“There is a tide in the affairs of men,
                            Which taken in the flood leads on to fortune;
                            Omitted, all the voyage of their life
                            Is bound in shallows and in miseries.”

                                                         Julius Caesar, IV. 3

Eventrics, like ordinary physics, divides into two parts: macro and micro. The micro part is covered in Ultimate Event Theory while macro-Eventrics, or just Eventrics for short, deals with ‘bulk events’, the only ones we perceive directly. As in physics, it is not at all clear whether the interplay of events at the macro-level is, or is not, ultimately reducible to behaviour at the micro level. In what follows, I shall for the moment simply take for granted that there are such things as ‘individuals’, ‘society’, ‘historical forces’ and so on, without attempting to ‘explain’ them in terms of more basic entities.
Nonetheless, the focus remains firmly fixed on ‘events’ (as opposed to persons or processes). In particular, it is assumed that particular bundles of complex macro-events have an intrinsic momentum that is to a considerable extent independent of the personalities involved. This does not, however, mean that individuals or close-knit associations of individuals are powerless, quite the reverse. The successful individual  ‘goes with the current’ when it suits him and immediately abandons it when it ceases to be favourable. Moreover, depending on where one is situated, some control over the direction of the current is possible: as the 19th century diplomat, Talleyrand, put it “L’homme supérieur épouse les évènements pour les conduire” (‘The great man welcomes events in order to redirect their course’) (Note 1).
The most important question in ‘Eventrics’ is to determine   whether there exists a completely general method for dealing with whatever one is confronted with, something that can be applied,  with appropriate modifications, to the specific context right across the board. Such a life-skill is what the Chinese Taoists referred to as the ‘tao’ (tao literally means ‘way’ or ‘path’). If there really is such a method, it follows that, when examining ‘world-historical figures’, we should expect to find very similar defining circumstances, roughly similar life trajectories and, above all, similar ‘event-strategies’. Is this the case? 


We start by asking to what extent conquerors and world-historical figures foreshadow their future greatness (good or bad) at an early age? Surprisingly, the answer seems to be ‘not very much’. The early lives of  Abraham Lincoln or Hitler, even Julius Caesar, showed no particular promise; the sense that they, and people like them, were destined to be world-movers and world-shakers often only came with maturity, and even then somewhat by accident (Note 2). As we know, Hitler was twice refused entry to the Viennese School of Architecture for lack of  talent and, incredibly for a future war leader and strategist, he started his military career as an Austrian draft dodger ─ though he volunteered promptly enough when World War I broke out. Lincoln was an ungainly, self-educated man from the backwoods who, though a reasonably successful lawyer, only got the Republican Presidential nomination because the support for the other, more popular, candidates was evenly divided. At the age of forty, Oliver Cromwell was a provincial squire, holding no office, local or national, and not even possessing the land on which he grazed his cattle. As for the Duke of Wellington ─ “Until his early twenties, Arthur showed little sign of distinction and his mother grew increasingly concerned at his idleness, stating, “I don’t know what I shall do with my awkward son Arthur” ”(Wikipedia). The list can be extended endlessly.
Even Julius Caesar, the most famous Roman of all,  though he had some minor military successes, was, up to the age of forty, notorious not for his victories but for his debts and dissipated life style ─ Curio referred to him contemptuously as “every man’s woman and every woman’s man”. Even in the case of military prodigies like Alexander the Great and the 17th century Charles XII of Sweden (now somewhat forgotten but hailed at the time as ‘the second Alexander’), circumstances played at least as great a part in their future celebrity as the drumroll of destiny. Both Alexander the Great and Charles XII came unexpectedly to the throne at a very young age (20 for Alexander, 15 for Charles XII). It was ‘sink or swim’ and, as it happened, their enemies, the anti-Macedon Greek states in the case of Alexander and Denmark in the case of Charles XII, got the shock of their lives when they took them on. But it was in both cases as much ‘forced to become great’ as ‘predestined to conquer’ (Note 3). In war and politics, it is often the case that, after an early success, the only way forward is up since retreat is actually more dangerous than the attempt to scale the peak ahead (Note 4).

Summarizing so far, one might even hazard a sort of  ‘power law’ of Eventrics, namely:
       An early disadvantage overcome gives rise to a much greater advantage than an outright advantage.

Macchiavelli even makes this a sine qua non:
“Fortune, when she wants to make a new ruler powerful….makes him start off surrounded by enemies and endangered by threats, so that he can overcome the obstacles and climb higher on a ladder supplied by his enemies”   The Prince, ch. 20

Ruthlessness and Luck

 It is sometimes said that such people as Hitler and Julius Caesar only got to the top because they were extremely ruthless and extremely lucky. Certainly, they were both, but this explanation doesn’t get you very far. Ruthlessness is, unfortunately, not a particularly rare human trait ─ every incumbent mafiosi has it, but how many get to be controllers of nations? Moreover, to demonstrate cold-bloodedness too readily, or too systematically, can be a liability, as it makes it extremely difficult to form alliances which every future leader needs at some stage. Psychopaths don’t usually become conquerors: even Genghis Khan, who is the nearest to being one, spent years forging (and unforging) alliances in the complicated world of Mongolian tribal politics before he was finally accepted as the ‘Great Khan’.
As for luck, Pasteur rightly said that it comes to the prepared mind and Macchiavelli agrees:
“You will find that they [Moses and Cyrus] were only dependent on chance for their first opportunity. They seized their chance to make it what they wanted. Without that first opportunity, their strength of purpose [virtù] would never have been revealed. Without their strength of purpose [virtù], the opportunity they were offered would not have amounted to anything”    The Prince ch. 6


Future commanders and world-leaders are rarely exceptionally intelligent in the ‘normal’ sense, I mean academically speaking. Napoleon is in this respect an exception, since he was a brilliant pupil at his École Militaire and is one of the few (only?) Western rulers who was a capable mathematician. Nonetheless, it is generally accepted today that Napoleon was not a great military theorist or even innovator:  he took almost all his ideas from the Maréchal de Saxe ─ but then again why not? “Napoleon was wise enough not to tinker with his legacy; [but] he knew how to exploit it to the full” writes Marshall-Cornwall in Napoleon as Military Commander.
Oliver Cromwell, one of the greatest cavalry leaders of all time, was certainly no intellectual and, indeed, prided himself on being a man of common sense, hence his approval (doubtless with himself in mind) of “the plain russet-coated captain that knows what he fights for and loves what he knows”. Stalin was an extremely capable Bolshevik hit-man (hence the nickname ‘Stalin’ or ‘man of steel’) but, unlike Lenin and Mao, he made no important contribution to Marxist theory apart from the nebulous doctrine of “Socialism in One Country” which was forced upon him by events. Hitler, surely the most unprepossessing  of all modern leaders, turned his lack of formal education and undistinguished appearance  (“He looks like the house painter he once was”) into an advantage since it enabled him to relate effectively to ‘ordinary people’ ─ and had the immense additional benefit of making aristocrats and educated people underrate him to their cost.

Similarity of Situation  

So, if we discount intellectual brilliance, ruthlessness and an early sense of mission as essentials, what does one notice about the rise and fall of famous historical figures? The four most powerful, non-hereditary Western leaders in recent centuries are probably Oliver Cromwell, Napoleon, Hitler and Stalin. Now, the first thing to note is that they all came to prominence in a fractured society near to breakdown: this gave them the chance they would never have had otherwise. Take Napoleon. Had Buonaparte been born just a few years earlier, he would never have been able to obtain a scholarship to a French École Militaire. For Corsica belonged to Genoa until 1768  and, anyway, it was well nigh impossible for someone outside the leading French families to get real advancement in the army prior to the revolution ─ as it was, the teenage Buonaparte was mocked by his fellow cadets for his dreadful accent and flimsy claim to noble birth. Moreover, the revolution came at exactly the right time for him: all but three of the cadets of Napoleon’s year offered their services to the monarchy ─ which meant the Republic desperately needed trained officers and was eager to promote them. Much the same applied to the Roundhead armies: the professional soldiers mostly fought for Charles I and, once Cromwell’s ability as an organiser of scratch troops was noticed, advancement followed.
As for Hitler, one can with difficulty see him getting anywhere at all in a different time and place, not because he had no talents but because a different environment might never have revealed them to him. He only discovered his uncanny ability as a public speaker by chance when addressing a tiny patriotic society in Munich in 1921 and, as for his military experience, he would never have had any but for the outbreak of WWI which enabled him to gain the Iron Cross and the respect of his comrades and superior officers.
But why, we must ask, did social breakdown favour these individuals? Because there was all of a sudden a power vacuum and someone had to fill it (Note 5). But this is not the only reason. A revolutionary situation drives  a society close to ‘tipping point’ and it may only require a very slight action on the part of a single individual to propel it irreversibly over a certain threshold. In normal circumstances this is almost never the case: a slight action produces a slight outcome but, when a complex system is  near to a ‘phase transition’ or ‘tipping point’, the effects of tiny actions are ‘non-linear’, i.e. can produce  disproportionately large consequences. Principe, the Serbian nationalist who shot the Austrian Archduke Ferdinand in Sarajevo in 1914 did not, as it happens, intend to bring about a European war but this is what ensued. The five great powers were locked in a tense, complex web of alliances, so much so that what was in itself a fairly trivial incident at once set off a frantic round of threat, bluff and counter bluff between Austria, Serbia, Russia and Germany which, within a couple of months,  culminated in the invasion of Belgium and we know the rest.
The 9/11 attack on the Two Towers is one of those rare historical ‘avalanche events’ that really was deliberate. Without the Two Towers there would almost certainly have been no invasion of Iraq and thus none of the sequels. Bin Laden seems to have known what he was doing, his aim being not to ‘overcome’ America militarily, which was and is impossible, but to tempt it into invading an Arab country in reprisal. The Middle East then, and even more so today, exhibits all four classic attributes of a ‘complex system’ on the brink:  the states involved are (1) diverse; (2) closely connected geographically; (3) interdependent; and (4) ceaselessly adapting to each other’s initiatives. 9/11 drew America directly into the fray (invasions of Afghanistan and Iraq) and this extra ingredient made the whole Middle East tip.

One lesson to draw from all this is that if someone, or some group, wishes to bring about really big changes, he or she must position himself at an ‘event hub’, somewhere that is extensively connected to diverse, rival, mutually interacting power groups. In such a position, minor personal initiatives really can have vast consequences ─ this is Archimedes’s “Give me a fixed point and I will move the world” translated into geopolitics. Napoleon and Hitler found themselves ‘by chance’ at such an event hub, revolutionary France at the end of the 18th century and Germany in the Twenties after her ignominious defeat in WWI  and subsequent hyper-inflation (Note 6).

