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In Keynes’ view — supported by the vast collection of unpublished papers Newton left after his death, which Keynes made it his mission to recover for Cambridge — Newton looked for a mathematical pattern in the movements of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 All his unpublished works on esoteric and theological matters are marked by careful learning, accurate method and extreme sobriety of statement.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.
A big difference is that physicists can literally touch the things they are measuring, so we can easily understand what a meter, or a gram, or an acceleration of 2m/s^2 is.
In economics instead, what is a “real” dollar? Utility? The marginal productivity of a worker? These are all logical constructs that do not have a real immediately measurable counterpart, so this makes checking (falsifying) mathematical models difficult and dubious.
I see what you mean but I would almost argue the exact opposite. If the biggest problem in economics (relative to physics) was that objects such as utility, marginal productivity etc. aren’t immediately measurable, surely this could be addressed by taking the same operationalist approach that seems viable in physics. We would test models involving ‘utility’ the same way a physicist would test models involving ‘force’, by testing their predictions involving observables. The real problem, and the reason this wouldn’t actually work, is that the phenomena studied by economists do not exhibit the same regularities, invariant across time and space and stable under interventions, that the phenomena studied by physicists exhibit (at least approximately).
If anything, the one advantage we have in studying economic behavior is that we have *more direct* knowledge about humans, their motives and intentions, etc., than physicists have about elementary particles. We should make the most of it.
This is an interesting question. It’s certainly true, from where I’m sitting, the many of the objects economic theory is organized around – utility, “real” aggregates, etc. – don’t correspond to any observable object in the world. It’s also true that human societies don’t exhibit the kinds of universal regularities that would be needed for the sort of theories economics seeks to offer. But are these two separate critiques, or two sides of the same problem? It’s not obvious to me.
I highly recommend the first half of Eric Beinhocker’s The Origin of Wealth, which is the best synthesis I’ve read on why the biggest mistake for traditional economics was to adopt the mathematics of 19th century physics and apply to economics.
Second, if you are not familiar with Stephen Wolfram’s theory of computational irreducibility I highly recommend you read his work on the subject, or even just watch one of his many videos he’s made of the subject. But to summarize:
The world is almost entirely computationally irreducible – meaning they’re are no short cuts you can take (ie equations that can be found) which allow you to skip ahead and know how the system will play out. But any computationally irreducible system will have small pockets that are computationally reducible. All of the scientific theories for which we have found mathematical equations that allow precise prediction correspond to these pockets of computational reducibility. But they are the exception in the universe.
For everything else you have to actually run the system to discover how it will play out.
The economy is a complex adaptive system. You can discover general properties for CAS but no mathematical equations will ever be discovered that allow you to skip ahead and make predictions like you can with quantum mechanics for ex.
The big transition in science today is from using equations to describe how everything works to using programs and computation to describe how things work.
“He looked on the whole universe and all that is in it as a riddle…”
And the answer to the riddle was 18.93 GBP per ounce of gold. Very Hitchhiker-esque. 😉
Interesting read, thanks.
This is an interesting discussion! I wonder if Newton is perhaps somewhat of an outlier in the history of science, a pure theorist who could ply his trade equally in matters of empirical soundness and fantasy. And even in his case, empirical foundations had already been laid by others. Galileo recorded the acceleration of a ball rolling down an incline, which indicated that instantaneous speed obeyed a power law (not his terminology of course) and that acceleration from one speed to another was continuous with an infinity of points of measurement.
What is striking about the development of mainstream economic theory is its relative independence from prior empiricism. Ricardo, Walras, Samuelson — not only were they not empiricists, they didn’t build on empiricists. Alas, most empirical tests, ex post, of modern theory are more exercises in calibration than serious tests of possible falsification.
Now does this perspective apply to quantum mechanics? Was there a prior or an accompanying empirical aspect to its development? Or is my belief in the value of empirical/theoretical dialogue in need of revision?
BTW, thanks for the mention about Types I and II error. It’s definitely a corollary that science has to have a high tolerance for acknowledging ignorance and uncertainty.
