Panspermia and the Black Death

Where and how did life begin?

Can/could there be a universe without life? Life without a universe? Contemporary science says yes to the first question and no to the second, whereas most religions tend towards the opposite point of view; indeed disagreement on the subject is perhaps the main bone of contention between the two camps. Given that there is such a thing as life, and that we know how to recognize it when and where it exists (no easy task), where did it start? For Galileo and Newton, there was only one place where it could possibly start, the Earth. And, as to how and why it began in the first place, few if any of the ‘classical’ physicists troubled themselves about the question since they were all believers, if not in Christ at least in God. The paradigm of a unique universe created once and for all by an omnipotent intelligence, and henceforth forced to obey rules laid down by this intelligence, served physics and mechanics well for several centuries. But it was not clear how ‘life’, especially human life,  could be fitted into this schema which is probably the reason why Newton, having sorted out the physical side of things, tried his hand at alchemy. One can (perhaps) reduce biology, the life science, to chemistry but not to mechanics and in Newton’s day chemistry scarcely existed.

Darwin was extremely reticent on the subject of the origins of life though he did famously speak of “a warm little pond with all sorts of ammonia and phosphoric salts present”, a place where “a protein compound was chemically formed ready to undergo still more complex changes”. This shows that Darwin was at least firmly committed to the idea that life developed ‘spontaneously’ without the need for supernatural intervention or planning. Eventually, in the nineteen-fifties, Miller caused a sensation by simulating in  a test-tube the Earth’s supposed early environment (water, ammonia, methane and carbon dioxide) and bombarding it with ultra-violet radiation. The result was the spontaneous formation of certain compounds, including amino-acids, the building blocks of proteins. However, it would seem that Miller and Urey got the composition of the early Earth’s environment wrong and there are other reasons why the Miller/Urey experiment is no longer considered to be a good indication of how life on Earth started. Since the discovery in the nineteen-seventies of sulphur consuming microbes in deep ocean hydro-thermal vents, and the copious eco-systems to which they give rise, the theory that life began under the surface of the Earth, rather than on it, has become more and more popular. Such bacteria do not require sunlight to produce energy, i.e. do not photosynthesize, and, because of their location, they would have been at least partially protected against the intense bombardment of the Earth’s surface by meteorites which was so characteristic of the early  years of the Earth’s history.

Life from elsewhere

There is, however, another way to explain the sudden appearance of primitive life on Earth about 3.85 billion years ago : it came from somewhere else in the universe. The idea that there might well be life outside the Earth goes back as far as the IVth century B.C. and demonstrates how astonishingly ‘modern’ many of the Greek thinkers were in their outlook. Although better known for his contention that the goal of human life is, and should be, pleasure, Epicurus also wrote extensively on physical matters. Unfortunately these works have been lost and are only known via his Roman follower, Lucretius, author of the long poem De Rerum Naturae. The latter writes

“If atom stocks are inexhaustible Greater than the power of living things to count, If Nature’s same creative power were present too To throw the atoms into unions — exactly as united now Why then confess you must That other worlds exist in other regions of the sky And different tribes of men, and different kinds of beasts.”

Note that this is a reasoned argument based on the premises that (1) there exists an abundant supply  of the building-blocks of life (atoms), (2) these building-blocks combine together in much the same way everywhere, and (3) Nature’s ‘creative power’ (‘energy’) is limitless. Therefore, there must exist other habitable worlds containing beings made of the same material as us but different from us. This is almost word for word the argument put forward by contemporary physicists that we are not alone in the universe. Lucretius does not go so far as to suggest that there could be, or ever had been, any interaction between these different ‘worlds’. However, the Gnostics (‘Knowers’, ‘Those who Know’), a half-pagan, half-Christian sect that flourished during the declining Roman Empire, taught that human kind did not originate here but came from what we would call ‘outer space’  —  indeed this is precisely what they knew and what ordinary  persons didn’t (Note 1). 


The belief that life did not begin here but was brought from elsewhere in the cosmos seems to have disappeared after the triumph of orthodox Christianity but eventually re-surfaced at the end of the nineteenth century in a place where one would not normally expect to find it, namely physical science. The 19th century German physicist von Helmholtz, a hard-nosed physicist if ever there was one, wrote in 1874: “…it appears to me a fully correct scientific procedure to raise the question whether life is not as old as matter itself and whether seeds have not been carried from one planet to another and have developed everywhere that they have found fertile soil.” (Note 2)               Lord Kelvin agreed, arguing that collisions could easily transport material around the solar system and thus ‘infect’ other planets with life, as he put it. And the Swedish chemist,  Svante Arrhenius, energetically took up the idea which he dubbed ‘Panspermia’ (‘seeds everywhere’). Nearer our own time, Francis Crick of DNA fame argues in his book Life Itself, Its Origin and Nature that “microorganisms ….. travelled at the head of an [unmanned] spaceship sent to Earth by a higher civilization which had developed elsewhere billions of years ago.”

 Life as a Cosmic Phenomenon   

But the theory that life came from outer space is above all associated with the work of Fred Hoyle and Chandra Wickramasinghe who have expounded it in great detail in a series of books and scientific papers. They summarize their position thus : “The essential biochemical requirements of life exist in very large quantities within the dense interstellar clouds of gas. This material [eventually] becomes deposited within the solar system, first in comet-type bodies, and then in the collisions of such bodies with the Earth. (…) The picture is of a vast quantity of the right kind of molecules looking for suitable homes, and of there being very many suitable homes [i.e. planets].” (Note 3)

As the two authors never tire of pointing out, ‘Panspermia’ is not just another scientific theory : it constitutes a paradigm shift only to be compared with the shift from a geocentric to a heliocentric viewpoint instigated by Copernicus. Just as humanity previously — and mistakenly — considered itself to be situated at the centre of the universe and the favoured creation of the Almighty, so biologists and astronomers today mistakenly tend to take it for granted that the Earth has been particularly favoured to be the unique seat of intelligent life. In its full development, as propounded in Hoyle’s The Intelligent Universe (the title says all), the theory of ‘panspermia’ really means what it says  : ‘seeds of life evrywhere’.  Hoyle and Wickramasinghe argue that life is so improbable an eventuality, requiring so much fine-tuning of physical constants, that it has either always existed (Hoyle’s preferred option) or has only come about once. A complicated circulation system, involving interstellar dust, comets and meteorites, is responsible for randomly disseminating the seeds of life throughout the universe in the expectation that at least one or two of them will fall on fertile ground somewhere sometime. As one might expect, the Hoyle/Wickramasinghe theory was, and is, highly controversial. In the past they would have run foul of the Inquisition — Giordano Bruno was burnt at the stake for propounding something vaguely similar —  but, this being the 20th century, their main opponents have come from within the scientific establishment. The two scientists, despite their impressive credentials, were met with what Hoyle describes  euphemistically as “a wall of silence”. It is even said that Hoyle’s outspoken advocacy of ‘panspermia’ is the main reason he was not granted the Nobel Prize for his seminal work on the carbon cycle in stars.

Evidence in favour of the Hoyle/Wickramasinghe Theory

 We require a new scientific theory to, (1) explain known data in a more elegant and satisfactory way than current theories and (2) make predictions which can be tested experimentally. Now the Hoyle/Wickramasinghe theory certainly does explain something that contemporary astro-physics struggles to make any sense of, namely the surprisingly early appearance of bacterial life on the Earth. The Earth is currently considered to have formed some 4.6 billion years ago but for most, if not all, of the first seven or eight million years it must have been a boiling inferno uninhabitable even for heat-loving microbes. However, the high level of carbon-12 in certain rocks that date back 3.85 billion years, suggests that microbial life already existed at that early date. We are not here talking about organic molecules but about unicellular organisms which, though ‘primitive’ compared to plants and mammals, possess DNA (or RNA). It is scarcely credible that the transition from a few diffuse chemicals to such a highly organized entity as a prokaryotic cell came about in  such a short time in evolutionary terms, especially since the subsequent transition from bacterial to multicellular life took around 3 billion years! But for Hoyle and Wickramasinghe, this is not a problem : primitive life arrived here ready-made, a seed quite literally falling from the sky either naked or enclosed in the remnants of a comet that, like Icarus, had ventured too near the Sun and had spilled its contents into the atmosphere (Note 4). So, is there any evidence that a microbial spore could exist in interstellar space and be wafted to Earth riding on a gas cloud or enclosed in the kernel of a wandering comet? In the seventies, when Hoyle and Wickramasinghe first advanced the general idea, it sounded more like science fiction than science — Hoyle was after all the author of a successful SF novel The Black Cloud. But since then the critics have had to eat their words — though in point of fact scientists never seem to actually bring themselves to do such a terrible thing — since it is now common knowledge that interstellar dust is full of molecules, many of them organic, and that comets contain most, and probably all, of the basic ingredients for life. “Analysis of the dust grains streaming from the head [of Halley’s comet] revealed that as much as one third was organic material. Common substances such as benzene, methanol, and acetic acid were detected, as well as some of the building blocks of nucleic acids. If Halley is anything to go by, then comets could easily have supplied Earth with enough carbon to make the entire biosphere.”      Davies, The Origin of Life, p. 136

It is also generally admitted now that there is a considerable exchange of (not necessarily organic) material throughout the galaxy : the very latest issue of Science (15 August 2014) contains an article “Evidence for interstellar origin of seven dust particles collected by the Stardust space craft”. So far, so good. But all this, of course,  stops well short of Hoyle and Wickramasinghe’s claim that actual bacterial spores and/or viruses can and do make the perilous journey from a cloud of interstellar dust to a comet in the Oort Cloud and then on to the interior of the solar system and us. A number of claims for the presence of fossilized organic material in meteorites have nonetheless  been made, for example by Claus and Nagy in the 1960s and, more recently, by two researchers from the University of Naples D’Argenio and Geraci who concluded that their results  constituted “clear evidence for the existence of extra-terrestrial life”. Those who wish to pursue the topic further are referred to a recent article by Chandra Wickramasinghe on DNA Sequencing and Predictions of the Cosmic theory of Life (and the extensive bibliography at the end). This is available free of charge at

Can bacteria and viruses reach the surface of the Earth? 

The suggestion that diseases can come from space follows on from Hoyle and Wickramasinghe’s belief that life came from space in the first place. For the cosmic bombardment continues unabated though, thankfully, on a lesser scale than during the first billion or so years of the Earth’s history. Suppose for the moment that a certain amount of interstellar ‘dust’, some of it organic, finds its way into a comet inhabiting the so-called Oort Cloud situated beyond the orbit of Pluto. Incredibly, there are an estimated billion or more such comets on highly eccentric orbits and a few enter the inner reaches of the solar system each year.  Near the Sun much of the comet melts, ejecting millions of tons of incandescent debris into space and the Earth, like the other planets, cannot avoid ploughing through this cosmic muck. So much is fact. But can any organic material make it to ground level without being burned up or crushed ? If the answer is no, there is no point in discussing the diseases from space theory. However, it seems that bacteria and viruses, especially if protected by some sort of coating, can enter the Earth’s atmosphere without burning up if they come in at an oblique angle. H & W have calculated that “to fit the heating requirement, according to our criteria bacteria are about as big as they can possibly be”. If a bacterium exceeds 1 micron in length it must, according to H & W, be rod-shaped, i.e. what we term a ‘bacillus’. (Yersinia pestis is rod-shaped incidentally). Small particles will be wafted this way and that by air currents or descend inside raindrops or snowflakes. Have any micro-organisms of suspected cometary origin been identified? This is difficult to establish since there is always the possibility of terrestrial contamination but high resistance to ultra-violet radiation would suggest an extra-terrestrial origin. Again various claims have been made, for example by Wainwright, Shivaji et al. and  one new bacterial species culled from the stratosphere has even been named Janibacter hoylei.sp.nov. !

Tell-tale signs of cosmic origin

What characteristics of epidemics/pandemics does official epidemiology have difficulty in explaining? Or, to put things the other way round, supposing for a moment that pathogens can and do arrive from outer space, what special features would we expect to find in the consequent epidemics ?  Basically, the following : 1. We would expect an epidemic/pandemic with an extra-terrestrial origin to be unusually severe because the immune systems of potential hosts would be taken unawares; 2. We would expect very rapid spread since the pathogens would not originally be dependent on human or animal vectors (would rain down on people from the air); 3. We would expect a very wide but somewhat patchy distribution since the pathogens would be taken here and there by air currents; 4. We would expect the attack to be ‘one-off” since only after several outbreaks would a new disease be able to establish itself with a permanent terrestrial focus − to begin with it would most likely be too lethal and kill off potential hosts.

So, are there any epidemics or pandemics that fit the bill? Yes, I can think of several candidates at once, the Vth century Plague of Athens (1, 2 and 4); the Plague of Justinian  (1, 2, 3 and 4); the ‘Sweats’ of the Reformation period (1, 2 and 4); and the 1917-18 outbreak of Spanish Flu (1, 2, 3 and 4). Unfortunately, almost all outbreaks of disease prior to the 19th century are poorly documented so this only leaves the 1917-18 Spanish Flu Pandemic on which H & W concentrate in their book (along with the Common Cold). Since the Spanish Flu killed rather more people than WWI worldwide − estimates vary from 26 million to 50 million deaths − there is no doubt about (1), the severity. Also, because the influenza virus is constantly mutating, it generally manages to keep ahead of the human immune system : each wave of infection is thus essentially new even if given the same general name. So Spanish Flu passes on 4, and also qualifies on 2 and 3.  .         However,  Spanish flu had the benefits of (from its point of view) modern transportation systems and is known to have been passed on by person to person contact (especially by sneezing). However, “The lethal second wave [of Spanish Flu] involved almost the entire world over a very short space of time…. Its epidemiological behaviour was most unusual. Although person-to-person spread occurred in local areas, the disease appeared on the same day in widely separated parts of the world on the one hand, but took days to weeks to spread over relatively short distances. It was detected in Boston and Bombay on the same day, but took three weeks to reach New York City, despite the fact there was considerable travel between the two cities….”       Who wrote the above − Hoyle and Wickramasinghe? In fact, not. The author is a certain Dr. Louis Weinstein cited by H & W and presumably a contemporaryof the pandemic. Likewise, H & W cite Professor Magrassi commenting on the 1948 influenza epidemic  “We were able to verify….the appearance of influenza in shepherds who were living for a long time alone, in solitary open country far from any inhabited centre; this occurred absolutely contemporaneously with the appearance of influenza in the nearest inhabited centre”.       It is on the basis of this kind of evidence, along with detailed maps showing the spread and distribution, that H & W make their case for extra-terrestrial origin. But everything they say about the Spanish Flu pandemic a fortiori applies to the best candidate of the lot, at least on counts (1, 2 and 3),  namely the Black Death itself.

Did the Black Death  come from Space?

H & W only devote five pages of their well-documented book to the Black Death and the treatment is sketchy indeed. When H & W were writing (late nineteen-seventies) the official view was that the Black Death was undoubtedly bubonic plague and that it was spread about by rats : even so learned an author as Shrewsbury does not for a moment question the received wisdom though he does state that the quantity of rats required to get such a pandemic going would be enormous. H & W also assume that the Plague of Justinian and the Black Death were caused by the same pathogen, an assumption Dr Twigg and others have questioned. H & W do, however make one or two valid points. They rightly ridicule the idea of an army of rats advancing like killer ants across most of Europe infecting all and sundry as they march. But, still keeping within the rat/bubonic plague schema, they point out that, if the pestilence was spread about by ship, at least to begin with, we would expect it to systematically spread inland from seaports, something they claim is not the case if we examine the evidence. For example, they cite the testimony of Carbonell, archivist to the Court of Aragon, who reports that the Black Death “began in Aragon, not at the Mediterranean coast or at the eastern frontier, but in the western inland city of Ternel.”        However, we have to distinguish between evidence that the Black Death was propagated by air (which I certainly believe) from the belief that it came from outer space in the first place. H & W emphasize the very extensive but strangely patchy distribution of Black Death mortality: while it attained remote hamlets and monasteries it spared Milan and Nuremburg almost completely. But again this is evidence for airborne dissemination rather than proof of extra-terrestrial origin. Dr Twigg has also pointed out to me that  a vast quantity of bacteria would be required to start the pandemic going in the manner H & W suggest. The Japanese experimented with bubonic plague as a biological weapon and dropped 36 kilos of bubonic plague infested fleas. Seemingly only 7,000 humans died, a statistic that was acquired fifty years later and so was more likely to have been amplified than reduced. Serious though this must have been for the unwilling recipients of this Japanese manna from heaven, this is not a fantastic death toll. And one would expect dropping infected fleas to be a more efficient method of spreading the disease than simply having bacteria drifting down spasmodically.

