Occam’s Razorburn

Stephen Hawking’s latest book raises far more questions than it answers. Such as, why hasn’t he been reading Thomas Kuhn, and what really is the benefit of unifying theories which don't seem to need unification?

In which we meet yet another first-class scientist who wishes to self-identify as a second-class philosopher and a comedian from the back end of steerage.

Since few will buy A Grand Design for its wit we can forgive Stephen Hawking's appalling attempts to be funny, but it's not so easy to forgive his philosophical ignorance. Certain physical scientists might be better off unacquainted with the modern philosophy of science (though those who know it possess a welcome sense of perspective and humility). But not world-renowned cosmologists. Their field continually bumps up against the boundary of what science even is (and it doesn't have a "no-boundary condition", whatever that might be).

So when Stephen Hawking claims that "philosophy has not kept up with modern science, especially physics" it suggests not only a lack of perspective and humility, but that Hawking has been skipping on some required reading.  Especially since, having written off the discipline, Hawking seems barely acquainted with it. He mentions few philosophers more recent than Rene Descartes (d. 1650). So it is hard to know who he thinks hasn't kept up.

Particularly when Hawking's first grand pronouncement is "model-dependent reality": the idea that there may be alternative ways to model the same physical situation with fundamentally different elements and concepts. "If [such different models] accurately predict the same events, one cannot be said to be more real than the other." Physics has, apparently, been forced into this gambit following recent failures to get unifying calculations to work themselves out. In any case it isn't quite the neat trick Hawking thinks it is.

Firstly, while model-dependent reality might be news to Stephen Hawking (he seems to think it the fruit of modern physics' womb) the philosophers he hasn't been reading have been talking about it for years, if not centuries, to the constant sound of scientists' excoriations. It is even part of Descartes' philosophical fabric (and, more tellingly, Darwin's, but picking a fight with modern evolutionists, while fun, is a story for another day). That is to say, it sounds like it is the physicists who are finally catching up with the philosophers and not the other way around.

Secondly, in the grand game of philosophers' football that Cosmology has become, the model-dependent reality play is something of a surrender before kick-off.  For if it is true that the same phenomenon can be plausibly accounted for in multiple, "incommensurate" (© Thomas Kuhn) ways, then the hard question is not about the truth in itself of any model, but the criteria for determining which of the (potentially infinite) models available we should choose in the first place. 

This question is not one for physics, but metaphysics. It necessarily exists outside any given model (© Paul Feyerabend). Here we meet our old friend, Occam's Razor. This isn't a scientific principle at all, but a pragmatic rule of thumb with no intellectual pedigree: all else being equal, take the simplest explanation. Occam's Razor is a favourite instrument for the torture of hapless Christians by grumpy biologists: all your tricksy afterlife wagers and so on fail because evolution is so much less complicated and has so much more explanatory value than the idea that an omniscient, intangible, invisible, omnipotent entity pulling strings we can't see to make the whole thing go.

But, alas, in seeking a grand unification of things that really aren't asking to be unified, cosmology reveals some almighty snags. Unification under Hawking's programme, if it is even possible, involves slaughtering some big old sacred cows. To name a few: causality, the conventional conception of space-time; the idea that scientific theories should be based on observable data and their outcomes testable. It bows to some truly heinous false idols too. For example: seven invisible space-time dimensions, a huge mass of invisible dark matter, an arbitrary cosmological constant, a potentially infinite array of unobservable universes which wink in and out of existence courtesy of a mathematically inferred "vacuum energy"). Hawking doesn't propose solutions to these problems, but seems to think they're a fair price for achieving grand unification.

I'm not so sure: other than intellectual bragging rights, the resulting unified theory has no obvious marginal utility. And it has political drawbacks: believing one's model to be the truth carries potentially unpleasant implications for the suppression of those who don't.

There are practical drawbacks, too. We are asked to reject existing theories, which still have quite a lot of utility, in favour of something that it infinitely harder to understand and work with. The accelerating expansion of the universe without any apparent acting force seems to violate Newton's second law of motion. Without an outrageous end-run, the first nanosecond of the Big Bang (wherein the universe is obliged to expand in size by ten squillion kilometres - i.e. far faster than the speed of light) seems to violate the fundamentals of general relativity. String theory requires seven necessarily unobservable space-time dimensions and/or entirely different universes, and even then doesn't yield a single theory but millions of the blighters, all slightly inconsistent with each other (hence the appeal to "model dependent reality).

From the camp which wielded Occam's Razor so heartily against the Christians, this seems a bit rich. If these are the options, then the razor might slice in favour of the big guy with the beard.