Opposing Strategies

Supposing one happens to find oneself in an ‘event-hub’ of potentially momentous importance, what then? Broadly speaking, there exist two opposing strategies for the ambitious person, the first active, deliberate, calculating, the second passive, indirect, instinctive. Nineteenth century Western thinkers such as Carlyle and Nietzsche emphasized ‘will’ and ‘character’ while Clausewitz stressed the importance of sheer numbers, i.e. the active approach. Eastern philosophies generally recommend the second, indirect approach. China’s most famous military theorist, Sun Tzu (who is said to have influenced Mao), recommends systematically avoiding direct confrontation and relying instead on manoeuvre and deception. (Not that China’s history is any less bloody than Europe’s for all that.)
To employ Taoist terms, the first method is ‘Doing’, the second ‘Not-Doing’ (wu-wei), a strange concept to our ears though it is central to Taoism. The Tao Te Ching is a peculiar work because it can be (and has been) interpreted in two mutually contradictory ways. On the one hand, it purports to preach a form of quietism: it recommends retirement from the ‘world’ with all its bustle and senseless striving in order to cultivate the ‘inner self’. The Tao Te Ching specifically condemns the use of brute force in government, viewing it as both inhumane and ultimately ineffective. At the same time the title Tao Te Ching means, literally, Way Power Book and it has been interpreted as a sort of manual for an aspiring ruler. According to this view, the aim of the book is to show the future ‘philosopher king’ how to rule effectively without appearing to govern at all. At first sight this sounds all very civilised ─ but is it really? Such a ruler, according to the Tao Te Ching, gets people to do what he thinks right because they admire him for his ‘moral authority’ and ‘inner poise’ ─ but this sounds dangerously close to the ‘charisma’ that mass-murderers like Hitler and Stalin undoubtedly possessed to a high degree.
What does all this mean in practice? ‘Not-Doing’ does not necessarily mean abstaining from action, though it can mean this ─ sometimes the best plan is simply to let things take their course. Sun Tzu speaks a great deal about ‘momentum’ which he sees as an intrinsic property of certain sequences of events ─ what in Ultimate Event Theory I term ‘dominance’. “Skilful warriors” he writes, “are able to allow the force of momentum to seize victory for them without exerting their strength”. And this ‘momentum’ is impersonal, does not depend on individuals: “Good warriors seek effectiveness in battle from the force of momentum, not from individual people”.
The Tao Te Ching assumes that only a ‘good’ man or woman can possess the mysterious moral authority that makes the use of force secondary, or even unnecessary. This is too optimistic by far, not to say dangerously naive. ‘Not-Doing’ is certainly useful (and preferable to coercion) but will not take you all the way: one thinks at once of Stalin’s immortal quip, “How many battalions can the Pope put in the field?”
          The truth seems to be that both ‘Doing’ and ‘Not-Doing’ are essential for success in practically every sphere, but above all in warfare and government. If we look at famous European leaders, especially Cromwell and Hitler, we find that they practised both ‘Doing’ and ‘Not-Doing’ in more or less equal doses, were alternately ‘active’ and ‘passive’ and at ease in  both modes. It is now known that a great deal of mental and physical activity is ‘unconscious’: in a routine situation, it is often better, and even safer, to put oneself in a state of ‘auto-pilot’. However, the ‘self’ must remain ultimately in control, able to step in and overrule learned behaviour when changing circumstances make it inappropriate. Warfare is inevitably an activity that requires intense training, since the aim is to turn a warm-blooded human being into a killing machine (Note 7). But the soldier who is completely incapable of taking initiative is a liability: part of Napoleon’s success lay precisely in his ability to maintain firm overall control of strategy while encouraging his subordinates to act independently when necessary. This is one reason why he outclassed the Prussians and Austrians who tended to make war strictly by rote and were thrown into confusion by the unexpected. Similarly, the historian Grant says that Julius Caesar’s “supreme qualities as a commander were speed, timing, and adaptability to suddenly changing circumstances” (my italics).

If we consider the English Civil War and the Protectorate, we see that Cromwell and the Roundheads in general owed much of their success to their belief system. The Puritan world-view, though hardly logical, proved to be a very suitable one for men of action whether soldiers or, at a later date, pioneers of the Industrial Revolution. For, while the Puritans, and Protestants generally, firmly believed that  ‘grace’ trumped virtue (since God chose whoever He wished), they simultaneously stressed the importance of an ‘active life in the world’ ─ as opposed, for example, to retreating into a monastery to ‘watch and pray’. Cromwell’s belief in Providence is central to his character and to his conduct as a military and political leader. The moral earnestness of the Puritan obliged him not only to ‘take up arms’ for a just cause, but also to plan ahead carefully since he could not expect any miraculous intervention from above. “Duties are ours, events are the Lord’s” as Samuel Rutherford put it in a nutshell. Such a belief system protected the Puritans from the dangers of cocksureness, and induced in Cromwell a state of mind somewhere in between ‘meditation’ and ‘rational analysis’. Typically, when a categorical decision one way or the other was required, Cromwell would retire to weigh up the situation and commune with God. In ‘event’ terms, he was trying to get the feel of the mysterious ‘momentum’ of which Sun Tzu speaks ─ except that, for Cromwell, this ‘momentum’ had something to do with Providence. But if a plan did not work, it was his fault, never God’s ─ he had not been sufficiently alert to the signs pointing the way. This was clearly a very favourable mind-set for the leader of a rebellion.
Cromwell’s admirers encouraged him in the belief that he was chosen by God: “Your victories have been given you of God himself, it is himself that has raised you up amongst men, and hath called you to high enjoyments” as John Desborough put it. This sense of being a ‘man with a mission’ obviously gave Cromwell enormous self-confidence as it always does but, again, the Puritan in him stopped him from being completely carried away: he did not, as Napoleon seems to have done, conclude that he was invincible or, like Hitler, that his judgment was infallible. Cromwell, thus combined to a remarkable degree the advantages of the indirect and the direct  approaches. His ‘Not-Doing’ was making himself a passive instrument for God and Providence, his ‘Doing’ was giving full attention to meticulous military planning and logistics. One of the reasons he was such a successful cavalry leader was the seemingly mundane one that he trained his troops to advance at a trot and regroup smartly in good order once they had penetrated enemy lines, whereas the Cavaliers charged at full gallop and typically wasted precious time ransacking the supply train behind the lines.
We find much the same combination of opposites in Hitler as we find in Cromwell. “I carry out the commands that Providence has laid upon me” might well have come from Cromwell, but it is in fact Hitler speaking. As for ‘Not-Doing’, we have Hitler’s  chilling statement, “I go to my goal with the precision and security of a sleep-walker”. But this sense of mission, even combined with Hitler’s oratory, would not have ‘taken him to his goal’ if he had only been a sleep-walker. Halder, his one time Chief of General Staff, writes of Hitler’s “astonishing grasp of technical detail” ─ and, since Halder was eventually sent to a concentration camp by Hitler, he was not playing the flatterer. We are talking about data such as the range of certain guns or the tonnage of certain ships, hardly the bedside reading of a visionary.
Bullock cites the diary of an ordinary German who heard Hitler speak long before he became Chancellor and who wrote, “I have never heard an orator so fanatical or so logical”. Logical? Hitler? In fact, yes, given his premises which were to make Germany great at all costs. Hitler saw more clearly than anyone else at the time that Germany could not become a world power in post-WWI circumstances for two reasons: (1) it did not produce enough food for its burgeoning population; and (2) it was woefully deficient in raw materials for a leading industrial power. His solution was simple: invade the Soviet Union to get hold of the wheat-growing areas of the Ukraine and the oil rich Caucasus. This was clearly stated in the so-called Holbach Memorandum where Hitler outlined (to his generals) the reasons for the forthcoming invasion of Russia. An additional plus for this strategy was that it did not involve war with Britain (or so Hitler supposed); there was no point, Hitler argued in trying to recover  Germany’s lost colonies in Africa ─ let Britain rule the waves and Germany the land. Furthermore, this devastatingly rational economic analysis dictated Hitler’s basic military strategy, Blitzkrieg. Aggression suited Hitler’s temperament, of course, but the main reason for ‘lightning war’ was that Germany would never have been able to sustain a long war because it needed imported food, oil and steel amongst many other commodities.
Bullock observes that most historians writing about Hitler either stress his “fanatical will” or “insist that he relied for his success on calculation and lack of scruple”. But Bullock goes on to say, correctly, that these interpretations are not mutually exclusive. “He [Hitler] was at once fanatical and cynical, unyielding in his assertion of will power and cunning in calculation”. In particular, “His foreign policy….combined consistency of aim with complete opportunism in method and tactics”. Now, this is an extremely unusual combination and shows where Hitler differed from Mussolini, “an opportunist who snatched eagerly at any chance that was going”. In summing up, Bullock writes, “Fixity of aim by itself, or opportunism by itself, would have produced nothing like the same results”.

Application to other areas

To what extent can these precepts be applied in more congenial areas of human activity than war and government?

Firstly, there is the importance of being at a cultural ‘event-hub’. It is possible for geniuses like Nietzsche to mature in more or less complete isolation but this is hardly to be recommended ─  it doubtless contributed to his mental collapse. Writers, painters and composers tend to congregate in particular spots where they cross-fertilize each other even if, or maybe above all, if they quarrel. For reasons that are none too clear, Elizabethan London suddenly produced more great dramatists than perhaps any other place or time. And the Restoration London coffee-houses were suddenly all agog at once with sparkling comedies, Locke’s philosophizing, Defoe’s political and social broadsheets and the revolutionary physical ideas emanating from the newly created Royal Society. Edinburgh at the end of the 18th century is another notable hub since it produced James Watt, Adam Smith and Hume alongside many lesser but still significant thinkers. Vienna at the beginning of the 20th century saw the birth of psycho-analysis, Boltzmann’s statistical physics, logical-positivism and early abstract painting. I have read somewhere that post-war Paris deliberately kept its exchange rate artificially low relative to the dollar and the pound in order to attract Americans and Britons; this along with the incredible profusion of cafés and cheap hotels made Paris the cultural world-centre for half the 20th century, spewing out surrealism, cubism, modernist fiction and finally existentialism. More recently, the cultural ‘world event-hub’ seems to have shifted to California since the latter state gave rise to two utterly opposed but strangely interrelated cultural phenomena, the hippie movement with all that it entailed and Silicon Valley. Today, the awakening giant, China, has given birth to an unexpected amalgam of laissez-faire capitalism and centralized government but has, so far, not produced anything equally new and wonderful in the cultural domain. Maybe this is to come.
So, the advice to an aspiring author, artist or entrepreneur is to position yourself near the coming (not actual) cultural centre-point, or at least pass through to absorb the vibes. (However, the existence of the world-wide web has, arguably, made geography far less important.) As for luck and ruthlessness, much the same principles apply to artists as to politicians and military commanders. In a writer, ruthlessness translates as clarity, precision and economy with respect to words and lack of sentimentality with respect to one’s own early productions ─ though it is also crucial not to overdo this. In mathematics, rigour is the rule but the really great mathematicians such as Leibnitz, Newton and Euler were very far from being logic-machines and relied to a large extent on their undefinable ‘mathematical intuition’ (which is why they sometimes made mistakes). And Bullock’s ‘consistency of aim combined with opportunism of execution’ certainly sounds as much a winning formula in the arts as in foreign policy.

