Monday, 13 May 2013

Richard Feynman's "The Relationship Between Mathematics and Physics" (1965)

Richard Feynman, in 1965, at the height of his powers and recognition, was moved to decry those who wondered "Why" a physical theory worked. He concludes this justly famous lecture with the following declaration: "The horizons are limited which permit such people to imagine that the centre of the universe of interest is man!"
It could equally well be said that the horizons are limited which permit people to imagine that the centre of the universe of interest is not man. 


It's 95 years since the birth of the theoretical physicist Richard Feynman.

In the past what we now call "physics" was philosophical speculation and commonly known as "natural philosophy". By the time Feynman was in his prime, it seems that physics was widely felt by its leading exponents to be a self-contained enterprise not connected with philosophy, at least to the extent that they need not be troubled by any supposed interface between physics and philosophy.

This is in evidence in Richard Feynman's entertaining and informative lecture on "The Relationship Between Mathematics and Physics", one of six "Messenger Lectures" he delivered at Cornell University, USA, in 1965. This lecture is, brilliantly, available to watch on youtube, and elsewhere, for free.

The lecture is punctuated with moments when Feynman appeals to his audience not to be tempted to ask why the mathematics that describes the phenomena works.

In his closing statement there is a clear note of exasperation with those of the "other culture" (a reference to C P Snow's Rede Lecture of 1959, "The Two Cultures and The Scientific Revolution"): "The horizons are limited which permit such people to imagine that the centre of the universe of interest is man!"

When I came across this lecture four or five years ago, I was very alert to the seeming cultural divide between the sciences and the humanities, and I was interested to find out how it surfaced and how it origintaed. (My interest was fuelled by a problems that emerged in my working life and personal life that I think began with a kind of over-extension of scientific thinking into realms outside science. I think the problems I met are not unusual. I have been glad to find writing on this phenomenon, even very recent writing, such as that of Marilynne Robinson in “Absence of Mind” (2010)).

Richard Feynman was evidently frustrated with the very idea of people, philosophers, setting out to ask why mathematical descriptions of the universe work, seem to give the “right” answers. When he presented this lecture, there was probably a good deal of academic debate, even within the world of theoretical physics, generated by the 1962 publication of Thomas Kuhn’s book “The Structure of Scientific Revolutions”. That “it" works was enough for Feynman. Yet I wonder if he might have been less averse to philosophical reflection if he had been given to appreciate the actual philosophical problems that had prompted people to ask these questions so persistently, not just in the 1950s and 60s, but ever since the time of Newton. Probably not, I feel.
Philosophy is not idle thinking, and there are such things as philosophical problems. My guess is that Feynman would simply not have been interested in them. 

Meaning is the concern of disciplines in which "the centre of the universe of interest is man".

It is meaningful for humans if, as Hume showed, certain knowledge of the world is not attainable through our senses, because a world that is purely contingent and governed by laws is emptied of meaning.

In the 18th century it was held that true knowledge had been attained in science through Newton's mathematical theories of dynamics, gravitation and light. This attainment of true knowledge had been anticipated ever since Descartes set down his method in pursuit of the indubitable ground of knowledge, fifty years before Newton.

Martin Heidegger wrote an essay on the development of Aristotelian into Cartesian metaphysics and Aristitelian to Galilean and Newton's mathematical descriptions of the universe, called "Mathematics, Metaphysics and Modern Science", which I recommend to any reader. I think this is an important essay because it offers a window onto what Heidegger outlines as the culmination of metaphysics in moden mathematical science: not modern science is free of metaphysics, but that the modern science is the culmination of metaphysics, which is to do with its mathematical character. 

Immanuel Kant saw that the attainment of precise warrantable knowledge of the world based on mathematics contradicted Hume’s argument that no such knowledge can be had through our senses. The rationalism of his time, the belief that truths of the world, and of God, can be attained through reason alone, was supported by Newton’s achievement. Hume’s argument placed rationalism, and metaphysical speculation in total, in doubt. That this was a real philosophical problem is something that Karl Popper sought to defend against the programme of logical positivism. I suppose a stepping-off point for someone who might be interested by the philosophical problem, is the notion that a completely law-bound universe includes human minds and so seems to contradict the supposed human capacity to will freely.

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