But these aren't the options. We could save a lot of angst, and perhaps could have avoided digging trillion dollar circular tunnel under Geneva, had we employed model dependent reality the way the philosophers saw it and not the scientists (and shouldn't we call a spade a spade and label it cognitive relativism, by the way?). Since it crossed the event horizon of observability modern cosmology has become arcane, stunt-mathematics. If there were a chance that it might deliver time-travel, hyperspace or a tool for locating wormholes to other galaxies or universes then one could see the point in this intellectual onanism. But none of that seems to be allowed. So we should therefore ask the question "but why? What's the point? What progress do you promise that we can't achieve some other way?" No one seems to be able to answer that question.

But if we park it, what's left of Stephen Hawking's latest book is some pretty ropey jokes.

The End – or the Start – of Ignorance

 

E.O. Wilson is just the latest biologist to try turning the base metal of scientific induction into the spun gold of existential truth. What is the allure of religious certainty for these folks, and why they can’t heed the lessons of their own discipline?

I’ve made  the observation before that scientists - especially biologists - make lousy philosophers, and it doesn’t take long for Professor E. O. Wilson - one of evolutionary biology’s most prominent lights - to place himself squarely in that camp.

“No one should suppose,” he asserts, “that objective truth is impossible to attain, even when the most committed philosophers urge us to acknowledge that incapacity. In particular it is too early for scientists, the foot soldiers of epistemology, to yield ground so vital to their mission. ... No intellectual vision is more important and daunting than that of objective truth based on scientific understanding.”

On the other hand not long afterwards, apparently without intending the irony with which the statement overflows, he says, “People are innate romantics, they desperately need myth and dogma.”

None more so, it would seem, that philosophising evolutionary biologists. 

Wilson’s Consilience is a long essay on objective truth that - per the above quotation, gratuitously misunderstands what epistemology even is, whilst at the same time failing to mention (except in passing) any of its most important contributors - the likes of Wittgenstein, Kuhn, Quine, Rorty or even dear old Popper. Instead, Wilson characterises objections to his extreme reductionism as “leftist” thought including - and I quote - “Afrocentrism, ‘critical’ (i.e., socialist) science, deep ecology, ecofeminism, Lacanian psychoanalysis, Latourian sociology of science and neo-Marxism.”

Ad hominem derision is about the level of engagement you’ll get, and the only concession - a self-styled “salute” to the postmodernists - is “their ideas are like sparks from firework explosions that travel away in all directions, devoid of following energy, soon to wink out in the dimensionless dark. Yet a few will endure long enough to cast light on unexpected subjects.” You could formulate a more patronising disposition, I suppose, but it would take some work.

“You could formulate a more patronising disposition, I suppose, but it would take some work.”

What is extraordinary is that of all scientists, a biologist should be so insensitive to the contingency of knowledge, as this is the exact lesson evolutionary theory teaches: it’s not the perfect solution that survives, but the most effective. There is no “ideal organism”.

In support of his own case, Wilson refers at some length to the chimerical nature of consciousness (taking Daniel Dennett’s not uncontroversial account more or less as read). But there is a direct analogy here: Dennett’s model of consciousness stands in the same relation to the material brain as Wilson’s consilience stands to the physical universe. Dennett says consciousness is an illusion - a trick of the mind, if you like (and rather wilfully double-parks the difficult question “a trick on whom?”).

But by extension, could not consilience also be a trick of the mind? Things look like they’re ordered, consistent and universal because that’s how we’re wired to see them. Our evolutionary development (fully contingent and path-dependent, as even Wilson would agree) has built a sensory apparatus which filters the information in the world in a way which is ever-more effective.  That’s the clever trick of evolutionary development. If it is of adaptive benefit to apprehend “the world” as a consistent, coherent whole, then as long as that coherent whole accounts effectively for our physiologically meaningful experiences, then its relation to “the truth” is really beside the point.

When I run to catch a cricket ball on the boundary no part of my brain solves differential equations to catch it (I don’t have nearly enough information to do that), and no immutable, unseen cosmic machine calculates those equations to plot its trajectory either. Our mathematical model is a clever proxy, and we shouldn’t be blinded by its elegance or apparent accuracy (though, in point of fact, practically it isn’t that accurate) into assuming it somehow reveals an ineffable truth. This isn’t a new or especially controversial objection, by the way: this was one of David Hume’s main insights - an Enlightenment piece of enlightenment, if you will. As a matter of logic, there must be alternate ways of describing the same phenomena, and if you allow yourself to implement different rules to solve the puzzle, the set of coherent alternative solutions is infinite.

