J. W. Mason – Keynes on Newton and the Methods of Science

How Isaac Newton thought and approached questions. Very different than one might think and why that is relevant for economics.

J. W. Mason is Associate Professor of Economics at John Jay College, City University of New York and a Fellow at the Roosevelt Institute.

This article  is cross posted from J. W. Masons blog The Slack Wire


Photo: Alina Zienowicz via Wikimedia Commons

Among the dazzling array of prose produced by John Maynard Keynes are a couple of short sketches of Isaac Newton, collected in his Essays in Biography. The two pieces are fascinating in their own right, but they’re particularly worthwhile for anyone who has wondered about the relationship between the methods and the subject matter of physics, and what it might mean to apply those methods in the social sciences.

Keynes’ 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.”

It’s not a secret, of course, that Newton had an interest in the occult, in 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In Keynes’ view — supported by the vast collection of unpublished papers Newton left after his death, which Keynes made it his mission to recover for Cambridge — Newton looked for a mathematical pattern in the movements of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 Michel Foucault’s discussion in The Order of Things of 16th century comparative anatomy. When an early-modern scholar like Pierre Belon carefully compares the structures of a bird’s skeleton to a human one, it may superficially resemble modern biology. But, says Foucault, it 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.”

In the same way, Newton’s scientific work was 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 television shows, intellectual work is almost never presented in any other way.) Some problems really do have answers like this. Many, of course, do not. And 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. (How much the imagined object of envy resembles actual physics is a topic for anther time.) 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 emphasizing, are hardly 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 application 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 physics envy in this sense. 

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, and often, as in Newton’s case, by the same people. We have not 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 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 lovely 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.

One way of reading this quote is 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 is arguably the essence of a scientific mindset – the willingness to accept ignorance and uncertainty. As the economist Peter Dorman has observed, the key thing that 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.

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