Conclusion that there is no conclusion

So where does that leave us? As far as I am concerned, I would say that Hoyle and Wickramasinghe have made  a fair case for the Black Death coming from outer space given the extreme severity, rapid spread and extended but patchy distribution of the pandemic, the worst in human history. As to (4), whether the Black Death was a ‘one-off’ outbreak that failed to establish itself or not, this depends on whether one considers that subsequent outbreaks during succeeding centuries were, or were not, the same disease. The jury is not out on this topic and both sides have made valid points. But there is no doubt that ‘plague’, whatever it was, suddenly and mysteriously disappeared from Europe in the early eighteenth century never to return apart from a few spasmodic 20th century cases. But I am not sure that a supposed extra-terrestrial origin has any particular bearing on this circumstance.
More specifically, I do not feel that H & W have said anything to shake my personal conviction that the Black Death was not bubonic plague. If the Black Death was plague and came from space, this suggests that the pandemic started off as the pneumonic variety since human beings would absorb it directly from the air, or from fresh water. It would subsequently pass from human beings to rats and the bubonic variety would dominate and the ‘normal’ scenario develop from then on. Now, an initial outbreak of bubonic plague amongst rodents can spread to humans and become a predominantly pneumonic outbreak, since this is what happened in Manchuria in 1910, but I do not know of any cases of an initial pneumonic epidemic giving rise to bubonic plague. Moreover, supposing for the moment the Black Death was plague, it is not possible that the outbreak was exclusively pneumonic since buboes do not have time to form and we have plenty of contemporary medieval descriptions of buboes, whatever it was that caused them. H & W’s suggestion that plague came from above does not help us to understand the spread of the 14th century pandemic, rather the reverse. It may well be that the cause of the Black Death, whatever it was, did come from space but this does not advance us in understanding what the disease was and how it propagated. Although H & W’s books have made me a likely convert to the general theory of panspermia, I do not feel they have brought us any closer to understanding the Black Death which remains as much of an enigma as ever.            SH 12/10/14

Note 1  According to the Gnostics, the universe was not deliberately created by an omnipotent God but was the result of a cosmic accident with tragic consequences, i.e. was the result of Chance rather than Necessity. They identify God with ‘the Light’ and, in one version, relate how Sophia, the ancestress of humanity, ‘fell’ from a domain of light into a dark, cold and empty universe. Some ‘seeds of light’ end up on the Earth which is ringed by hostile powers (archons) who prevent those who have become aware of their true nature from returning to their place of birth. This schema is really quite close to what we, and especially H & W, currently believe to be the case. It would seem that all the heavier elements including carbon and oxygen were created by nuclear fusion in the heart of stars and were subsequently disseminated throughout the universe in a supernova explosion. Any material ejected would certainly have found itself in a cold, dark and hostile world. Also, since our bodies are made of carbon, hydrogen and oxygen, we are indeed “stardust”. And if Hoyle and Wickramasinghe are right and the first organisms formed in space, we are aliens or the progeny of aliens since the Earth is not humanity’s place of birth.

Note 2 Quoted by Paul Davies in The Origin of Life (p. 125)

Note 3 From Hoyle & Wickramasinghe, Life Cloud (1978). The original schema given in this book and Diseases from Space (1979) goes something like this :

(1) The cycle starts with outflows of gaseous material from the surfaces of stars;
(2) High-density clouds give rise to ‘dust’, “solid particles with dimensions comparable to the wavelength of visible light”(H & W)
(3) Under compression, organic molecules present in the gas clouds “condense in solid form onto the dust grains” (H & W);
(4) In particular formaldehyde (H2CO), which is “one of the commonest organic molecules actually found by actual observation in interstellar space” condenses onto grains and a process of polymerization is induced by cosmic rays;
(5) Sugars and polysaccharides form — and “it has been shown by C. Ponnamperuma that this can happen when formaldehyde is exposed to ultra-violet radiation”;
(6) All of the basic building blocks of life are formed in a similar way and are transported randomly around the galaxy by comets;
(7) Primitive living organisms evolve inside some comets;
(8) One or two comets are drawn within the inner solar system and, on partially melting, deposit clouds of living material some of which falls onto the Earth.

Wickramasinghe has  subsequently extended this model to one where “the genetic products of evolution on a planet like the Earth were mixed on a galactic scale with products of local evolution on other planets elsewhere” (from the paper on DNA sequencing mentioned earlier).

Note 4   At first sight it might seem that Hoyle and Wickramasinghe have not answered the problem of the origins of life but have simply shelved it by situating it somewhere else. Their reply would be that, firstly, rather more suitable environments for the development of life than the early Earth have certainly existed, and, secondly, given the vast number of galaxies and the age of the universe (between 14 and 15 billion years) even such an improbable event as the emergence of microbial life might conceivably have occurred (and apparently did). The point is that, given the cosmic circulation system they propose, life need only occur once somewhere for it to eventually reach practically everywhere (though it would of course not catch on equally well everywhere). And this is assuming the Big Bang scenario. If we assume Hoyle’s modified Steady State model, life has always existed and always will.  



Napoleon Buonaparte : Case Study in Eventrics

“There is a tide in the affairs of men                Which taken in the flood, leads on to fortune”

                                         Shakespeare, Julius Caesar

 Eventrics, a term I have coined, is the theory of events and their interactions. Up to now, I have almost entirely given my attention to the ‘micro’ end of Eventrics, that is to Ultimate Event Theory, an ‘ultimate event’ being the smallest possible event, roughly the equivalent of an atom or elementary particle. But it is now time to turn to ‘macro-Eventrics’ and, in particular, human power politics. Any principles that underlie massive human-directed complexes of events have, on the face of it, little or nothing to do with the sort of things I have been discussing up to now [on the website] ─ but that is just as true of matter-based physics when we shift from the world of the electron to the world of matter in bulk. As a disbeliever in continuity, I ought to be prepared for such a difference, but I would never have expected it to be so large. It is notoriously difficult to say exactly what this extra ingredient is, which is why reductionist theories have, in the last two hundred years or so, decisively gained the upper hand over ‘vitalist’ or ‘system’ theories. For the moment, the question of how and at what exact scale groups of causally bonded ultimate events start behaving in a qualitatively different manner from their individual components will be laid aside. Chief features of ‘power’ event-chains  In the last post I mentioned a few features of power politics viewed from the standpoint of Eventrics and, in particular, enunciated the basic doctrine that “it is events, not human beings that drive history”. I stressed the importance of a so-called ‘tipping point’ or ‘moment of opportunity’ in the fortunes of famous individuals. Persons become powerful, so I argued, not because they have outstanding intelligence, looks or charm ─ though clearly such things are assets ─ but because they (1) “fit the situation they find themselves in” and (2) because they seize with both hands the passing opportunity that presents itself (if it presents itself). I also advanced the notion that the recommended way to seize power and hold it is based on two, and essentially only two items, which are summed up in the codeword used by the US for the invasion of Panama : “Shock and Awe”. Descending the stairs immediately after putting this post on the Internet, my eye was drawn to a battered second-hand book on Napoleon (Napoleon by Paul Johnson) that I remembered only vaguely (Note 1). I opened it and came across the following passage that I had marked in red in the margin : “Victor Hugo, a child of one of Bonaparte’s generals, was later to write: Nothing is more powerful than an idea whose time has come. It is equally true to say : No one is more fortunate than a man whose time has come. Bonaparte was thus favoured by fortune and the timing of the parabola, and he compounded his luck by the alacrity and decision with which he snatched at opportunities as they arose”. Paul Johnson, Napoleon   Exactement, c’est ça. Certainly, the author would seem to be wholly in agreement with the ‘First and Second Principles of Eventrics’. I then wondered how some of the other general principles I tentatively outlined applied to Napoleon. Did he have his ‘moment of opportunity’? Did he apply “Shock and Awe” as his principal methods? In fact, yes, on both counts but first let us enquire a little more into the thesis that it is not the man who commands events but rather the events that offer the opportunity to the man. This is not quite the same thing as saying a successful person is ‘lucky’, though as a matter of fact a surprising number of very successful people do say this, and not out of modesty. Three Dictators If we exclude Russia as being somewhat out on its own, and thus Stalin, the three most powerful non-elected individuals in Western history are Cromwell, Napoleon and Hitler. It is worthwhile examining their backgrounds carefully. None came from a rich, well-educated, aristocratic background ─ but none of them came from a working-class background either (Note 1). Oliver Cromwell, though distantly related to Henry VIII’s all-powerful minister Thomas Cromwell, came from the ‘lower gentry’ and even for a while apparently worked his own land. He did attend Oxford for one year but made no sort of mark there. More to the point, he had absolutely no formal military training, perhaps a blessing in disguise since it forced him to improvise and innovate. As for Hitler, he was the son of an Austrian Customs Official and had at least enough education to be able to present samples of his work to the Viennese School of Architecture (which twice refused him). Bonaparte’s family were small-time impoverished Corsican gentry turned lawyers “just rich enough to own their own house and garden and employ servants” as Johnson puts it. Coming from the lower gentry or the ‘upwardly mobile’ lower middle class can actually be an advantage if you have your eye on the heights : such persons have enough of a leg up to obtain one or two useful contacts and a minimum of education and professional training  — but not enough to spare them the titanic effort needed if they want to seriously improve their condition.

The Young Napoleon  

Napoleon JPEGOf the three ‘dictators’ Napoleon was without a doubt the most talented in the ‘normal’ sense of the word. He had outstanding powers of concentration and application and a memory for “facts and locations” that never ceased to astonish people; he was a better mathematician than any Western ruler I can think of and such a good map-reader that he would be considered a ‘genius’ if we treated cartography on a level with, say, astronomy . At school he was not quite a prodigy ─ real prodigies rarely achieve anything in later life ─ but he was not far short of being one. Whereas the military training at the Ecole Militaire, Paris, usually took two or three years, Napoleon passed all his exams in a single year and qualified as a 2nd Lieutenant at the ripe age of 16. His examiner in mathematics was the world-famous mathematician and astronomer, Laplace.
So, what would Buonaparte have been in another time and place? There have been extremely few eras in history when talent alone could win out over entrenched interests and tradition. All three of our ‘dictators’ came to power in extremely uncertain times, Cromwell during the English Civil War, Hitler during the chaotic post-war German Weimar Republic and Napoleon himself emerged from obscurity after the most famous revolution of all time. Even so, Napoleon, a ‘provincial’ with a Corsican accent and an obscure titre de noblesse that his fellow students didn’t take seriously, and with no family money behind him, nearly missed the boat since most of the best places were already filled by the time he hit Paris. Under the Directory, most important appointments were controlled by a self-serving clique that ruled France from the centre of Paris, and the ambitious young Buonaparte had little direct access to this circle. At one point he thought of offering his services to the Sultan or emigrating to India where he might well have been a rather less successful Clive ─ less successful only because France did not bother so much about India as England did.
My conclusion is that, in another time and place, Buonaparte would certainly have been someone, but equally certainly he would not have been Napoleon.

A Strange Combination of Circumstances” 
As countless historians have pointed out, had Napoleon been born a decade or so earlier when his native Corsica was owned by Genoa, he would not have been a French citizen at all and so would not have qualified to become a boursier (paid student) first at Brienne and later at the Ecole Militaire in Paris. The teaching seems to have been pretty good and by a second stroke of luck, the young officer shortly after receiving his commission, was assigned to an artillery regiment commanded by Baron Duteil, “perhaps the most distinguished gunner in the French army” (Marshall-Cornwall, Napoleon as Military Commander). The Baron was extremely impressed by the cadet officer, who had not yet been under fire, and helped him as much as he could. And the scarcely credible slackness of a young officer’s life under the ancien régime (when there wasn’t actually a war on) meant that the young Napoleon had plenty of time to supplement his formal education with intensive personal study, not just military theory but also politics and ancient history (Note 2).
After the revolution, virtually all the top officers went over to the royalist side so the fledgling republic needed all the trained soldiers it could find and was ready to promote them accordingly. Nonetheless, Napoleon very nearly squandered the chance of a lifetime because he got embroiled in the struggle for Corsican Independence, changing sides more than once, until he finally opted for Revolutionary France. But then, while inspecting the coastal defences of the South of France he had three amazing strokes of luck. (1) The General in charge of the forces near Toulon, Carteaux, was incompetent and soon to be relieved of his functions (2) Carteaux’s artillery commander, Dugommier was badly wounded and (3) Napoleon ‘happened’ to come across a certain Saliceti, an old Corsican friend of the family, now a leading politician in the Paris Convention. Saliceti arranged for the promising but still relatively inexperienced officer, scarcely out of his teens, to be put in charge of the artillery for the relief of Toulon. As Marshall-Cornwall says, “It was a strange combination of circumstances”.

First Moment of Opportunity : Awe
Toulon was the first and most important ‘tipping point’ in Napoleon’s career and though it was ‘Fortune’ that gave him the golden opportunity, it was Napoleon who seized it firmly with both hands and never let it go. The siege of Toulon, more correctly the attack on the forts and batteries surrounding Toulon, was an impeccably executed manoeuvre conducted largely according to plans drawn up by Napoleon himself and enthusiastically endorsed by the new commander, du Teil, the brother of Napoleon’s artillery mentor (another amazing stroke of luck). Napoleon himself took part in the final assault on the key position, Fort Mulgrave, and was wounded by a bayonet. His commander du Teil sent a glowing report to the War Minister Words fail me to describe Buonaparte’s merits. He has great knowledge and as much intelligence and courage, and that is only a faint outline of the qualities of this rare officer”.
        Toulon was, militarily speaking, an awesome performance and at the age of 24 the young artillery officer found himself promoted to général de brigade ( Brigadier) skipping all the intermediary ranks including Colonel. This could surely never have happened in any national army in the world except perhaps during the American War of Independence. Shortly before the successful conclusion of the siege, Napoleon was brought to the notice of a ‘political commissar’ ─ one feels oneself already in the 20th century ─ sent by the Paris Convention to scout around for promising talent, but doubtless also to check on people’s political correctness. The person in question was a Royalist officer turned Republican, Paul Barras. This remarkable man was to play a key role in Napoleon’s life since he later downloaded onto him an attractive but aging mistress with bad teeth, Josephine de Beauharnais, and, more important still, provided Napoleon with his first chance to show his political mettle. It is well to remember that it was Barras that spotted Napoleon and not the reverse, and that Napoleon came to his notice not through social contacts but by his actions. Although Barras was an opportunist who wanted to use Napoleon for his own purposes, the other senior figures, the two du Teils and Napoleon’s new superior General Dugommier, all war-hardened veterans, seem to have been literally spell-bound by the young officer, somewhat as Beauregard was spell-bound by Jeanne d’Arc.

Second Moment of Opportunity : Shock
I mentioned in the last post that the recipe for power is Shock & Awe (not necessarily in that order). Occasionally, figures achieve eminence without the first element but they are almost always religious or artistic figures, not political or military ones. Machiavelli is quite adamant about the importance of Shock and advises the would-be usurper to get this part over with as quickly and decisively as possible : “If you take control of a state, you should make a list of all the crimes you have to commit and do them all at once. He who acts otherwise, either out of squeamishness or out of bad judgment, has to hold a bloody knife in his hand all the time. (…) Do all the harm you must at one and the same time, that way the full extent of it will be noticed, and it will give least offence” (Note 3
        We do not know at what point Napoleon decided he wanted not only military but political power as well. Actually, he did not have a lot of choice. While the chaotic aftermath of the French Revolution gave able young officers like Napoleon their chance, it also made them extremely vulnerable to the vicissitudes of party politics. After such a brilliant start Napoleon was briefly imprisoned when the Jacobins were guillotined since he had been on good terms with the younger Robespierre. The ever ready Corsican Saliceti came to his aid, arguing that France needed officers like Napoleon ─ but from then on he was regarded by the authorities with some distrust, though returned to his duties. After the collapse of the first attempt to invade Italy (with plans partly drawn up by Napoleon himself), Napoleon must have felt that his promising career had been nipped in the bud. There he was, poor, regarded with some suspicion at Paris and despite his striking looks, gauche and unsuccessful with women.
But Barras was now the leading figure of the Directory. This man, even more than Napoleon in a sense, was an absolute master of what I call Eventrics since, incredibly, while starting off as a Royalist officer, he went through all the vicissitudes of the Revolution unscathed, changing sides exactly at the right time and like a political Soros always backing the winner. In 1795 Napoleon was called to the bureau topographique (sort of Planning Office) in Paris. The political situation was extremely serious : the poorer population of Paris, feeling that the revolution had been snatched out of their hands by a lot of devious politicians and currency speculators, were getting ready for the third stage of the Revolution. Barras was granted full powers to restore order while the other members of the new government barricaded themselves in the Tuileries. Napoleon’s job was to quell the revolt. According to Johnson, on 13 vendémiaire (5 October) about 30,000 malcontents (??), many of them armed, rampaged through the centre of Paris. This sounds like an enormous number of people given the smaller populations at the time and much of Paris was an ideal battleground for urban guerrilla ─ as parts of it remained right up to the ‘student revolution’ of May 1968.
It is not clear whether Buonaparte seized this second opportunity to distinguish himself because of ambition, or because of conviction (most likely both). Politically, Napoleon was what we would today consider ‘Centre-Left’. He was sincere in his dislike of the ancient régime, opposed to the power of the Catholic Church, believed everyone should be equal before the law and was an active patron of the arts and sciences. But, like all other ‘middle-class’ people at the time, he would have been horrified by the idea of giving power to ‘the mob’ (Note 3).
Buonaparte applied the Machiavellian principles to the letter. He realized that in hand-to-hand fighting the rebels, even if poorly armed, would probably get the upper hand by sheer weight of numbers. His plan, then, was to lure the rioters away from the lethal alleyways of much of central Paris into an open space, of which there were not so many then, where he could unleash his artillery on them. Fortunately for him, the Tuileries, siege of the government and target of the populace’s anger, did have some open space around it. Johnson goes so far as to suggest that Napoleon deliberately chose ‘grapeshot’ rather than balls or shells because “it scattered over a wide area, tending to produce a lot of blood” but maiming rather than killing its victims. If this is the case, Buonaparte possibly did the ‘right thing’ ─ or so at any rate Machiavelli would have said ─ since it was more politically expedient (and even more humane) to frighten once and for all than to kill. A heavy initial death toll after a massed charge would have enraged the assailants and made them even more desperate, thus more dangerous. As it was, the operation went off as successfully as the raising of the siege of Toulon : the mob recoiled, bloodied and terrified out of their wits by the noise of the big guns at point-blank range, and never got together in such numbers again until the July Revolution of 1830 by which time Napoleon was long dead.