SH 15/2/2018

 Note 1 Talleyrand was the ultimate survivor: he not only lived through, but flourished during, (1) the French Revolution, (2) the Directorate, (3) the Napoleonic period and (4) the Bourbon Restoration, eventually dying quietly in his bed.  

Note 2 Hitler, the proto-typical modern ‘man of destiny’, only got the first intimations of his future role in the trenches in 1915 when he was twenty-six. And it was only during his brief imprisonment in 1923 after the failed ‘Beer-hall putsch’ that he finally cast himself in the role of Germany’s predestined leader. As a youth Hitler had no interest in warfare and little enough in politics: his passion was, and remained, architecture. 

Note 3 If it is true that Alexander’s mother had Philip of Macedon assassinated, as some historians think, she has a better claim than Cleopatra to being a woman who changed the course of history.

Note 4 In the case of Julius Caesar, he absolutely had to stay continuously in office once launched on his career since, like certain contemporary heads of state, this gave him immunity from prosecution.

Note 5 I had the occasion to personally witness something similar, albeit on a much smaller scale, during the May 1968 ‘student revolution’ and ensuing General Strike. For a few weeks, the Parisian faculties were occupied and even the police didn’t dare to go in. It was amazing to see, alongside genuine ‘revolutionaries’, future Robespierres and Stalins manouevering shamelessly in committees to get themselves into positions of power (see my reminiscences ‘Le Temps des Cérises, May ’68 and aftermaths’ in the anarchist quarterly The Raven No. 38).

Note 6 In Hitler’s case, it was perhaps not entirely chance that had him end up in Germany: some obscure instinct made him leave Vienna for what, as it transpired, was an even more suitable locale, Munich ─ since Germany offered far greater scope to his ambitions than Austria. Hitler, though Austrian by birth, was permitted, by special demand, to enlist in the German (not Austrian) army in WWI. 

Note 7 “The aim [of military training]…..is to reduce the conduct of war to a set of rules and a system of procedures ─ and thereby make orderly and rational what is essentially chaotic and instinctive” ( Keegan, The Face of Battle p. 20).


Benjamin Lee Whorf seems to have been the first person to point out how much English, and other European languages, are ‘thing-languages’, ‘object-languages’. By far the most important part of speech is the noun and though it is now accepted that not all sentences are of the subject-predicate form, once regarded as universal, quite a lot are. We have a person or thing, the grammatical subject, and the rest of the sentence tells us something about this thing, for example localizes it (‘The cat was sitting on the mat’), or enumerates some property possessed by the ‘thing’ in question (‘The cover of the book is red’). And if we have an active verb, we normally have an agent doing the acting, a person or thing.
There’s nothing ‘wrong’ with such a linguistic structure, of course, but we are so used to it we tend to assume it’s perfectly  reasonable and irreplaceable by any other basic structure. However, as Whorf points out, it is not just applied to sentences of the type ‘A is such-and-such’, where it is appropriate, but also to sentences where it makes little sense. “We are constantly reading into nature fictional acting entities, simply because our verbs must have substantives. We have to say “It flashed” or “A light flashed”, setting up an actor to perform what we call an action, “to flash”. Yet the flashing and the light are one and the same!” (from Whorf, Language, Thought and Reality p. 242, M.I.T. edition).
The quantum physicist and philosopher, David Bohm,  seemingly unaware of Whorf’s prior work, makes exactly the same point.  “Consider the sentence ‘It is raining.’ Where is the ‘It’ that would, according to the sentence, be ‘the rainer that is doing the raining’? Clearly, it is more accurate to say: ‘Rain is going on’ (from Bohm, Wholeness and the Inplicate Order p. 29 ).
Whorf and Bohm clearly have a point here and the general hostility of the academic world to Whorf’s ‘Theory of Linguistic Relativity’ is doubtless in part due to their irritation at an outsider ─ Whorf trained as a chemical engineer ─ pointing out the obvious. Moreover, one would expect the syntax and vocabulary of languages to tell you something about the general conceptions, day to day concerns and modes of thought of the people whose language it is. After all, people talk about what interests them, and languages typically evolve to make communication about common interests more efficient (Note 1).

Even if this is granted for the sake of argument, one might still object that the subject-predicate structure and the role of nouns in English simply reflects ‘how things are’ ─ and there is only ‘one way for things to be’. Since ‘reality’ consists essentially of ‘things’, and relations between these things, isn’t it inevitable that nouns should have pride of place? Well, maybe, but maybe not. And Whorf, one of the very first ‘Westerners’ to actually speak various American Indian languages, was in a good position to question what practically everyone else had so far taken for granted. Amerindian native languages certainly are very different from any European or even Indo-European language. For a start, “Nearly all American Indian languages are either distinctly ‘polysynthetic’ or have a tendency to be so. At the risk of oversimplification, polysynthetic languages can be thought of as consisting of words that in European languages would occupy whole sentences” (from Lord, Comparative Linguistics). Out and out literal  translations from other European languages into English may sound clunky but are perfectly comprehensible, but literal translations from Shawnee or Nitinat sound, not just awkward, but half crazy. Whorf writes, “We might ape such a compound sentence in English thus: ‘There is one who is a man who is yonder who does running which traverses-it which is a street which elongates’ …... the proper translation [being] ‘A man yonder is running down the long street’.” Whorf adds, “Of such a polysynthetic tongue it is sometimes said that all the words are verbs, or again that all the words are nouns with verb-forming elements added. Actually the terms verb and noun in such a language [as Nitinat] are meaningless.”

Secondly, approaching things from the physical/conceptual side, there can be no doubt that native American tribal societies, untouched as they were by Christianity or Newtonian physics, really did have very different conceptions about the world from those of the incoming European settlers, which is one reason why this meeting of the cultures was so catastrophic. Sapir (Whorf’s first teacher) and Whorf believed that this double dissimilarity was not an accident and that the structure of native American languages indeed reflected a very different ‘view of the world’.
So what, in a nutshell, were these linguistic and ‘metaphysical’ differences? According to Whorf, most Amerindian languages are ‘verb-based’ rather than ‘noun-based’ ─ “Most metaphysical words in Hopi are verbs, not nouns as in European languages”. Worse still, “When we come to Nootka, the sentence without subject or predicate is the only type….Nootka has no parts of speech”. Why were they ‘verb-based’, or at any rate not ‘noun-based’? Because, Whorf argues, the Amerindian world-view was not ‘thing-based’ or ‘object-based’ but ‘event-based’. “The SAE (Standard Average European) microcosm has analysed reality largely in terms of what it calls ‘things’ (bodies and quasibodies) plus modes of extensional but formless existence that it calls ’substances’ or ‘matter’. The Hopi microcosm seems to have analysed reality largely in terms of EVENTS” (Whorf, op. cit. p. 147).

         Again, there seems little to quarrel with in Whorf’s claim that the SAE world-view, which we can trace right back to Greek atomism for its physics, really was ‘thing-based’ ─ “Nothing exists except atoms and void” as Democritus put it. The subsequent, more sophisticated Newtonian world-view nonetheless reduces to a world consisting of ‘hard, massy’, indestructible atoms colliding with each other and influencing each other from afar through universal attraction. Whether, the world of native American Indians really was ‘event-based’ in the way Whorf imagined it to be, few of us today are qualified to say ─ since hardly anyone speaks Hopi any more and even the most remote Amerindian tribes have long since ceased to be independent cultural entities. In any case, the complex metaphysics/physics of the Hopi as interpreted by Whorf is in itself interesting and original enough to be well worth investigating further.

To return to language. Assuming for the moment there is some truth in the Sapir-Whorf theory that language structure reflects underlying physical and metaphysical preconceptions,  what sort of structures would one expect an ‘event-language’ to have?  Bohm asked himself this but sensibly concluded  that “to invent a whole new language  implying a radically different structure of thought is….not practicable”. I asked myself a similar question when,  in my unfinished SF novel The Web of Aoullnnia,  I tried to rough out the principles underlying ‘Lenwhil Katylin’, a future language invented by the Sarlang, the first of the  Parthenogenic types that dominate Sarwhirlia (the future Earth).
For his part, Bohm proposes to introduce, “provisionally and experimentally”, a new mode into English that he calls the rheomode (‘rheo’ comes from the Greek ‘to flow’). This mode is meant to signal and reflect the “movement of growth, development and evolution of living things” in accordance with Bohm’s ‘holistic’ philosophy. Whorf, for his part, finds most of what Bohm is looking for already present in the Hopi language which typically emphasizes ‘process’ and continuity rather than focusing on specific objects and/or moments of time. Although both these thinkers were looking for  a ‘verb-based’ language, they were also firm believers in continuity and the ‘field’ concept in physics (as opposed to the particle concept). My preferences, or prejudices if you like, take me in the opposite direction, towards a physics and a language that reflect and represent  a ‘universe’ made up of staccato events that never last long enough to become ‘things’ and never overlap enough with their successor events to become bona fide processes.