“It is extraordinary that a biologist should be so insensitive to the contingency of knowledge, it being the exact lesson of evolutionary theory.” 

So our self-congratulation at the cleverness of the model we have arrived at (and, sure, it is very clever) shouldn’t be overdone. It isn’t the “truth” - it’s an effective proxy, and there is a world of difference between the two. And there are uncomfortable consequences of taking the apparently harmless step of conflating them.

For one thing, “consilience” tends to dissuade inquiry: if we believe we have settled on an ineffable truth, then further discussion can only confuse and endanger our grip on it. It also gives us immutable grounds for arbitrating against those who hold an “incorrect” view. That is, to hold forth a theory which is inconsistent with the mainstream “consiliated” view is wasteful and given it has the potential to lead us away from the “true” path, may legitimately be suppressed.

You can see this style of reasoning being employed by two groups already: militant religious fundamentalists, and militant atheists. Neither is prepared to countenance the pluralistic, pragmatic (and blindingly obvious) view that there are not just many different *ways* of looking at the world but many different *reasons* for doing so, and each has its own satisfaction criteria. While these opposing fundamentalists go hammer and tongs against each other, their similarities are greater than their differences, and their greatest similarity is that neither fully comprehends, and as a consequence neither takes seriously, the challenge of the “postmodern” strands of thought against which they’re aligned.

Hence, someone like Wilson can have the hubris to say things like: “Yet I think it is fair to say that enough is known to justify confidence in the principle of universal rational consilience across all the natural sciences”

Try telling that to Kurt Gödel or Bertrand Russell, let alone Richard Rorty or Jacques Derrida.

Vanquishing magic by sleight of hand

Douglas Hofstadter’s essay on the incompleteness of “loopy” logical systems starts out brightly, but makes a disappointing and strangely unimaginative resort to reductionism in the end. Pity.

Philosophy, to those who are disdainful of it, is a sucker for a priori sleights of hand: purely logical arguments which do not rely for grip on empirical reality, but purport to explain it all the same: chestnuts like “cogito ergo sum”, from which Descartes concluded a necessary distinction between a non-material soul and the rest of the world.

Douglas Hofstadter is not a philosopher (though he’s friends with one), and in I am a Strange Loop he is mightily disdainful of the discipline and its weakness for cute logical constructions. All of metaphysics is so much bunk, says Hofstadter, and he sets out to demonstrate this using the power of mathematics and in particular the fashionable power of Gödel’s incompleteness theory.

Observers may pause and reflect on an irony at once: Hofstadter’s method - derived a priori from the pure logical structure of mathematics - looks suspiciously like those tricksy metaphysical musings on which he heaps derision. As his book proceeds this irony only sharpens.

But I’m getting ahead of myself, for I started out enjoying this book immensely. Until about halfway I thought I’d award it five stars - but then found it increasingly unconvincing and glib, notably at the point where Hofstadter leaves his (absolutely fascinating) mathematical theorising behind and begins applying it. He believes that from purely logical contortion one may derive a coherent account of consciousness (a purely physical phenomenon) robust enough to bat away any philosophical objections, dualist or otherwise.

Note, with another irony, his industry here: to express the physical parameters of a material thing - a brain - in terms of purely non-material apparatus (a conceptual language). In the early stages, Professor Hofstadter brushes aside reductionist objections to his scheme which is, by definition, an emergent property of, and therefore unobservable in, the interactions of specific nerves and neurons. Yet late in his book he is at great pains to say that that same material thing cannot, by dint of the laws of physics, be pushed around by a non material thing (being a soul), and that configurations of electrons correspond directly to particular conscious states in what seems a rigorously deterministic way (Hofstadter brusquely dismisses conjectures that your red might not be the same as mine). Without warning, in his closing pages, Hofstadter seems to declare himself a behaviourist. Given the excellent and enlightening work of his early chapters, this comes as a surprise and a disappointment to say the least.

Hofstadter’s exposition of Gödel’s theory is excellent and its application in the idea of the “Strange Loop” is fascinating. He spends much of the opening chapters grounding this odd notion, which he says is the key to understanding consciousness as a non-mystical, non-dualistic, scientifically respectable and physically explicable phenomenon. His insight is to root consciousness not in the physical manifestation of the brain, but in the patterns and symbols represented within it. This, I think, is all he needs to establish to win his primary argument, namely that Artificial Intelligence is a valid proposition. But he is obliged to go on because, like Darwin’s Dangerous Idea, the Strange Loop threatens to operate like a universal acid and cut through many cherished and well-established ideas. Alas, some of these ideas seem to be ones Douglas Hofstadter is not quite ready to let go. Scientific realism, for example.