A classic case  Napoleon’s career is almost too pat as a study in Eventrics power politics. First, an ideal situation to step into, two ‘moments of opportunity’, one military and one political, a steady ascent to absolute power, finally decline due to overconfidence and unnecessary risk-taking (invasion of Russia). When the tide of events left him stranded, his dash and mastery changed to bluster and obstinacy. Napoleon could easily have got a better deal for himself, and certainly for France, if he had accepted the Allied offers of returning France to its 1799 or 1792 frontiers instead of fighting on against Allied forces that outnumbered him eight or ten to one. And most historians think that, even if he had won the Battle of Waterloo after his return from Elba (which he nearly did), he could never have remained in power. Nothing particularly surprising here from the point of view of ‘Eventrics’, simply the trap of believing yourself to command events when they always, at the end of the day, control you. Byron apparently thought Napoleon should have died fighting and certainly that would have been better for his posthumous image. Hitler committed suicide on the advice of Goebbels in order precisely to “maintain the Fuhrer legend” which was judged to be more important than the man himself.     SH 24/3/14  

Note 1 Surprisingly, Thomas Cromwell, Henry VIII’s (for a while) all-powerful minister, was the son of a Putney blacksmith. But Thomas Cromwell’s position was always precarious and he did not last long. Henry VIII put into practice Machiavelli’s golden rule of getting someone to do the dirty work and, then, when his services were no longer needed, getting rid of him, thus earning the gratitude of the common people.

Note 3 “Apart from his service duties, Buonaparte plunged into an intensive course of self-education, devouring in particular books on military and political history. In order to train     his memory, he wrote out a preface for every book he read, and these voluminous digests still survive; they cover a wide range of subjects…”          Marshall-Cornwall, Napoleon as Military Commander p. 18  

Note 3 The  quotation is form Machiavelli, The Prince ch. VIII (edited and translated David Wootton)  
Machiavelli praises Cesare Borgia for putting Remiro d’Orco, “a man both cruel and efficient” in charge of the Romagna. “D’Orco in short order established peace and unity and acquired immense authority. At that point the duke decided such unchecked power as no longer necessary, for he feared people might come to hate it. (…) In order to purge the ill-will of the people and win them completely over to him, he [Cesare Borgia] wanted to make it clear that, if there had been any cruelty, he was not responsible for it and that his hard-hearted minister was to blame. One morning, in the town square of Cesena, he had Remiro d’Orco’s corpse laid out in two pieces, with a chopping board and a bloody knife beside it. This ferocious sight made the people of the Romagna simultaneously happy and dumbfounded.” Machiavelli,  The Prince ch. 7 translated Wootton  

Note 4 Today, at a safe distance of two centuries, one tends to feel sympathetic to the rioters and, as a socialist and a romantic, I used at one time to think that “the people” were automatically in the right especially when attacked by the military. However, I hardly think much good would have come of this popular uprising : there would just have been more pointless bloodshed and general chaos. In effect, the ‘Third Revolution’ was postponed until the 1871 Paris Commune. In this case grape-shot was not enough : some 22,000 people, mainly civilians, were killed in a single week, the notorious ‘semaine de sang’ 21-28 May 1871.                              

Reappearance Rates and Ultimate Event Theory

 [Note :   This post is taken from the website where the basic ideas are explained in previous posts.]

Although, in modern physics,  many elementary particles are extremely short-lived, others such as protons are virtually immortal. But either way, a particle, while it does exist, is assumed to be continuously existing. And solid objects such as we see all around us like rocks and hills, are also assumed to be ‘continuously existing’ even though they may undergo gradual changes in internal composition. Since solid objects and even elementary particles don’t appear, disappear and re-appear, they don’t have a ‘re-appearance rate ’ ─ they’re always there when they are there, so to speak.
However, in UET the ‘natural’ tendency is for everything to flash in and out of existence and virtually all  ultimate events disappear for ever after a single appearance leaving a trace that would, at best, show up as a sort of faint background ‘noise’ or ‘flicker of existence’. All apparently solid objects are, according to the UET paradigm, conglomerates of repeating ultimate events that are bonded together ‘laterally’, i.e. within  the same ksana, and also ‘vertically’, i.e. from one ksana to the next (since otherwise they would not show up again ever). A few ultimate events, those that have acquired persistence ─ we shall not for the moment ask how and why they acquire this property ─ are able to bring about, i.e. cause, their own re-appearance : in such a case we have an event-chain which is, by definition,  a causally bonded sequence of ultimate events.
But how often do the constituent events of an event-chain re-appear?  Taking the simplest case of an event-chain composed of a single repeating ultimate event, are we to suppose that this event repeats at every single ksana (‘moment’ if you like)? There is on the face of it no particular reason why this should be so and many reasons why this would seem to be very unlikely.    

The Principle of Spatio-Temporal Continuity 

Newtonian physics, likewise 18th and 19th century rationalism generally, assumes what I have referred to elsewhere as the Postulate of Spatio-temporal Continuity. This postulate or principle, though rarely explicitly  stated in philosophic or scientific works,  is actually one of the most important of the ideas associated with the Enlightenment and thus with the entire subsequent intellectual development of Western society. In its simplest form, the principle says that an event occurring here, at a particular spot in Space-Time (to use the current term), cannot have an effect there, at a spot some distance away without having effects at all (or at least most?/ some?) intermediate spots. The original event sets up a chain reaction and a frequent image used is that of a whole row of upright dominoes falling over one by one once the first has been pushed over. This is essentially how Newtonian physics views the action of a force on a body or system of bodies, whether the force in question is a contact force (push/pull) or a force acting at a distance like gravity.
As we envisage things today, a blow affects a solid object by making the intermolecular distances of the surface atoms contract a little and they pass on this effect to neighbouring molecules which in turn affect nearby objects they are in contact with or exert an increased pressure on the atmosphere,  and so on. Moreover, although this aspect of the question is glossed over in Newtonian (and even modern) physics, each transmission of the original impulse  ‘takes time’ : the re-action is never instantaneous (except possibly in the case of gravity) but comes ‘a moment later’, more precisely at least one ksana later. This whole issue will be discussed in more detail later, but, within the context of the present discussion, the point to bear in mind is that,  according to Newtonian physics and rationalistic thought generally, there can be no leap-frogging with space and time. Indeed, it was because of the Principle of Spatio-temporal Continuity that most European scientists rejected out of hand Newton’s theory of universal attraction since, as Newton admitted, there seemed to be no way that a solid body such as  the Earth could affect another solid body such as the Moon thousands  of kilometres with nothing in between except ‘empty space’.   Even as late as the mid 19th century, Maxwell valiantly attempted to give a mechanical explanation of his own theory of electro-magnetism, and he did this essentially because of the widespread rock-hard belief in the principle of spatio-temporal continuity.
The principle, innocuous  though it may sound, has also had  extremely important social and political implications since, amongst other things, it led to the repeal of laws against witchcraft in the ‘advanced’ countries ─ the new Legislative Assembly in France shortly after the revolution specifically abolished all penalties for ‘imaginary’ crimes and that included witchcraft. Why was witchcraft considered to be an ‘imaginary crime’? Essentially because it  offended against the Principle of Spatio-Temporal Continuity. The French revolutionaries who drew the statue of Reason through the streets of Paris and made Her their goddess, considered it impossible to cause someone’s death miles away simply by thinking ill of them or saying Abracadabra. Whether the accused ‘confessed’ to having brought about someone’s death in this way, or even sincerely believed it, was irrelevant : no one had the power to disobey the Principle of Spatio-Temporal Continuity.
The Principle got somewhat muddied  when science had to deal with electro-magnetism ─ Does an impulse travel through all possible intermediary positions in an electro-magnetic field? ─ but it was still very much in force in 1905 when Einstein formulated the Theory of Special Relativity. For Einstein deduced from his basic assumptions that one could not ‘send a message’ faster than the speed of light and that, in consequence,  this limited the speed of propagation of causality. If I am too far away from someone else I simply cannot cause this person’s death at that particular time and that is that. The Principle ran into trouble, of course,  with the advent of Quantum Mechanics but it remains deeply entrenched in our way of thinking about the world which is why alibis are so important in law, to take but one example. And it is precisely because Quantum Mechanics appears to violate the principle that QM is so worrisome and the chief reason why some of the scientists who helped to develop the theory such as Einstein himself, and even Schrodinger, were never happy with  it. As Einstein put it, Quantum Mechanics involved “spooky action at a distance” ─ exactly the same objection that the Cartesians had made to Newton.
So, do I propose to take the principle over into UET? The short answer is, no. If I did take over the principle, it would mean that, in every bona fide event-chain, an ultimate event would make an appearance at every single ‘moment’ (ksana), and I could see in advance that there were serious problems ahead if I assumed this : certain regions of the Locality would soon get hopelessly clogged up with colliding event-chains. Also, if all the possible positions in all ‘normal’ event-sequences were occupied, there would be little point in having a theory of events at all, since, to all intents and purposes, all event-chains would behave as if they were solid objects and one might as well just stick to normal physics. One of the main  reasons for elaborating a theory of events in the first place was my deep-rooted conviction ─ intuition if you like ─ that physical reality is discontinuous and that there are gaps between ksanas ─ or at least that there could be gaps given certain conditions. In the theory I eventually roughed out, or am in the process of roughing out, both spatio-temporal continuity and infinity are absent and will remain prohibited.
But how does all this square with my deduction (from UET hypotheses) that the maximum propagation rate of causality is a single grid-position per ksana, s0/t0, where s0 is the spatial dimension of an event capsule ‘at rest’ and t0 the ‘rest’ temporal dimension? In UET, what replaces the ‘object-based’ image of a tiny nucleus inside an atom, is the vision of a tiny kernel of fixed extent where every ultimate event occurs embedded in a relatively enormous four-dimensional event capsule. Any causal influence emanates from the kernel and, if it is to ‘recreate’ the original ultimate event a ksana later, it must traverse at least half the ‘length’ (spatial dimesion) of one capsule plus half of the next one, i.e. ½ s0 + ½ s0 = 1 s0 where s0 is the spatial dimension of an event-capsule ‘at rest’ (its normal state). For if the causal influence did not ‘get that far’, it would not be able to bring anything about at all, would be like a messenger who could not reach a destination receding faster than he could run flat out. The runner’s ‘message’, in this case the recreation of a clone of the original ultimate event, would never get delivered and nothing would ever come about at all.
This problem does not occur in normal physics since objects are not conceived as requiring a causal force to stop them disappearing, and, on top of that, ‘space/time’ is assumed to be continuous and infinitely divisible. In UET there are minimal spatial and temporal units (that of the the grid-space and the ksana) and ‘time’ in the UET sense of an endless succession of ksanas, stops for no man or god, not even physicists who are born, live and die successively like everything else. I believe that succession, like causality, is built into the very fabric of physical reality and though there is no such thing as continuous motion, there is and always will be change since, even if nothing else is happening, one ksana is being replaced by another, different, one ─ “the moving finger writes, and, having writ, moves on” (Rubaiyat of Omar Khayyam). Heraclitus said that “No man ever steps into the same river twice”, but a more extreme follower of his disagreed, saying that it was impossible to step into the same river once, which is the Hinayana  Buddhist view. For ‘time’ is not a river that flows at a steady rate (as Newton envisaged it) but a succession of ‘moments’ threaded like beads on an invisible  chain and with minute gaps between the beads.

Limit to unitary re-appearance rate

So, returning to my repeating ultimate event, could the ‘re-creation rate’ of an ultimate event be  greater than the minimal rate of 1 s0/t0 ? Could it, for example, be  2, 3 or 5 spacesper ksana? No. For if and when the ultimate event re-appeared, say  5 ksanas later, the original causal impulse would have covered a distance of 5 s0   ( s0 being the spatial dimension of each capsule) and would have taken 5 ksanas to do  this. Consequently the space/time displacement rate would be the same (but not in this case the individual distances). I note this rate as c* in ‘absolute units’, the UET equivalent of c, since it denotes an upper limit to the propagation of the causal influence (Note 1). For the very continuing existence of anything depends on causality : each ‘object’ that does persist in isolation does so because it is perpetually re-creating itself (Note 2).

But note that it is only the unitary rate, the distance/time ratio taken over a single ksana,  that cannot be less (or more) than one grid-space per ksana or 1 s0/t0 : any fractional (but not irrational) re-appearance rate is perfectly conceivable provided it is spread out over several ksanas. A re-appearance rate of m/n s0/t0  simply means that the ultimate event in question re-appears in an equivalent spatial position on the Locality m times every n ksanas where m/n ≤ 1. And there are all sorts of different ways in which this rate be achieved. For example, a re-appearance rate of 3/5 s0/t0 could be a repeating pattern such as

Reappearance rates 1
















and one pattern could change over into the other either randomly or, alternatively, according to a particular rule.
As one increases the difference between the numerator and the denominator, there are obviously going to be many more possible variations : all this could easily be worked out mathematically using combinatorial analysis. But note that it is the distribution of ™the black and white at matters since, once a re-appearance rhythm has begun, there is no real difference between a ‘vertical’ rate of 0™˜™˜●0● and ˜™˜™™˜™˜™˜™˜●0™˜™˜●0 ™˜™™˜™˜ ˜™˜™ ─ it all depends on where you start counting. Patterns with the same repetition rate only count as different if this difference is recognizable no matter where you start examining the sequence.
Why does all this matter? Because, each time there is a blank line, this means that the ultimate event in question does not make an appearance at all during this ksana, and, if we are dealing with large denominators, this could mean very large gaps indeed in an event chain. Suppose, for example, an event-chain had a re-appearance rate of 4/786. There would only be four appearances (black dots) in a period of 786 ksanas, and there would inevitably be very large blank sections of the Locality when the ultimate event made no appearance.

Lower Limit of re-creation rate 

Since, by definition, everything in UET is finite, there must be a maximum number of possible consecutive gaps  or non-reappearances. For example, if we set the limit at, say, 20 blank lines, or 200, this would mean that, each time this blank period was observed, we could conclude that the event-chain had terminated. This is the UET equivalent  of the Principle of Spatio-Temporal Continuity and effectively excludes phenomena such as an ultimate event in an event-chain making its re-appearance a century later than its first appearance. This limit would have to be estimated on the  basis of experiments since I do not see how a specific value can be derived from theoretical considerations alone. It is tempting to estimate that this value would involve c* or a multiple of c* but this is only a wild guess ─ Nature does not always favour elegance and simplicity.
Such a rule would limit how ‘stretched out’ an event-chain can be temporally and, in reality , there may not after all be a hard and fast general rule  : the maximal extent of the gap could decline exponentially or in accordance with some other function. That is, an abnormally long gap followed by the re-appearance of an event, would decrease the possible upper limit slightly in much the same way as chance associations increase the likelihood of an event-chain forming in the first place. If, say, there was an original limit of a  gap of 20 ksanas, whenever the re-appearance rate had a gap of 19, the limit would be reduced to 19 and so on.
It is important to be clear that we are not talking about the phenomenon of ‘time dilation’ which concerns only the interval between one ksana and the next according to a particular viewpoint. Here, we simply have an event-chain where an ultimate event is repeating at the same spot on the spatial part of the Locality : it is ‘at rest’ and not displacing itself laterally at all. The consequences for other viewpoints would have to be investigated.

