Keynes on Newton and the Methods of Science

I’ve just been reading Keynes’ short sketches of Isaac Newton in Essays in Biography. (Is there any topic he wasn’t interesting on?) His thesis is that Newton was not so much the first modern scientist as “the last of the magicians” — “a magician who believed that by intense concentration of mind on traditional hermetics and revealed books he could discover the secrets of nature and the course of future events, just as by the pure play of mind on a few facts of observation he had unveiled the secrets of the heavens.”

The two pieces are fascinating in their own right, but they also crystallized something I’ve been thinking about for a while about the relationship between the methods and the subject matter of the physical sciences.

It’s no secret that Newton had an interest in the occult, astrology and alchemy and so on. Keynes’ argument is that this was not a sideline to his “scientific” work, but was his project, of which his investigations into mathematics and the physical world formed just a part. In Keynes’ words,

He looked on the whole universe and all that is in it as a riddle, as a secret which could be read by applying pure thought to … mystic clues which God had laid about the world to allow a sort of philosopher’s treasure hunt to the esoteric brotherhood. He believed that these clues were to be found partly in the evidence of the heavens and in the constitution of elements… but also partly in certain papers and traditions … back to the original cryptic revelation in Babylonia. …

In Keynes’ view — supported by the vast collection of unpublished papers Newton left after his death, which Keynes made it his mission to recover for Cambridge — Newton looked for a mathematical pattern in the movements of the planets in exactly the same way as one would look for the pattern in a coded message or a secret meaning in a ancient text. Indeed, Keynes says, Newton did look in the same way for secret messages in ancient texts, with the same approach and during the same period in which he was developing calculus and his laws of motion.

There was extreme method in his madness. All his unpublished works on esoteric and theological matters are marked by careful learning, accurate method and extreme sobriety of statement. They are just as sane as the Principia, if their whole matter and purpose were not magical. They were nearly all composed during the same twenty-five years of his mathematical studies. 

Even in his alchemical research, which superficially resembled modern chemistry, he was looking for secret messages. He was, says Keynes, “almost entirely concerned, not in serious experiment, but in trying to read the riddle of tradition, to find meaning in cryptic verses, to imitate the alleged but largely imaginary experiments of the initiates of past centuries.”

There’s an interesting parallel here to Foucault’s discussion in The Order of Things of 16th century comparative anatomy. When someone like Pierre Belon carefully compares the structures of a bird’s skeleton to a human one, it superficially resembles modern biology, but really “belongs to the same analogical cosmography as the comparison between apoplexy and tempests,” reflecting the idea that man “stands in proportion to the heavens just as he does to animals and plants.”

Newton’s “scientific” work was, similarly, an integral part of his search for ancient secrets and, perhaps, for him, not the most important part. Keynes approvingly quotes the words that George Bernard Shaw (drawing on some of the same material) puts in Newton’s mouth:

There are so many more important things to be worked at: the transmutations of matter, the elixir of life, the magic of light and color, above all the secret meaning of the Scriptures. And when I should be concentrating my mind on these I find myself wandering off into idle games of speculation about numbers in infinite series, and dividing curves into indivisibly short triangle bases. How silly!

None of this, Keynes insists, is to diminish Newton’s greatness as a thinker or the value of his achievements. His scientific accomplishments flowed from this same conviction that the world was a puzzle that would reveal some simple, logical, in retrospect obvious solution if one stared at it long enough. His greatest strength was his power of concentration, his ability to

hold a problem in his mind for hours and days and weeks until it surrendered to him its secret. Then being a supreme mathematical technician he could dress it up… for purposes of exposition, but it was his intuition which was pre-eminent … The proofs … were not the instrument of discovery. 

There is the story of how he informed Halley of one of his most fundamental discoveries of planetary motion. ‘Yes,’ replied Halley, ‘but how do you know that? Have you proved it?’ Newton was taken aback—’Why, I’ve known it for years,’ he replied. ‘ If you’ll give me a few days, I’ll certainly find you a proof of it’—as in due course he did. 

This is a style of thinking that we are probably all familiar with — the conviction that a difficult problem must have an answer, and that once we see it in a flash of insight we’ll know that it’s right. (In movies and tv shows, intellectual work is almost never presented in any other way.) Some problems really do have answers like this. Many, of course, do not. But you can’t necessarily know in advance which is which. 

Which brings me to the larger point I want to draw out of these essays. Newton was not wrong to think that if the motion of the planets could be explained by a simple, universal law expressible in precise mathematical terms, other, more directly consequential questions might be explained the same way. As Keynes puts it,

He did read the riddle of the heavens. And he believed that by the same powers of his introspective imagination he would read the riddle of the Godhead, the riddle of past and future events divinely fore-ordained, the riddle of the elements…, the riddle of health and of immortality. 

