Thank Terry for your explanation of the utility of both heuristics and rigor. Sometimes, though I am unable to grasp the relation between the two. For example ,we use Lebesgue integrals with real numbers knowing very well that charge is actually quantized in nature. Then how do we actually check the consistency of the assumptions. In fact, any place where we use real numbers, I find it hard to see how our approximations to natural phenomenon can be rigorously proved without knowing whether real numbers exist in nature.

Also could you please explain the difference between rigorous proof of a theorem and consistency of a theorem. Is consistency just checked by some easy test cases?

And according to Karl Popper, mathematics is about establishing equivalences between different entities . Mathematical statements are close to analytic statements or tautologies within the axiomatic framework and they help to change statements into a form that is empirically verifiable or falsifiable . And there, the statistical method provides the interaction between mathematical model and empirical testing. So nothing is proved, only things are accepted till the hypothesis cannot be rejected.

Do you agree with this analysis?

]]>Feynman, who liked going there (“after a hard day dealing with oscillating bodies, it’s nice to see some oscillating bodies”), succeeded in keeping the place open a few more months. When the city tried enforcing the anti-topless-bar ordinance, the owner could now say: “we’re not a topless bar. We’re a topless restaurant.”

The other Feynman sandwich anecdote: Leonard Susskind and Feynman are getting a “Feynman sandwich” at the local deli, and Feynman remarks that a “Susskind sandwich” would be similar, but with “more ham”.

]]>“When I was a kid, my dad was friends with Richard Feynman before he’d won his Nobel Prize in physics. Always an iconoclast, Feynman never let anyone tell him how to act or behave. He would go to topless bars to sit there and do calculations on the tablecloth. He wasn’t there to look at naked girls; he just liked the ambience.”

Topless bars? Ambience?

That’s not as unusual though as the next physicist she talked about:

“Yet another physicist at Caltech insisted on working in the buff in his office. There was a picture in one of the hallways in the physics department of him sitting naked at his desk, taken tastefully from the side.”

]]>Sorry, somehow hit the wrong thread in referring to polymath. The point is that there is a difference between physics and maths. Maths can live in its own world, physics is answerable to experiment.

]]>Doesn’t this simply mean that Newton’s systematic understanding of Gravity was superseded by Einstein – so Newtonian Gravity, which once looked fundamental, was a mere approximation.

On the other hand, conservation of angular momentum, which was a by-product of Newtonian dynamics, survives, and is in fact now understood to reflect the fact that there is no privileged direction in space – it expresses the fundamental symmetry of things under rotation.

Mathematics builds on axioms it regards as fundamental – provided the axioms and rules of deduction remain the same and are consistent, the conclusions are unaltered.

Feynman expressed many times that the test of science was experiment, and if theory did not fit experiment it was the theory which had to change. But some surprising elements may remain.

This is philosophically interesting, but I’m not sure what it has to do with polymath.

]]>A somewhat surprising statement. I wonder if what he meant is that in physics a finite set of incomplete examples can establish the law, and that this is not possible in mathematics.

Say, borrowing from his example, if physicists experimentally observe conservation of angular momentum in three or four rather disparate settings the physical law is considered established.

The analogy in mathematics would be to consider it established that the integral is an antiderivative from the mere fact that it holds for a few disparate functions. Mathematicians will certainly use this as evidence to conjecture the general theorem, but the result still needs to be proven in its full generality on its own.

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