Thus, in Lenwhil Katylin, a language deliberately concocted to reflect the Sarlang world-view, the verb (for want of a better term) is the pivot of every communication and refers to an event of some kind. In many cases there is no need for  a grammatical subject at all: events simply happen, or rather ‘become occurrent’, like the ‘lightning flash’ mentioned by Whorf ─ in the Sarlang world-view, all events are, at bottom,  ‘lightning flashes’. The rest of a typical LK sentence provides the ‘environment’ or ‘localization’ of the central event, e.g. for a ‘lightning-flash’ the equivalent of our ‘sky’, and also gives the causal origin of the event (if one exists). We have thus a basic structure Event/Localization/Origin ─ although in many cases the ‘localization’ and ‘origin’ might well be what for us is one and the same entity.
As to the central events themselves, the Katylin language applies an  inflection to show whether the event is ‘occurrent’ or, alternatively, ‘non-occurrent’. One might compare the inflection with Bohm’s ‘is going on’ in his formulation “Rain is going on” ― in LK we just get Irhil~ where ‘~’ signifies “is occurrent”. Being ‘occurrent’ means that an event occupies a definite location on the Event Locality and has demonstrable physical consequences, i.e. brings into existence at least one other event. Such an event is what we would perhaps call an ‘objective’ event such as a blow with a hammer, as opposed to a subjective one like a wish to be somewhere else (which does not get you there). But the category ‘non-occurrent’ is much larger than our ‘subjective’ since it covers all ‘general’ entities, indeed everything that is not specific and precisely localized in space and time (as we would put it). On the other hand, the Sarlang consider a mental event that is infused with deep emotion, such as a flash of hatred or empathy, to be ‘occurrent’ even if it is completely private since, they would argue, such events can have observable physical consequences. This is somewhat similar to the Buddhist distinction between ‘karmic’ and ‘non-karmic’ events: the first have consequences (‘karma’ means ‘action’ or ‘activity’) while the second do not.
After the ‘occurrent/non-occurrent’ dichotomy, the most important category in Lenwhil Katylin is discontinuity/continuity. Although the Sarlang believe that, in the last analysis, all events are a succession of point-like ‘ultimate events’ (the dharma(s) of Hinayana Buddhism), they nonetheless distinguish between ‘strike-events’ such as a blow and ‘extend-events’ such as a ‘walk’, a ‘run’ and so on. Suffixes or inflections make it clear, for example, whether the equivalent of the verb ‘to look’ means a single glance or an extended survey. And the suffix –y or –yia turns a ‘strike-event’ into an ‘extend-event’  when both cases are possible. Moreover, ‘spread-out’ verbs themselves fall into two classes, those that are repetitions of a selfsame ‘strike-event’ and those that contain dissimilar ‘strike-events’. The monotonous beating of a drum is, for example, a ‘strike spread-event’ while even a single note played on a violin is classed as a ‘spread strike-event’ because of the overtones that are immediately brought into play.
A further linguistic category distinguishes between events which are caused by events of the same type and events brought about by events of an altogether different type. In particular, a physical event brought about by a physical event is sharply distinguished from a physical event brought about by a mental or emotional event: the latter case exhibits ‘cause-effect-dissimilarity’ and is usually, though not invariably, signalled by the suffix -ez. This linguistic distinction has its origin in the division of perceived reality into what is termed ‘the Manifest Occurrent’, very roughly the equivalent of our objective physical universe, and the Manifest Non-Occurrent which consists of wishes, dreams, desires, myths, legends, archetypes, indeed the whole gamut of mental and internal emotional occurrences. Nonetheless, these two domains are not absolutely independent and the Sarlang themselves claimed to have developed a technique (known as witr-conseil) that transferred whole complexes of events from the Manifest Non-Occurrent into the Manifest Occurrent and, more rarely, in the opposite direction. Whatever the truth of this claim, the technique, supposing it ever existed, was lost for ever when the Sarlang, reaching the end of their term, committed mass extinction.                                       SH  13/1/18

Note 1 The standard argument against the ‘Linguistic Relativity Theory’ is that, if it were correct, translation would be impossible which is not the case. This argument carries some weight but we must remember that almost all books successfully translated into English come from societies which share the same general religious and philosophic background and whose languages employ similar grammatical structures. Few books have been translated from so-called ‘primitive’ societies because such societies had a predominantly oral culture, while Biblical translators ‘going the other way’ have typically found it extremely difficult to get their message across when communicating with  animists.
There may be something in Whorf’s claim that the Hopi world-view was closer to the modern ‘field of energy’ paradigm than to the ‘force and particle’ paradigm of classical physics. ‘Energy’ (a term never used by Newton) is essentially a ‘potential’ entity since it refers to what an object ‘possesses  within itself’, not what it is actually doing at any particular moment. Generally speaking, primitive societies were quite happy with ‘potential’ concepts, with the idea of a ‘latent’ force locked up within an object but which was not accessible to the five senses directly. It is in fact possible to formulate mechanics strictly in energy terms (via the Hamiltonian) rather than on the basis of Newton’s laws of motion, but no one ever learned mechanics this way, and doubtless never will, because it requires such advanced mathematics. It is hard to imagine a society committed from the start to an ‘energy’ viewpoint on the world ever being able to develop an adequate symbolic system to flesh out such a vision.

What is random? That which cannot be predicted with any confidence. But there is a weak and a strong sense to ‘unpredictable’. We might say that the motion of a leaf blown about by the wind is ‘random’ ― but then that may simply be because we don’t know the exact speed and direction of the wind or the aerodynamic properties of this particular leaf. In classical mechanics, there is no room for randomness since all physical phenomena are fully determined and so could in principle be predicted if one had sufficient data. Indeed, the French astronomer Laplace claimed that a super-mind, aware of the current positions and momenta of all particles currently in existence could predict the entire future of the universe from Newtonian principles.

In practice, of course, one never does know the initial conditions of any physical system perfectly. Whether this is going to make a substantial difference to the outcome hinges on how sensitively dependent on the initial conditions the system happens to be. Whether or not the flap of a butterfly’s wings in the bay of Tokyo could give rise to a hurricane in Barbados as chaos theory claims, systems that are acutely sensitive to initial conditions undoubtedly exist, and this is, of course, what makes accurate weather forecasting so difficult. Gaming houses retire dice after a few hundred throws because of inevitable imperfections creeping in and a certain Jagger made a good deal of money because he noted that certain numbers seemed to come up slightly more often than others on a particular roulette wheel and bet on them. Later on, he guessed that the cause was a slight scratch on this particular wheel and there seems to have been something in this for eventually the management thwarted him by changing the roulette wheels every night (Note 1). All sorts of other seemingly ‘random’ phenomena turn out, on close examination, to exhibit a definite bias or trend: for example, certain digits turn up in miscellaneous lists of data more often than others (Bensford’s Law) and this bias, or rather its absence, has been successfully used to detect tax fraud.

There is, however, something very unsatisfactory about the ‘unpredictable because of insufficient data’ definition of randomness: it certainly does not follow that there is an inherent randomness in Nature, nor does chaos theory imply that this is the case either. Curiously, quantum mechanics, that monstrous but hugely successful creation of modern science, does maintain that there is an underlying randomness at the quantum level. The radioactive decay of a particular nucleus is held to be not only unforeseeable but actually ‘random’ in the strong sense of the word ― though the bulk behaviour of a collection of atoms can be predicted with confidence. Likewise, genetic mutation, the pace setter of evolution, is regarded today as not just being unpredictable but, in certain cases at least, truly ‘random’. Randomness seems to have made a strong and unexpected come-back since it is now a key player in the game or business of living ― a bizarre volte-face given that science had previously been completely deterministic.

The ‘common sense’ meaning of randomness is the lack of any perceived regularity or repeating pattern in a sequence of events, and this will do for our present purposes (Note 2). Now, it is extremely difficult to generate a random sequence of events in the above sense and in the recent past there was big money involved in inventing a really good random number generator. Strangely, most random number generators are not based on the behaviour of actual physical systems but depend on algorithms deliberately concocted by mathematicians. Why is this? Because, to slightly misquote Moshe, “complete randomness is a kind of perfection”(Note 3).

The more one thinks about the idea of randomness, the weirder the concept appears since a truly ‘random’ event does not have a causal precursor (though it usually does have a consequence). So, how on earth can it occur at all and where does it come from? It arrives, as common language puts it very well, ‘out of the blue’.

Broadly speaking there are two large-scale tendencies in the observable universe: firstly the dissipation of order and decline towards thermal equilibrium and mediocrity because of the ‘random’ collision of molecules, secondly the spontaneous emergence of complex order from processes that appear to be, at least in part, ‘random’. The first principle is enshrined in the 2nd Law of Thermo-dynamics : the entropy (roughly extent of disorder) of a closed system always increases, or (just possibly) stays the same. Contemporary biologists have a big problem with the emergence of order and complexity in the universe since it smacks of creationism. But at this very moment the molecules of tenuous dispersed gases are clumping together to form stars and the trend of life forms on earth is, and has been for some time, a movement from relative structural simplicity (bacteria, archaea &c.) to the unbelievable complexity of plants and mammals. Textbooks invariably trot out the caveat that any local ‘reversal of entropy’ must always be paid for by increased entropy elsewhere. This is, however, not a claim that has been, or ever could be, comprehensively tested on a large scale, nor is it at all ‘self-evident’ (Note 4). What we do know for sure is that highly organized structures can and do emerge from very unpromising beginnings and this trend seems to be locally on the increase ― though it is conceivable that it might be reversed.

For all that, it seems that there really are such things as truly random events and they keep on occurring. What can one conclude from this? That, seemingly, there is a powerful mechanism for spewing forth random, uncaused events, and that this procedure is, as it were, ‘hard-wired’ into the universe at a very deep level. But this makes the continued production of randomness just as mysterious, or perhaps even more so, than the capacity of whatever was out there in the beginning to give rise to complex life!

The generation of random micro-events may in fact turn out to be just about the most basic and important physical process there is. For what do we need to actually produce a ‘world’? As far as I am concerned, there must be something going on, in other words we need ‘events’ and these events require a source of some sort. But this source is remote and we don’t need to attribute to it any properties except that of being a permanent store of proto-events. The existence of a source is not enough though. Nothing would happen without a mechanism to translate the potential into actuality, and the simplest and, in the long run, most efficient mechanism is to have streams of proto-events projected outwards from the source at random. Such a mechanism will, however, by itself not produce anything of much interest. To get order emerging from the primeval turmoil we require a second mechanism, contained within the first, which enables ephemeral random events to, at least occasionally, clump together, and eventually build up, simply by spatial proximity and repetition, coherent and quasi-permanent event structures (Note 5). One could argue that this possibility, namely the emergence of ‘order from chaos’, however remote, will eventually come up ― precisely because randomness in principle covers all realizable possibilities. A complex persistent event conglomeration may be termed a ‘universe’, and even though an incoherent or contradictory would-be ‘universe’ will presumably rapidly collapse into disorder, others may persist and maybe even spawn progeny.