It’s a cliché that economists suffer from physics envy. There is definitely some truth to this (though how much the object of envy resembles actual physics I couldn’t say.)  The positive content of this envy might be summarized as follows: The techniques of physical sciences have yielded good results where they have been applied, in physics, chemistry, etc. So we should expect similar good results if we apply the same techniques to human society. If we don’t have a hard science of human society, it’s simply because no one has yet done the work to develop one. (Economists, it’s worth noting, are not alone in believing this.)

In Robert Solow’s critical but hardly uniformed judgement,

the best and the brightest in the profession proceed as if economics is the physics of society. There is a single universal model of the world. It only needs to be applied. You could drop a modern economist from a time machine … at any time in any place, along with his or her personal computer; he or she could set up in business without even bothering to ask what time and which place. In a little while, the up-to-date economist will have maximized a familiar-looking present-value integral, made a few familiar log-linear approximations, and run the obligatory familiar regression. 

It’s not hard to find examples of this sort of time-machine economics. David Romer’s widely-used macroeconomics textbook, for example, offers pre-contact population density in Australia and Tasmania (helpfully illustrated with a figure going back to one million BC) as an illustration of endogenous growth theory. Whether you’re asking about GDP growth next year, the industrial revolution or the human population in the Pleistocene, it’s all the same equilibrium condition.

Romer’s own reflections on economics methodology (in an interview with Snowdon and Vane) are a perfect example of what I am talking about. 

As a formal or mathematical science, economics is still very young. You might say it is still in early adolescence. Remember, at the same time that Einstein was working out the theory of general relativity in physics, economists were still talking to each other using ambiguous words and crude diagrams. 

In other words, people who studied physical reality embraced precise mathematical formalism early, and had success. The people who studied society stuck with “ambiguous words and crude diagrams” and did not. Of course, Romer says, that is now being corrected. But it’s not surprising that with its late start, economics hasn’t yet produced as definite and useful knowledge as the physical science have.  

This is where Newton comes in. His occult interests are a perfect illustration of why the Romer view gets it backward. The same techniques of mathematical formalization, the same effort to build up from an axiomatic foundation, the same search for precisely expressible universal laws, have been applied to the whole range of domains right from the beginning — often, as in Newton’s case, by the same people. We have not, it seems to me, gained useful knowledge of orbits and atoms because that’s where the techniques of physical science happen to have been applied. Those techniques have been consistently applied there precisely because that’s where they turned out to yield useful knowledge.

In the interview quoted above, Romer defends the aggregate production function (that “drove Robinson to distraction”) and Real Business Cycle theory as the sort of radical abstraction science requires. You have “to strip things down to their bare essentials” and thoroughly grasp those before building back up to a more realistic picture.

There’s something reminiscent of Newton the mystic-scientist in this conviction that things like business cycles or production in a capitalist economy have an essential nature which can be grasped and precisely formalized without all the messy details of observable reality. It’s tempting to think that there must be one true signal hiding in all that noise. But I think it’s safe to say that there isn’t. As applied to certain physical phenomena, the idea that apparently disparate phenomena are united by a single beautiful mathematical or geometric structure has been enormously productive. As applied to business cycles or industrial production, or human health and longevity, or Bible exegesis, it yields nonsense and crankery. 

In his second sketch, Keynes quotes a late statement of Newton’s reflecting on his own work:

I do not know what I may appear to the world; but to myself I seem to have been only like a boy, playing on the sea-shore, and diverting myself in now and then finding a smoother pebble or a prettier shell than ordinary, whilst the great ocean of truth lay all undiscovered before me. 

I’m sure this quote is familiar to anyone who’s read anything about Newton, but it was new and striking to me. One way of reading it as support for the view that Newton’s scientific work was, in his mind, a sideshow to the really important inquiries which he had set aside. But another way is as a statement of what I think is arguably the essence of a scientific mindset – the willingness to a accept ignorance and uncertainty. My friend Peter Dorman once made an observation about science that has always stuck with me – that what distinguishes scientific thought is the disproportionate priority put on avoiding Type I errors (accepting a false claim) over avoiding Type II errors (rejecting a true claim). Until an extraordinary degree of confidence can be reached, one simply says “I don’t know”.

It seems to me that if social scientists are going to borrow something from the practices of Newton and his successors,  it shouldn’t be an aversion to “ambiguous words,” the use calculus or geometric proofs, or the formulation of universal mathematical laws. It should be his recognition of the vast ocean of our ignorance. We need to accept that on most important questions we don’t know the answers and probably cannot know them. Then maybe we can recognize the small pebbles of knowledge that are accessible to us.

Nonoverlapping Magisteria

This looks like an interesting book.