If we speak of the labour theory of value (Ricardo), while the theory as a whole is quite complex, the basic idea was demonstrated during the industrial revolution: some objects, like cloth, that earlier had a certain price suddenly fell in value, so that many artisans had to change job.
While this isn’t really an empirical proof of the LTV it is a strong suggestion. I see this because it seems to me people today tend to think the LTV is some mistical religious concept, whereas Ricardo and others tought of is as an empirical reality (though their concept of empiricism would not be considered scientific today).
It seems to me that for the LTV to work as a generalization, several things must be true:
1. Prices are proportional to production costs.
2. Labor is the only ultimate input.
3. Production takes place under conditions of constant returns.
4. We have some way of aggregating labor performed at different dates.
The first is not a big problem at the level of theory – almost everyone involved in these debates is willing to set aside monopoly rents and so on as a first approximation. (It is of course an issue when we go to the data.) The second is probably fine for modern economies – it’s much easier to set aside land (as opposed to improvements, which are of course the product of labor) than it was 200 years ago. The third is also fine imo, and is enough to eliminate demand (consumer preferences and so on) as an influence on price. The big problem is 4. This is the Sraffa-Steedman critique of the LTV, which seems to me the only decisive one. If production takes place using a combination of current labor and past labor which is embodied in tools of various kinds, we cannot aggregate that into a single quantity of labor unless we already have a rate of profit or interest from somewhere else. To me tho, this falls into the category of a limitation rather than a refutation.
Also of course labor needs to be homogeneous. That this is tendentially true under capitalism is an important sociological fact that contributes to the LTV’s relevance. To the extent that labor is not homogeneous because of training/education/etc., this is just a subcase of point 4.
My understanding is that this is a problem that was already known to Smith, who wrote something about whisky casket with differential ages of whisky. Smith couldn’t solve the problem, Marx was conscious of the problem and “solved” it by assuming an overall capital to income ratio (that he calls organic composition of capital) and retrofitting prices with his dubious multipliers.
Sraffa came with a different model but IMO it is bascally a more elegant solution for Marx’s multipliers, that depend on the rate of profit (while Marx didn’t realize that the multipliers depend on the rate of profit).
In the real world prices do not really stay exactly on their long term equilibrium positions but bounce a lot, so the problem is quite moot and, if the LTV is correct (as I believe) it is only at a very large approximation.
Ps: Sraffa also reasoned at high level math and not empirically. This reminds me of Jung’s psychological types, where introvert thinkers tend to build very complex systems.
Dear Professor,
I wonder if you’ve ever come across Boris Hessen’s Social and Economic Roots of Newton’s Principia, which was part of the Soviet presentation to the Congress of the History of Science in London in 1931. I think it’s just incredible in explaining the development of Newton’s thought
https://www.surplusvalue.org.au/Science_Environment/Hessen%20Social%20&%20Economic%20Roots%20Newtons%20Principia.pdf
I have not. Looks fascinating – thanks!
Many thanks for this. The extent to which Newton’s mathematical researches were, if anything, an adjunct to his wider project of divining God’s plan (as he supposed it) was touched upon in this relatively recent and well-received work: https://global.oup.com/academic/product/priest-of-nature-9780199995356?cc=us&lang=en&
However, Newton needed to keep some of his heterodox religious views under wraps lest he be deprived of his Trinity fellowship, which was then an overwhelmingly clerical foundation. The symbiotic nature of science, theology, astrology, etc., was characteristic of the age, and some of the most eminent 17th century English mathematicians with whose works he would have been very familiar (Barrow, Oughtred, Wallis, etc.) were first and foremost divines. Oughtred, for example, in addition to being a parson at Albury in Surrey was also actively interested in alchemy and astrology.
Thanks, I hadn’t seen this. I assume that nothing in Keynes’ essays would be new to historians who write about Newton and his milieu. But it was new to me.
Hari Seldon got there. I would be amazed if Asimov had no effect on the push to develop Economics as a mathematical field. Of course, I have no evidence either way. Thanks for this post on Newton and Keynes! Your writing sparked all kinds of connections that I will now have to pin down and think about.