The implication of the Strange Loop, which I don’t think Hofstadter denies, is that a string of symbols, provided it is sufficiently complex (and “loopy”) can be a substrate for a consciousness. That is a Neat Idea (though I’m not persuaded it’s correct: Hofstadter’s support for it is only conceptual, and involves little more than hand-waving and appeals to open-mindedness.

“Perhaps, rather than slamming the door on mysticism, Hofstadter has unwittingly blown it wide open. After all, why stop at human consciousness as a complex system?” 

But all the same, some strange loops began to occur to me here. Perhaps rather than slamming the door on mysticism, Douglas Hofstadter has unwittingly blown it wide open. After all, why stop at human consciousness as a complex system? Conceptually, perhaps, one might be able to construct a string of symbols representing God. Would it even need a substrate? Might the fact that it is conceptually possible mean that God therefore exists?

I am being mendacious, I confess. But herein lie the dangers (or irritations) of tricksy a priori contortions. However, Professor Hofstadter shouldn’t complain: he started it.

Less provocatively, perhaps a community of interacting individuals, like a city - after all, a more complex system than a single one, QED - might also be conscious. Perhaps there are all sorts of consciousnesses which we can’t see precisely because they emerge at a more abstract level than the one we occupy.

This might seem far-fetched, but the leap of faith it requires isn’t materially bigger than the one Hofstadter explicitly requires us to make. He sees the power of Gödel’s insight being that symbolic systems of sufficient complexity (“languages” to you and me) can operate on multiple levels, and if they can be made to reference themselves, the scope for endless fractalising feedback loops is infinite. The same door that opens the way to consciousness seems to let all sorts of less appealing apparitions into the room: God, higher levels of consciousness and sentient pieces of paper bootstrap themselves into existence also.

This seems to be a Strange Loop Too Far, and as a result we find Hofstadter ultimately embracing the reductionism of which he was initially so dismissive, veering violently towards determinism and concluding with a behavioural flourish that there is no consciousness, no free will, and no alternative way of experiencing red. Ultimately he asserts a binary option: unacceptable dualism with all the fairies, spirits, spooks and logical lacunae it implies, or a pretty brutal form of determinist materialism.

There’s yet another irony in all this, for he has repeatedly scorned Bertrand Russell’s failure to see the implications of his own formal language, while apparently making a comparable failure to understand the implications of his own model. Strange Loops allow - guarantee, in fact - multiple meanings via analogy and metaphors, and provide no means of adjudicating between them. They vitiate the idea of transcendental truth which Hofstadter seems suddenly so keen on. The option isn’t binary at all: rather, it’s a silly question.

In essence, all interpretations are metaphorical; even the “literal” ones. Neuroscience, with all its gluons, neurons and so on, is just one more metaphor which we might use to understand an aspect of our world. It will tell us much about the brain, but very little about consciousness, seeing as the two operate on quite different levels of abstraction.

To the extent, therefore, that Douglas Hofstadter concludes that the self is that is an illusion his is a wholly useless conclusion. As he acknowledges, “we” are doomed to “see” the world in terms of “selves”; an a priori sleight-of-hand, no matter how cleverly constructed, which tells us that we’re wrong about that (and that we’re not actually here at all!) does us no good at all. Neurons, gluons and strange loops have their place - in many places this is a fascinating book, after all - but they won’t give us any purchase on this debate.

How to philosophise with a hammer

I am a hopeless handyman. I have poor attention to detail and lack patience. I am disorganised. When hanging a picture, rather than finding a hammer, I bash the tack in with whatever first comes to hand. Recent examples: A tin of Rawleigh's Medicated Ointment (reasonably effective), an ornamental porcelain donkey (bad - it didn't survive) and a book (a hard-backed edition of E. O. Wilson's Consilience: better than nothing, but now pocked with pinholes).


That we tend to do that sort of thing lies at the root of a big problem with the ideas inside Professor Wilson's book (just as well, therefore, it has some use for hammering in picture hooks). Using a familiar object to do an unfamiliar job is rather like coining a metaphor: It's a creative act. As well as being pragmatic, it has its advantages. (It must have some advantages - convenience; it overcomes the lack of botheredness to find the hammer - or you wouldn't do it). But while my tin of ointment (or ornamental donkey, for that matter)  might not be conventional (and, in the donkey's case, might not work awfully well) it's not wrong. It is as good as the job it does. A "proper" tack hammer has been designed, to the exclusion of all other purposes, for hammering in tacks. You can imagine other objects being better or worse at functioning like hammers. Blu-tack, for example, would be hopeless. But not wrong. Just not much use.