So, which tendency is going to win out, the tendency towards increasing order or reversion to primeval chaos? It certainly looks as if a recurrent injection of randomness is necessary for the ‘health’ of the universe and especially for ourselves ― this is one of the messages of natural selection and it explains, up to a point, the extraordinarily tortuous process of meiosis (roughly sexual reproduction) as against mitosis when a cell simply duplicates its DNA and splits in two (Note 6). But there is also the “nothing succeeds like success” syndrome. And, interestingly, the evolutionary biologist John Bonner argues that microorganisms “are more affected by randomness than large complex organisms” (Note 7). This and related phenomena might tip the balance in favour of order and complexity ― though specialization also makes the larger organisms more vulnerable to sudden environmental changes.                                                                 SH


Note 1 This anecdote is recounted and carefully analysed in The Drunkard’s Walk by Mlodinow.

 Note 2 Alternative definitions of randomness abound. There is the frequency definition whereby, “If a procedure is repeated over and over again indefinitely and one particular outcome crops up as many times as any other possible outcome, the sequence is considered to be random” (adapted from Peirce). And Stephen Wolfram writes: “Define randomness so that something is considered random only if no short description whatsoever exists of it” (Stephen Wolfram).

 Note 3 Moshe actually wrote “Complete chaos is a kind of perfection”.

Note 4 “The vast majority of current physics textbooks imply that the Second Law is well established, though with surprising regularity they say that detailed arguments for it are beyond their scope. More specialized articles tend to admit that the origins of the Second Law remain mysterious” (Stephen Wolfram, A New Kind of Science p. 1020

 Note 5 This is essentially the principle of ‘morphic resonance’ advanced by Rupert Sheldrake. Very roughly, the idea is that if a certain event, or cluster of events, has occurred once, it is slightly more likely to occur again, and so on and so on. Habit thus eventually becomes physical law, or can do. At bottom the ‘Gambler’s Fallacy’ contains a grain of truth: I suspect that current events are never completely independent of previous similar occurrences despite what statisticians say. Clearly, for the theory to work, there must be a very slow build-up and a tipping point after which a trend really takes off. We require in effect the equivalent of the Schrodinger equation to show how initial randomness evolves inexorably towards regularity and order.

Note 6. In meiosis not only does the offspring get genes from two individuals rather than one, but there is a great deal of ‘crossing over’ of segments of chromosomes and this reinforces the mixing process.

Note 7 The reason given for this claim is that there are many more developmental steps in the construction of a complex organism and so “if an earlier step fails through a deleterious mutation, the result is simple: the death of the embryo”. On the other hand “being small means very few developmental steps, with little or no internal selection” and hence a far greater number of species, witness radiolaria (50,000) and diatoms (10,000). See article Evolution, by chance? in the New Scientist 20 July 2013 and Randomness in Evolution by John Bonner.








“He who examines things in their growth and first origins, obtains the clearest view of them” Aristotle.

Calculus was developed mainly in order to deal with two seemingly intractable problems: (1) how to estimate accurately the areas and volumes of irregularly shaped figures and (2) how to predict physical behaviour once you know the initial conditions and the ‘rates of change’.
We humans have a strong penchant towards visualizing distances and areas in terms of straight lines, squares and rectangles ― I have sometimes wondered whether there might be an amoeba-type civilization which would do the reverse, visualizing straight lines as consisting of curves, and rectangles as extreme versions of ellipses. ‘Geo-metria’ (lit. ‘land measurement’) was, according to Herodotus, first developed by the Egyptians for taxation purposes. Now, once you have chosen a standard unit of distance for a straight line and a standard square as a unit of area, it becomes a relatively simple matter to evaluate the length of any straight line and any rectangle (provided they are not too large or too distant, of course). Taking things a giant step forward, various Greek mathematicians, notably Archimedes, wondered whether one could in like manner estimate accurately the ‘length’ of arbitrary curves and the areas of arbitrarily shaped expanses.

At first sight, this seems impossible. A curve such as the circumference of a circle is not a straight line and never will become one. However, by making your unit of length progressively smaller and smaller, you can ‘measure’ a given curve by seeing how many equal little straight lines are needed to ‘cover’ it as nearly as possible. Lacking power tools, I remember once deciding to reduce a piece of wood of square section to a cylinder using a hand plane and repeatedly running across the edges. This took me a very long time indeed but I did see the piece of wood becoming progressively more and more cylindrical before my eyes. One could view a circle as the ‘limiting case’ of a regular polygon with an absolutely enormous number of sides which is basically how Archimedes went about things with his ‘method of exhaustion’ (Note 1).

It is important to stop at this point and ask under what conditions this stratagem is likely to work. The most important requirement is the ability to make your original base unit progressively smaller at each successive trial measurement while keeping them proportionate to each other. Though there is no need to drag in the infinite which the Greeks avoided like the plague, we do need to suppose that we can reduce in a regular manner our original unit of length indefinitely, say by halving it at each trial. In practice, this is never possible and craftsmen and engineers have to call a halt at some stage, though, hopefully, only when an acceptable level of precision has been attained. This is the point historically where mathematics and technology part company since mathematics typically deals with the ‘ideal’ case, not with what is realizable or directly observable. With the Greeks, the gulf between observable physical reality and the mathematical model has started to widen.

What about (2), predicting physical behaviour when you know the initial conditions and the ‘rates of change’? This was the great achievement of the age of Leibnitz and Newton. Newton seems to have invented his version of the Calculus in order to show, amongst other things, that planetary orbits had to be ellipses, as Kepler had found was in fact the case for Mars. Knowing the orbit, one could predict where a given planet or comet would be at a given time. Now, a ‘rate of change’ is not an independently ‘real’ entity: it is a ratio of two more fundamental items. Velocity, our best known ‘rate of change’, does not have its own unit in the SI system ― but the metre (the unit of distance) and the second (the unit of time) are internationally agreed basic units. So we define speed in terms of metres per second.

Now, the distance covered in a given time by a body is easy enough to estimate if the body’s motion is in a straight line and does not increase or decrease; but what about the case where velocity is changing from one moment to the next? As long as we have a reliable correlation between distance and time, preferably in the form of an algebraic formula y = f(t), Newton and others showed that we can cope with this case in somewhat the same way as the Greeks coped with irregular shapes. The trick is to assume that the supposedly ever-changing velocity is constant (and thus representable by a straight line) over a very brief interval of time. Then we add up the distances covered in all the relevant time intervals. In effect, what the age of Newton did was to transfer the exhaustion procedure of Archimedes from the domain of statics to dynamics. Calculus does the impossible twice over: the Integral Calculus ‘squares the circle’, i.e. gives its area in terms of so many unit squares, while the Differential Calculus allows us to predict the exact whereabouts of something that is perpetually on the move (and thus never has a fixed position).

For this procedure to work, it must be possible, at least in principle, to reduce all spatial and temporal intervals indefinitely. Is physical reality actually like this? The post-Renaissance physicists and mathematicians seem to have assumed that it was, though such assumptions were rarely made explicit. Leibnitz got round the problem mathematically by positing ‘infinitesimals’ and ultimate ratios between them : his ‘Infinitesimal Calculus’ gloriously “has its cake and eats it too”. For, in practice, when dealing with an ‘infinitesimal’, we are (or were once) at liberty to regard it as entirely negligible in extent when this suits our purposes, while never permitting it to be strictly zero since division by zero is meaningless. Already in Newton’s own lifetime, Bishop Berkeley pointed out the illogicality of the procedure, as indeed of the very concept of ‘instantaneous velocity’.

The justification of the procedure was essentially that it seemed to work magnificently in most cases. Why did it work? Calculus typically deals with cases where there are two levels, a ‘micro’ scale’ and a ‘macro scale’ which is all that is directly observable to humans ― the world of seconds, metres, kilos and so on. If a macro-scale property or entity is believed to increase by micro-scale chunks, we can (sometimes) safely discard all terms involving δt (or δx) which appear on the Right Hand Side but still have a ‘micro/micro’ ratio on the Left Hand Side of the equation (Note 2). This ‘original sin’ of Calculus was only cleaned up in the late 19th century by the key concept of the mathematical limit. But there was a price to pay: the mathematical model had become even further away removed from observable physical reality.

The artful concept of a limit does away with the need for infinitesimals as such. An indefinitely extendable sequence or series is said to ‘converge to a limit’ if the gap between the suggested limit and any and every term after a certain point is less than any proposed non-negative quantity. For example, it would seem that the sequence ½; 1/3; ¼……1/n gets closer and closer to zero as n increases, since for any proposed gap, we can do better by making n twice as large and 1/n twice as small. This definition gets round problem of actual division by zero.

But what the mathematician does not address is whether in actual fact a given process ever actually attains the mathematical limit (Note 3), or how near it gets to it. In a working machine, for example, the input energy cannot be indefinitely reduced and still give an output, because there comes a point when the input is not capable of overcoming internal friction and the machine stalls. All energy exchange is now known to be ‘quantized’ ― but, oddly, ‘space’ and ‘time’ are to this day still treated as being ‘continuous’ (which I do not believe they are). In practice, there is almost always a gulf between how things ought to behave according to the mathematical treatment and the way things actually do or can behave. Today, because of computers, the trend is towards slogging it out numerically to a given level of precision rather than using fancy analytic techniques. Calculus is still used even in cases where the minimal value of the independent variable is actually known. In population studies and thermo-dynamics, for example, the increase δx or δn cannot be less than a single person, or a single molecule. But if we are dealing with hundreds of millions of people or molecules, Calculus treatment still gives satisfactory results. Over some three hundred years or so Calculus has evolved from being an ingenious but logically flawed branch of applied mathematics to being a logically impeccable branch of pure mathematics that is rarely if ever directly embodied in real world conditions.                                         SH




Note 1 It is still a subject of controversy whether Archimedes can really be said to have invented what we now call the Integral Calculus, but certainly he was very close.

Note 2 Suppose we have two variables, one of which depends on the other. The dependent variable is usually noted as y while the independent variable is, in the context of dynamics, usually t (for time). We believe, or suppose, that any change in t, no matter how tiny, will result in a corresponding increase (or decrease) in y the dependent variable. We then narrow down the temporal interval δt to get closer and closer to what happens at a particular ‘moment’, and take the ‘final’ ratio which we call dy/dt. The trouble is that we need to completely get rid of δt on the Right Hand Side but keep it non-zero on the Left Hand Side because dy/0 is meaningless ― it would correspond to the ‘velocity’ of a body when it is completely at rest.