General Balance:
Accumulation = (Input – Output) + (Generation – Consumption)
Given the initial state of a physical system, and provided with a reasonable model for a physical process, characterize the deterministic change in state of the system (accumulation) as input minus output plus generation minus consumption. This is the basic pattern for applying differential equations or finite difference equations in physics, chemistry, and other domains of applied math.
If we can’t find a deterministic model we still apply the concept of a physical process or state transformation except the changes of state are random or otherwise uncertain.
Economics is distinct because the inputs to the system of production are inherently things that we dis-value and the outputs are inherently things that we value. I had a professor of legal philosophy, Hugh Gibbons, who wanted me to draw “liberty curves”. This is the idea that if criminals cause private constraints on individual liberty then the State is justified to impose public constraints in order to maximize liberty under the circumstances. I refused to draw such curves because there was measurement model to apply math – it was only a sketch to discuss the idea that individuals want maximum liberty and freedom from either private constraints or public constraints. I agree with Hugh that a social value exists, “the will of each person”, and that consentual political systems are based on the principle that the will of each person is worthy of respect. I don’t see any way to maximize or optimize the will of each person via any political system or system of “free markets”. I think economics uses buzz words to indirectly make an effort to recognize the will of each person in conflict via political strife or market competition. The math is arbitrary.
Appreciate your comment, but I have to say that this is the sort of thinking that the post is intended to criticize. We are not going to be able to create a mathematical formalization act says anything interesting about “systems” in general. If we want to understand whatever real social phenomena we group under economics, we have to study the historical evolution of real economies.
JW I always appreciate your reasoning in terms of conventional and other economic theory. But as a student of electrical engineering and jurisprudence I see the history of economics as: (1) the political problem of social plans; and (2) the economic problems of scarcity, counter-factual uses of resources, and econometrics. The folk psychology of human values, which I recognize as ethical and moral in dimension, pervade both problems.
Ethical values are two efforts. First, to identify what is good. Second, to identify how a person or group should act to cause the good. Social planning must identify the good and how to coordinate activity to cause the good. People in small and large groups often do not agree on what is good or do not agree on how to cause the good. So in my model of folk psychology there is the perpetual ethical planning problem that I call “politics”.
Moral values pertain to the social judgment of human actions and perceived outcomes. If an outcome is not caused by a moral agent then we attribute it to God or Nature rather than a moral agent. We recognize moral agents and we generate and impose moral judgments concerning the behavior of moral agents.
Hugh Gibbons, my professor of legal philosophy, was an economist turned legal philosopher. He describes the political problem in terms of the will. To define the will he uses an I-statement: I am the cause of my desired perceptions. Hugh thought that the law can be a means to optimize or maximize liberty – the will of each person – and I think this is what the conventional economist means unconsciously by their concept of “economic efficiency” or the Pareto optimum.
I think of the Pareto efficient model as a three lane highway with spare capacity in the lanes and car engines – so everyone who wants to go faster than the next guy can do so! But in the real world the marginal next guy is using up all the spare capacity and the result is a traffic jam!
If anyone is following my comments this time-indexed lecture provides an illustration of “Utility Curves” associated with Bentham’s philosophy of government:
https://youtu.be/U0iS4Ax3LXc?list=PL2FD48CE33DFBEA7E&t=1992
Econometrics per se applies to things we can measure using an objective method and this maps into the methods that I am calling the General Balance Equation. We can measure populations of people, goods, and financial instruments, for example, and measure the change in populations over time. But I think all economic theory is concerned with the political problems that I am calling ethical and moral values. Any math model or curve drawn to map these values is an arbitrary construct with no objective measurement methods. An economist can survey or poll the opinions of others to fashion a utility curve, which appears to be objective, but the next instant the utility of the subjects involved in the poll can change with no way to measure that change except to take another poll and construct another arbitrary curve. I don’t know if these thoughts are “on point” concerning Newton – the methods of Newton are pretty damn good in their domain of application which is non-ethical and non-moral observations that map to the General Balance Equation.