And so it is with metaphors:  they deliberately take a conventional concept and put it to work in a concept it wasn't designed for. As a result metaphorical meanings are different from literal meanings (in a manner of speaking) but no worse or better - while they might be more or less effective, effectiveness is in the eye of the beholder.

Often, a metaphor can more elegantly or succinctly some aspects of its "target" (which Julian Jaynes would call a "metaphrand") than a literal construction. "Love is a rose": I suppose you might take this to mean love is a delicate, beautiful, fragile, thing that can prick you if you aren't careful with it. Or that is is a soft, rich and complexly enfolded collection of different facets. These aren't mutually exclusive metaphors, but they're not entirely consistent either. Both of them make some sense, where a literal interpretation of "love is a rose" doesn't.

Now while I was bashing in my picture hook with Professor Wilson's book I got to thinking about what was inside his book, and how Professor Wilson's whole enterprise, his desired end state, is one which overlooks the metaphor. This is some irony as metaphors, and rich ones at that, are scattered prodigally around his text.

Professor Wilson, in Consilience, sees the possibility (not yet arrived) of a unified, unique, continuous, contiguous spectrum of knowledge, encompassing not merely the physics and the physical sciences, but all of the humanities too. In fact, I think he sees the necessity of it. Wilson is an unabashed reductionist. Wilson embraces a hierarchy of physical sciences (physics at the bottom, grounding everything else; Chemistry sitting atop it, Biology atop that, and so on. Higher sciences can be reduced to lower ones; all sciences are consistent with each other, and it is only a lack of data which prevents completion of the total blueprint of the physical universe. Thereafter the social sciences and even the arts will fall into a pre-ordained and logical place and will similarly be logical, consistent and unambiguously explicable. Wilson is excited by this idea (it horrifies me, personally), and sets out in his book to give it some intellectual underpinning.

Wilson is running before he can walk. Metaphor gets in the way - literally, and metaphorically. The same thing happened to Bertrand Russell following a similarly hubristic exercise restricted to the logical underpinnings of mathematics. In the infancy of the twentieth century Russell tried to chart the entirely cosmos of the mathematical universe by reference to a single, finite set of well-defined logical axioms. By limiting himself to numbers, Russell took up an easier challenge, you would think, than Wilson has. Mathematics was, Russell supposed, a closed logical system: finite, reducible and therefore well susceptible to his kind of enterprise.

But Russell failed to complete his mathematical globe. Russell didn't just not manage to get to all points in a large whole; he failed totally: his entire project, so pointed out a precocious young German chap by the name of Goedel, was logically flawed. Doomed.

The reason? Metaphor. Even though Russell had decreed some ad-hoc rules to guard against logical cul-de-sacs - for example, no item was allowed to be a member of its own set - it was possible to run mathematical operations by analogy - metaphorically, in other words, that could tell you things that a literal mathematical operation could not. And any ostensibly complete description of a language which forbade expressions such as "the set of all possible sets" was going to be practically useless anyway. There are some excellent accounts of Goedel's dramatic insight, Douglas Hofstadter's a particularly good one (though his ultimate conclusion seems wildly wrong).

When he does refer to metaphor, Wilson's is a rather unimaginative account: what he describes isn't metaphor so much as definitional drift occasioned by metaphor. To use one of his examples, by the time "plot" - a physical site and a building plan - came to mean "plot" - the narrative structure of a story - any figurative content in the expression had long since evaporated; seawater gone, a residue of salt.

Wilson's idea of a metaphor therefore is a dead one: these are the ones "normal scientists" like, of course, because dead metaphors can't get up and bite you by suggesting what you meant to say might be taken in a number of ways. If there were a substantive distinction between art and scientific literature - and like Wilson, but for radically different reasons, I'm inclined to think there isn't one - it might be found in the systematic exclusion of metaphor from scientific discourse. Science is about exactitude; consensus on a literal way of speaking enhances that end.

But at some cost, and not just in the notorious dullness of scientific literature. Literalness encourages and perhaps compels compliance with orthodoxy. Paul Feyerabend - another conspicuous absentee from Wilson's reading list - makes the inspired observation that scientific revolutions rely on inspired observations: a willingness to disregard the formal language of the discipline. If you stick rigidly to the rules of the prevailing scientific paradigm it is not possible to see, much less formulate, contradictions to it: Anything which looks like a contradiction, by the terms of the theory, must be explicable some other way (wind interference; malfunctioning equipment).

To find a new solution to a conundrum you are forced to use existing concepts in a new way. You can only do it by being creative with your language.

