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In Keynes’ view — supported by the vast collection of unpublished papers Newton left after his death, which Keynes made it his mission to recover for Cambridge — Newton looked for a mathematical pattern in the movements of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 All his unpublished works on esoteric and theological matters are marked by careful learning, accurate method and extreme sobriety of statement.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.

Links for September 23

I am going to strive to make these posts weekly. People need things to read.

 

The trouble with macro. I haven’t yet read any of the latest big-name additions to the “what’s wrong with macroeconomics?” pile: Romer (with update), Kocherlakota, Krugman, Blanchard. I should read them, maybe I will, maybe you should too. Here’s my own contribution, from a few years ago.

 

Tankus notes. You may know Nathan Tankus from around the internet. I’ve been telling him for a while that he should have a blog. He’s finally started one, and it’s very much worth reading. I’m having some trouble with one of his early posts. Well, that’s how it works: You comment on what you disagree with, not the things you think are smart and true and interesting — which in this case is a lot.

 

The shape of the elephant. Branko Milanovic’s “elephant graph” shows the changes in the global distribution of income across persons since 1980, as distinct from the more-familiar distribution of income within countries or between countries. The big story here is that while there has been substantial convergence, it isn’t across the board: The biggest gains were between the 10th and 75th percentiles of the global distribution, and at the very top; gains were much smaller in the bottom 10 percent and between the 70th and 99th percentiles. One question about this has been how much of this is due to China; as David Rosnick and now Adam Corlett of the Resolution Fondation note, if you exclude China the central peak goes away; it’s no longer true that growth was unusually fast in the middle of the global distribution. Corlett also claims that the very slow growth in the upper-middle part of the distribution — close to zero between the 75th and 85th percentiles — is due to big falls in income in the former Soviet block and Japan. Initially I liked the symmetry of this. But now I think Corlett is just wrong on this point; certainly he gives no real evidence for it.  In reality, the slow growth of that part of the distribution seems to be almost entirely an artifact due to the slow growth of population in the upper part of the distribution; correct for that, as Rosnick does here, and the non-China distribution is basically flat between the 10th and 99th percentiles:

Source: David Rosnick
Source: David Rosnick

Yes, there does seem to be slightly slower growth just below the top. But given the imprecision of the data we shouldn’t put much weight on it. And in any case whatever the effect of falling incomes in Japan and Eastern Europe (and blue-collar incomes in the US and western Europe), it’s trivial compared to the increase in China. Outside of China, the global story seems to be the familiar one of the very rich pulling ahead, the very poor falling behind, and the middle keeping pace. Of course, it is true, as the original elephant graph suggested, that the share of income going to the upper-middle has fallen; but again, that’s because of slower population growth in the countries where that part of the distribution is concentrated, not because of slower income gains.

It’s important to stress that no one is claiming that Branko’s figures are wrong, and also that Branko is on the side of the angels here. He’s been fighting the good fight for years against the whiggish presumption of universal convergence.

 

Equality of opportunity and revolution. Speaking of Branko, here he is on the problem with equality of opportunity:

Upward mobility for some implies downward mobility for the others. But if those currently at the top have a stronghold on the top places in society, there will no upward mobility however much we clamor for it. … In societies that develop quickly even if a lot of mobility is about positional advantages, … it can be compensated by creating enough new social layers, new jobs and by making people richer. …

In more stagnant societies, mobility becomes a zero-sum game. To effect real social mobility in such societies, you need revolutions that, while equalizing chances or rather improving dramatically the chances of those on the bottom, do so at the cost of those on the top. … The French Revolution, until Napoleon to some extent reimposed the old state of affairs, was precisely such an upheaval: it oppressed the upper classes (clergy and nobility) and promoted the poorer classes. The Russian revolution did the same thing; it introduced an explicit reverse discrimination against the sons and daughters of former capitalists, and even of the intellectuals, in the access to education.

I think this is right. The principle of equality of opportunity is incompatible, not just practically but logically, with the principle of inheritance. The only way to realize it is to deprive those at the top of their power and privileges, which by definition is possible only in a revolutionary situation. This is one reason why I have no interest in a political program defined, even in its incremental first steps, in terms of equality of income or wealth. The goal isn’t equality but the abolition of the system which makes quantitative comparisons of people’s life-situations possible.

