffering became too great, and you know that as soon as suffering becomes acute enough, one goes forward. Brother H. was led to despair in his test, and despair is the result of each earnest attempt to understand and vindicate human life. Despair is the result of each earnest attempt to go through life with virtue, justice and understanding and to fulfill their requirements. Children live on one side of despair, the awakened on the other side. Defendant H. is no longer a child and is not yet fully awakened. He is still in the midst of despair.’

So: Despair is what you enter when you are no longer a child, when you become a questing adult, and before you are initiated or awakened.

Now President Leo initiates H.H. for a second time, giving him a replacement ring and welcoming him back into the ranks of the League.

This really is nothing at all about any literal Journey To The East, is it? It is about adventures of the spirit, or maybe psychological experiences, in a quiet Swiss town.

Now the President leads H.H. to the final test. He is shown the League archives about himself. Specifically, he is shown several other accounts written by members of his group or party on his Journey of ten years ago. Here he is horrified to read that it is he, H.H. that the other members of the group blamed for Leo’s disappearance, for accusing Leo of having taken key documents with him, it was he, H.H. who was blamed by the rest of the group for spreading dissension.

He learns something about trying to write ‘the truth’ (something which is, to be blunt, fairly obvious), which is that everyone has a different account of what happened, and no ‘truth’ can ever be arrived at.

If the memory of this historian was so very confused and inaccurate, although he apparently made the report in all good faith and with the conviction of its complete veracity – what was the value of my own notes? If ten other accounts by other authors were found about Morbio, Leo and myself, they would presumably all contradict and censure each other.

No, our historical efforts were of no use; there was no point in continuing with them and reading them; one could quietly let them be covered with dust in this section of the archives. ..

How awry, altered and distorted everything and everyone was in these mirrors, how mockingly and unattainably did the face of truth hide itself behind all these reports, counter-reports and legends! What was still truth? What was still credible ?

The final few pages end on an enigmatic moment and symbol. Tucked away in the shelf where his records are stored, he finds a grotesque little statuette, like a pagan idol. Only slowly does he realise it is two-sided, shows two human figures joined at the back. And then slowly makes out that one is a depiction of himself, with blurred features, weak and dying. And as he lights another candle he sees something stirring in the heart of the glass statuette, and realises that some kind of life force is moving from his half of the statuette over into Leo’s

And in the last few sentences of the book he remembers a conversation he had with the servant Leo on the Journey, ten years earlier, amid a wonderful festival early in the journey, where Leo had explained that a pet or writer drains himself in order to give eternal life to his work, just as a mother suckles a baby and gives the babe life, at her own expense. So the poet.

And on this slightly ominous, pregnant image the book ends. The narrator feels very sleepy. He turns to find somewhere to sleep. Maybe enacting exactly the gesture whereby the poet, writer or maker, gives all their spirit and life force to their creation and then expires.

Thoughts

Well, it turns out not to be a literal Journey To The East in the slightest. Anyone expecting a straightforward narrative of a pilgrimage to India will be disappointed and puzzled.

However, anyone familiar with Hesse will be less surprised by its combination of the strangely mundane and the wildly phantasmagorical. This is the same combination as in Steppenwolf, which evolved from being a dull account of a middle-aged boarder in a provincial boarding house into the giddy surrealism of the Magic Theatre.

And Steppenwolf also covered a similar range of emotional or psychological states – to be more precise, it displayed a similar, almost schizophrenic, tendency to jump between extremes of Despair and the giddy heights of ecstatic imaginative delirium.

I had this impression of Hesse as being a lofty propounder of high-minded Eastern philosophy. I wasn’t prepared to encounter so many characters who were so full of despair, self-loathing and so many discussions of suicide.

And I’m still reeling from the way the book is not about a Journey To The East at all; it’s much more about the psychological adventures or journey of a middle-aged man living in a Swiss town. All the key events happen in the narrator’s mind. It is a psychological odyssey.

Building a universe

It’s a small detail, but it’s interesting that Hesse includes among fellow members of the League, not only some of his real-life friends, but characters from his other books.

Thus the character ‘Goldmund’, one of the two leads in Narziss and Goldmund, crops up in his initial memories of the Journey, as does the painter Klingsor, who is the fictional lead of Hesse’s earlier novel Klingsor’s Last Summer.

And when I started reading Hesse’s final novel, The Glass Bead Game, early in the introduction the narrator mentions the League of Journeyers To The East as forerunners of the game. Hesse was quite obviously creating a kind of larger imaginative canon, an imaginarium, in which characters not only from history, not only actual writers and composers, along with mythical and legendary figures, but figures from his own earlier fictions, could meet and mingle on equal terms.


Images of war in The Journey To The East

I am always interested in the social history revealed by older texts. It is striking that Hesse doesn’t just launch straight into his fairy-tale journey, but feels the need to define the times, the era, the period against which his pilgrim is reacting, and that he defines these times by repeated references to the social, economic, cultural and spiritual chaos following Germany’s defeat in the Great War.

Ours have been remarkable times, this period since the World War, troubled and confused, yet, despite this, fertile…

It was shortly after the World War, and the beliefs of the conquered nations were in an extraordinary state of unreality. There was a readiness to believe in things beyond reality…

Have we not just had the experience that a long, horrible, monstrous war has been forgotten, gainsaid, distorted and dismissed by all nations? And now that they have had a short respite, are not the same nations trying to recall by means of exciting war novels what they themselves caused and endured a few years ago?…

At the time that I had the good fortune to join the League – that is, immediately after the end of the World War – our country was full of saviors, prophets, and disciples, of presentiments about the end of the world, or hopes for the dawn of a Third Reich. Shattered by the war, in despair as a result of deprivation and hunger, greatly disillusioned by the seeming futility of all the sacrifices in blood and goods, our people at that time were lured by many phantoms, but there were also many real spiritual advances. There were Bacchanalian dance societies and Anabaptist groups, there was one thing after another that seemed to point to what was wonderful and beyond the veil. There was also at that time a widespread leaning towards Indian, ancient Persian and other Eastern mysteries and religions…

His name is Lukas. He had taken part in the World War and had published a book about it which had a large circulation…

And indeed, from a structural point of view, this editor, Lukas, is included mainly for the discussion he promotes about the struggle he had to write his memoirs of the war, and his eventual conclusion that it was better to write something rather than nothing – even if untrue or less than perfect – if only because the act of writing was so therapeutic and saved him from terrible feelings of despair and suicide.

I’m doing no more than suggest that Hesse, who is generally thought of as a kind of high-minded explorer of timeless values was, in fact, very much a man of his times, and that his thinking was marked and shaped by the great cataclysm which he and his nation lived through just as much as all the other authors of the Weimar period.

Credit

Die Morgenlandfahrt by Hermann Hesse was published in German in 1932. The English translation by Hilda Rosner was published by Peter Owen Ltd in 1956. All references are to the 1995 Picador paperback edition.


Related links

20th century German literature

The Weimar Republic

German history

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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