She’s arguing, as I understand it, that science cannot be ontologically complete, that it always coexists with other kinds of truth:

There is always ‘room left’ for alternative ontologies in cognitive-intellectual space, a realm that is neither cramped nor finite but, on the contrary, appears – both historically and for humans individually – exceedingly and perhaps infinitely elastic. … For many people … accepting, applying, and/or producing scientific knowledge and being religiously observant are no more in conflict than would be, for any of us, both playing the violin and practising law.

Interesting, maybe, as a bare assertion; more for the particular argument. Let’s say, on the one hand, that we accept a scientific view of religion. It’s a pattern of human behavior created by the interaction of our biological brains and our social environment; the potential for it was favored by its usefulness to our savannah ancestors and its actual existence by its usefulness for some social-political purpose today. Group cohesion then, the ploys of the Jesuits now, something like that.

The problem with this isn’t that it isn’t true; it is true, within some limits. The problem is that it explains too much. Every human belief system is the product of our Darwinianly-evolved brains and our social environment. You can fully explain religion, in principle, by a combination of genetic predisposition and practical advantage, but you can just as fully explain science, or anything else that people do. After all, we’re natural beings in the natural world; everything we do has a natural explanation. The most you can say in this framework is that science has displaced religion from many areas of life because of its greater utility; but by the same token you have to concede that religion has held on in other areas thanks to its greater utility. A purely naturalistic account of human beliefs has no place for them being true or false. People adopt them all for the same kind of reasons.

(Sraffa to Wittgenstein: “If the rules of language can be constructed only by observation, there can never be any nonsense said. This identifies the cause and the meaning of a word. The language of birds, as well as the language of metaphysicians can be interpreted consistently in this way. It is only a matter of finding the occasion on which they say a thing, just as one finds the occasion on which they sneeze.”)

On the other hand, almost anyone who cares about science prefers to believe it corresponds to some external truth about the world. One can’t object to this (Thomas Nagel, in this review, accuses Smith of objecting, but I suspect he’s got her wrong), but it’s not consistent with science being ontologically complete. A scientific account of scientific beliefs can offer various reasons for why people happen to hold them, but it has nothing to say about whether they are true. You may believe, if you like, that Betelgeuse would be 630 light years from the Earth whether anyone had measured the distance or not; but in a naturalistic account of why people do believe that, it all comes down to the measurements; independent of those the “objective” distance has no effect on anyone.

Put it another way: science offers heuristics for sorting beliefs into relatively confirmed and relatively falsified piles; but it doesn’t, and can’t, tell you why should prefer to hold the beliefs in the confirmed pile. Oh, say the new atheists, because they’re more useful. But right there they’ve conceded that if someone finds some social or psychological advantage in being religious, that’s as justified as anyone’s belief in science. To get along with your neighbors, to be free of angst about The Point of It All: aren’t those useful too?

Galileo is a hero of science and of civilization for eppur si muove. But what’s he saying? With respect to the heavens, he’s asserting that the demands of reality take precedence over what we think is right. But with respect to the earth, it’s just the opposite: He’s insisting on the priority of abstract right over concrete reality. After all, if he applied the same unromantic empiricism to his life as he did to his astronomy, he’d take one look at the instruments and conclude that practical experimentation revealed that the Earth goes around the Sun. (As did Brecht’s Galileo.) A belief that’s liable to get you tortured to death is pretty clearly less practically useful than a belief that leaves you torture-free. Galileo’s insistence that one should believe in science, come what may, is entirely unscientific, and — Brecht struggled with this — so much the better for Galileo.

The thing about the contradiction between the scientific method and belief in science is that it can be resolved either way. Nagel thinks that Smith is trying to apply the naturalistic, constructivist view of human beliefs “all the way down”. Me, I prefer to think she’s showing that’s exactly what you cannot do.

How biologists think about genes

From Tangled webs: Tracing the connections between genes and cognition, by Simon E. Fisher:

The deceptive simplicity of finding correlations between genetic and phenotypic variation has led to a common misconception that there exist straightforward linear relationships between specific genes and particular behavioural and/or cognitive outputs. The problem is exacerbated by the adoption of an abstract view of the nature of the gene, without consideration of molecular, developmental or ontogenetic frameworks. … Genes do not specify behaviours or cognitive processes; they make regulatory factors, signalling molecules, receptors, enzymes, and so on, that interact in highly complex networks, modulated by environmental influences, in order to build and maintain the brain. …

What is a gene? Answering this question is far from trivial, but a useful operational definition might be ‘‘a stretch of DNA whose linear sequence of nucleotides encodes the linear sequence of amino acids in a specific protein’’. … It is important to realise that the appearance and biology of a mature organism is the result of a complex series of ontogenetic events unfolding over time, moderated by environmental and stochastic influences. Genomes are much more like knitting patterns or recipes than blueprints (although even the former are poor analogies for the peculiarities of the genome). …