Note 3   Contrary to what is generally believed, practically all the sequences we are interested in do not actually attain the limit to which they are said to converge. Mathematically, this does no9t matter — but logically and physically it often does.


What is time? Time is succession. Succession of what? Of events, occurrences, states. As someone put it, time is Nature’s way of stopping everything happening at once.

In a famous thought experiment, Descartes asked himself what it was not possible to disbelieve in. He imagined himself alone in a quiet room cut off from the bustle of the world and decided he could, momentarily at least, disbelieve in the existence of France, the Earth, even other people. But one thing he absolutely could not disbelieve in was that there was a thinking person, cogito ergo sum (‘I think, therefore I am’).
Those of us who have practiced meditation, and many who have not, know that it is quite possible to momentarily disbelieve in the existence of a thinking/feeling person. But what one absolutely cannot disbelieve in is that thoughts and bodily sensations of some sort are occurring and, not only that, that these sensations (most of them anyway) occur one after the other. One outbreath follows an inbreath, one thought leads on to another and so on and so on until death or nirvana intervenes. Thus the grand conclusion: There are sensations, and there is succession.  Can anyone seriously doubt this?

 Succession and the Block Universe

That we, as humans, have a very vivid, and more often than not  acutely painful, sense of the ‘passage of time’ is obvious. A considerable body of the world’s literature  is devoted to  bewailing the transience of life, while one of the world’s four or five major religions, Buddhism, has been well described as an extended meditation on the subject. Cathedrals, temples, marble statues and so on are attempts to defy the passage of time, aars long vita brevis.
However, contemporary scientific doctrine, as manifested in the so-called ‘Block Universe’ theory of General Relativity, tells us that everything that occurs happens in an ‘eternal present’, the universe ‘just is’. In his latter years, Einstein took the idea seriously enough to mention it in a letter of consolation to the son of his lifelong friend, Besso, on the occasion of the latter’s death. “In quitting this strange world he [Michel Besso] has once again preceded me by a little. That doesn’t mean anything. For those of us who believe in physics, this separation between past, present and future is an illusion, however tenacious.”
Never mind the mathematics, such a theory does not make sense. For, even supposing that everything that can happen during what is left of my life has in some sense already happened, this is not how I perceive things. I live my life day to day, moment to moment, not ‘all at once’. Just possibly, I am quite mistaken about the real state of affairs but it would seem nonetheless that there is something not covered by the ‘eternal present’ theory, namely my successive perception of, and participation in, these supposedly already existent moments (Note 1). Perhaps, in a universe completely devoid of consciousness,  ‘eternalism’ might be true but not otherwise.

Barbour, the author of The End of Time, argues that we do not ever actually experience ‘time passing’. Maybe not, but this is only because the intervals between different moments, and the duration of the moments themselves, are so brief that we run everything together like movie stills. According to Barbour, there exists just a huge stack of moments, some of which are interconnected, some not, but this stack has no inherent temporal order. But even if it were true that all that can happen is already ‘out there’ in Barbour’s Platonia (his term), picking a pathway through this dense undergrowth of discrete ‘nows’ would still be a successive procedure.

I do not think time can be disposed of so easily. Our impressions of the world, and conclusions drawn by the brain, can be factually incorrect ― we see the sun moving around the Earth for example ― but to deny either that there are sense impressions and that they appear successively, not simultaneously, strikes me as going one step too far. As I see it, succession is an absolutely essential component  of lived reality and either there is succession or there is just an eternal now, I see no third possibility.

What Einstein’s Special Relativity does, however, demonstrate is that there is seemingly no absolute ‘present moment’ applicable right across the universe (because of the speed of light barrier). But in Special Relativity at least succession and causality still very much exist within any particular local section, i.e. inside a particular event’s light cone. One can only surmise that the universe as a whole must have a complicated mosaic successiveness made up of interlocking pieces (tesserae).

In various areas of physics, especially thermo-dynamics, there is much discussion of whether certain sequences of events are reversible or not, i.e. could take place other than in the usual observed order. This is an important issue but is a quite different question from whether time (in the sense of succession) exists. Were it possible for pieces of broken glass to spontaneously reform themselves into a wine glass, this process would still occur successively and that is the point at issue.

Time as duration

‘Duration’ is a measure of how long something lasts. If time “is what the clock says” as Einstein is reported to have once said, duration is measured by what the clock says at two successive moments (‘times’). The trick is to have, or rather construct, a set of successive events that we take as our standard set and relate all other sets to this one. The events of the standard set need to be punctual and brief, the briefer the better, and the interval between successive events must be both noticeable and regular. The tick-tock of a pendulum clock provided such a standard set for centuries though today we have the much more regular expansion and contraction of quartz crystals or the changing magnetic moments of electrons around a caesium nucleus.

Continuous or discontinuous?

 A pendulum clock records and measures time in a discontinuous fashion: you can actually see, or hear, the minute or second hand flicking from one position to another. And if we have an oscillating mechanism such as a quartz crystal, we take the extreme positions of the cycle which comes to the same thing.
However, this schema is not so evident if we consider ‘natural’ clocks such as sundials which are based on the apparent continuous movement of the sun. Hence the familiar image of time as a river which never stops flowing. Newton viewed time in this way which is why he analysed motion in terms of ‘fluxions’, or ‘flowings’. Because of Calculus, which Newton invented, it is the continuous approach which has overwhelmingly prevailed in the West. But a perpetually moving object, or one perceived as such, is useless for timekeeping: we always have to home in on specific recurring configurations such as the longest or shortest shadow cast. We have to freeze time, as it were, if we wish to measure temporal intervals.

Event time

The view of time as something flowing and indivisible is at odds with our intuition that our lives consist of a succession  of moments with a unique orientation, past to future, actual to hypothetical. Science disapproves of the latter common sense schema but is powerless to erase it from our thoughts and feelings: clearly the past/present/future schema is hard-wired and will not go away.
If we dispense with continuity, we can also get rid of  ‘infinite divisibility’ and so we arrive at the notion, found in certain early Buddhist thinkers, that there is a minimum temporal interval, the ksana. It is only recently that physicists have even considered the possibility that time  is ‘grainy’, that there might be ‘atoms of time’, sometimes called chronons. Now, within a minimal temporal interval, there would be no possible change of state and, on this view, physical reality decomposes into a succession of ‘ultimate events’ occupying  minimal locations in space/time with gaps between these locations. In effect, the world becomes a large (but not infinite) collection of interconnected cinema shows proceeding at different rates.

Joining forces with time 

The so-called ‘arrow of time’ is simply the replacement of one localized moment by another and the procedure is one-way because, once a given event has occurred, there is no way that it can be ‘de-occurred’. Awareness of this gives rise to anxiety ― “the moving finger writes, and having writ/ Moves on, nor all thy piety or wit/Can lure it back to cancel half a line….”  Most religious, philosophic and even scientific systems attempt to allay this anxiety by proposing a domain that is not subject to succession, is ‘beyond time’. Thus Plato and Christianity, the West’s favoured religion. And even if we leave aside General Relativity, practically all contemporary scientists have a fervent belief in the “laws of physics” which are changeless and in effect wholly transcendent.
Eastern systems of thought tend to take a different approach. Instead of trying desperately to hold on to things such as this moment, this person, this self, Buddhism invites us to  ‘let go’ and cease to cling to anything. Taoism goes even further, encouraging us to find fulfilment and happiness by identifying completely with the flux of time-bound existence and its inherent aimlessness. The problem with this approach is, however, that it is not clear how to avoid simply becoming a helpless victim of circumstance. The essentially passive approach to life seemingly needs to be combined with close attention and discrimination ― in Taoist terms, Not-Doing must be combined with Doing.

Note 1 And if we start playing with the idea that  not only the events but my perception of them as successive is already ‘out there’, we soon get involved in infinite regress.


Time and place

“Absolute, true and mathematical time, of itself, and from its own nature, flows equably without relation to anything external”  (Newton, Principia Scholium to Definition VIII)

Newton does not say whether there are any absolute units or measures to his absolute time, i.e. whether any exact meaning is to be given to the term ‘moment’. Rather he implies that there are no such units since time ‘flows’, i.e. is continuous. He does, however, contrast ‘absolute time’ with “relative, apparent, and common time” which is “some sensible and external (whether accurate or unequable) measure of duration by the means of motion…. such as an hour, a day, a month, a year”.

He also believes that each object has what he calls a ‘place’ which fixes it in absolute space and absolute time. “All things are placed in time as to order of succession; and in space as to order of situation. It is from their essence or nature that they are places; and that the primary places of things should be movable, is absurd. These are therefore the absolute places; and translations out of these places are the only absolute motions” (Ib.)

This view is to be contrasted with Leibnitz’s which sees the position and motion of bodies as essentially relative: a body’s ‘place’ merely indicates where it is in relation to other bodies at a given moment. This ‘relational’ approach has been adopted by several modern physicists beginning with Mach. As Lee Smolin puts it, “Space is nothing apart from the things that exist; it is only an aspect of the relationships that hold between things” (Smolin, Three Roads to Quantum Gravity p. 18). Much the same goes for time: “Time also has not absolute meaning…..Time is described only in terms of change in the network of relationships that describes space” (Smolin, Ib.) 


 What about ‘change of place with respect to time’ or motion? To determine a body’s motion we have to establish what a body’s ‘place’ was before motion began and the same body’s ‘place’ when motion has ceased. Newton concedes that the ‘parts of space’ cannot be seen and so we have to assume that there is a body which is immoveable and measure everything with respect to it. “From the positions and distances of things from any body considered as immovable, we define all places” (p. 8). But is there such a thing as an immovable body ? Newton is undecided about this though he would like to answer in the affirmative. He writes, “It may be that there is no body really at rest” but a few lines further on he adds that “in the remote regions of the fixed stars, or perhaps far beyond them, there may be some body absolutely at rest”. However, since such bodies are so far away, they are of little use as reference points practically speaking while “absolute rest cannot be determined from the position of bodies in our region”.

Newton concludes that we have to make do with ‘relative places’ though he is clearly bothered by this since it means that motion will also have to be treated as relative. This leads straight on to the Galilean ‘law’ that rest and constant straight line motion cannot be distinguished. Newton’s position is, however,  to be contrasted with the modern interpretation of Galileo’s claim. For Newton is not saying that ‘rest’ and ‘constant straight line motion’ are ‘equivalent’. Instinctively, he feels that there must be such a thing as ‘absolute place’ and ‘absolute rest’ and is chagrined that he cannot provide a reliable test to distinguish true rest from motion.