Re-appearance Rate as an intrinsic property of an event-chain  

Since Galileo, and subsequently Einstein, it has become customary in physics to distinguish, not between rest and motion, but rather between unaccelerated motion and  accelerated motion. And the category of ‘unaccelerated motion’ includes all possible constant straight-line speeds including zero (rest). It seems, then,  that there is no true distinction to be made between ‘rest’ and motion just so long as the latter is motion in a straight line at a constant displacement rate. This ‘relativisation’ of  motion in effect means that an ‘inertial system’ or a particle at rest within an inertial system does not really have a specific velocity at all, since any estimated velocity is as ‘true’ as any other. So, seemingly, ‘velocity’ is not a property of a single body but only of a system of at least two bodies. This is, in a sense, rather odd) since there can be no doubt that a ‘change of velocity’, an acceleration, really is a feature of a single body (or is it?).
Consider a spaceship which is either completely alone in the universe or sufficiently remote from all massive bodies that it can be considered in isolation. What is its speed? It has none since there is no reference system or body to which its speed can be referred. It is, then, at rest ─ or this is what we must assume if there are no internal signs of acceleration such as plates falling around or rattling doors and so on. If the spaceship is propelling itself forward (or in some direction we call ‘forward’) intermittently by jet propulsion the acceleration will be note by the voyagers inside the ship supposing there are some. Suppose there is no further discharge of chemicals for a while. Is the spaceship now moving at a different and greater velocity than before? Not really. One could I suppose refer the vessel’s new state of motion to the centre of mass of the ejected chemicals but this seems rather artificial especially as they are going to be dispersed. No matter how many times this happens, the ship will not be gaining speed, or so it would appear. On the other hand, the changes in velocity, or accelerations are undoubtedly real since their effects can be observed within the reference frame.
So what to conclude? One could say that ‘acceleration’ has ‘higher reality status’ than simple velocity since it does not depend on a reference point outside the system. ‘Velocity’ is a ‘reality of second order’ whereas acceleration is a ‘reality of first order’. But once again there is a difference between normal physics and UET physics in this respect. Although the distinction between unaccelerated and accelerated motion is taken over into UET (re-baptised ‘regular’ and ‘irregular’ motion), there is in Ultimate Event Theory, but not in contemporary physics, a kind of ‘velocity’ that has nothing to do with any other body whatsoever, namely the event-chain’s re-appearance rate.
When one has spent some time studying Relativity one ends up wondering whether after all “everything is relative” and quite a lot of physicists and philosophers seems to actually believe something not far from this : the universe is evaporating away as we look it and leaving nothing but a trail of unintelligible mathematical formulae. In Quantum Mechanics (as Heisenberg envisaged it anyway) the properties of a particular ‘body’ involve the properties of all the other bodies in the universe, so that there remain very few, if any, intrinsic properties that a body or system can possess. However, in UET, there is a reality safety net. For there are at least two  things that are not relative, since they pertain to the event-chain or event-conglomerate itself whether it is alone in the universe or embedded in a dense network of intersecting event-chains we view as matter. These two things are (1) occurrence and (2) rate of occurrence and both of them are straight numbers, or ratios of integers.
An ultimate event either has occurrence or it does not : there is no such thing as the ‘demi-occurrence’ of an event (though there might be such a thing as a potential event). Every macro event is (by the preliminary postulates of UET) made up of a finite number of ultimate events and every trajectory of every event-conglomerate has an event number associated with it. But this is not all. Every event-chain ─ or at any rate normal or ‘well-behaved’ event-chain ─ has a ‘re-appearance rate’. This ‘re-appearance rate’ may well change considerably during the life span of a particular event-chain, either randomly or following a particular rule, and, more significantly, the ‘re-appearance rates’ of event-conglomerates (particles, solid bodies and so on) can, and almost certainly do, differ considerably from each other. One ‘particle’ might have a re-appearance rate of 4, (i.e. re-appear every fourth ksana) another with the same displacement rate  with respect to the first a rate of 167 and so on. And this would have great implications for collisions between event-chains and event-conglomerates.

Re-appearance rates and collisions 

What happens during a collision? One or more solid bodies are disputing the occupation of territory that lies on their  trajectories. If the two objects miss each other, even narrowly, there is no problem : the objects occupy ‘free’ territory. In UET event conglomerates have two kinds of ‘velocity’, firstly their intrinsic re-appearance rates which may differ considerably, and, secondly, their displacement rate relative to each other. Every event-chain may be considered to be ‘at rest’ with respect to itself, indeed it is hard to see how it could be anything at all if this were not the case. But the relative speed of even unaccelerated event-chains will not usually be zero and is perfectly real since it has observable and often dramatic consequences.
Now, in normal physics, space, time and existence itself is regarded as continuous, so two objects will collide if their trajectories intersect and they will miss each other if their trajectories do not intersect. All this is absolutely clearcut, at least in principle. However, in UET there are two quite different ways in which ‘particles’ (small event conglomerates) can miss each other.
First of all, there is the case when both objects (repeating event-conglomerates) have a 1/1 re-appearance rate, i.e. there is an ultimate event at every ksana in both cases. If object B is both dense and occupies a relatively large region of the Locality at each re-appearance, and the relative speed is low, the chances are that the two objects will collide. For, suppose a relative displacement rate of 2 spaces to the right (or left)  at each ksana and take B to be stationary and A, marked in red, displacing itself two spaces at every ksana.

Reappearance rates 2

Clearly, there is going to be trouble at the  very next ksana.
However, since space/time and existence and everything else (except possibly the Event Locality) is not continuous in UET, if the relative speed of the two objects were a good deal greater, say 7 spaces per 7 ksanas (a rate of 7/7)  the red event-chain might manage to just miss the black object.

This could not happen in a system that assumes the Principle of Spatio-Temporal Continuity : in UET there is  leap-frogging with space and time if you like. For the red event-chain has missed out certain positions on the Locality which, in principle could have been occupied.

But this is not all. A collision could also have been avoided if the red chain had possessed a different re-appearance rate even though it remained a ‘slow’ chain compared to the  black one. For consider a 7/7 re-appearance rate i.e. one appearance every seven ksanas and a displacement rate of two spaces per ksana relative to the black conglomerate taken as being stationary. This would work out to an effective rate of 14 spaces to the right at each appearance ─ more than enough to miss the black event-conglomerate.

Moreover, if we have a repeating event-conglomerate that is very compact, i.e. occupies very few neighbouring grid-spaces at each appearance (at the limit just one), and is also extremely rapid compared to the much larger conglomerates it is likely to come across, this ‘event-particle’ will miss almost everything all the time. In UET it is much more of a problem how a small and ‘rapid’ event-particle can ever collide with anything at all (and thus be perceived) than for a particle to apparently disappear into thin air. When I first came to this rather improbable conclusion I was somewhat startled. But I did not know at the time that neutrinos, which are thought to have a very small mass and to travel nearly at the speed of light, are by far the commonest particles in the universe and, even though millions are passing through my fingers as I write this sentence, they are incredibly difficult to detect because they interact with ordinary ‘matter’ so rarely (Note 3). This, of course, is exactly what I would expect ─ though, on the other hand, it is a mystery why it is so easy to intercept photons and other particles. It is possible that the question of re-appearance rates has something to do with this : clearly neutrinos are not only extremely compact, have very high speed compared to most material objects, but also have an abnormally high re-appearance rate, near to the maximum.
RELATIVITY   Reappeaance Rates Diagram         In the adjacent diagram we have the same angle sin θ = v/c but progressively more extended reappearance rates 1/1; 2/2; 3/3; and so on. The total area taken over n ksanas will be the same but the behaviour of the event-chains will be very different.
I suspect that the question of different re-appearance rates has vast importance in all branches of physics. For it could well be that it is a similarity of re-appearance rates ─ a sort of ‘event resonance’ ─ that draws disparate event chains together and indeed is instrumental in the formation of the very earliest event-chains to emerge from the initial randomness that preceded the Big Bang or similar macro events.
Also, one suspects that collisions of event conglomerates  disturb not only the spread and compactness of the constituent events-chains, likewise their ‘momentums’, but also and more significantly their re-appearance rates. All this is, of course, highly speculative but so was atomic theory prior to the 20th century event though atomism as a physical theory and cultural paradigm goes back to the 4th century BC at least.        SH  29/11/13



Note 1  Compared to the usual 3 × 108 metres/second the unitary  value of s/t0 seems absurdly small. But one must understand that s/t0 is a ratio and that we are dealing with very small units of distance and time. We only perceive large multiples of these units and it is important to bear in mind that s0is a maximum while t0 is a minimum. The actual kernel, where each ultimate event has occurrence, turns out to be s0/c* =  su so in ‘ultimate units’ the upper limit is c* su/t0.  It is nonetheless a surprising and somewhat inexplicable physiological fact that we, as human beings, have a pretty good sense of distance but an incredibly crude sense of time. It is only necessary to pass images at a rate of about eight per second for the brain to interpret the successive in images as a continuum and the film industry is based on this circumstance. Physicists, however, gaily talk of all sorts of important changes happening millionths or billionths of a second and in an ordinary digital watch the quartz crystal is vibrating thousands of times a second (293,000 I believe).

 Note 2  Only Descartes amongst Western thinkers realized there was a problem here and ascribed the power of apparent self-perpetuation to the repeated intervention of God; today, in a secular world, we perforce ascribe it to ‘ natural forces’.
In effect, in UET, everything is pushed one stage back. For Newton and Galileo the  ‘natural’ state of objects was to continue existing in constant straight line motion whereas in UET the ‘natural’ state of ultimate events is to disappear for ever. If anything does persist, this shows there is a force at work. The Buddhists call this all-powerful causal force ‘karma but unfortunately they were only interested in the moral,  as opposed to physical, implications of karmic force otherwise we would probably have had a modern theory of physics centuries earlier than we actually did.

Note 3  “Neutrinos are the commonest particles of all. There are even more of them flying around the cosmos than there are photons (…) About 400 billion neutrinos from the Sun pass through each one of us every second.”  Frank Close, Particle Physics A Very Short Introduction (OUP) p. 41-2 


Power ─ what is power? In physics it is the rate of ‘doing Work’ but this meaning has little or no connection to ‘power’ in the political or social sense.
Power is the capacity to constrain other people to do your bidding whether or not they wish to do so. This sounds pretty negative and indeed power has had a bad sense ever since the Romantics from whom we have never really recovered. Hobbes spent a good deal of his life trying to persuade the ‘powers that be’ of his time, i.e. King and/or Parliament, to make themselves absolute ─ even though he himself was exactly the sort of freewheeling and freethinking individual no absolute ruler would want to have as a citizen. But Hobbes lived through the Civil War which the Romantics didn’t. Prior to the nineteenth century most people of all classes were more afraid of the breakdown or absence of power (‘chaos’, ‘anarchy’) than of ‘abuse of power’: indeed they would find modern attitudes not only misguided but scarcely comprehensible.
If you wish to live in society, there has to be some way of constraining people since otherwise everyone pulls in different directions and nothing gets done. If you don’t believe me, go and spend a few weeks or even days in a situation where no one has power. I have lived in ‘communities’ and they are intolerable for this very reason. What usually happens is that someone soon steps into the power vacuum and he (less often she) is the person who shouts loudest, pushes hardest, is the most unscrupulous and generally the most hateful ─ though sometimes also the most efficient. In more traditional communities it is not so much the more assertive as the ‘older and wiser’ who wield the power, the obvious example being the Quakers. This sounds a lot better but in my experience it isn’t that much of an improvement. People like the Quakers who forego the use of physical force tend to be highly manipulative ─ they have to be ─  and it would be quite wrong to believe that a power structure in the Quakers or the Amish does not exist for it certainly does. In fact no society can exist for more than a month without a power structure, i.e. without someone (whether one or many) holding power.

Necessity of power
So, my thesis is the unoriginal one that some form of power invested in specific  human beings (whether initially elected or not) is inevitable and not necessarily a bad thing. Lord Acton was being extremely silly when he made the endlessly repeated statement “All power corrupts, absolute power corrupts absolutely” with the implication is that it is better to keep away from power altogether. Although I don’t know much about Lord Acton’s life, I can be pretty sure that he didn’t know what it was like to be powerless. One could just as well say, “All lack of power corrupts, absolute powerlessness corrupts absolutely”. It is lack of physical or financial muscle that makes people devious, treacherous, deceitful : one more or less has to be like this to survive. And it is simply not true that ‘absolute power corrupts absolutely’. You can’t get much nearer to absolute power than the position of the Roman Emperor. But Rome produced one or two quite good Emperors, e.g. Augustus himself and Hadrian, also one entirely admirable, indeed saintlike (though woefully ineffective) one, Marcus Aurelius. President Obama has currently more power in his hands than anyone who has ever existed, at least in the  military sense, and although not everyone agrees with his policies not even his enemies have accused him of being corrupt or corrupted by power.

Liberty to Order
One alarming and unexpected aspect of the dynamics of power is that when an existing power structure is overthrown, the ‘order’ that emerges from the usually brief period of chaos is a good deal more restrictive than what preceded it, witness the Commonwealth under Cromwell, Russia under Stalin &c. &c. In the ‘mini-revolution’ of Paris in May 1968, I and one or two others, watched open-mouthed, hardly believing what we were witnessing,  as a single individual, in whom at one stage most of us had full confidence, concentrated all the power of an occupied University faculty into his hands exactly like Robespierre or Stalin. And he did it without striking a blow.
Actually, such a dénouement is virtually inevitable ─ or at any rate  the danger of such a development will always be there. Immediately after a revolution there is usually a counter-attack by the ousted elite, so the revolutionaries find themselves with their backs to the wall. In such a situation, it is survival that counts, not liberty ─ because if you, or the social order you represent, don’t survive, then there won’t be any more liberty either, it will just be ancien régime all over again, only worse. So the revolutionaries enact repressive legislation to protect themselves, legislation which is rarely repealed when things eventually calm down.

Power and Eventrics
Why am I writing a post about power on this site? Because, as a friend has just this very day reminded me, I must beware of giving the impression that ‘Eventrics’, the theory of events and their interactions, only deals with  invisible ‘ultimate events’, equally invisible ‘Event Capsules’ and generally is about as irrelevant to everyday life as nuclear physics. Ultimate Event Theory is the microscopic branch of Eventrics but the theory applies right across the board and it may be that its strength will be in the domain of social thinking and power politics. Just as the physics of matter in bulk is very different from the physics of quarks and electrons, that part of Eventrics that deals with macro-events, i.e. with massive repeating bundles of ultimate events that behave as if they were independent entities, has on the face of it little in common with micro-eventrics (though presumably ultimately grounded in it).
So what has the Theory of Events and their Interactions to say about power? Well, firstly that it is events and their internal dynamism that drive history, not physical forces or even persons. Mechanics, electro-magnetism and so on are completely irrelevant to human power politics and indeed up to a point the less science you know the more successful you are likely to be  as an administrator  or politician. Biology is a little more relevant than physics because of the emphasis on struggle but it is all far too crude and ridiculously reductionist to apply directly to human societies. Human individuals certainly do not strive to acquire power in order to push their genes around more extensively : Casanova pushed his around more effectively than Hitler, Mussolini and Cromwell combined. And the widespread introduction of birth-control in Western societies demonstrates that modern human beings are certainly not under the thumb of their ‘selfish genes’ (as even Dawkins belatedly admits). Nor is this the only example. Just as virtue really is its own reward, at least sometimes, so apparently is the pursuit of power, and indeed at the end of the day so are most things.

Irrelevance of Contemporary Science to Power Politics
More fashionable contemporary ‘sciences’ such as complexity theory do  have something of interest to say about human affairs but their proponents have yet to make any predictions of import that have come true as far as I know. The financial crash of 2008, only anticipated by a handful of actual investors and traders such as Nessim Taleb and Soros (the former even pinpointed where the bubble would start, Fanny Mac and Fanny Mae), makes a mockery of the application of mathematics to economics and indeed of economics in toto as an exact science.
The reason for official science’s impotence when addressing human affairs is very  easy to explain :  almost all living scientists are employed either by universities or by the State. That is, they have never fought it out in the cut-throat world of business nor even, with one or two exceptions, dirtied their hands with investment, have never been under fire on a battlefield or even played poker for money. But it is in business, warfare and gambling that you can detect the ‘laws’ of power inasmuch as there are any, i.e. how to acquire power when you don’t have it and how to keep it when you do. Hitler was an auto-didact dismissed as a buffoon by the Eton and Oxbridge brigade that staffed the Foreign Affairs Department then as now : but he ran rings around them because he had learned his power politics strategy at the bottom, in the hard school of Austrian YMCA Hostels and German beer-halls.

Qualitative ‘Laws of Power’
There are most likely no specific laws of power in the sense that there are ‘laws of motion’ but there are certain recurrent features well worth mentioning. They are ‘qualitative’ rather than ‘quantitative’ but this is as it should be. It is stupid to put numbers on things like fashions and revolutions because it is not the specifics that matter, only the general trend. Indeed, the person who is obsessed with figures is likely to miss the general trend because the actual shapes and sizes don’t look familiar. Rutherford’s much quoted remark that “Qualitative is just poor quantitative” may have its uses in his domain (nuclear physics), but in human affairs it is more a matter of “quantitative is lazy or incompetent qualitative”.

Tipping Points and Momentum
So what noticeable trends are there? One very general feature, which sticks out a mile, is the ‘tipping point’ or ‘critical mass’.  Malcolm Gladwell, a non-scientist and a qualitative rather than quantitative thinker, wrote a justly praised bestseller called The Tipping Point, which demonstrates his sound understanding of the mechanisms at work. A movement, fashion, revolution &c. must seemingly attain a certain point : if it does not attain it, the movement will fail, fade away. If it does attain this point, the movement takes off and it does not take off in a ‘linear’ fashion but in a runaway ‘exponential’ fashion, at least for a while. Anyone who has lived through a period of severe social unrest or revolution knows what I am talking about. My own experience is based on the May 1968 ‘Student Revolution’ in Paris. But much the same goes for a new style in clothes or shoes : indeed fashions have something alarming precisely because they demonstrate power, sudden, naked power which sweeps aside all opposition. The fashion industry is in its way as frightening as the armaments industry and for the same reasons.
OK. There is a ‘tipping point’ (generally only one) and, following it, a consequent sudden burst of momentum : these are the first two items worth signalling. And these two features seem to have very little to do with particular individuals. It is the events themselves that do the work : the events pull the people along, not the reverse. Companies that found they had launched a trend overnight ─ Gladwell cites the Hush Puppies craze ─ were often the first to be surprised by their own success. As for political movements, I know for a fact, since I was part of the milieu, that the French left-wing intelligentsia was staggered out of its wits when a few scuffles in the Sorbonne for some reason turned almost overnight into the longest general strike ever known in a modern industrialized country.

