Coincidence: shadow and fact

 

1.

In 1850, Dickens began a novel with an exemplary sentence: “Whether I shall turn out to be the hero of my own life, or whether that station shall be held by someone else, these pages will tell.”  It was, in fact, obviously the nature of these pages – the novel – to tell this story. It went without saying that for Dickens, as well as for other Victorian novelists, the interest of the novel was tied to interest in the individual. If there was an anxiety here, it was about heroism in Carlyle’s key, a heroism that passes the moral tests of life – but there was no doubt that a life was definitely not a matter determined within a larger social pattern, and only of interest insofar as it could be grouped with a subpopulation in order to display certain tendencies. In this sense, the novel bet everything on the ideology of heroism.

 

Even so, at the same time, in mid nineteenth century, there were indications that a radically different point of view, the statistical mindset, was winning minds outside the circle of literature.  Quetelet, for instance, in 1835 had already tried to show that crime should not be understood through its individual instances, but through statistics demonstrating its likelihood of incidence. From this, Quetelet inferred that it was society, and not the criminal, which produced crime, just as an orange tree produced oranges. We would not hold an orange responsible being an orange, although we might pluck it and squeeze it to death for its juice – just as we might take down a criminal and cut off his head to satisfy the principles of social hygiene.

 

Dicken’s notion of the novel and the individual produced what Robert Musil called a naïve, or old fashioned story form, which was very difficult to break with. In his view –a view, it must be admitted, conditioned by Musil’s envy of the fame of the great modernists – Ulysses and A la recherche are still footed in the archaic world of certainty and heroism, instead of the world in which that ground had disappeared and criminals could be considered the fruit of society, rather than bad actors making bad decisions, while characters could be considered as hybrids of the interior thoughts that, they delusively believe, guide them, and the administrative purposes for which they employed by exterior forces.

 

It is in this context that Musil thought a lot about coincidence – Zufall. Chance, after all, is felt as coincidence in a story, especially when science shatters our confidence that a life and a life story are one and the same thing.  In his diaries,  Musil piled up references to popular work on probability and chance in the field of math and physics. One of his sources was Erwin Schroedinger’s essay on the Gesetz der Zufall – the Law of Chance – in Koralle, a popular science magazine, which appeared in 1928.

 

It is a small, lucid essay, with two themes. One is that our understanding of the physical world is based not on certainty, but on probability. The other theme is that the second law of thermodynamics, which posits that systems advance from order to larger degrees of disorder, doesn’t free us from the link of determinism, if by determinism we mean unpredictability. Rather, entropy is highly predictable.

 

To make this point, Schroedinger uses an example that would have struck a writer like Musil – the example of the library.

 

He asks us to imagine a library that has been organized so that all the books in it are numbered and put in their proper places. And then he imagines a horde coming in on Monday – surely, students right before exam time – and going through the library and taking out books and putting them back with no regard for their proper place:

 Now the astonishing feature is that this process proves to be subject to very definite laws, especially if we suppose that the valumes are taken from the shelves in the same haphazard way as they are put back…. If we suppose that there were eighty volumes of Goethe’s works, for instance, neatly arranged in one section of the library when the casual mob entered, and if we find that only sixty volumes are now in their places while the other twenty are scattered about here and there, then we can expect during the second week about fifteen volumes will disappear from the row, and about eleven volumes will vanish during the third week, etc. For since we have supposed that the books are taken out quite at random, the probability that one of the remaining volumes will meet with this misfortune decreases as their number decreases.”

 

Schroedinger concedes that his example is stylized – really, for the predictions to be more exact, the numbers must be bigger. If the collected works amounted to 80,000 among millions of volumes, the deviations from the predicted number of remaining books would be smaller.

 

Schroedinger’s library example is interesting to follow through. If this were a real library, then some of the Goethe volumes would be checked out, and some of the books that were scattered around would be discovered by library assistants and put back in their place. In terms of the second law, what this would mean is that the system had feedbacks – which means that it is not entirely closed.

“ We do not wish to asseert anything more than that the total balance of disorder in nature is steadily on  the increase. In individual sections of the universe, or in definite material systems, the movement may  cvery well be towards a higher degree of order, which is made possible because an adequate compensation  occurs in some other systems.”