The post continues:

There is also an age element to such revolutions which fundamentally alter societies and lift those from below to the top. The young people benefit. In a beautiful short novel entitled “The élan of our youth” Alexander Zinoviev, a Russian logician and later dissident, describes the Stalinist purges from a young man’s perspective. The purges of all 40- or 50-year old “Trotskyites” and “wreckers” opened suddenly incredible vistas of upward mobility for those who were 20- or 25-year old.  They could hope, at best, to come to the positions of authority in ten or fifteen years; now, that were suddenly thrown in charge of hundreds of workers, became chief designers of airplanes, top engineers of the metro. What was purge and Gulag for some, was upward mobility for others.

As this suggests, the overturning ofhierarchies didn’t stop with the revolutions themselves — that was the essential content of the various purges, to prevent a new elite from consolidating itself. I’ve always wondered how much vitality revolutionary France and Russia gained from these great overturnings. There are an enormous number of working-class people in our society, I have no doubt, who would be much more capable of running governments and factories, designing airplanes and subways, or teaching economics for that matter, than the people who get to do it.

 

We simply do not know — but we can fake it. Aswath Damodaran has a delicious post on the valuations that Elon Musk’s bankers came up with to justify Tesla’s acquisition of Solar City. The basic problem in these kinds of exercises is that the same price has to look high to the shareholders of the acquired company and low to the shareholders of the acquiring company. In this case, the Solar City shareholders have to believe that the 0.11 Tesla shares they are getting are worth more than the Solar City share they are giving up, while the Tesla shareholders have to believe just the opposite — that one Solar City share is worth more than the 0.11 Tesla shares they are giving for it. You can square this circle by postulating some gains from the combination — synergies! efficiencies! or, sotto voce, market power — that allows the acquirer to pay a premium over the market price while still supposedly getting a bargain. Those gains may be bullshit but at least there’s a story that makes sense. But as Damodaran explains, that isn’t even attempted here. Instead the two sets of advisors (both ultimately hired by Musk) simply use different assumptions for the growth rates and cost of capital for the two companies, generating two different valuations. For instance, Tesla’s advisors assume that Solar City’s existing business will grow at 3-5% in perpetuity, while Solar City’s advisors assume the same business will grow at 1.5-3%. So one set of shareholders can be told that a Solar City share is definitely worth less than 0.11 Tesla shares, while the other set of shareholders can be told that it is definitely worth more.

So what’s the interest here? Obviously, it’s always fun to se someone throwing shoes at the masters of the universe. But with my macroeconomist hat on, the important thing is it’s a snapshot of the concrete sociology behind the discounting of future cashflows. Whenever we talk about “the market” valuing some project or business, we are ultimately talking about someone at Lazard or Evercore plugging values into a spreadsheet. This is something people who imagine that production decisions are or can be based on market signals — including my Proudhonist friends — would do well to keep in mind. Solar City lost money last year. It lost money this year. It will lose money next year. It keeps going anyway not because “the market” wants it to, but because Musk and his bankers want it to. And their knowledge of the future isn’t any better founded than the rest of ours. Now, you could argue that this case is noteworthy because the projections are unusually bogus. Damodaran suggests they aren’t really, or only by degree. And in any case this sort of special pleading wouldn’t work if there were an objective basis for computing the true value of future cashflows. I suspect it was precisely Keynes’ experience with real-world financial transactions like this that made him stress the fundamental unknowability of the future.

 

Uber: The bar mitzvah moment. While we’re reading Damodaran, here’s another well-aimed shoe, this one at Uber. As he says, pushing down costs is not enough to make profits. You also need some way of charging more than costs. You need some kind of monopoly power, some source of rents: network externalities; increasing returns, and the financing to take advantage of them; proprietary technology; brand loyalty; explicit or implicit collusion with your competitors. Which of these does Uber have? maybe not any? Uber’s foray into self-driving cars is perhaps a way to generate rents, though they’re more likely to accrue to the companies that actually own the technology; I think it’s better seen as a ploy to convince investors for another quarter or two that there are rents there to be sought.

Izabella Kaminska covers some of the same territory in what may be the definitive Uber takedown at FT Alphaville. Though perhaps she focuses overmuch on how awful it would be if Uber’s model worked, and not enough on how unlikely it is to.

 

On other blogs, other wonders. 

San Francisco Fed president John Williams writes, “during a downturn, countercyclical fiscal policy should be our equivalent of a first responder to recessions.” Does this mean that MMT has won?

Mike Konczal: Trump is full of policy.

My friend Sarah Jaffe interviews my friend Vamsi, on the massive strikes going on in India.

The Harry Potter books are bad books and and have a bad, childish, reactionary view of the world. So does J. K. Rowling.

The Mason-Tanebaum household has its first byline in the New York Times this week, with Laura’s review of the novel Black Wave in the Sunday books section.