From our Foreign Correspondent... a working theory about Warsaw

This one coming at you live, courtesy of the cellular network, from the steps of Pałac Kultury i Nauki in downtown Warsaw, an unwanted gift from Stalin to Poland, a solitary long-lost cousin to Stalin’s “Seven Sisters” in Moscow.

This is my fist visit to Poland, and some forty minutes of daylight into it, the excitement of being in a genuinely former Eastern bloc country hasn’t worn off. I walked through the catacombs of underground newsagents and jewellers around Warsaw’s central railway station and then around the Pałac this morning and have wound up on the steps in the shadow of a suitably heroic working class statue looking to kill some time before my meeting and, I suppose, looking for some evidence to fit my working theory about the place: I always do this in a new locale: try to figure it out, in very basic terms. What makes the people tick; why do they do what they do; how will they react to me. It’s a form of preservation. This morning, my theory’s predictably unimaginative: the Poles are a defiant and long-suffering people still overhung with the shroud of Mother Russia, nonetheless looking west, the rude shoots of sprouting capitalism pushing gaudily through cracks in the concrete of the former era, today’s inhabitants caught uneasily in the crosstalk between two incommensurate regimes.

And, of course, I find plenty of evidence of that sort – you don’t have to look for long: the grand Soviet building, a sort of stunted, baroque Empire State Building, formerly grand but latterly muted; hemmed in – besieged – by parked western European cars; its heroic spire now barnacled with cellular receivers and satellite dishes; its heroic working class figures and athletes strangely emasculated (Discobolus modestly wears underpants, a variation on the Greek ideal I’d not seen before), and just across the street, a block of new and shoddy skyscrapers, like ugly priapic weeds, thin vertical high-rises boasting, to the memory of Marx and Engels, sacrilegious names: Hotel Intercontinental; Sharp; Bank Austria. As a piece of municipal scenery, the Pałac bears the comparison well: it is no Chrysler Building, but it has a permanence and grandeur singularly lacking from the more modern constructions in its environment. In a century, it will still stand; I wouldn’t lay that bet about any of the new buildings. Still, all the time its Communist roots are being re-explained. Stalin, who commissioned the structure, has been obliterated from the book – literally, a volume carried by one of the bas-reliefs has his name plastered out (Marx, Engels and Lenin lived on to tell their tale), as part of a process apparently known as “de-Stalinisation”.

Back to my working theory. Unimaginative it may be, but it’s a coherent and simple theory, if outrageously condescending – I’ve barely been in the place half an hour – and it is one I presume locals wouldn’t recognise. They’d see it as either utterly false, or at least so ignorant of nuance, undercurrent and competing cross-current as to be meaningless and worthless to a local who must to navigate the cultural and social dynamics of this place every day. Communism died twenty years ago, it was only around for seventy years in the first place, and in that time other transformative revolutions would have affected life more profoundly than any centrally planned economy could, no matter how oppressive (the Second World War, for one). And Poland wasn’t invented in 1918, after all.

Painting with a broad brush and the limited palette of a narrow (or ignorant) historical perspective is a tourist’s luxury (and prerogative); a tourist’s picture isn’t designed to be heavy duty or to carry much content (enough to make for an interesting trip and competently flag down taxis and order coffee). A six month stay in Warsaw would be a different proposition and might yield a very different and more detailed painting; I’d be obliged to flesh out my telling of the Warsaw story a very different way. But there would be vestiges of my caricatured first impression.

That is how, invariably, we arrive at conclusions. My strong suspicion is that, in most walks of life, when confronted with a novel situation, as a point of entry we exercise our tourist’s prerogative: form preliminary views based on whatever small and imperfect knowledge we happen to have, and if none, draw analogies to things we do know, test them, meld them, fine tune them. What we don’t – can’t – do is come at a new situation with a completely open mind. There is no point at which we have no view at all – there is no “perfectly rational and unbiased” stance.

But observe that as we progress from our rough-hewn preliminary working model, assuming we don’t immediately reject it outright, as we progress in our understanding, our hypothesis will grow increasingly more elaborate and sophisticated (in the sense of being detailed and complex, as opposed to “representative of reality” as such). Assuming it survives, the more detailed and complex it is, the better will be able to fit “facts”, though there may be isolated portions that don’t reconcile awfully well (if they really are isolated from each other we will tend not to notice the discontinuity and in any case it won’t matter much). At length we will have invested a lot of time and energy and we may find our initial hypothesis has spawned new hypotheses, applications we hadn’t originally contemplated and, as a result, we have new analytical techniques available to us.

