Provocation # 120 Math and economics.
Math has a dampening effect on an economics of observation and participation in real lives. Prep for war, chaos of poverty, dynamics of hope and despair eddy around all economic activity – but is largely ignored in main stream economics which favors formalism.
We know that in the ancient world: Mesopotamia and then Greece and in the background China, accounting created numbers that it was important for the state to be able to predict: how much tax could be collected (bags of grain), how much grain would be grown next year. We know that contracts were written that specified payback times and included interest. Calculation merged with accounting and then with mathematics. The new power was used by temple managers and priests representing an elite support class, obviously for its power, and this becomes a major part of the math story for economics. Math and its supported economics is the plumbing so to speak for the flow of wealth in the society benefitting the elites. I think it is obvious that this attraction for economists to use math is to show they have tools that are useful to elites. Though often not directly, because the elites don’t actually use the results but as a sign of sophistication and expertise.
But deeper was and still is the attraction to math by many economists because of its power as an unseen force. A drawn triangle was known to be imprecise but Pythagoras knew that [a squared plus b squared = c squared] was true for all time, invariant and that the real triangle drawn in the sand was a mere approximation. The imagined triangle is more real than the drawn one. There is behind appearances, so the thinking from Pythagoras to the present went, a deeper truth of invariant relations, approximately true in the material world but unequivocally true in the world of the mind, as somehow representative of the forces of the universe, the creative power of number, the ultimate force of the universe. The cosmos was lawful, the microcosm down here reflects the big cosmos up there. The truth of math precedes the first humans and will still be true when there are no humans.
After Newton further advanced the move toward understanding the motions of planets as mathematical, the success was so profound, it seemed magical, god-given, the model of what knowledge should be: true, invariant in time, and elegant.
Reality is created, again following Pythagorians, out of something not material. Math is architectural for everything that can be. The body, with its harmonies, balances of energies, is an effect of the abstract harmonies organizing the material as an unseen equilibrating entity. It was assumed by later economists that Adam Smith’s Unseen Hand had real effects.
Because the material world of Newton’s time was strongly based on trade and empire, navigation made the realm of the stars seriously important for investment in voyages and this was only enhanced as mathematical representation came to seem more real than the thing it represented.
The impact on economics can be seen in the following: imagine a globe with the land masses and all the lines of latitude, longitude the tropics, the constellations projected downward onto the surface. For economists the lines and measurements became increasingly more real than the land masses underneath. Even if the earth vaporizes, the pythagorian belief in number says the lines and numbers persist for all time and are an essential part of the non material universe.
Math had an appeal because of its success, its power, its hint at things unseen but true. It avoided the noise of the world for the complete clarity of the mental in touch with the essence.
For Plato following Pythagoras, all things were relational and relations were math and math was numbers. Plato was interested in harmony of the heavens and of music. The discovery that music was relational (attributed to Pythagoras) and precise CEG for example with its harmonized relations, you can hear the beats of the mismatch when two slightly out of tune strings are plucked, as on a guitar)
There were other trends in Greek thought. Heraclitus (before Plato) saying you can’t step into the same river twice, all things are flux, but the platonic won out because it could lead to calculations and predictions whereas the heraclitian world was a nice story but didn’t lead to action.
Part of the appeal of math was its relation to contemplation, an extreme denial of the body as a distraction from the real. Contemplation to get to the real avoids day to day affairs in order to get to the ultimate nature of things.
That math is more real than material appeals to economists, many of whom are drawn to careers in economics because of the formalism, more than to it as the science of pragmatic action or as a guide to public policy. Undergrads in economics courses have these broader interests nut get sorted out by the series of required courses leading to a higher degree.
You will notice than any use of math must assume some constancy in the referred to system, for example the constancy of the sample space over time. Otherwise calculation is not possible.
The tendency of math to seek for and represent constant relationship suggests that the economics that prefers math is perhaps unconsciously support ing a conservative view thta things basically don’t change. Change is seen only a perturbation within a fixed system. The struggle between economics as observational, journalistic, humanitarian and motivated by interests will remain in tension with an economics that seeks hidden patterns and causal formal systems.
From Wikipedia on math.
Galileo Galilei (1564–1642) said, “The universe cannot be read until we have learned the language and become familiar with the characters in which it is written. It is written in mathematical language, and the letters are triangles, circles and other geometrical figures, without which means it is humanly impossible to comprehend a single word. Without these, one is wandering about in a dark labyrinth.” Carl Friedrich Gauss (1777–1855) referred to mathematics as “the Queen of the Sciences”. Benjamin Peirce (1809–1880) called mathematics “the science that draws necessary conclusions”. David Hilbert said of mathematics: “We are not speaking here of arbitrariness in any sense. Mathematics is not like a game whose tasks are determined by arbitrarily stipulated rules. Rather, it is a conceptual system possessing internal necessity that can only be so and by no means otherwise.” Albert Einstein (1879–1955) stated that “as far as the laws of mathematics refer to reality, they are not certain; and as far as they are certain, they do not refer to reality.”
Well , can you imagine a book written only in geometrical figures? In economics texts you will see a formula followed by a few english sentences which have the form A=,Q=.. Etc. My view is that the real understanding is in understanding what A, Q etc are, not in the math, which while often interesting is secondary to the hard work of figuring out things like income, wealth, ownership, contract. Take “unemployment” for example. All the equations hide the debate about what it is, perhaps the idea that unemployment means talents that are not used in work.
If math is method, the real science is in the understanding of the things counted, not so much in the counting.. For an alternative view of some attempts at interesting use of quantification see for example
Another site full of interesting perspectives is
From within Economics the series of book reviews by Diane Coyle is a good education.
My discussion of math and economics is a prelude to a discussion of the division in economics between calculation and the humanities, especially literature.
The shift from math to statistics is another story of an apparent gain in accuracy and computability but a loss of underlying understanding. It is very hard, in a statistical discussion, to introduce a nuanced shift in the meaning of one of the variables because it would throw off the whole basis for calculation. A story for another time.