The notion of feedbacks gives us a new way of thinking about the game played between the novel and the author, in as much as the author keeps adding and subtracting from the novel, as well as that played between the reader and the novel, in that the reader keeps decoding the novel. But the question Musil was gnawing on was whether the novel as a system could accommodate the character as a point determined by the irreversible progress from order to disorder inherent in the other administrative systems within the social world that give the character a content. 

2.

E.T. Jaynes was a mathematician and philosopher who, in the twentieth century, did perhaps the most to counter and wrongfoot the frequentist tradition in possibility theory. Jaynes tried to prove that the possibility calculus is rooted in logic – that it is, indeed, as Laplace said, “the calculus of inductive reasoning” – of which random experiments are merely a subset. In other words, Jayne tried to harden the hearts of all who were interested in probability against the idea that probability represented some objective property of objects – or a Popper put it, a propension. To Jayne’s mind, at the same time that the frequentist line attempted to demonstrate that probabilty was something objective, instead of subjective, it also abstracted, absurdly, from the laws of physics. His central case for this was the discourse around coin tossing. Coins, as Jayne points out, are physical objects, and their rise and fall is completely described by the physics of ballistics. (I take this example from Jayne’s book, Probability theory: the logic of the sciences). Thus, to say that a coin with heads and tails has a fairly equal chance of landing on either side, with a lean a bit to heads over a long series of tosses, is to speak nonsense. Rather, everything depends on how a coin is tossed, as a physical object.

 

The laws of mechanics now tell us the following. The ellipsoid of inertia of a thin disc is

an oblate spheroid of eccentricity 1/√2. The displacement x does not affect the symmetry of this ellipsoid, and, so according to the Poinsot construction, as found in textbooks on rigid dynamics (such as Routh, 1905, or Goldstein, 1980, Chap. 5), the polhodes remain circles concentric with the axis of the coin. In consequence, the character of the tumbling motion of the coin while in flight is exactly the same for a biased as an unbiased coin, except

that for the biased one it is the center of gravity, rather than the geometrical center, which describes the parabolic ‘free particle’ trajectory.”

 

Given these physical facts, this is what Jayne suggests:

Therefore, in order to know which face will be uppermost in your hand, you have only

to carry out the following procedure. Denote by k a unit vector passing through the coin

along its axis, with its point on the ‘heads’ side. Now toss the coin with a twist so that k and

n make an acute angle, then catch it with your palm held flat, in a plane normal to n. On

successive tosses, you can let the direction of n, the magnitude of the angular momentum,

and the angle between n and k, vary widely; the tumbling motion will then appear entirely

different to the eye on different tosses, and it would require almost superhuman powers of

observation to discover your strategy.

 

Thus, anyone familiar with the law of conservation of angular momentum can, after some

practice, cheat at the usual coin-toss game and call his shots with 100% accuracy.”

 

Jayne’s point is that probability is not a spooky physical property connected with the two sidedness of the coin, but is a logical abstraction describing the physical event, including in its reference set the manner of the tossing.

 

Jayne goes on to demolish other examples from the frequentist literature. Here’s his conclusion:

 

“… those who assert the existence of physical probabilities do so in the belief that this establishes for their position an ‘objectivity’ that those who speak only of a ‘state of knowledge’ lack. Yet to assert as fact something which cannot be either proved or disproved by observation of facts is the opposite of objectivity; it is to assert something that one could not possibly know to be true. Such an assertion is not even entitled to be called a description of a ‘state of knowledge’.”

 

This conclusion led Jaynes to some radical and unorthodox positions. In particular, it led him to stress lack of knowledge, rather than physicalism, when accounting for quantum mechanics. He is famous for applying this, as well, to thermodyamics:  “entropy is an anthropomorphic concept, not only in the well known statistical sense that it measures the extent of human ignorance as to the microstate. Even at the purely phenomenological level entropy is an anthropomorphic concept. For it is a property not of the physical system but of the particular experiments you or I choose to perform on it.”