All this hard work is cumulative and is put to good use, and none of it is predicated on the original rough-cast view being accurate, as such. But something else happens as our hypothesis progresses in complexity: the opportunity cost of abandoning it increases. In the first half hour of my visit I ran two or three working hypotheses and quickly rejected two; six months afterwards I have invested a great deal of energy, and achieved some workable success, with the one that remained: the price of throwing it away now and starting from scratch becomes increasingly unpalatable unless there is something jarringly wrong with it. 

Foghorns, mist and grammar

But if each of us can see only our own segment of blackly shining asphalt, how can we extrapolate that to a common picture of the world to share with our fellow travellers? We need signposts, foghorns, landmarks, lighthouses – a map, in short – by which we can navigate the terrain.

Some like Steven Pinker see evidence for a lingua franca: a common grammar shared by all human languages which is pre-wired by evolution into the cognitive faculties all human beings. On this view language – and therefore the particular rendition of the universe it affords – is as much a product of our biology as our arms or eyes, and through the office of this grammar there is a universal means of perceiving the world. In other words, after all, there is a single common map by which we do orient ourselves and avoid colliding with each other, and by reference to which all uncertainties and misunderstandings can be resolved.

It is courtesy of just this innate universal grammar that we can “shape events in each other’s brains with exquisite precision”.

As we pass the 200^th anniversary of Charles Darwin’s birth, one might remark in the margin at the huge variety of social, political and philosophical literature which claims Darwin’s intellectual antecedence. Some might see this as evidence of the rude health in which Darwin’s Dangerous Idea finds itself a couple of centuries on – universal acid indeed, as Daniel Dennett termed it. Others might wonder whether such universal acidity is symptomatic of weakness in Darwin’s programme: a theory which can be all things to all people ends up being nothing to anyone; there’s a point where flexibility needed for multiple applications tips into ambiguity and incoherence.

For me, Pinker’s account or universal grammar, Darwin-certified or not, leaves something out. Even if it were sufficiently, exquisitely, precise as to permit only a single literal interpretation for a given statement (as far as I can tell, it isn’t), there would still be an infinite universe of possible figurative interpretations of the same statement, and grammar – the rules for constructing meanings from words – cannot help us with our vocabulary. When Lou Reed tells us, at the end of his exquisitely miserable single Perfect Day, “You’re going to reap just what you sow”, grammar is no help in determining whether or not he was talking about gardening, and whether it really was a “perfect day”, or perhaps there was just a little bit of irony interlaced. 

But – and here’s the thing – the ambiguity conferred by the possibility of metaphor is not an obstacle only for our poets and novelists. Exactly the same ambiguity, the susceptibility to figurative meaning, infests every statement, however strictly empirical or even mathematical. Indeed, that was the very problem with Bertrand Russell’s Principia Mathematica, so deftly exposed by Goedel. This is significant, because it suggests there is no difference between literature and science might not be as ontological as scientists tend to suppose.

So how are we meant to identify each time, from the infinite set of possible meanings, the right one? Like any natural language, English is no more and no less than a formal logical system, like Mathematics. In these technologically revolutionary times we are confronted, as never before, by the fact that English is a numeric system: Every character can in theory be and, for the purpose of electronic processing of data, is assigned its own digit – the ASCII code. A computer can only understand text by reducing it to numbers.

And in the same way that a mathematical system is, English is (non-viciously) circular (you can only validly define an English expression in terms of other English expressions: evidence: the Shorter Oxford Dictionary, a document which defines and explains the set of “every word in the English language” wholly in terms of words taken from that very same set).

Ultimately, the meanings we hang on the intricate latticework of words we create each day comes from beyond the formal set of symbols which comprise the English language. “Meaning in the world” when we apply our own respective vocabularies to the formal symbols in the language. Notwithstanding the Shorter Oxford Dictionary, the set of formal symbols in practical use in any single person’s language will almost certainly be unique, and the precise meanings which that person assigns to that set of symbols, being completely functional on that person’s individual life history, definitely will be.

Einstein, Newton, Markopolos and Madoff - and what they teach us

Imagine Albert Einstein lived not at the beginning of the twentieth century, but in the early Eighteenth Century. Imagine he was an Austrian patent clerk without any scientific credentials or standing, but nonetheless had managed to devise and publish his theory of relativity, exactly as it was finally published, only in 1730, just 43 years after Newton originally published his Philosophae Naturalis Principia Mathematica. At this time classical mechanics (of the Force = Mass x Acceleration variety) was widely accepted and was a perfectly well functioning, pragmatic, simple account of celestial (and every day) mechanics).
Let’s say Einstein had correctly anticipated, in broad-brush terms, all the supporting scientific development which would be needed for Relativity to be a coherent scientific, well formed and operational thesis.