The apparent ease of correlating genotype with phenotype without reference to molecular/developmental mechanisms promotes an erroneous impression of neurogenetics; one in which individual genes are able to mysteriously control specific behaviours or cognitive abilities, leading to talk of ‘‘language genes’’, ‘‘smart genes’’, ‘‘gay genes’’, ‘‘aggressive genes’’ and so on. It is indisputable that variations of gene sequence can contribute to variability in cognitive abilities and personality traits (sometimes in a dramatic manner) and that apparently straightforward genotype-phenotype correlations can sometimes emerge in our datasets. But the simplicity of these relationships is merely an illusion; genes do not (and indeed can not) specify particular behavioural outputs or cognitive processes, except in the most indirect way. … The gross activities of the human brain are the products of a complex interplay between factors at multiple levels; be they genetic, cellular, developmental, anatomical, or environmental, and the routes linking genes to cognition will inevitably be tortuous…

… the gap between genes and cognition can only be bridged by a thorough systems biology account of brain development and function. Even pure candidate gene approaches can be victims of the ‘‘abstract gene’’ perspective. In many cases, when researchers find statistical evidence to support association between a particular variant of a gene and a common trait, it is erroneously assumed on the basis of this that the variant is likely to be causative and that there is a simple pathway connecting gene to trait. … There is a large gulf between finding statistical evidence for a genotype-phenotype correlation and demonstrating a convincing causal relationship…

There is no doubt that the gene known as FOXP2 is relevant to linguistic ability. However, any characterisation of this as a ‘‘gene for grammar’’ clearly becomes untenable once we are able to view it within a more complete biological framework. … Reduced amounts of functional FOXP2 protein can lead to disordered brain development or function, in a manner that primarily interferes with speech and/or language abilities. … this is emphatically not the same as saying that FOXP2 is a ‘‘gene for speech’’ or a ‘‘gene for language’’… FOXP2 [also] regulates key pathways in the developing lung, heart and gut. …. The recycled use of the same regulatory factors to control multiple pathways in different developmental contexts is a common feature of complex biological systems; it is rare to find a transcription factor that has an exclusive role specific to only one context. Thus, calling FOXP2 a ‘‘language gene’’ makes no more sense than referring to it as a ‘‘lung gene’’… the data on FOXP2 from molecular and developmental biology confounds any expectations that one might have for a hypothetical ‘‘language gene’’; and the reason for this is that this entire concept is flawed, being rooted in an abstract view of the nature of the gene. …

How to think about genes

Pre-scientific or magical thinking has several key features:

* The idea of a direct or intrinsic connection between things, i.e. that if two things influence each other or are associated in some way, they are bound by an occult link, are subject to the same invisible forces. One can instantly affect the other with nothing linking them.
* The idea that the visible characteristics of something are the expression of an invisible essence.
* The failure to distinguish between perceptions an reality, so that anything we see or imagine or experience is assumed to have an independent existence in the objective world.

Popular thinking about genetics has exactly these characteristics. Anything we can say about an organism, any description we give it, is reified as an objective trait of the organism. (As if the placement of an animal in Borges’ Library of Babel was a property of the animal.) These traits are then assumed to be present in the organism’s inner being, i.e. its genes. And the genes are then believed to produce and modify the trait by occult direct action, without any need for specific intermediate transmission mechanisms.

It’s just scholasticism. They said a person who behaved intelligently must have a property of intelligence. We say they must have a gene for it.

The alternative, scientific view insists that until we know the mechanism by which something happens, we don’t know anything about it at all. And there’s no expectation that the mechanism has any formal or inherent resemblance to the observed phenomenon.

The beginning of wisdom is that genes code for proteins. (Or for RNA.) The only thing a gene does is produce a particular protein. Nothing except the protein is the product of the gene, there’s no sense in which a gene is “for” anything else.

These proteins then participate in causal pathways. These pathways always involve the organism’s pre-existing physical state, the products of other genes, and the external environment, and almost always involve the organism’s behavior. Each protein may participate in many pathways, and at least as important, various pathways converge at points where they are interchangeable. Great proportions of this protein or that protein or this dietary change or that behavioral stimulus will all produce the exact same developmental response. And multiple points along the pathway may be sites of selective pressure – there is no sense in which the influence of the gene stops at the point we’ve chosen to identify as a “trait”.

There are many wonderful examples of what this means in practice in Mary Jane West-Eberhard’s Developmental Plasticity and Evolution. There she also makes the somewhat related point that organisms constantly lean on the self-organizing capacities of inorganic matter — another way the whole “code” metaphor is wrong.