Often, while following a philosophical train of thought, one encounters a moment when the values one has been using strangely seem to inverse themselves. It is like the child's game of closing your eyes and spinning around and around: at the moment you stop and open your eyes, it seems that it is the world that is spinning around and around and you are standing still in the eye of it. The argument about probability partakes of that vertigo. The classical school inherits from Laplace the confidence that the world is a totally determined system, in which all phenomena can eventually traced back to material causes. And yet, to get to this argument, the school has to advance the thesis that probability is simply a measure of knowledge - or, to use the modern term, information. This means that, in classical terms, possibility is subjective. On the other side is the world picture that rejects crude determinism and accords chance a very real place. This school, then, takes possibility as as a real property, or in Popper's terminology, propensity, of events. This is, ultimately, an argument that makes possible an ontologically distinct thing called subjectivity. But, in grounding subjectivity in chance, in making possibility objective, this school entangles itself in all the logical problems adduced by Jaynes. And so, as the first group bases its determinism, which ultimately dissolves subjectivity, on the subjectivity of the probability calculus, the other group bases its indeterminism on the reification of a spooky non-cause. As I've pointed out, what goes for chance goes for coincidence. Perhaps here a Kantian probabilist could claim that we have reached the limit of our reason - the antinomies of chance are undecidable. But I'm pretty sure Jaynes would question whether, ultimately, we are not just making undecidable a case of our lack of knowledge, thus forcing us back towards his school.

3.

In Mill’s Logic, that grand old lumber room, in Chapter 18 of Book three,  a principle is spelled out that, in our day, has been shorthanded into the sometimes tendentious phrase,  correlation does not prove causation:

“Although two or more cases in which the phenomenon a has been met with may have no common antecedent except A, this does not prove that there is any connection between a and A, since a may have many causes, and may have been produced, in these different instances, not by any thing which the instances had in common, but by some of those elements in them which were different.”

Mill, in keeping with his practical bent, distills from this a question: “After how many and what sort of instances may it be concluded that an observed coincidence between two phenomena is not the effect of chance?”

Another way of putting this question is: when is a coincidence really a coincidence?

As Francois Mentre has pointed out, the French mathematician and scientist, Cournot, was also intested in this question, or at least in one of its guises: the reality of probability. Cournot worked in the shadow of Laplace; but where Laplace, finally, came down on the side of a universal determinism, Cournot was sure that this move was not justified by Laplace’s mathematics.  “He could not admit that chance was nothing  but a “vain sound, flatus vocis, which we use, as Laplace said, to disguise our ignorance of true causes.” For him [Cournot], chance had an objective reality independent of our knowledge.” (144) Cournot spelled out his ontological conviction by way of a critique of Laplace. Laplace wrote that Nature obeys “a small number of immutable laws.” Cournot’s disprove of Laplace’s determinism moves from this idea: “it suffices, said Cournot, that there be only two, perfectly independent one from the other, in order that we must make a place for the fortuitous in the government of the world. Whether or not  we do or do not know the literal law for each of the independent two series, as soon as they intersect, there is chance. Chance thus does not derive from our ignorance of the laws of the universe, no more than it diminishes as the measure of our knowledge extends. It subsists in the eyes of the expert as well as those of the ignoramus. It is necessary to accept it as an irreducible, sui generis fact that has a notable part in the government of the world.” (209)

This, though, is hard to accept, either for the expert or the ignoramus or that hybrid of the two, the modern mystic..

One can see that Cournot’s observation blocks two popular explanations of coincidence (or chance – in fact, I am using coincidence here as a proxy for a semantic family that includes the French hasard and the German Zufall). True coincidence can neither be purely the effect of human ignorance of the causes in place, nor can itself be characteristic of some autonomous law – a law of synchronicity or seriality. The same reasoning Cournot applies to other laws would apply in this case, so that any law of synchronicity would inevitably generate coincidences that would fall outside its domain as it intersected with other universal laws, creating, if you will, hypercoincidences.

One way of looking at physics in the 20^th century is that the physicists were both moved by the fact that the world given by a structure that was governed by two or more irreducible laws would have to accord a large place to chance – such that probability was no longer a way of mathematically stylizing elements that were, to an all powerful intelligence, always certain – and a movement to unify the laws of physics, to reduce them to some grand single principle, which would drive out coincidence.