Now, in those circumstances as they were: an unknown Austrian clerk pitting himself against a man who was Lucasian Professor of Mathematics at Cambridge University and President of the Royal Society, and whose theory of mechanics appeared to work perfectly well, what is more – would Einstein’s theory would have gained any currency in the scientific community?
Allow that Einstein might have argued for this theory on the grounds that, at extremely high velocities, the supposed relations between acceleration, mass and force would not hold up: that, at the limit, classical mechanics was wrong.
I contend that Einstein’s theory would have been rejected for certain (for all we know such a theory was proposed, but hasn’t survived the ensuing centuries). Here are some of the reasons that would have been given for rejection:

• You have no credentials. You’re a crackpot. You’re quesrtioning one of the greatest scientific minds in the history of the western intellectual tradition. Go away, get properly credentialised as a scientist (by studying the works of people like Isaac Newton), and then see if you still agree with your deluded theory.
  
• Your theory is hopelessly complicated, counter-intuitive, and involves the absurd requirement that we reject the constancy of space and time, and instead agree on the constancy of the speed of light. It fails, utterly, the principle of Occam’s Razor.
  
• There is simply no need for this theory. Mr. Newton’s existing theory is perfectly adequate for our needs.
  

Of course, this is speculation, and probably idle speculation. But were we to know the answer, we would have a real insight into how science – or any community of experts – works.
Recently there has been a fascinating example of just such a situation, not in the annals of science, but in the arcane and highly specialised world of fund management.


Bernard Madoff was little known outside the New York investment community before late 2008. Nonetheless, before that time he was one of the most respected and successful senior members of the New York financial community – itself the most sophisticated gathering of financial experts anywhere in the world. He chaired the Nasdaq stock exchange, at one stage was the largest market maker on it, and ran a hedge fund for 48 years, which he grew from a $5,000 investment in 1960 to a portfolio, of of 2008, with something like $50 billion under management.
His firm, Madoff Securities LLC, was the largest single hedge fund on the planet. Amongst his clients were some of the most storied names in international finance, including Fairfield Greenwich, Banco Santander and HSBC, each of whom invested more than a billion dollars. Madoff’s returns over serveral years were consistent, regular, and immensely impressive: They averaged 12-13 per cent, after fees, every year.


Yet, as we all now know, Bernard Madoff was running a giant, fraudulent Ponzi Scheme. The returns, the positions he purported to be invested in and the cashflows were all fictional. To the best of anyone’s knowledge now, it seems Madoff was using the continuing stream of new customer investments to pay returns to existing customers.


Now, with the benefit of hindsight, commentators say Madoff’s claims are laughable; his supposed returns preposterous: they defied known laws of mathematics as much as economics given the strategy he purported to pursue.


We can only stare bewildered into vacant space wondering how an industry apparently based on the very principle of excellent management of just this sort of risk, where self-interested individuals with literally hundreds of million dollars of their own (and their clients’) money at stake, can have possibly let this happen. We do know that it did, and that is that.
So let’s consider the 17^th Century Einstein scenario. What would have happened if, say three years ago, the appropriate regulatory authorities were warned, in minute detail, that the only possible explanation for Bernard Madoff’s returns were that he was fraudulent? If the equivalent of our anonymous patent clerk from Austria set out in a single, clear, concise and compelling document, entitled “The World’s Largest Hedge Fund is a Fraud”. Imagine if that 15 page document alleged that it was highly likely that Madoff Securities is the world’s largest Ponzi Scheme”, and outlined nearly 30 “red flags” correctly predicting analysis existing publicly available evidence that was only consistent with insider trading or a Ponzi Scheme.

Now this is far more striking than the evidence Einstein could have hoped to level against Newton. What would have been the likelihood of the Securities and Exchange Commission acting on that information. Again, I would say – admittedly, with the benefit of hindsight – it would be low. I say wit the benefit of hindsight because that’s exactly what someone did do – an options trader by the name of Harry Markopolos, in November 2005. You can see his document for yourself online, and now he's published a book about it. The SEC took absolutely no action.

This isn’t offered in indictment of securities regulation in the United States (not by me, at any rate; Markopoulos feels differently)  – almost the contrary. What I think this speaks to is the limitations of rational argument – the same limitations apply not just in finance and politics, but also in science and academia. These collective self-delusions don’t only arise in the absence of free debate contrary, but more or less in spite of it, and in almost any intellectual field: science, sociology, politics, ethics, finance, sport – all are susceptible to mass delusion.

This ought to tell us something about how we collectively think about things. Our claim to rationality seems not to be as robust as we might like it to be. With irony, we wonder, is our belief in our own rationality itself a product of mass delusion?