When discussing circular motion Newton invokes the backdrop of the ‘fixed stars’ which “ever remain unmoved and do thereby constitute immovable space”. Thus, it is, according to Newton, possible to distinguish between relative and absolute circular motion because in the latter case there is a force at work which makes a body “recede from the axis of circular motion”.  He gives the celebrated example of a bucket of water suspended by a chord which is twisted and then released so that the water climbs up the sides of the vessel. Today we would use the example of a merry-go-round which is, according to Newton’s test, a genuine case of absolute circular motion since we feel a definite force pushing us towards the outer edge.

Continuous and Discontinuous

 When analysing the perceived motion of bodies, Newton treats motion as at once continuous and discontinuous: a projectile or a planet is never at rest as it pursues its path (unless interrupted by something in the way). But if a body is accelerating it does not have a constant velocity at that instant, and if it is in motion at any particular instant it cannot have a precise position. At the end of the day, provided we make the time interval small enough, it would appear that everything is at rest. However, the use of ‘infinitesimals’ allows one to decrease the time interval down to ‘almost nothing’ so that we can speak of  a body’s  ‘instantaneous velocity’ ― despite this being a contradiction in terms. In effect, the Infinitesimal Calculus which Newton co-invented, allows him to have his cake and eat it too as Bishop Berkeley pointed out to Newton and his supporters. This is probably the main reason why Newton avoids calculus methods as such in the Principia employing instead cumbersome geometrical constructions which in effect treat motion as an infinite succession of stills. Newton struggles to defend the logic behind his treatment in the beginning of Book I which treats the Motion of Bodies. But he cannot decide whether the ‘ultimate ratio’ of distance versus time ― what we call dy/dt ― is ever actually attained, a rather important point (Note 1).

More precisely, Bishop Berkeley made it clear that Newton was contradicting himself by first assuming that x has an increment and then, “in order to reach the result, allows the increment to be zero, i.e. assumes that there was no increment.” Modern mathematics gets round this problem by defining the ‘limit’ to an ‘infinite series’ in such a way that it is not required that this limiting value is actually attained ― indeed in practically all cases of interest it cannot be. The price we have to pay for this rationalization of the Calculus is loss of contact with physical reality. Even if Newton  had been capable of formulating the concept of a ‘limit’ in the precise modern sense I doubt if he would have employed it. Why not? Because Newton, like Leibnitz, and like practically every other ‘natural philosopher’ of the time, was a realist. In Newton’s time mathematics had not yet separated into ‘pure’ and ‘applied’ and the question as to whether infinitesimals ‘existed’ or not was the same sort of question as asking whether atoms existed. Pre-modern mathematics required infinitesimals to get tangible results which could be checked and usually turned out to be correct. But Newton was pragmatist enough to realize that, taken literally, Calculus methods made little sense.

Boyer naturally champions the modern view. “His [Berkeley’s] argument is of course absolutely valid as showing that instantaneous velocity has no physical reality, but this is no reason why, if properly defined or taken as an undefined notion, it should not be admitted as a mathematical abstraction” (Boyer, The History of the Calculus p. 227).
But  why should one allow mathematics to wag the tail of physics to this extent? The real world cannot be handwaved into irrelevance just because it hampers the style of pure mathematicians. It is in fact deeply shocking that contemporary physics, on the face of it  the most ’down to earth’ of the sciences, has been transformed into a piece of recondite pure mathematics. For mathematics, as a logico-deductive system, does not and cannot guarantee the existence of anything. Yet, for all that,  most of us would like to know what is ‘really real’ and what is imagination: science is not the same thing as science fiction.

Boyer claims that mathematics only deals in ‘relations’ not actualities which is all right up to a point ― but one has to ask, ‘relations between what sort of things?’ Since mathematics is a symbolic system, either its symbols ‘represent’  or stand in for realities of some  sort or they do not, in which case they are simply decorative in the same sort of way in which embroidery patterns are decorative. It is quite conceivable that a different intelligent species might use embroidery or textile design as a way of communicating truths about the cosmos but our species has not gone down this route and has restricted its scientific pattern-making to geometrical drawings and algebra.

Newton’s Approach and UET

 How does Newton’s idea of ‘absolute time and place’ play out in terms of the basic assumptions of Ultimate Event Theory? In UET ‘ultimate events’ replace Newton’s ‘bodies’ and ‘time’ is the rate at which ultimate events succeed each other. Newton’s assumption of ‘absolute time’ is tantamount to suggesting that there is a fixed, universal and absolute rate at which certain events succeed each other and which is entirely regular. Most sequences of events, of course, probably only approximate to this measure in principle it is always there in the background. There is, then, a sort of metronome according to whose ticks all other sequences can be measured, and towards which all actual rates of actual events tend.

Is such an ‘absolute rate’ conceivable? (This is a different question to whether it actually exists.) If we assume, as I do, that all ultimate events have the ‘same extent’, i.e. occupy spatially  equivalent ‘places’ on the Locality, and last for exactly the same ‘length of time’, we obtain a basic regular rate if (and only if) the intervals between successive ultimate events are equal. And the simplest case would be when the interval between successive events is a minimum, i.e. just enough to keep the events separate, like a cell membrane that is one molecule thick.

As far as I am concerned, I believe that Newton was right in thinking that every object must have a ‘place’: this strikes me as even more necessary when dealing with events, which are by definition transitory, than with semi-permanent objects. I simply cannot conceive of ‘space’, or whatever is out there, as being simply composed of ‘relations’. But the UET conception is not the same as Newton’s concept of absolute space and time since the latter provide a fixed framework whether or not anything exists  inside this framework or not. One should conceive of an ‘ultimate’ rate for event chains as a constraint or asymptotic limit to which actual event sequences may tend, rather than something existing independently of all actual events. What it means, however, is that the time variable δt cannot be arbitrarily diminished, so there is always a final ratio of distance versus time for consecutive events. Moreover, one could state as a postulate that a ‘rest’ event sequence, the equivalent of a stationary object, proceeds at the minimal rate, i.e. one ksana at a time (sic) with the distance between any two consecutive events in an event-chain being  a minimum ― or, alternatively, a maximum.

SH  18/03/15

Note 1 Newton writes, “There is a limit which the velocity at the end of the motion may attain, but not exceed. This is the ultimate velocity”. But, a little further on, he changes tack and writes, “those ultimate ratios with which quantities vanish are not truly the ratios of ultimate quantities, but limits towards which the ratios of quantities decreasing without limit do always converge, and to which they approach nearer than by any given difference, but never go beyond, nor in effect attain to, till the quantities are diminished in infinitum”.

Note 2 And again, “Berkeley was unable to appreciate that mathematics was not concerned with a world of “real” sense impressions. In much the same manner today some philosophers criticize the mathematical conceptions of infinity and the continuum, failing to realize that since mathematics deals with relations rather than with physical existence, its criterion of truth is inner consistency rather than plausibility in the light of sense perception or intuition”.



Minkowski, Einstein’s old teacher of mathematics, inaugurated  the hybrid ‘Space-Time’ which is now on everyone’s lips. In an address delivered not long before his death in 1908 he said the now famous lines,

“Henceforth space by itself, and time by itself, are doomed to fade away into mere shadows, and only a kind of union of the two will preserve an independent reality.”

         But why should Minkowski, and whole generations of scientists, have ever thought that ‘space’ and ‘time’ could be completely separate in the first place? Certain consequences of a belief in ‘Space-Time’ in General Relativity do turn out to be  scarcely credible, but there is nothing weird or paradoxical per se about the idea of ‘time’ being a so-called fourth dimension. To specify an event accurately it is convenient to give three spatial coordinates which tell you how far the occurrence of this event is, or will be, along three different directions relative to an agreed  fixed point.  If I want to meet someone in a city laid out like a grid as New York is (more or less), I need to specify the street, say Fifth Avenue, the number of the building and the floor (how high above the ground it is). But this by itself will not be enough for a successful meet-up : I also need to give the time of the proposed rendez-vous, say, three o-clock in the afternoon. The wonder is, not that science has been obliged to bring time into the picture, but that it was possible for so long to avoid mentioning it (Note 1)


 Now, if you start off with ‘events’, which are by definition ‘punctual’ and impermanent, rather than things or ‘matter’ you cannot avoid bringing time into the picture from the start: indeed one  might be inclined to say that ‘time’ is a good deal more important than space. Events happen ‘before’ or ‘after’ each other; what happened yesterday preceded what happened this morning, and you read the previous sentence before you started on the current one. The very idea of ‘simultaneous’ events, events that have occurrence ‘at the same time’, is a tricky concept even without bringing Special Relativity into the picture. But  the idea of succession is both clearcut and basic and one could, as a first bash, even define ‘simultaneous’ events negatively as bona fide  occurrences that are not temporally ordered.

So, when I started trying to elaborate an ‘event-orientated’  world-view, I felt I absolutely had to have succession as a primary ingredient : if anything it came higher up the list than ‘space’. Originally I tried to kick off with a small number of basic assumptions (axioms or postulates) which seemed absolutely unavoidable. One such assumption was that most events are ‘ordered temporally’, that they have occurrence successively, ‘one after the other’ ─ with the small exception of so-called ‘simultaneous events’. Causality also seemed to be something I could not possibly do without and causality is very much tied up with succession since it is usually the prior event that is seen as ‘causing’ the other event in a causal pair. Again, one might tentatively  defined ‘simultaneous events’ as events which cannot have a direct causal bond, i.e. function as cause and effect (Note 2). And,  in an era innocent of Special Relativity and light cones, one might well define space as  the totality of all distinct events that are not temporally ordered.

From an ‘event-based’ viewpoint,  chopping up reality into ‘space’ and ‘time’ is not fundamental : all we require is a ‘place’ where events can and do have occurrence, an  Event Locality. Such a Locality starts off empty of events but has the capacity to receive them, indeed I have come to regard ultimate events as in some sense concretisations or condensations of an underlying substratum.

 Difference between Space and Time

 There is, however, a problem with having a single indivisible entity whether we call it ‘Space-Time’ or simply ‘the Locality’. The two parts or aspects of this creature are not at all equivalent. Although I believe, as some physicists have suggested, that, at a certain level, ‘space’ is ‘grainy’, it certainly appears to be continuous : we do not notice any dividing line, let alone a gap, between the different spatial ‘dimensions’ or between different spatial regions. We don’t have to ‘add’ the dimension height to pre-existing dimensions of length and width for example : experience always provides us with a three-dimensional physical block of reality (Note 3). And the fact that the choice of directions, up/down, left/right and so on, is more often than not completely arbitrary suggests that physical reality does not have inbuilt directions, is ‘all-of-a-piece’.