However, there was also a tradition, a fringe tradition, that rejected the whole idea that coincidence wasn’t subject to its own proper law. Instead, it sought that law. This was an especially popular theme in Germany in the 20s, coexisting with a faddish interest in psychoanalysis, physiognomics, graphology, paranormal psychology, etc. Psychoanalysis had a tentative relationship with these things, which fascinated Freud, but which, finally, he diagnosed as cultural symptoms of a mass psychopathology.

4.

The ever resourceful, ever peculiar Arthur Koestler devoted two books to a minor figure in the history of science: Paul Kammerer. One book, The case of the Midwife Toad, detailed Kammerer’s search for proof that Lamarkian evolution – the inheritance of acquired traits – actually exists. The other book, The Roots of Coincidence, explored Kammerer’s fascination with what he called seriality, which found its way into Kammerer’s 1919, Das Gesetz der Serie. As I pointed out, if we take Cournot’s reasoning to be correct, there shouldn’t be a “law” of coincidence, since coincidence is, by definition, a byproduct of the fact that the laws of physics are both plural and independent one from the other. Thus, a law of coincidence would simply create another kind of coincidence that it couldn’t encompass, and thus would not be a law of all coincidences at all – eliminating it from consideration as a law of physics.

Nevertheless, while 20^th century physicists did follow, reluctantly, the probabilistic path scouted out by Cournot, there were intellectuals – sometimes including physicists of note, such as Wolfgang Pauli – who couldn’t resist the impulse of trying to discover some law to explain the interstices of chance.

Mostly, these intellectuals were not physicists, however. Rather, they were, many of them, concerned that the geometric spirit was strangling the poetry of the world, and sought places at the spiritual front where they could fight back. Often, however, they ended up fighting back using the methods of their opponents – that is, instead of claiming poetry as a power in its own right, they claimed that they were making scientific discoveries.

Kammerer, according to Koestler, made notebooks in which he recorded coincidences. He was on the lookout for them. A coincidence notebook is something to dream about – what a wonderful form for a novel!  Here’s what it looks like, in an extract from Koestler:

Kammerer's book contains a hundred samples of

coincidences. For instance:

(7) On September 18, 1916, my wife, while waiting for her turn in the consulting rooms of Prof. Dr.j.

v. H., reads the magazine Die Kunst; she is impressed by some reproductions of pictures by a painter named Schwalbach, and makes a mental note to remember his name because she would like to see the originals. At that moment the door opens and the receptionist calls out to the patients: "Is Frau Schwalbach here? She is wanted on the telephone."

(22) On July 28, 1915, I experienced the following progressive series: (a) my wife was reading about

"Mrs. Rohan", a character in the novel Michael by Hermann Bang; in the tramway she saw a man who looked like her friend, Prince Rohan; in the evening Prince Rohan dropped in on us. (b) In the tram she overheard somebody asking the pseudo-Rohan whether he knew the village of Weissenbach on Lake Attersee, and whether it would be a pleasant place for a holiday. When she got out of the tram, she went to a delicatessen shop on the Naschmarkt, where the attendant asked her whether she happened to know Weissenbach on Lake Attersee-he had to make a delivery by mail and did not know the correct postal address.”

Those who have the ear for these things will be impressed by the similarity (the coincidence?) of this kind of prose with Freud’s cases from ordinary life in the Psychopathology, which contains the famous (and much disputed) analysis of a “Freudian slip”. The coincidence, in fact, seems to be a sort of slip by fate itself – as though some secret law governing human events slips quickly into and out of view. Kammerer, like Freud, was concerned with repetition. He defined the series as "a lawful recurrence of the same or similar things and events -a recurrence, or clustering, in time or space whereby the individual members in the sequence-as far as can be ascertained by careful analysis-are not connected by the same active cause".

What they are connected by is the same person, depending on the case.

