Comments | gustavolacerda: quotes: Babylonian vs Euclidean method, why physicists dread precision

gustavolacerda

quotes: Babylonian vs Euclidean method, why physicists dread precision

Mar 01, 2005 00:22

There are two kinds of ways of looking at mathematics... the Babylonian tradition and the Greek tradition... Euclid discovered that there was a way in which all the theorems of geometry could be ordered from a set of axioms that were particularly simple... The Babylonian attitude... is that you know all of the various theorems and many of the ( Read more... )

phil.sci, formal_ed, formal_math, phil.math, philosophy

Comments 15

jcreed February 28 2005, 23:59:57 UTC

I pretty much agree with everything you're saying. There's a bit of a fallacy in Schwartz's comment --- maybe more than one.

First of all the idea that a heuristic for accepting or rejecting arguments is better the more permissive it is, is ridiculous. Though I want to believe that I'm just setting up a straw man, Schwartz does say "rightly dreads" not "rightly apporaches with caution" or something. Of course I acknowledge that we may, by demanding more formal, more rigorous proofs, throw out some arguments that (by our new standard) wrongly reach what were actually right concluisions. But there is always tension between (to use fundamentally like terminology from several fields) soundness and completeness, (from formal language transformations) between "safety" and "expressiveness" (from programming language design) between type one and type two errors, (from experimental psychology) between precision and recall (from machine learning).

There's always an opportunity for making mistakes saying "yes" when you should say "no" to an ( ... )

pbrane March 2 2005, 02:38:09 UTC

The physicist can exhibit a thousand proofs that were fallacious in the formal system and that are still fallacious to her informal intuition, but this does not convince me that there is no informal argument yet to be discovered that passes her intuitive test, but cannot be correctly formalized.
I think the point for physics is that we don't rely on "proofs" at all, really. We often 'prove' things to some degree of satisfaction using formal systems (renormalization of the Standard Model being a good example - Physics Nobel 2000), but we know that the real final arbiter of correctness for a theory is *experiment*: regardless how hokey and seemingly inconsistent a theory seems (mathematicians are pretty sure that QFT as a whole is inconsistent on numerous levels: each term in the perturbation theory is ill defined, even once regulated, the sum of the series diverges, and the defining generating function of the whole system is an integral with a completely undefined measure over an infinite dimensional space), if it produces predictions ( ... )

jcreed March 2 2005, 02:57:02 UTC

So, I don't dispute that consistency with experiment is the right thing to be looking for. However, isn't there still a process that takes the a proposed model and derives what experimental predictions it actually makes? I think that process could (or, really, already does) benefit from improving and deploying more formal understanding. Just because QFT produces formal objects that are foreign to how mathematicians usually think about calculus doesn't mean that there isn't some consistent formal system that encapsulates our current physical theory in that domain.

If the mathematics is irreparably inconsistent (which I doubt) then it falls to mere intuition and the community social dynamics of physicists to even decide what the theory is predictably and what it isn't. But I bet instead that it's a very well-behaved formal system that just hasn't been exactly delineated yet.

pbrane March 2 2005, 05:16:12 UTC

But I bet instead that it's a very well-behaved formal system that just hasn't been exactly delineated yet.Certainly, I agree with you on this. My point is just that for all the work that mathematicians have done on trying to make advances in finding this well-behaved formal system, we've gained pretty much *no* new insights about physics, and have made no new predictions, and don't really have any new way of seeing what's going on ( ... )

Thread 10

Perhaps English is irremediably vague triple_entendre March 1 2005, 01:07:25 UTC

I really like that Feynman quote.

I also like your overall goal here. Metaphorically, it sounds a lot like some of the thought processes that happen in my head when going from an idea of what I want a computer program to do, to actually writing the program.

This is an open problem in computer science (or, if you like, "computer engineering"). The complaint is that too much of software development is an art when it (or at least parts of the process) could be formalized into something that you'd call engineering.

If you are interested a concrete example of an almost "provable" method of software development, I'll suggest a book called Database Design for Mere Mortals by Michael J. Hernandez. I have actually used the methods outlined in this book to train a non-programmer, non-technical person to do database application development! The process described by the book begins with gathering information in conversational English, and then applying small, mechanical, formal steps to that input in a way that transforms and reduces it to an ( ... )

Re: Perhaps English is irremediably vague darius March 1 2005, 07:22:29 UTC

That database thing you describe reminds me of compilation by program transformation. Interesting.

Dijkstra quote fare March 1 2005, 17:24:21 UTC

A quote that I think applies here:

Being abstract is something profoundly different from being vague... The purpose of abstraction is not to be vague, but to create a new semantic level in which one can be absolutely precise. -- E. Dijkstra

What you're looking for is the correct abstraction for a logical argument. Now, the core of logic is probably pretty well established and extensively studied, I believe. What might be more interesting, and has to date been untractable, is the way that arguments ramify when you take into consideration the fact that manipulated representations are dynamically found to not match the represented reality closely enough. Even in classical logic, you get some ramification. Just imagine having to add subjective evaluations to the matter. They add a whole new world of potential break downs, and it would be interesting to exhibit the structure of the space of such break downs (and ways to cope with them ( ... )

Re: Dijkstra quote gustavolacerda March 6 2005, 02:56:26 UTC

What do you mean by ramification?

What does reverse mathematics have to do with ramification? The fact that it's more "Babylonian"?

Cool quote anonymous May 9 2008, 10:09:33 UTC

Show me a man who is a good loser and I'll show you a man who is playing
golf with his boss.

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