Another point worth mentioning is that we seem to have a strong sense of being ‘at rest’ spatially : not only are we ‘where we are’, and not where we are not, but we actually feel this to be the case. Indeed we tend to consider ourselves to be at rest even when we know we are moving : when in a train we consider that it is the other things, the countryside, that are in motion, not us. It is indeed this that gives Galileo’s seminal concept of inertia its force and plausibility; in practice all we notice is a flagrant disturbance of the ‘rest’ sensation, i.e. an ‘acceleration’.

What about time? Now it is true that time is often said to ‘flow’ and we do not notice any clearcut temporal demarcation lines any more than we notice spatial ones. Nonetheless, I would argue that it is much less natural and plausible to consider ‘time’ as a continuum because we have such a strong sense of sequence. We continually break up time into ‘moments’ which occur ‘one before the other’ even though the extent of the moment varies or is left vague. Sense of sequence is part of our world and since our impressions are themselves bona fide events even if only subjective ones, it would appear that sequence is a real feature of the physical world. There is in practice always an arrow of time, an arrow which points from the non-actual to the actual. Moreover, the process of ‘actualization’ is not reversible : an event that has occurrence cannot be ‘de-occurred’ as it were (Note 4).

And it is noteworthy that one very seldom feels oneself to be ‘at rest’ temporally, i.e. completely unaware of succession and variation. The sensation is so rare that it is often classed as  ‘mystical’, the feeling of being ‘out of time’ of which T.S. Eliot writes so eloquently in The Four Quartets. Heroin and certain other drugs,  by restricting one’s attention to the present moment and the recent past, likewise ‘abolish time’, hence their appeal. In the normal way,  even when deprived of all external physical stimuli, one still retains the sensation of there being a momentum and direction to one’s own thoughts and inner processes : one idea or internal sensation follows another and one never has any trouble assigning order (in the sense of sequence) to one’s inner feelings and thoughts. It is now thought that the brain uses parallel processing on a big scale but, if so, we are largely unaware of this incessant multi-tasking. Descartes in his thought experiment of being entirely cut off from the outside world and considering what he simply could not doubt, might well have concluded that sequence, rather than the (intemporal) thinking ego, was the one item that could not be dispensed with. For one can temporarily disbelieve in one’s existence as a particular person but not in the endless succession of thoughts and subjective sensations that stream through one’s mind/brain.

All this will be dismissed as belonging to psychology rather than physics. But our sense impressions and thoughts are rooted in our physiology and should not be waved aside for that very reason : in a sense they are the most important and inescapable ‘things’ we have for without them we would be zombies. Physical theories that deny sequence, that consider the laws of physics to be ‘perfectly reversible’, are both implausible and seemingly  unliveable, so great is our sense of ‘before and after’. Einstein towards the end of his life decided that it followed from General Relativity that everything happened in an ‘eternal present’. He took this idea seriously enough to mention it in a letter to the son of his college friend, Besso, on receiving news of the latter’s death, writing “For those of us who believe in physics, this separation between past, present and future is only an illusion, however tenacious”.

Breaks in Time

 If, then, we accept succession as an unavoidable feature of lived reality, are we to suppose that one moment shifts seamlessly into the next without any noticeable demarcation lines, let alone gaps? Practically all physicists, even those who toy with the idea that Space-time is in some sense ‘grainy’, seem to be stuck with the concept of a continuum. “There is time, but there is not really any notion of a moment in time. There are only processes that follow one another by causal necessity” as Lee Smolin puts it in Three Roads to Quantum Gravity..

But I cannot see how this can possibly be the case, and this is precisely why the ‘time dimension’ of the Event Locality is so different from the spatial one. If I shift my attention from two items in a landscape, from a rock and its immediate neighbourhood to a tree, there is no sense that the tree displaces the rock : the two items can peaceably co-exist and do not interfere with each other. But if one moment follows another, it displaces it, pushes it out of the way, as it were, since past and present moments, prior and subsequent events, cannot by definition co-exist ─ except perhaps in the inert way they might be seen to co-exist in an Einsteinian perpetual now. And all the attributes and particular features of a given moment must themselves disappear to make way for what follows. We do not usually see this happening, of course, because most of the time the very same objects are recreated and our senses do not register the transition. We only notice change when a completely different physical feature replaces another one, but the same principle must apply even if the same feature is recreated identically. Since a single moment is, in its physical manifestation, three-dimensional, all these three dimensions must go if a new moment comes into being.

Whether there is an appreciable gap between moments apart from there being a definite change is an open question. In the first sketch of Ultimate Event Theory I attribute a fixed extent to the minimal temporal interval, the ksana, and I allow for the possibility of flexible gaps between ksanas. The phenomenon of  time dilation is interpreted as the widening of the gap between ksanas rather than as an extension of the ‘length’ of a ksana itself. This feature, however, is not absolutely essential to the general theory.

What we actually perceive and consider to constitute  a ‘moment’ is, of course, a block containing millions of ksanas since the length of a ksana must be extremely small (around the Planck scale). However, it would seem that ksanas do form blocks and that there are transitions between blocks and that sometimes, if only subliminally, we are aware of these gaps. Instead of being a flowing river, ‘time’ is more like beads on a string though the best image would be a three-dimensional shape pricked out in coloured lights that is switched on and off incessantly.

Mosaic Time

Temporal succession is either a real feature of the world or it is not, I cannot see that there is a possible third position. In Einstein’s universe “everything that can have occurrence already has occurrence” to put things in event terms. “In the ‘block universe’ conception of general relativity….the present moment has no meaning ─ all that exists is the whole history of the universe at once, timelessly. When laws of physics are represented mathematically, causal processes which are the activity of time are represented by timeless logical implications…. Mathematical objects, being timeless, don’t mhave present moments, futures or pasts”  (Lee Smolin, It’s Time to Rewrite time in New Scientist 20 April 2014)  

This means that there is no free will since what has occurrence cannot be changed, cannot be ‘de-occurred’. It also makes causality redundant as Lee Smolin states. One could indeed focus on certain pairs of events and baptise them ‘cause and effect’ but, since they both have occurrence, neither of them has brought the other about, nor has a third ‘previous’ event brought both of them about simultaneously. Causality becomes of no account since it is not needed.

Even a little acquaintance with Special Relativity leads one to conclude that it is impossible to establish a universally valid ‘now’. Instead we have the two light cones, one leading back to the past and one to the future (the observer’s future), and a large region classed as ‘elsewhere’. It is notorious that the order of events in ‘elsewhere’, viewed from inside a particular light cone, is not fixed for all observers : for one observer it can be said that event A precedes event B and for another that event B precedes A. This indeterminacy if of little or no practical consequence since there is (within SR) no possibility of interaction between the two regions. However, it does mean that it is on the face of it impossible to speak of a universally valid ‘now’ ─ although physicists do use expressions like the “present state of the universe”.

I personally cannot conceive of a ‘universe’ or a life or indeed anything at all without succession being built into it : the timeless world of mathematics is not reality but a ‘take’ on reality. The only way to conceptually save succession while accepting some of the more secure aspects of Relativity would seem to be to have some sort of ‘mosaic time’, physical reality split up into zones. How exactly these zones, which are themselves subjective in that they depend on a real or imagined ‘observer’, fit together is not a question I can answer though certain areas of research into general relativity can presumably be taken over into UET.  One could perhaps define the next best thing to a universal ‘now’ by taking a weighted average of all possible time zones : Eddington suggested something along these lines though he neglected to give any details. Note that if physical reality is a mosaic rather than a continuum, it would in principle be possible to shift the arrangement of particular tesserae in a small way, exchange one with another and so on.                     SH 23/01/15


 Note 1 Time was left out of the picture for so long, or at any rate neglected, because the first ‘science’ to be developed to a high degree of precision in the West was geometry. And the truths of (Euclidian) geometry, if they are truths at all, are ‘timeless’ which is why Plato prized geometry above all other branches of knowledge except philosophy. Inscribe a triangle in a circle with the diameter as base line and you will always find that it is right-angled. And if you don’t, this is to be attributed to careless drawing and measurement : in an ‘ideal’ Platonic world such an angle has to be a right angle. How do we know? Because the theorem has been proved.

This concentration on space rather than time meant that although the Greeks set out the basic principles  of statics, the West had to wait another 1,600 years or so before Galileo more or less invented the science of dynamics from scratch. And the prestige of Euclid and the associated static view of phenomena remained so great that Newton, perversely to our eyes, cast his Principia into a cumbrous geometrical mould using copious geometrical diagrams even though he had already invented a ‘mathematics of motion’, the Calculus.

 Note 2   Kant did in point of fact defend the idea of ‘simultaneous causation’ where each of two ‘simultaneous’ events affects the other ‘at the same time’. He gave the example of a ball resting on a cushion arguing that the ball presses down on the cushion for the same amount of time as the cushion is deformed by the presence of the ball. And if we take Newton’s Third Law as operating exactly at the same time on or between two different objects, we have to accept the possibility of simultaneous causation.

Within Ultimate Event Theory, what would normally be  called ‘causality’ is (sometimes) referred to as ‘Dominance’. I chose this term precisely because it signifies an unequal relation between two events, one event, referred to as the ‘cause’, as it were ‘dominating’ the other, the ‘effect’. In most, though perhaps not all, cases of causal relations I believe there really is priority and succession despite Newton’s Third Law. I would conceive of the ball pressing on the cushion as occurring at least a brief moment before its effect ─ though this is admittedly debatable. One could introduce the category of ‘Equal Dominance’ to cover cases of  Kant’s ‘simultaneous causality’ between two events.

Note 3  I have always found the idea of Flatland, which is routinely trotted out in popular books on Relativity, completely unconvincing. I can more readily conceive of there being more than three spatial dimensions as there being a world with less than three : a line, any line, always has some width and height.

 Note 4. If it is possible for an event in the future to have an effect ‘now’, this can only be because the ‘future’ event has already somehow already occurred, whereas intermediate events between ‘now’ and ‘then’ have not. I cannot conceive of a ‘non-event’ having any kind of causal repercussion — except, of course, in the trivial sense that current wishes or hopes about the future might affect our behaviour. Such wishes and desires belong to the present or recent past, not to the future.