 

Six years before Kammerer’s book, Freud had published one of his more adventurous works: Totem and Taboo. In this book, he develops the idea of projection as a process by which the ambiguity of feelings one has about a person are relieved – in the case of “primitives”, by imputing hostility to the spirits of the dead, a hostility that has its real origin in the hostility one felt about them living. This idea has had a long career, and merged into the ordinary way of thinking about how we negotiate feeling and interactions with others so that it no longer seems or is even recognized, much of the time, as Freudian. Of course, it is a word that coincided with a technology – the projection of images on a screen – that also characterized one of the long events in the cultural life of the twentieth century. Freud sees, in a sense, the false divide that separates the “primitive” from the modern, even if the only moderns that he compares to primitives are neurotics. As to neurotics – in essence, you have successful ones, who sublimate their neuroses, and unsuccessful ones, who exibit it, and that is the psychopathology of everyday life. Mental illness is  a matter of degree, not a difference in kind.

Which is why projection is fundamentally based, according to Freud, on the human setup:

“But projection exists not only as a defense mechanism, but it also arises where there are no conflicts. The projection of inner perceptions to the outside is a primitive mechanism which underlies, for instance, our sense perceptions, which thus have the greatest share in shaping our outer world. Under not sufficiently fixed conditions, our inner perceptions will also project outward our feeling and thought processes as well as our sense perceptions, applying them to the forming of the outer world while they should remain bound to the inner world. This is connected genetically, perhaps, to the fact that the function of attention is not originally directed to the inner world, but instead to stimuli streaming in from the outer world, receiving from the endopsychic processes only reports of the development of pleasure or pain. Only with the construction of an abstract thought language, through the conjunction of sense-related remnants of verbal representations with inner processes, does this become gradually perceptible. Up to this point the primitive person through projection of inner perceptions on the outside develops a picture of the outer world that we only now, with a heightened sense of consciousness in psychology, are forced to retranslate.”  

6.

Nabokov played around with the coincidence device himself, in his novel, Despair. There, the hero, a prosperous businessman named Hermann, mistakenly supposes that he looks like a certain much poorer man. Hermann befriends this man on behalf of a plot to make make money and get out of a relationship with his cheating wife. The plot involves getting the double to dress as Hermann and then killing him. After this, the life insurance money will come rolling in, and Hermann can collect it. Hermann, then, is very much writing the “plot” for his characters, and banking on a coincidence. But what he doesn’t reckon on is his own blindspot with regard to what he looks like. There’s a character in a Turgenev story who says, somewhere, that he can keep a sharp mental image of strangers, but more familiar faces, including his own, never fix themselves in his imaginagtion. Hermann seems to be in a similar case – in fact, nobody else thinks his double looks like Hermann. Thus, the coincidence by which the murderer hopes to make his escape ends up being no coincidence at all – which is a very funny variation on the coincidence plot.
An Israeli sociologist, Ruma Falk, has made a career long study of coincidence stories. Like a disillusioned Hermann, Falk claims to have shown that our coincidence stories often depend on obtaining a statistically significant result from a deliberately chosen extreme example instead of basing that conclusion on a random sample”. The emphasis here on the random sample indicates the frequentist bias of Falk’s work – but at the same time, what really interests here is a cognitive property – the “surprising” effect of the coincidence. If Hermann had interviewed other candidates for doppelganger, or consulted his friends, he might well have found someone who, according to consensus, looked like him – which would of course be a coincidence, but one founded in the pool of types, cultural and genetic, in which Hermann existed, like some dictator looking for a body double to use as a security measure. But Hermann didn’t, because the coincidence surprised him to the extent that he didn’t question it.
Falk, then, looked at the element of surprise in coincidence stories. They divide stories of coincidence taken from a pool of subjects between self-coincidence and other-coincidence. They asked their subjects to judge the degree of surprise elicited by these stories – that is, stories the subject told about his or her experience, and stories the subject read about others’ experiences. “On the average, authors judged their self-coincidences somewhat more surprising than they judged others’ coincidences. However, the mean rating of the control subjects revealed that the other-stories were objectively more surprising than the self-stories. Taken together, authors found their own coincidences more surprising than others’ coincidences despite the fact that the latter were objectively more surprising.”
This is a complex response, no? One might speculate that the surprisingness of coincidence operates in more important ways in ordinary life than it is given credit for. At least, in listening to people talk about their lives, and about accidents that have befallen them, I get the sense that coincidence operates as a sort of guiding shadow to making sense of the incidents in a life - making the life seem fated, necessary, telic.