Comments on: The Unreasonable Effectiveness of Physics

By: A Little Arithmetic at Steven Landsburg | The Big Questions: Tackling the Problems of Philosophy with Ideas from Mathematics, Economics, and Physics

Fri, 13 Nov 2009 07:05:00 +0000

[...] so we have one more example of the (apparently) unreasonable effectiveness of pure mathematics —indeed, mathematics at its purest—as a description of the physical world—a [...]

By: michael webster

michael webster — Sat, 07 Nov 2009 16:42:37 +0000

@Barry, Ok read Lakoff’s “Where Mathematics Comes From”, Michael Dummett’s Intuitionism, and then defend naive realism about mathematical entities.

Or you could just start with Simon Blackburn’s observation that Frege showed us that numbers were not objects but rather adverbs.

And it is possible that smart physicists could be very dumb about ontology? Sure, and it may be a requisite for doing science.

By: Al V.

Al V. — Thu, 05 Nov 2009 14:27:38 +0000

This leads one to wonder where the difference between mathematics and physics lies. Are the laws of mathematics inherent in our universe, and therefore really a product of physics (and not the other way around), or are they supra-universal?

By: Barry Semmer

Barry Semmer — Thu, 05 Nov 2009 06:28:07 +0000

Thank you very much for that enlightening comment, Michael. I shall make sure to disinter that hack Wigner and castigate him.

By: michael webster

michael webster — Mon, 02 Nov 2009 14:57:00 +0000

Miracles as an explanation of the possibility of successfully using mathematics is empty. Embedded cognition theories at least have a chance at avoiding empty platonism.

By: Snorri Godhi

Snorri Godhi — Mon, 02 Nov 2009 10:12:51 +0000

a curious use of physical reasoning to reveal a purely mathematical truth

Hmm … I would rather call it the use of a mathematical truth to obtain a simple and elegant proof of a physical law. The logic that I see is as follows. We start from the following propositions:

a. the arithmetic mean is never smaller than the geometric mean (a mathematical truth);
b. in the system under consideration, neglecting gravitational energy and other factors which we assume constant, the energy is proportional to the average temperature (this can be considered either a physical law or a definition of temperature);
c. again neglecting other constant factors, the entropy of the system is proportional to the geometric mean of the temperatures of the various buckets of water (again, this can be considered a definition of entropy);
d. the energy of a system is a constant (first law of thermodynamics).

Combining all of the above, we can derive
e. the second law of thermodynamics.

OTOH propositions from b to e (all physical laws or physical definitions) do not appear sufficient for a mathematical proof of proposition a, because physical laws are always at risk of being falsified.