Key Individuals
This general point (that it is not human beings that direct history) needs some qualification, however. There are indeed individuals who unleash a vast movement by a single act but this happens much less often than historians pretend, and usually the result is not at all what was intended. Princeps, the high-school boy who shot the Archduke at Sarajevo and precipitated WWI did have a political agenda of a kind but he neither wished nor intended to cause a European war.

To recap. We already have a few features to look out for. (1) tipping point; (2) sudden, vertiginous take-off when there is a take-off; (3) lack of anyone instigating or controlling the movement but (4) certain individuals who achieve what seems to be impossible by simply ‘moving with the events’.


Today we tend to trace the study of power back to Machiavelli and certainly it would be foolish to downplay his importance. Nonetheless, the historical situation in which Machiavelli worked and thought, Quattrocento Italy, is completely different from the modern world, at any rate what we call the ‘advanced’ modern world. Would-be rulers in Machiavelli’s time acquired power either by being promoted by some clique or by direct annexation and murder. But no 20th century head of an important state acquired power by a coup d’etat : he or she  generally acquired it by the ballot box — and incredibly this even applies to Hitler who obtained the votes of a third of the German population. And though Machiavelli does have some useful things to say about the importance of getting the common people on your side, he has nothing to say about the power of political oratory and the use of symbolism.
Possibly, the sort of brazenness that Machiavelli advocates actually did work in the Italian Quattrocento world of small city-states and condottieri. But even then it would certainly not have worked in any of the larger states. No one who aims at  big power admits duplicity or advocates its use; if you are ambitious, the first person you usually have to convince is yourself and this is no easy task. You have to carry out a sort of self-cheat whereby you simultaneously believe you really are acting for the general good while simultaneously  pursuing a ruthlessly egotistical policy. This is not quite hypocrisy (though perilously close to it): it is rather the Method actor temporarily ‘living the role’ ─ and running the risk of getting caught in his own noose. Indeed it is because Machiavelli has a sort of  basic honesty, and hence integrity, that no clear-sighted upstart ruler would want to give such a man high office ─ he would either be utterly useless or a serious danger because too formidable. And, interestingly, the Medicis did not employ Machiavelli although he was certainly angling to be taken on by them.

The Two Ways to Power
There seem to be two ways to achieve power which are interestingly summed up in the codeword employed by the greatest military power of all time, America, when it invaded Panama : Shock and Awe. (I think that was the codeword but if not it is very apposite.)
Shock and awe are distinct and even to some extent contradictory. By ‘shock’ we should understand showing the enemy, or anyone in fact, that you have the means to do a lot of damage and, crucially, that you are prepared to go the whole way if you have to. It can actually save lives if you make an initial almighty show of force ─ exactly what the US Army did in Panama ─ since the opposition will most likely cave in at once without risking a battle. (This doesn’t always work, however : the bombing raids on civilian targets of both the English and the Germans during WWII seem to have stiffened opposition rather than weakened it.)
Awe has a religious rather than a military sense though the great commanders of the ancient world, Alexander, Caesar, Hannibal, had the sort of aura we associate more with religious leaders. Time and again isolated figures with what we vaguely, but not inaccurately, call ‘charisma’ have suddenly attained enormous power and actually changed the course of history : the obvious example being Joan of Arc. Hitler, having failed to ‘shock’ the country, or even Munich, by holding a revolver to the Governor of Bavaria (literally) and rampaging around the streets with a handful of toughs, was sharp enough to realize that he must turn to awe instead, using his formidable gifts of oratory to obtain power via  the despised ballot-box. Mahomet did fight but no one doubts that it was his prophetic rather than strictly military abilities that returned him against all odds to Mecca.

The Paradox of Christ
What of Christ? It seems clear that there were at the time in Palestine several movements that wished to rid the country of the Romans (even though they were by the standards of the time quite tolerant masters) and to revive the splendours of the House of David. There is some hesitation and a  certain ambivalence in Christ’s answer under interrogation which suggests he had not entirely made up his mind on the crux of the matter, i.e. whether he did or did not intend to establish himself as ‘King of the Jews’. He did not deny the attribution but qualified it by adding “My kingdom is not of this world.” This is a clever answer to give since it was only Christ’s political pretensions that concerned the Romans, represented here by  Pontius Pilate. It is not an entirely satisfactory answer, however. If a ‘kingdom’ is entirely of, or in, ‘another world’, one might justifiably say, “What’s the use of it, then?” Christianity has in fact changed the everyday here-and-now world enormously, in some ways for the better, in some ways not. And Pontius Pilate’s blunt refusal to remove the inscription, “Jesus of Nazareth, the King of the Jews” suggests that Pilate thought the Jews could have done a lot worse than have such a man as ‘king’.
It seems probable that some of Christ’s followers, including one disciple, wanted to nudge Christ into taking up a more openly political stance which, subsequently, it would  have been difficult to draw back from. According to this interpretation, Judas did not betray Christ for money or protection : he tried to bring about an open conflict ─ and he very nearly succeeded since Peter drew his sword and struck off the servant of the High Priest’s ear in the Gethsemane stand-off. But Christ seemingly had by now (after a final moment of intercession and prayer) decided to stick entirely to ‘awe’ as a means of combat with the forces of evil (in which he clearly believed). In a sense, Christ was not so much a victim as a resolute and exceedingly skilful strategist. No one expected him to give in and actually be put to death as a common felon, and for a moment Christ himself seems to have been hoping for a miracle hence the cry “Why, oh why hast Thou forsaken me?” (a quotation from Isaiah incidentally). It has been suggested by certain commentators  that Christ was using ‘goodness’ and the respect and awe it inspires to actually take the ‘Evil One’ by surprise and, as it were, wrong-foot him. Seemingly, there are suggestions of this ‘unorthodox way of combatting evil’ in the writings of the Old Testament prophets which Christ knew off by heart, of course.           And, incredibly, the stratagem worked since Christ’s small band of followers rallied and went from strength to strength whereas the other Jewish would-be Messiahs of the time who really did take up arms against the Romans perished completely ─ and provoked the greatest disaster in Jewish history, the complete destruction of the Temple and the diaspora. Certainly there are moments when ‘awe’ without shock works. Saint  Francis, Fox, the founder of the Quakers, Gandhi and Martin Luther King have all used the ‘awe’ that a certain kind of disinterested goodness inspires to excellent effect. It is, however, a perilous strategy since you have to be prepared to ‘go the whole way’ if necessary, i.e. to die, and the public is not likely to be easily fooled on this point.

“Be as cunning as serpents and as innocent as doves”
The case of Christ is a very interesting case viewed from the standpoint of Eventrics. But before examining it in more detail, may I make it clear that by analysing the behaviour of figures such as Christ or Mahomet in terms of event strategy, no offence to religious people is intended. Eventrics, like all sciences is ethically neutral : it merely  studies, or purports to study what goes on. But as a matter of fact, most great religious leaders had a pretty good grasp of day to day tactics as well. Charisma by itself is not enough, and Christ himself said, “Be as cunning as serpents and as innocent as doves”.
The trouble with the ‘innocent’ is that they are usually completely ineffective, either because they don’t understand Realpolitik or consider it beneath them. But there is actually not a lot of point in being ‘good’ if you don’t actually do any good ─ at any rate from society’s point of view. And there is a way of getting things done which is identical whether you are good or bad. Nor need the ‘good’ person feel himself or herself to be as much at a disadvantage as he usually does. Bad people themselves have weak points : they tend to assume everyone else is as selfish and unscrupulous as they themselves are and in consequence make catastrophic errors of judgement. The really dangerous bad person is the one who understands ordinary people’s wish to be ‘good’, at least occasionally, ‘good’ in the sense of unselfish, ready to devote oneself to a higher cause and so on. Hitler was able to simultaneously play on people’s baser instincts but also on their better instincts, their desire not only to be of service to their country but to sacrifice themselves for it (Note 1).

The paradox of Christ
Christ at the zenith of his mission was swept along by what seemed a well-nigh irresistible tide of events fanned by the growing irritation with Roman rule, the preachings of holy men like John the Baptist, widespread  expectations of a sudden miraculous cataclysm that would wind up history and bring about the Jewish Golden Age, and so on. Christ was borne along by this current : it took him into the lion’s den, Jerusalem itself, where he was acclaimed by an adoring multitude.
So far, so good. The tide was strong but not quite strong enough, or so Christ judged. The most difficult thing for someone who has a string of successes behind him is to pull out at the right moment, and very few people are capable of doing this since the power of the event-train not only exerts itself on spectators but above all on the protagonist himself. He or she gets caught in his own noose, which only proves the basic law of Eventrics that it is events that drive history not the person who directs them, or thinks he does.
Over and above any moral priority which puts pacifism higher than combat, or a desire to broaden his message to reach out to the Gentiles, on the strictly tactical level Christ seemingly judged that the Jewish resistance movement was not strong enough to carry the day against the combined force of the official priesthood and Rome. So he decided to combat in a different way ─ by apparently giving in. He withdrew deliberately and voluntarily from the onward surge of events and, miraculously, this unexpected strategy worked (but only posthumously).
Napoleon made a fatal mistake when he invaded Russia, as did Hitler, and both for basically the same reasons (though the case of Hitler is more problematical) : they had swum along with a tide of events that took them to the pinnacle of worldly power but were unable, or unwilling, to see that the moment had come to pull out. In a roughly similar situation, Bismarck, a far less charismatic leader than either Napoleon or Hitler, proved he was a far better practitioner of Eventrics. Having easily overwhelmed Denmark and crushed Austria, Bismarck halted, made a very moderate peace settlement with Austria, indeed an absurdly generous one, because he had the wit to realize he required at least the future neutrality and non-intervention of Austria for his larger aims of creating a united Germany under Prussian leadership and prosecuting a successful war with France. As H.A.L. Fisher writes, “There is no more certain test of statesmanship than the capacity to resist the political intoxication of victory.”
It is the same thing with gambling. Despite all the tut-tutting of scientists and statisticians who never risk anything and know nothing about the strange twists and turns of human events, I am entirely convinced that there really is such a thing as a ‘winning streak’, since successive events can and do reinforce each other ─ indeed this is one of the most important basic assumptions of Eventrics. What makes gamblers lose is not that they believe in such chimeras as ‘runs’ or ‘winning streaks’ : they lose because they do not judge when it is the right moment to leave the table, or if they do judge rightly do not have the strength of character to act on this belief. They are caught up by the events and taken along with them, and thus become helpless victims of events. There is I believe a Chinese expression about ‘riding’ events and this is the correct metaphor. A skilful rider gives the horse its head but doesn’t let it bolt ─ and if it shows an irresistible inclination to do so,  he jumps off smartly. This gives us the double strategy of the practitioner of Eventrics : go with the tide of events when it suits you and leave it abruptly when, or better still just before, it turns against you. The ‘trend’ is certainly not “always your friend” as the Wall Street catchphrase goes. The successful investor is the person who detects a rising tide a little bit earlier than other people, goes with it, and then pulls out just before the wave peaks. Timing is everything.     SH

[This post appeared on the related site] 

Note 1  Curiously, at least in contemporary Western society, there is not only very little desire to be ‘good’, but even to appear to be good. Bankers and industrialists in the past presented themselves to the public as benefactors, and some of them actually were (once they had made their pile): this is a million miles from the insolent cocksureness of “Greed is good”. We have thus an unprecedented situation. People who not only lack all idealism but scorn it are very difficult to manipulate because it is not clear what emotional buttons to push. Today Hitler would never get anywhere at all, not just because his racial theories don’t really hold water but, more significantly, because most people would just laugh at all this high-sounding talk about the “fatherland” and “serving your country”. This clearly is a good thing (that Hitler wouldn’t get anywhere today), but one wonders whether a rolling human cannon, a lynch mob looking for someone to lynch (anyone will do) may not turn out to be an even greater danger. In terms of Eventrics, we now have large numbers of people literally “at the mercy of events” in the sense that there are today no ringleaders, no people calling the shots, no conductors of orchestras, only a few cheerleaders making a lot of noise on the sidelines. The resulting human mass ceases to be composed of individuals and event dynamics takes over, for good or ill. The charismatic power figure has himself become outdated, irrelevant : it is Facebook and Google that control, or rather represent, the future of humanity but who controls Facebook and Google?

Footbridge over the Seine (Cont.)

La Passerelle des Arts



Stefan is painting as before, this time it is the original canvas with the model in it. Josette arrives with pastries. She sits down on the bench.

JOSETTE I brought something.

She shows pastries. Stefan covers over the painting.

JOSETTE I didn’t bring any coffee.
STEFAN It’s all right, I’ve got some.

He sits down and pours coffee from a thermos. He has brought two plastic cups.

JOSETTE I saw you yesterday at the Canal Saint-Martin.
STEFAN That’s possible.
JOSETTE That how you spend your days, just walking around ?
JOSETTE All day?

Stefan nods. Background music based on the overture to “Attila” by Verdi in the background, very quiet at first.

JOSETTE Which parts of Paris?

Stefan shrugs.

STEFAN Anywhere.
JOSETTE Just drifting?
JOSETTE Like a leaf?

Stefan nods. Josette looks down at the water flowing under the bridge.

STEFAN Or a piece of paper.

Josette tears off a piece of paper  from the wrapping of the pastries, screws it up a little and throws it into the air.  We watch it being taken up by a gust of wind, eventually falling into the water on the right side of the bridge and then taken rapidly  downstream. Josette rushes to the other side to see if it has re-appeared and leans over the side of the bridge.  The current takes it away and we watch it going down through other bridges, past Les Invalides and onward.

JOSETTE It’s gone for ever. We’ll never see it again.

She sits down on the bench again. Music stops.

JOSETTE (Inquisitorial) You looking for someone or something when you’re wandering around?
STEFAN  (Decisive) No. Sometimes I do get in conversation with odd people I come across but that’s not the point.
JOSETTE What is the point ?

Stefan shrugs.
STEFAN Just to feel the pulse of life in the great city. That is enough.


La Passerelle des Arts

A very beautiful Parisian woman, stylishly dressed, crosses the Pont des Arts. Josette follows her with her eyes and looks at Stefan quizzically to see how he is reacting. We see the woman moving away very slowly with a special grace until she is eventually lost in the crowds in front of the Louvre. The camera switches to the water and we see various twigs and bits of paper taken away by the current.

Suddenly, a young North African rushes onto the bridge hotly pursued by two policemen. He is about to knock over Stefan’s easel in his flight and Stefan hastily moves it to one side of the bridge. Other police appear from nowhere at the other end of the bridge barring the way. The North African  looks desperately over the side of the bridge but then allows himself to be seized. Stefan watches with a pained expression as the man is bundled into a police van.

JOSETTE Bastards!

We hear the main theme bursting out but this time it is much more sombre. It trails away into nothingness and the scene on the bridge fades into jumbled shots of police vans circulating around the streets of Paris, angry demonstrators, disconsolate young French conscripts getting on a train taking them to Algeria, French soldiers patrolling an Algerian casbah and a victim of a shoot-out lying on the pavement.

Conscripts going to Algeria

Conscripts going to Algeria


Victim on pavement




Were Rats to Blame?

Rat “From April 18 onwards, quantities of dead or dying rats were found in storehouses and public buildings (…) The situation worsened in the following days. There were more and more dead vermin in the streets and the scavengers had bigger cartloads every morning. On the fourth day the rats began to come out and die in batches. From basements, cellars and sewers they emerged in long wavering files into the light of day, swayed helplessly, then did a sort of little dance and fell dead at the feet of the horrified onlookers. People out at night would often feel underfoot the squelchy roundness of a still warm body. It was as if the earth on which our houses stood was being purged of their secreted humours….”

An extract from Boccacio’s account of the Black Death in Florence in 1348 which serves as a preface to his Decameron ?  No. The passage is taken from the opening of Camus’s famous novel La Peste in Stuart Gilbert’s translation (with two or three words altered so as not to give the game away). In Camus’ novel the plague which attacks Oran in Algeria (where Camus was born) commences as an epizootic (animal epidemic) amongst the rat population of the town. This is how one would expect an outbreak of bubonic plague to begin since the usual carrier of the bacillus, the flea Xenopsylla cheopis, is a parasite on rodents  and normally only transfers to humans when there are no available (living) rodents.

