Am I a crank?
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From: Han de Bruijn on 30 Aug 2006 03:23 Gerry Myerson wrote: > Somewhere along the way you should check to see whether what you have > done (or what you are planning to do) has already been done. [ ... ] Precisely! And there are a lot of things out there which have NOT been done. To mention an example. Take a couple of (3-D) bricks and find out how to make a discretization of the equations describing incompressible and irrotational 3-D flow with the least squares finite element method. But ah .. nobody will appreciate (or even comprehend) if you have done such an uncommon thing. Han de Bruijn
From: Han de Bruijn on 30 Aug 2006 03:43 schoenfeld.one(a)gmail.com wrote: > Han de Bruijn wrote: > >>Jesse F. Hughes wrote: >> >>>*Fortunately* mathematics is not an experimental science. >> >>Not true. Part of modern mathematics _is_ an experimental science. >>In very much the same way as physics is: theory as well as experiment. >>Or would you like to say that structural (numerical) analysis is not >>a form of mathematics? And how about computing a large prime number? >> >>Welcome to the 21th century! > > Wouldn't that be computer science? Is a simple calculation by hand (like 1 + 1 = 2) "computer science" ? Or is it just mathematics? In the latter case, computing a large prime is also mathematics, because it could be done - in principle - by hand. (What else does computer science add except more speed and more space.) Han de Bruijn
From: schoenfeld.one on 30 Aug 2006 04:02 Han de Bruijn wrote: > schoenfeld.one(a)gmail.com wrote: > > > Han de Bruijn wrote: > > > >>Jesse F. Hughes wrote: > >> > >>>*Fortunately* mathematics is not an experimental science. > >> > >>Not true. Part of modern mathematics _is_ an experimental science. > >>In very much the same way as physics is: theory as well as experiment. > >>Or would you like to say that structural (numerical) analysis is not > >>a form of mathematics? And how about computing a large prime number? > >> > >>Welcome to the 21th century! > > > > Wouldn't that be computer science? > > Is a simple calculation by hand (like 1 + 1 = 2) "computer science" ? No. > Or is it just mathematics? In the latter case, computing a large prime > is also mathematics, because it could be done - in principle - by hand. > (What else does computer science add except more speed and more space.) Then there is no experiementation. Mathematics is not an experimental science, it is not even a science. The principle of falsifiability does not apply. > Han de Bruijn
From: Jeremy Boden on 30 Aug 2006 04:14 On Wed, 2006-08-30 at 09:15 +0200, Han de Bruijn wrote: > Jesse F. Hughes wrote: > > > *Fortunately* mathematics is not an experimental science. > > Not true. Part of modern mathematics _is_ an experimental science. > In very much the same way as physics is: theory as well as experiment. > Or would you like to say that structural (numerical) analysis is not > a form of mathematics? And how about computing a large prime number? > > Welcome to the 21th century! Do you mean that there are theories of numerical analysis which are accepted until found to be wrong due to practical experiments? Actually, I don't think anyone has discovered a practical method of *computing* a large prime number - although there are methods of performing primality checking on a given number. The faster methods are only probabilistic - but slower methods will give a definite answer. -- Jeremy Boden
From: Proginoskes on 30 Aug 2006 04:47
schoenfeld.one(a)gmail.com wrote: > Han de Bruijn wrote: > [...] > > Or is it just mathematics? In the latter case, computing a large prime > > is also mathematics, because it could be done - in principle - by hand. > > (What else does computer science add except more speed and more space.) > > Then there is no experiementation. Mathematics is not an experimental > science, it is not even a science. The principle of falsifiability does > not apply. Written by someone who has not done any math research. One of many examples: Try dividing 2^n by n and keeping track of the remainders. You won't get 1; you get 2 a lot, but you never seem to get a 3. So you conjecture: CONJECTURE: The remainder of 2^n divided by n is never 3. However, this conjecture is false; in particular, the remainder of 2^n divided by n is 3 if n = 4,700,063,497 (but for no smaller n's). --- Christopher Heckman |