So why didn’t Boccacio and other fourteenth century chroniclers of the ‘Great Mortality’ of 1348-50 mention a preliminary wave of very heavy rat mortality preceding human cases? There are no convincing answers to this question. Most writers state, or rather assume without stating, that the inhabitants of fourteenth century Europe were so thoroughly unscientific, filthy and unobservant that they either failed to notice, or deemed unworthy of mention, the enormous quantities of dead rats that must have accompanied bubonic plague as it swept through Europe at breakneck speed, taking less than three years to get from Sicily to upper Norway and visiting most rural areas, even very remote ones,  on its way. As for being ‘unscientific’, well, I personally do not expect fourteenth century man to have a knowledge of microbiology centuries before the construction of a decent microscope ¾ it was only in 1894 that the French doctor, Yersin, identified the plague bacillus during the so-called Plague of Canton. Whatever the ‘Great Pestilence’ was — the term ‘Black Death’ is of much later date — it was almost certainly a bacterial or viral disease and, equally certainly, there was very little that medieval doctors and Public Health authorities could have done other than what they did do, which was to  recommend flight to those who had somewhere else to go such as Boccacio’s wealthy Florentines, to clean up the streets and to enforce strict quarantine on incoming vessels in ports. Although there was a certain amount of talk about ‘God’s judgment on man’, and naturally some attempts to blame minority groups such as Jews, medieval Health authorities and doctors did make an attempt to understand the phenomenon in a ‘scientific’ manner and the theories proposed were by no means idiotic. It was, for example, suggested that the origin of the pestilence was probably ‘vapours’ emitted by rotting corpses and this same theory was proposed by Creighton in the latter nineteenth century.

It is essential to continually bear in mind that medieval man was not an animal lover : the cultural and religious climate of medieval Europe was utterly different from that of, say, India where devout Hindus stubbornly resisted the attempts of authorities to exterminate the rats that shared their habitations as late as the  early twentieth century. As to medieval men and women being indifferent to dirt and filth, this assumption needs some qualification, at any rate as regards the towns which one would expect to be the most promising foyers of infection. To judge by the frequency and venom of ecclesiastical tirades, bath-houses during the later Middle Ages were only too well-attended, though it was perhaps more the nudity of these unisex establishments that attracted men rather than the opportunity to get a good wash. Public latrines existed in large towns — there were at least thirteen on London Bridge — and municipal authorities were extremely concerned about the dangers that, notably, butchers’ offal represented. Boccacio himself, who lived through the Black Death, speaks of “the cleansing of the city [of Florence] by officials appointed for this purpose, the refusal of entry to sick folk, and the adoption of many precautions for the preservation of health  (Decameron, p. 5 Everyman Edition). But, though Boccacio does mention a pig dying in the street, nowhere is there any mention of rats.

There is, moreover, one very good reason why medieval man would have been more, not less, attentive to rat mortality than people living today, for he would have envisaged a wave of dying rats as a portent. Folklore and folk wisdom in China, India and many parts of Africa have traditionally associated mortality of rodents with human epidemics. There is a Chinese poem quoted by the plague specialist Wu Lien-Teh  containing the lines

“A few days after the death of rats
Men pass away like falling walls.”

likewise an Indian saying, “When the rats begin to fall it is time for people to leave their houses”.

In the country, although peasants may well have become resigned to the permanent presence of unwanted guests under their roofs, they can scarcely have felt much affection for them. I myself  have inhabited a traditional  one room ‘long house’ in a remote area of France, and was extremely annoyed by the racket that rodents living in the eaves made each night. But no medieval poet or chronicler writer mentions rats. During a visitation as severe as that of 1348, dying rats would have been falling down into the living quarters and dwelling-places everywhere must have stank of putrefying rat corpses.

For we are speaking of a very substantial rat presence across the whole of Europe. Shrewsbury, an out-and-out bubonic plague believer, estimated that around 69 rats per square mile were needed to sustain an epizootic of the scale of the Black Death — the term incidentally was not used until two centuries later — and this works out, given the population density of the time, at the incredible figure, as Shrewsbury himself admits, of over a 100 rats per two-room peasant cottage in many rural areas of Great Britain !  It is only too typical of otherwise reputable historians that, instead of questioning the hypothesis (that the Black Death was bubonic plague), Shrewsbury dismisses the medieval evidence as unfounded rumour and categorically affirms that the pestilence could not have visited large areas of Great Britain.

But are rats indispensable for an epidemic, or pandemic (world-wide epidemic), of the disease we now, rather irritatingly, call plague?  The answer is that rodents, not necessarily rats, are absolutely indispensable for an initial outbreak of bubonic plague and it seems most unlikely that there were any other rodent candidates available in fourteenth century Europe. There exist permanent reservoirs of plague amongst squirrels in North America, but they cause little harm since individual squirrels very rarely interact intimately enough with humans to infect them. And in Asia there are enormous foci of plague amongst burrowing rodents such as marmots, which, again, considering the numbers involved, cause very little damage.

Bubonic plague is not properly speaking a disease of humans, nor even of rodents, but of fleas. It is caused by the bacillus Yersinia pestis, named after the scientist who identified it at the end of the nineteenth century, which, in certain conditions, gets established in the stomach of certain fleas, especially Xenopsylla cheopis. The bacteria multiply, filling the stomach entirely and, because of this, the flea cannot take in nourishment and, in desperation, feeds all the more frantically, or tries to. In the process it regurgitates some of the blood it cannot ingest, and also defecates, depositing bacteria in the faeces (see Illustration I). The bacteria infect the host, the host infects other fleas and so on.

It is not in the interests of a parasite to kill off too many of its potential hosts, fortunately for us or pandemics would be more frequent than they actually are, and in general a status quo results as in the bacillus-flea-rodent tripartite biological system. Only about 12% of the fleas get blocked, and we can assume that only a small percentage of rodents such as marmots die, since marmots were, and still are, extremely numerous. Epizootics flare up, of course, from time to time, on occasion spreading to other rodents and thus to man who gets involved quite co-incidentally. Since the black rat, Rattus rattus, the only rat present in Medieval Europe, is an almost exclusively domestic animal who, typically, lives in houses, warehouses or ships, i.e. in close proximity to man, Rattus rattus is a good deal more dangerous than the rest of the rodents put together from our point of view. Xenopsylla cheopis will normally only transfer to a human being when there are no available living rats — it leaves the corpse as soon as the body temperature cools. And the bacteria can only enter the human body by flea-bite or, just conceivably, very close physical contact such as wound-to-wound, so, contrary to what most people believe, bubonic plague is not a contagious disease. The human flea, Pulex irritans, is a much less efficient transmitter of plague since it rarely becomes blocked even when feeding on infected humans : there is widespread (though not quite total) agreement that it can be ruled out as an insect vector for plague except in the case of septicaemic plague, a complication of bubonic plague that remains very rare.

We know a considerable amount about bubonic plague today because the last big outbreak, the so-called Plague of Canton, occurred when there were plenty of trained doctors and Health Officials available and the secret of bacterial infection was at long last known. Officials from the Plague Research Commission chronicled the relentless spread of bubonic plague through India in great detail, though they were incapable of doing much more than taking preventative measures prior to the discovery of antibiotics.

The most striking feature of the Plague of Canton was its extremely slow rate of dissemination despite the availability of modern methods of transport. It is thought that the pandemic originated in the Yunnan during the eighteen-fifties, but it was only in 1894 that it reached Canton and Hong Kong. It reached Calcutta in 1895, presumably by sea, and a year later found ideal conditions in the teeming, insanitary city of Bombay (Mumbai). Something of the Camus scenario of rats coming out to die on the streets was in fact observed, though not usually quite so dramatically. Plague maintained itself at these locations spreading outwards throughout much of India for some thirty years and, in Bombay itself, its progress was often no more than two or three miles a year!  Compare this with the lightning sweep of the 1348-50 Black Death which covered the ground from Messina in Sicily to Northern Norway in less than three years!

George Christakos and fellow authors (Interdisciplinary Public Health Reasoning and Epidemic Modelling: The Case of the Black Death, 2005, Springer), using advanced modelling techniques estimates that “plague advanced at an accelerated pace that peaked in October of 1348, when it infected a quarter of a million km2 in one month” (p. 230). To get an idea of what this area represents, I have roughly marked it out on a map of France (see Illustration II), though I hasten to add that the actual territory allegedly covered was not restricted to France and was a much more elongated shape.

The assumption that the Black Death so-called was caused by rats is of relatively recent date, since it only goes back to the late nineteenth century,  when Yersinia pestis was discovered and Koch, amongst others, immediately identified the bacillus as the cause of the 1348 pestilence. Practically all history books today, when discussing the issue, speak of three main onslaughts of bubonic plague in Europe, the Plague of Justinian, the medieval Black Death and the Plague of Canton. It is somewhat alarming to see how quickly an assumption becomes unassailable dogma, for that is what the rat theory has become. The principal; stumbling blocks to the identification of the Black Death with plague are, then :

1. Bubonic plague requires a rodent epizootic to get going, while contemporary witnesses nowhere mention rats in connection with the pestilence;

2. A very large native rodent population is required, and references to rats throughout the entire medieval period are few and far between, to say the least;

3.  The rate of spread was phenomenal and the mortality enormous — between a quarter and a third of the entire population of Europe.

On (2) further evidence that there can hardly have been a substantial rat population in the mid fourteenth century in Britain comes from the design of dovecotes. Everyone is agreed that the more familiar Brown Rat, Rattus norvegicus, only arrived in Britain in the early eighteenth century rapidly spreading inland from ports. According to Dr Twigg, who cites McCann, The Dovecotes of Suffolk (Suffolk Institute of Archaeology & History 1998 p. 21 -2), dovecotes were re-designed at around this period because of rats which climbed inside and ate both doves and eggs. Staddle stones, large toadstool-like constructions of stone on which barns, and even small houses, were laid, and which are very common in the area where I live (Dorset) appear to date from this period also. Now, in Tudor and late medieval times, one would expect there to have been more, not less, dovecotes as, apart from their value for food in monasteries and such establishments, the droppings were collected, mixed with earth and boiled to produce saltpetre, the main ingredient in gunpowder. Rattus rattus is actually a better climber than the Brown Rat so, had there been a substantial rural rat population in the preceding centuries, one would have expected to find mentions of it as a pest. Also, since  grain losses from manorial granaries were a recurring bone of contention, one would have expected bailiffs to have attributed them to rats, which, as far as we know, they never did.

Incidentally, for what it is worth, the story of the Pied Piper of Hamelin does not go back to the mid fourteenth-century (though conceivably based on earlier sources) and the first versions do not specifically mention rats as carriers of disease. Defoe, in Journal of the Plague Year, a partly fictionalized account of the seventeenth century Plague of London, does mention rats though he nowhere suggests that they were responsible for the epidemic. Black rats may well have become something of a nuisance in cities by Stuart or Commonwealth times, but the problem remains that the Black Rat is a strictly sedentary animal that has rarely been found even more than a mile or two from its, usually urban, birth-place.

Some readers are perhaps already getting impatient because I have not, as yet, mentioned pneumonic plague. Pneumonic plague is simply bubonic plague which affects the lungs : it is, however, a very different kettle of fish in many ways. Prior to the discovery of antibiotics, it was almost invariably lethal and can be spread person to person rather like influenza through droplets released into the air, by sneezing for example. This ties in quite nicely with the common medieval belief, not so long ago dismissed by historians as rank superstition, that you could ‘catch the pestilence’ simply by being in the same room as an afflicted person. Medieval doctors were themselves so worried about the possibility of contagion that they often refused to visit their patients !

However, the pneumonic plague hypothesis does not quite do what many people think it does. We know a lot about pneumonic plague, because of the 1910/11 and 1920 Plagues of Manchuria, voluminously recorded by a practising physician on the spot, Lien-Teh. In the first place, if the Black Death actually was plague, it cannot have been entirely, or even mainly, the pneumonic variety. For all medieval observers mention buboes (swellings) especially at the groin or armpit as being the principal symptom. In the case of pneumonic plague, there is not enough time for the buboes to form — in fact, paradoxical though it may sound, pneumonic plague is too deadly to make it a good candidate for a pandemic. For an epidemic to develop, we need an abundance of healthy carriers, or at any rate persons who appear healthy — precisely why AIDS is such a danger, likewise influenza, the cause of the last major pandemic in the West, that of 1918 which killed far more people than World War I. In the case of septicaemic plague the afflicted person dies within six hours, which makes it a very unlikely candidate for even a local epidemic. But pneumonic plague does not rate much better : it has been officially estimated that an afflicted person dies within an average of 1.8 days.

Why, then, the substantial mortality in Manchuria? The Manchurian outbreak had the benefit of extremely favourable conditions (from the bacillus’s point of view) which are most unlikely to repeat themselves  : migrant workers in the trapping industry travelled about in winter on heated trains and by night slept on platforms in crowded steam-heated hostels. Moreover, the authorities were taken by surprise in 1910 with the result that the 1920 outbreak was a good deal less serious though practically the only methods available were the ‘medieval’ ones of isolation and quarantine. And the Manchurian outbreaks, though severe, do not even remotely compare with the Black Death. Not everyone in 1349 could have avoided all contact with other human beings, since they had to procure food, but, as we know from Boccacio, people certainly kept as far away from each other as they possibly could with the honourable exception of the clergy called in to hear bedside confessions — they paid for their zeal by heavier mortality than amongst other professions especially in Germany. So the same difficulties for the rapid transmission of pneumonic plague by person to person contact would have applied in the fourteenth century, only more so given the absence of railways and steamships.

The second point to be stressed is that pneumonic plague does not get rid of the need for rats. Infected rodents in serious numbers are still required to start the epidemic, and we simply have no evidence to suppose that there were enough rats around in 1348 — except the circular ‘reasoning’,  “No rats, no plague”.  In the Manchurian case, it was marmots who started the epidemic : the first human victims handled them directly on a day to day basis and, it has been observed, were largely inexperienced migrant workers unaware of the dangers involved. Whether an outbreak of pneumonic plague can persist without an accompanying epizootic amongst rodents, is still a matter of learned debate, or rather controversy, but it seems more probable to me that an outbreak restricted to humans would burn itself out fairly quickly. Note that, if we accept de Mussis’ account (which almost everyone does with some reservations), the Black Death entered Europe via a Genoese galley hailing from the Crimea. The trip, even under very favourable conditions, would have taken a good six weeks, and this is ample time for an outbreak of any known form of plague to have either burned itself out, or, at the very least, to have killed off enough of the crew to make the harbour authorities at Messina most suspicious, which apparently they were not.

Frankly, the case for the identification of the Black Death with plague as we know it, just doesn’t stack up. As an amateur with no vested interests either way, when I first did some research into the Black Death for an article back in the eighties, it was not a matter of whether I did, but whether I could, in all honesty believe the two were one and the same. I decided I couldn’t, especially after reading Dr Twigg’s epoch making book, The Black Death (Batsford, 1984), also the very interesting Ph. D thesis of Palmer into the history of plague in Venice (though this does not cover the 1348 period). Since then, the small band of bubonic plague sceptics has been swelled by various other figures, notably Scott and Duncan (Return of the Black Death, Wiley 2004), Professor Cohn (Epidemiology of the Black Death and Successive Waves of Plague), Lerner (Fleas : Some Scratchy Issues Concerning the Black Death, Journal of the Historical Society June 2008) and, most recently of all, Gummer (The Scourging Angels, 2009) to mention only the main authors known to me.

The best that can be said for the bubonic plague hypothesis — and that is all it is — is that the description of the surgeon Guy de Chauliac and one or two other contemporaries of the symptoms of the disease does sound rather like bubonic plague. The buboes are not specific to plague but there is no doubt that they are distinctive. Bubonic plague can also give rise to small, black pustules, which fits the description of ‘God’s tokens’ as they were often called. However, these are much less distinctive than the buboes and it is worth noting that these marks, the “ring, a ring of roses’ of the (18th century) nursery rhyme, seem, over the years, to have become a more typical symptom than the buboes, assuming that subsequent outbreaks of ‘pestilence’ had the same cause, which they may well not have done. There is, annoyingly, just enough plausibility to the bubonic plague theory to keep it alive. Though far from being as lethal as the Black Death, or even, globally, smallpox and malaria, no one is going  to deny that plague is a serious disease since it caused over 12.5 million deaths in India during the twentieth century (over a period of forty-three years though, not two and a half).

What of DNA testing ? The jury is still out on this issue. A French team led by Michel Drancourt and Didier Raoult tested three skeletons from a grave pit in Montpellier for bubonic plague and reported positive results. However, various geneticists and archaeologists such as Mike Prentice, Alan Cooper, Carsen Pusch and others have disputed these claims, some attributing them to laboratory contamination. No one has, since then, managed to repeat these positive results and we await a more extensive and thorough investigation which, according to some unconfirmed reports, is currently underway.

The trouble with disbelieving that the Black Death was plague is that it is a negative option : its advocates find themselves pushed into making risky guesses about what the Black Death really was, and this has proved to be a dangerous game. Dr.  Twigg came up with anthrax as a possible alternative. This suggestion does have the advantage that it solves the problem of rapid dissemination since anthrax spores can be spread about by the wind, and are extremely resistant to extremes of temperature (which fits what we know of the Black Death). One might seriously doubt that, given medieval population density levels, any disease could have covered such a vast area so swiftly other than by dispersion in air currents. For what it is worth — and in my eyes is worth something — contemporary (medieval) observers thought that the pestilence was spread both by direct contact and by ‘vapours’, perhaps emanating from decaying corpses. This suggestion was by no means idiotic : the ‘miasmic’ theory of disease was still going strong in the late nineteenth century amongst the scientific establishment.

In other respects, however, Dr Twigg’s mention of anthrax proved to be an unfortunate suggestion since anthrax, in its present form at any rate, is not very contagious as we know from the post 9/11 scare. To invoke a ‘stronger strain of anthrax’ is a dangerous ploy, since it invites the plague lobby to counter by claiming that the bubonic plague bacillus of 1348 was a ‘stronger strain’ than what we are used to today. Dr Twigg’s suggestion, though it is contained only in the ten last pages of his book, simply gave his opponents a good excuse to dismiss, or simply not to read, the remaining densely argued two hundred odd pages.

Scott and Duncan have since then come up with haemorrhagic fever or ebola, a deadly viral disease. Much of their work is outside the remit of this article, since it deals with successive waves of ‘pestilence’ in Europe, not just, or principally, the 1348-50 outbreak, but deserves mention nonetheless. Using modern statistical methods, they have worked out an “average time from infection to death” for plague cases over a period of centuries and have come up with the figure of 37 days. This fits quite well with the ebola hypothesis but, more strikingly, with the Venetian institution of 40 days quarantine for incoming vessels, a period which soon came to be accepted throughout the whole of Italy. There were, subsequent to 1348, only 11 outbreaks of ‘pestilence’ in 300 years in Italy, which compares very favourably indeed with France and other countries. This quarantine was a considerable annoyance to merchants and may even have contributed to the commercial decline of Venice, so the Venetian Health authorities must, at least in their own eyes, have had serious reasons for instituting it. Of course, on the bubonic plague hypothesis, any quarantine is entirely pointless.

One  reason why the rat theory of the Black Death is still up and going, is that we do not, as humans, much like rats, viewing them as ugly and dirty creatures. If a similar pandemic had been initiated by squirrels, as just conceivably it might have been, one wonders whether the bubonic plague hypothesis would have remained established dogma for over a hundred years with very few daring to question it. Even if it were eventually proved to be utterly misguided, people for a long time to come will unthinkingly associate rats with the Black Death much as we automatically associate Nero with the burning of Rome or Louis XIV with the Man in the Iron Mask  — indeed I sometimes find it hard to get rid of the association myself despite having been in the non-bubonic camp for at least twenty-five years already. As a matter of fact, rats have probably been a good deal more serviceable to mankind than squirrels, who we find cute, since, apart from the rather unpleasant IQ maze experiments, rats have long been used to detect unexploded mines because of their excellent sense of smell.

There must, anyway, have been plenty of diseases which have disappeared without a trace, since diseases, being merely forms of life that we, as humans, do not view favourably, are subject to evolutionary pressures like everything else. One such is “the sweats”, a very serious disease prevalent at the time of the Reformation and which no one has subsequently successfully identified.  So it may well be that we shall never know with certainty the micro-organism responsible for what someone called, with not too much exaggeration, “the most nearly successful attempt to wipe out the human species” — a worthy adversary indeed !

Sebastian Hayes

Footbridge over the Seine

As the credits run we see a middle-aged man, Stefan, reasonably good-looking without being handsome, rummaging through canvases in his small flat cum studio. He pulls out a canvas and holds it at arm’s length, examining it quizzically. It represents a slim young girl posing nude on a divan with one hand behind her head. The painting is unfinished, in particular the background is not yet filled in.

We hear for the first time a theme which comes up at moments throughout the film : it is taken from the overture to Verdi’s little known opera, Attila.

Back to a group of students in the Beaux-Arts who are sketching the model in the painting. Stefan, twenty years younger, is one of the group working on the painting we have just seen.

Stefan looks up at the clock and says something which we do not hear. The students pack up and go off. Stefan remains to rearrange chairs and tables as if he is responsible for the class, though he does not look old enough to be a full-time teacher. The model continues to lie there lazily without making any attempt to get dressed. He notices this and she glances up at him  provocatively. He looks away, embarrassed. Irritated, the girl grabs a counterpane, throws it around herself and stalks out to get dressed.

During this time we hear the first two verses of “The Fugitive” (Lyrics and Melody Sebastian Hayes) in the background

I never planned this mission
Where I stay I never know ;
For I let the movement send me
Wherever it wants me to go.

So if the Germans ask you
Have you seen me passing by,

Tell them you never knew me,
Tell them it was not I.

No sign will mark my passing,
No tomb will bear my name,
But I’ll not be forgotten
When I go back to where I came,
When I go back to where I came.


Bridge over the Seine
Mist which clears gradually. Workers in blue denims cross the bridge, one or two better dressed office workers, maids with baguettes de pain. STEFAN, a man of about fifty wearing a floppy trilby and casual wear, carrying an easel and painting equipment walks halfway across the bridge (which is pedestrian only) and sets up his easel. The canvas is covered by a sheet of paper so we do not see the painting at first. In the background a Juliette Greco or Lucienne Delyle song of the era, very quiet. The man is Stefan.

Stefan on bridge

He lifts the protective wrapping from the canvas we see that it is a half-finished nude executed in the style of Modigliani; The slim model is stretched out on her back with her left hand behind her head, she has black hair and a mischievous expression. The painter sketches rapidly the background for the picture, namely what he sees in front of him —  the rest of the Pont des Arts and the Louvre : this is an imagined backdrop for the nude which has obviously been painted previously in a studio.

A group of noisy students, some carrying musical instruments arrive from the left (the camera side) and one of them flops down on a metal bench on the bridge slightly in front and to the right of the painter. The girl, JOSETTE, is in her early twenties, she is  wearing  expensive high heeled shoes but  is wrapped up in a somewhat shabby red coat. She is slim and has delicate features,  but there is something feverish about her appearance, half drunkenness, half fatigue. She closes her eyes

Boy. Coming, Josette ?

Josette. No.

Boy. Ok, please yourself.

Josette. (Slightly drunken tone) Yes, yes.

(She waves her hand and the students disappear towards the Right Bank. Josette stretches out on the bench exhausted. The painter, whom we see only from the back or the side, looks at her with interest and sets up his easel so that he can get a better view in order to use her as a model. His glance goes from the girl on the bench to the canvas and back to the girl. He gives a few touches to the painting.

The girl wakes up with a start and looks around.)

Josette. You painting me ?

Stefan. Well, not exactly.  In a way.

Josette. I pose for students  in the Beaux Arts sometimes.

Stefan. Do you ?

(Carries on painting.)

Josette. Yes.  (Pause) They pay me though.

Stefan. How much ?

Josette. I charge…..  fifty francs for a half hour.

(To her amazement the painter takes out some notes and hands them to her. She looks at them and him trying to make him out, then stuffs them hastily into a pocket of her coat.)

Josette. Is the pose all right ?

Stefan. Just move your right leg a little. Yes. Now put your  left arm behind your head and look up at the sky. Yes, that’s better.


Josette. Say something, I’m getting bored.

Stefan. I’ve more or less finished for today actually.

(Josette jumps up and comes round to look at the painting.)

Josette. But that’s not me !

Stefan. (A bit embarrassed) No.

Josette. She does look a bit like me, it’s true.  Who was she ?

Stefan. Oh, just a model at the Beaux-Arts.

Josette. But all this time you’ve just been doing the background ! What is this ?

Stefan. I did do something to the arm. But, yes, I did the figure years ago.

Josette. Anyway, it’s a crap painting.

(The painter smiles weakly, not taking offence.)

Josette. In fact it’s so bad I’m going to throw it in the Seine.

(Josette picks up the painting. The painter makes no attempt to stop her. She pulls her arm back as if about to hurl the painting into the water, but thinks better of it and eventually replaces it on the easel. She turns to face him.)

Josette. I’ll let you off this time. (Indicating the painting) Actually, it’s maybe sort of got something nonetheless. (Slight pause.) But it’s still a crap painting.

(Josette takes the notes out of her pocket, screws them tightly into a ball and tosses it at the painting.)

Keep your money.

(She stalks off.)

Man. Hey!

(Josette stops at once and turns.)

Man. (While packing up his easel and preparing to go off) Have breakfast on me at least.

(He puts a few coins down on the bench.

He walks off without turning round, taking his equipment with him. Josette stares after him with a puzzled air.)


(Josette is sitting at a table in a café drinking coffee and eating croissants. A few old workers at the bar pay no attention to her, but a young man at a nearby table tries to make conversation. She frowns and looks away.

Groups of police are milling around outside, talking amongst themselves or on walkie-talkie. Police vans pass incessantly. The radio at the bar gives out the 10 o’clock news. Josette looks up at once and listens attentively.)

RADIO ANNOUNCER In the Algerian capital French Algerian protesters have thrown up barricades in the streets and seized certain government buildings. The police have opened fire on the rioters and there is at this very moment intense fighting around Boulevard Laferrière. General de Gaulle has called on all members of the police and military to remain faithful to the Republic and has denounced the parachute regiment commander, Stefan Lagaillarde, as the instigator of this movement whose aim is clearly to sabotage the recent peace agreements.

(Josette gets up suddenly, pays at the counter and rushes out.)


La Passerelle des Arts

A few days later. Same scene as before a little later in the morning. Stefan has his easel set up in the same place. His back is towards us and we do not see the canvas.
Josette arrives from the left bank side of the bridge, so Stefan does not see her arriving. She is in slightly better shape though she wears the same threadbare coat. She surveys Stefan for a while, then flops down on the same bench, deliberately taking up the same pose. She looks up provocatively in a way slightly reminiscent of the model.
Stefan pretends not to notice her. Silence. After a bit both smile despite themselves. Josette throws off her coat and gets up to have a look at the painting. The centre of the painting is blank, Stefan is roughing in the Louvre and the Pont des Arts as a background in pastel.

JOSETTE (Shocked) What happened to the model?

Stefan carries on painting.

JOSETTE What do you mean, dead?
STEFAN I decided I didn’t need her any more. So I threw the painting into the Seine.
JOSETTE (Genuinely perturbed) No, no, you couldn’t have done that.
STEFAN Why not?
JOSETTE You just couldn’t.

Stefan keeps on painting, smiling to himself slightly.

STEFAN It’s all right. The original’s in my studio.
JOSETTE I’m very glad to hear that.

Slight pause.
Stefan puts his hand in his pocket and pulls out a note which he hands to Josette.

STEFAN Why don’t you go and get some pastries ?
JOSETTE What do I get for you?
STEFAN Oh, pain au chocolat.

Josette walks off slowly down to the other end of the bridge still looking somewhat troubled. The camera follows her.


Stefan and Josette are now sitting on the bench drinking coffee and eating pastries.

JOSETTE So what do you spend the rest of your day doing?  Painting?
STEFAN No. I only do it as a hobby now. I did go to the Beaux-Arts once but I dropped out before getting a diploma.

Slight pause. Josette looks at him, calculating his age.

JOSETTE Why’d you drop out? Because the Germans were after you?
STEFAN No. Nothing as heroic as that.
JOSETTE What, then?
STEFAN Personal reasons.
JOSETTE All very mysterious. (Scrutinising him) You don’t look old enough to be retired. You got money, then?

Stefan laughs.

STEFAN Pots. No. But last year I came into a small inheritance, enough to live on for a year or two.
JOSETTE (Stretching her arms lazily) It’s never too late in the day to start doing nothing. What work did you do  when you were active?
STEFAN Teaching a bit. More recently I worked for a firm translating technical manuals into Polish.
JOSETTE Sounds absolutely ghastly.
STEFAN I quite enjoyed it. You?
JOSETTE Oh, officially I’m enrolled at the Sorbonne. Political Science and Economics.
STEFAN What’s it like?
JOSETTE Complete crap. Everybody’s just interested in money and power in this shitty society — you don’t need to do Science-Po to see that. I don’t get a grant – I only enrolled so I could go to the Student Restaurant. Everybody has to eat.
STEFAN Yes, quite.

Pause. Stefan gets up and begins to pack up his things.

JOSETTE You going already?
STEFAN I’ve got to get back to take some medication.

Josette picks up his easel without being asked.

JOSETTE Here, I’ll carry that. Where’d you live?
STEFAN Not far from here.


A typical Parisian street. The 19th century five storey houses have balconies with iron railings.

JOSETTE This it?

Stefan nods. Close up of entrance showing the street number and a column of names with bell pushes. The top one is STEFAN WOZINSKY.

JOSETTE Yes. I’m at the top.

Josette looks at the entrance door again. She dumps the easel on the ground.

JOSETTE See you.

She saunters off without looking back. Stefan pushes a button, pulls open the heavy doors and enters with his equipment.


Stefan without his painting equipment is wandering aimlessly along the Canal Saint Martin. From time to time he exchanges the time of day with old men sitting on benches or playing boules, at one point he goes into a small grocery store to buy some fruit  and then resumes his stroll.
Josette and a group of students, mostly male, emerge from a Métro station and walk along in a group purposively as if going to a meeting. One of them consults a piece of paper. He presses the bell. Looking back idly Josette catches sight of Stefan. She stares  at him curiously. He does not see her. The others go in.

MALE STUDENT You coming, Josette?
JOSETTE Oh, yes.

She follows them in. The heavy double door slams to. We see Stefan continuing to wander  along  the canal bank.

To be continued

Leibnitz's Formula

Leibnitz’s Formula for π


one of the peculiarities  of π, the ratio of circumference of a circle to its diameter and thus a strictly geometric entity, is that it comes up in all sorts of unexpected places, thus giving rise to the belief, common amongst pure mathematicians, that Nature has a sort of basic kit of numbers, including notably π, e, i and Γ that She applies here, there and everywhere. Buffon, the eighteenth-century French naturalist, worked out  a formula giving the probability of a needle of length l dropped at random onto a floor ruled with parallel lines at unit intervals cutting at least one line. If l  is less than a unit in length, the formula turns out to be 2l/π  and this result has even been tested experimentally by a modern scientist, Kahan. Actually, in this case and very many others, there is a perfectly rational connection between the formula and the properties of circles, but I must admit that I am floored by the connection between π and the Gamma Function in the weird and rather beautiful result  Γ(1/2) =  √π

          π also turns up as the limit to various numerical series, a matter which in the past was of considerable importance as manufacturing methods required better and better estimates of the value of π. Today, computers have calculated the value of π to over a million decimal places so the question of exactitude has become academic — although computers still use formulae originally discovered by pure mathematicians such as Euler or Ramanujan.

          Leibnitz, co-inventor of the Calculus, produced several centuries ago, somewhat out of a hat, the remarkable series    


                   π/4  =  1/3  +  1/5  – 1/7  +  ……


          British mathematicians, eager to give as much credit as possible to Newton, pointed out that a Scot, Gregory, had already derived, using Newton’s version of the calculus, the formula


                   tan-1 x = x  1/3 x2 + 1/5 x2  ……  


and that you obtain Leibnitz’s formula by setting x = 1.

          However, apart from the question of priority, one might reasonably wonder why it should be necessary to bring in calculus to validate such a simple-looking series. A problem in so-called elementary number theory should, so I feel at any rate, make no appeal to the methods of analysis or any other ‘higher’ mathematics but rely uniquely on the properties of the natural numbers. I feel so strongly about this that I had at one point even thought of offering a small money reward for a strictly numerical proof of Leibnitz’s famous series, but I am glad I did not do so, since I have subsequently come across one in Hilbert’s excellent book, Geometry and the Imagination.

          The complete proof is not at all easy — ‘elementary’ proofs in Number Theory are not necessarily simple, far from it — but the general drift of the argument is straightforward enough.

          Consider a circle whose centre is at the origin with radius r , r a positive integer (> 0). The formula for the circle is thus x2 + y2 = r2 .

          We  mark off lattice points to make a network of squares (or use squared paper), and take each lattice as having a side of unit length.

          For any given choice of circle (with r > 1), there will be squares which ‘overlap’, part of the square falling within the circumference and part falling outside the circumference and a single point counts as ‘part’ of a square.

          We define a function f(r) with r a positive integer to be the sum total of all lattices where the bottom left hand corner of the lattice is either inside or on the circumference of a circle radius r. (Any other criterion, such as counting a square ‘when there is more than half its area inside the circle’, would do so long as we stick to it, but there are good reasons for choosing this ‘left hand corner’ criterion, as will shortly be apparent.)

          It is not clear at a glance whether the lattice area, evaluated according to our left hand corner criterion, is larger or smaller than the true area of the circle. However, as we make the lattices smaller and smaller, i.e. increase r, we expect the difference to diminish progressively. 

           f(1) = 5   — remember we are counting the squares where only  the left hand corner point lies on the circumference. I make f(2) come to 13 and f(3) come to 29, while the two higher values given below are taken from Hilbert’s book Geometry and the Imagination :


                   f(2)     =       13             

                   f(3)     =       29  

                   f(10)   =     317

                   f(100) = 31417       


          The absolute value of the difference between the lattice area, f(r), evaluated simply by counting the relevant lattices, and the area of the circle, π r2, is |f(r) – π r2|  If we use f(r) as a rough and ready estimate of the area of the circle and divide by r2 we thus get an estimate of the value of π  obtaining


          π   13/4   = 3.125

 π     29/9  = 3.222222…

 π      317/100  =  3.17

 π      31417/1000 = 3.1417


          Now, since the diagonal of a unit square lattice is 2, all the ‘borderline cases’ will be included within a circular annulus bounded within by a circle of radius of (r Ö2)  and without by a circle of radius (r + 2).

          The area of this annulus is the difference between the larger and smaller circles, i.e.


          [(r + 2)2 π  –  (r + 2)2 π]  =  4 2 π r 


          |f(r)  – π r2|, the discrepancy between the lattice area and the area  of the circle, is bound to be less than the annulus area since some lattices falling within the annulus area get counted in f(r), and certainly f(r) cannot be greater than the annulus area.   


                   |f(r)  – π r2|  ≤  4 2 π r   


which, dividing right through by r2 gives


                             |f(r)/r2 π| ≤   4 2 π/r          …………………..(i)


          Now, assuming Cartesian coordinates with 0 as the centre of the circle, for any value of r there will be a certain number of points which lie on the circumference of the circle, those points (x, y) which satisfy the equation


                   (x2 + y2) = r2  where r is a positive integer (> 0).


          But we must count all the negative values of x and y as well. For example, with r = 2, the circumference will pass through the lattice points (2, 0), (2, 0), (0, 2) and (0, 2) and no others.

          We now introduce a new variable n = r2 making the radius Ön and the equation of the circle becomes x2 + y2 = n   Although n must be an integer, we lift the restriction on r so that the radius is not necessarily an integer, e.g. r = √7, r = 13 and so on.     

          Now, the number of lattice points on the circumference of a circle with radius n is equivalent to four times the number of ways that an integer n can be expressed as the sum of two squares — four times because we allow x and y to take minus values. This is strictly a problem in Number Theory and an important theorem states that


          The number of ways in which an integer can be expressed as the sum of the squares of two integers is equal to four times the excess of the number of factors of n having the form 4k + 1 over the number of factors having the form 4k + 3.


          Take 35 = 5 × 7. We have as factors of 35 : 1, 5, 7 and 35 which are respectively

                   1 (mod 4)

                   1 (mod 4)

                   3 (mod 4)

                   3 (mod 4)


          Since there are two of each type and 2 –- 2 = 0 there is no excess of the (4k+ 1) type and so, if the theorem is correct, 35 cannot be represented as the sum of two squares, which is the case.

          The proof of the theorem is quite complicated and will not be attempted here. What we can show at once is that


          No prime p which is 3 (mod 4) can be represented as the sum of two (integer) squares.


          This is so because any odd number, whether it be 1 or 3 (mod 4), will be 1 (mod 4) when squared. And every even number, whether 2 or 0 (mod 4) will be 0 (mod 4) when squared. So if p happens to be 3 (mod 4) like 7 or 11, it will have no representation as the sum of two squares, i.e. the equation a2 + b2  = 3 (mod m) is insoluble in integers.

          However, if p prime is 1 (mod 4) it may be possible to find a representation in two squares since (4k+1)2 + even2 = 1 (mod 4) is possible. A theorem given by Fermat, which goes some way towards establishing the principal theorem, states that


          An odd prime p is expressible as the sum of two squares if and only if p = 1 (mod 4)      


          The ‘if’ part means that every odd prime p such as 5, 13, 17 and so on can be expressed as the sum of two squares.  13 = 32 + 22 for example and 17 = 42 + 12.


          From our point of view, any representation such as 5 = 12 + 22 gives us eight  lattice points, four for the different ways of forming (12 + 22) and four for the different ways of forming (22 + 12) i.e. the lattice points with coordinates


                  (1, 2), (1, 2), (1, 2), (1, 2)


and those with coordinates


                    (2, 1), (2, 1), (2, 1), (2, 1) 


          65 = 5 ´ 13   has factors, 1, 5, 13 and 65 all of which are positive integers which are 1 (mod 4).  There should, then, be four different ways of representing 65 as the sum of two squares, where the order in which we write the two squares matters. And in effect we have


          65 = (12 + 82) = (82 + 12)  =   (42 + 72) = (72 + 42)


We end up with eight lattice points for each combination, namely


          (1, 8), (1, 8), (1, 8), (1, 8),

          (8, 1), (8, 1), (8, 1), (8, 1), 


          (4, 7), (4, 7), (4, 7), (4, 7),

          (7, 4), (7, 4), (7, 4), (7, 4), 

           The idea now is that, by considering every number n £ r2 , working out how many times it can be expressed as a sum of two squares and adding the results, we will obtain f(r) on multiplying by 4 . Actually, this would include the origin, the point (0, 0), which we do not want to consider, so, excluding this, we have

          (f(r) 1)     = 4   representations of n ≤  r2  as two squares.


          Now 1 has a representation since 12  = 12 + 02 giving the four points (1, 0), (0, 1), (1, 0) and (0, 1), 2 = 12 + 12  has a representation giving four points, 3 none and 4 = 22 + 22  gives four points  giving twelve  in all. I made f(2) = 13  which checks out with the above since (f(2) – 1)  = 12. 

          Actually, rather than work out the excess for each number n individually, it is much more convenient to add up the number of factors of all numbers of the form (4k+1) and then subtract the number of factors of all numbers of the form (4k+3). In the first list we have


1, 5, 9….  (4k+1)   r2    and in the second


3, 7, 11…… (4k+3) ≤  r2


          Each of the numbers above must appear in the total for its class as many times as there are multiples of it that are at most r2. 1 will obviously appear r2 times, but 5 will only appear [r2/5] where the square brackets indicate the nearest integer r2/5 

          Finally, since we are not removing or adding anything, we can  subtract the first term in the (4k+3) category from the first term in the (4k+1) category, the second term from the second and so on. We end up with the open-ended series, depending on the choice of r


(f(r) 1)     =   4   representations of n ≤  r2  as two squares.

                   =   4  { [r2] – [r2/3] + [r2/5] – [r2/7] + [r2/9] ……..} ..(ii)


Now the ‘least integer’ series [r2] [r2/3] + [r2/5] [r2/7] + [r2/9] …

unlike the series r2 r2/3  +  r2/5   r2/7  +  …… is not an infinite series since it terminates as soon as we reach the point where r2/(4k+1)  < 1  making all subsequent terms = 0.

          We assume for simplicity that r is odd and of the type 4k+1 so that r1 is a multiple of 4. Since all the terms with 4k+1 as denominator are positive, we can split the series into two, and then add up the pairs, where the first member of a pair is taken from the  +  and the second from the  Series. The ‘+ Series’ contains [r2/r] and the final non-zero term is [r2/(r2].


[r2/1]   +  [r2/5]  + [r2/9]  …+ [r2/r]    +    [r2/(r+4] + ……..[r2/r2]  


0           +  [r2/3]  + [r2/7]  …+ [r2/(r2)] + [r2/(r+2)] +…[r2/(r22)]   


          If we cut off the series at [r2/r] the error involved, namely the rest of the original series, will be less than r, or a r where a is some proper fraction, i.e.


[r2/(r+4] – [r2/(r+2)] …………… [r2/(r22)] + [r2/r2]   < r 


          To see this, we write all terms after [r2/r] as [r2/(r+k)] where k is even and ranges from 2 to (r2 r) since (r+ (r2 r)) is the denominator of the final non-zero term. The absolute values of all these terms are less than [r2/r] = r and they come in pairs which alternate in sign.

          Also, all terms where 2(r+k) > r2 or k > (r2/2 r) = r(r 2)/2 will make [r2/(r+k)] = 1 The first such term comes when k = r(r 2)/2 + 1/2 (since k is even) i.e. when k = (r1)2/2  From this point on all pairs will sum to zero so we can ignore them  and only need consider the pairs between [r2/r] and ending [r2/(r+(r1)2/2)]. There will be (r1)2/8 such pairs with a maximum difference of 1 in each case, and so the sum total of the error cannot exceed (r1)2/8  < r since  (r1)2  < 8r for r ≥ 2

          An example may make this more intelligible. Take r = 9 which is a number of the form 4k+1. Then [92/9] = 9  and all terms from then on have their absolute values < 9 while the final last term is [92/92] = [92/(9+72)] The last term where [92/(9+k)] 2 comes when k = 30 and we can neglect all pairs where k has values > 32 (we make the last value k = 32 to make up the pair). k even thus ranges from 2 to 32


 2        4

 6        8

10      12


30      32


          The maximum absolute amount possible will thus be 32/4 = 8 (in this case (8)) and 8 < 9 = r

          A similar argument can be used to establish the case where r is odd and of the form 4k+3 and any even value of r will be sandwiched between the two cases.

          We thus have, returning to (ii)


¼ (f(r) 1) =   [r2] [r2/3] + [r2/5] [r2/7] + [r2/9] ± [r2/r] ± a r

where a < 1

          To lift the square brackets, we note that the error in each term is less than 1 and that there will be, for r odd, (r+1)/2  terms if we cut the series off at [r2/r]. The total possible error is thus < (r+1)/2  <  r  for r ³ 2  and can be written as ± b r where  b < 1   

          We can thus write


¼ (f(r) 1)     =  r2 r2/3 + r2/5 r2/7 ……. ± a r ± b r  ………..(iii)



         Dividing right through by r2 we obtain


1/4r2 (f(r) 1)   =  1 1/3 + 1/5   1/7 ……. ± a/r ± b/r




1/4 (f(r)/r2  1/r2) = 1 1/3 + 1/5   1/7 ……. ± a/r ± b/r


which has limit as r →  ∞    f(r)/4r2  = 1 1/3 + 1/5   1/7 …….


          Finally, we note that the discrepancy between the area of the circle and the lattice representation is


          |f(r)/r2 π| ≤  4 2 π/r   with limit 0 as r →  giving us the desired


limit  r →     1 1/3 + 1/5   1/7  + 1/9  ……. ± 1/(2r+1)  =     π/4





                                                                         Sebastian Hayes  

Catherine Pozzi : Immortal Longings

born into a very select Parisian family during the latter nineteenth century — her father was a fashionable surgeon and a Senator while her mother presided over a salon patronised by Sarah Bernhardt and Leconte de l’Isle — ‘Karin’ developed into a withdrawn, very intense young woman “tall, gracious and ugly” as Jean Paulhan describes her cattily. She traversed various emotional and religious crises, which she recounts in her voluminous Journals, before making a disastrous marriage which never survived the honeymoon. Not that she was frigid: a few years on, already suffering from the tubercular complaint which eventually killed her, she embarked on a tempestuous affair with Paul Valéry and committed the unforgivable faux-pas, not of having an affair with a married man, but of openly avowing the liaison.

If ever there was a poète manqué(e) — I am tempted to say génie manqué — it was Catherine Pozzi. In a rather pathetic passage from her Journals, she asks ‘Dieu Esprit’ to forgive her for not having fulfilled her sacred mission and having wasted too much time on trivialities. While her contemporary, Marcel Proust, also a chronic invalid and insomniac, managed to write the longest novel in the world, Catherine Pozzi left us only her Journals, one or two inconclusive philosophical prose pieces and….six poems. Out of these six, only one was published during her lifetime — though this was according to her own wishes.

Like the English Romantic poet Beddoes, Catherine Pozzi spent much of her life vainly searching for some faculty or lost sense, which would enable humanity to overcome the dreadful duality matter/spirit. To this end, she undertook serious studies in biology and physics during her maturer years, and, piecing together scattered passages from her Journals and prose pieces, it would seem that she was groping towards a theory similar to that of ‘morphic resonance’ currently advanced by Dr. Rupert Sheldrake, whereby each of our sensations, and ultimately the whole of our lives, is a sort of recapitulation of what has already been : “Je sens ce que j’ai déjà senti” as she puts it. More’s the pity she did not leave us a body of work as substantial as that of, say, Blake.

 Sebastian Hayes

That peerless love that was your gift to me,
The wind of days has rent beyond repair,
High burned the flame, strong was our destiny,
As hand in hand we stood in unity
Together there ;

Orb that for us was single and entire,
Our sun, its flaming splendour was our thought,
The second sky of a divided fire,
And double exile by division bought ;

These scenes for you evoke ashes and dread,
Places that you refuse to recognize
And the enchanted star above our head
That lit the perilous moment our embracing shed,
Gone from your eyes…..

The future days on which your hopes depend
Are less immediate than what’s left behind;
Take what you have, each harvest has an end,
You’ll not be drunk however much you spend
On scattered wine.

I have retrieved those wild celestial days,
The vanished paradise where anguish was desire ;
What we were once revives in unexpected ways,
It is my flesh and blood and will, after death’s blaze,
Be my attire ;

Your name acts like a spell, lost bliss I knew,
Takes shape, becomes my heart; I live again
That golden era memory makes new,
That peerless love that I once gave to you,
And lived in pain.


Love of my life, my fear is I may die
Not knowing who you are or whence you came,
Within what world you lived, beneath what sky,
What age or time forged your identity,
Love beyond blame,

Love of my life, outstripping memory,
O fire without a hearth lighting my days,
At fate’s command you wrote my history,
By night your glory showed itself to me,
My resting-place…

When all I seem to be falls in decay,
Divided infinitesimally
An infinite number of times, all I survey
Is lost, and the apparel of today
Is stripped from me,

Broken by life into a thousand shreds,
A thousand disconnected moments — swirl
Of ashes that the pitiless wind outspreads,
You will remake from what my spirit sheds
A single pearl.

Yes, from the shattered debris of my days,
You will remake a shape for me, remake a name,
A living unity transcending time and space,
Heart of my spirit, centre of life’s maze,
Love beyond blame.

Descending layer by layer the silt of centuries,
Each desperate moment always takes me back to you,
Country of sun-drenched temples and Atlantic seas,
Legends come true.

Soul ! word adored by me, by destiny made black,
What is it but the body when the flame has fled ?
O time, stand still ! O tightened weft of life, grow slack !
A child again, the trail toward the dark I tread.

Birds mass, confront the sea-wind blowing from the West,
Fly, happiness, towards the summer-time of long ago,
The final bank once gained, all is by sleep possessed,
Song, monarch, rocks, the ancient tree cradled below,
Stars that from old my original face have blessed,

A sun all on its own and crowned with perfect rest.


Far in the future is a world that  knows not me,
It has not taken shape beneath the present sky,
Its space and time not ours, its customs all awry,
Point in the lifespan of the very star I flee,
There you will live, my glory and my ruin — I
Will live in you, my blood your heart will fructify,
Your breathing, eyesight, mine, while everything of me
That is terrestrial will be lost, and lost eternally !

Image that I pursue, forestall what is to be !
(Acts I once cherished, you have wrought this agony)
Undo, unmake yourself, dissolve, refuse to be,
Denounce what was desired but not chosen by me.

Let me not see this day, fruit of insanity,
I am not done — let fall the spool of destiny !


The wine that courses through my vein
Has drowned my heart and in its train
I navigate the endless blueI am a ship without a crew
Forgetfulness descends like rain.

I am a just discovered star
That floats across the empyrean —
How new and strange its contours are!
O voyage taken to the sunAn unfamiliar yet persistent hum
The background to my night’s become.

My heart has left my life behind,
The world of Shape and Form I’ve crossed,
I am saved   I am lostInto the unknown am tossed,
A name without a past to find.

A Louise aussi de Lyon et d’Italie

O you my nights  O long-awaited dark
O noble land   O  secrets that endure
O lingering glances    lightning-broken space
O flights approved beyond shut skies

O deep desire  amazement spread abroad
O splendid journey of the spellstruck mind
O worst mishap O grace descended from above
O open door through which not one has passed

I know not why I sink, expire
Before the eternal place is mine
I know not who made me his prey
Nor who it was made me his love

Catherine Pozzi

Translation Sebastian Hayes

Ni Zan : Classical Chinese Painter

ni zan (1301-1374) is regarded as one of the four masters of Chinese landscape painting during the Yüan (Mongol) dynasty. Originally a wealthy landowner, he spent the latter part of his life living on houseboats wandering around the lakes and rivers of Songjiang and Suzhou, sometimes staying with literati friends. There is an article on him by Jane Dwight in the July 2009 issue of the Newsletter of the Chinese Brush Painters Society, and he is the speaker of the following monologue taken from The Portrait Gallery by Sebastian Hayes (Brimstone Press, 2008).

On the Great Lakes        

My works are colourless, the outlines clear
But never bold, dry, even strokes; the scene

Is much the same, a bank with mainly leafless trees,
Stretches of open water, in the distance, hills;
The season, autumn (though it might be early spring);
Mid-morning; human shapes never appear, at most
A makeshift shelter in the foreground with a roof of reeds
Made by a passing traveller; no wind,
The very slightest flutter at the tips of trees,
But at ground level nothing, even a rowing-boat
Would mar the perfect stillness and the silence…
Rain; the sound of it agreeable, light rain
Coming in from the south, my travelling-boat
Rocks idly in the creek, securely moored;
Behind me dark land-masses, misty peaks,
Bent pine and tangled scrub; Ma Yüan’s scrolls

Reach out towards the indistinct but mine do not,
All is contained and definite, hillsides rise up
And lakes are bright with water, always, endlessly

                                                                                    Sebastian Hayes

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