Am I a crank?
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From: Chip Eastham on 30 Aug 2006 09:37 Robert Israel wrote: > In article <1156822962.655075.212160(a)i3g2000cwc.googlegroups.com>, > david petry <david_lawrence_petry(a)yahoo.com> wrote: > > > >Nathan wrote: > >> david petry wrote: > >> > >> > It could be argued that since the mathematics community does expend a > >> > great deal of energy in the search for formal proofs of conjectures > >> > having ridiculously high probabilities of being true, and often turns a > >> > blind eye to the probabilistic arguments, the mathematics community > >> > itself engages in crank-like behavior. > >> > >> I have read many heuristic arguments advanced by mathematicians to > >> suggest what *might* be true, especially in number theory. I disagree > >> that the community "often turns a blind eye" to such. It's just that > >> these still leave the actual question unanswered. > > > >It all depends on what the "actual" question is. If mathematics is > >thought of as a science having the purpose of explaining why we observe > >the phenomena that we do observe, then the heuristic argument really > >does answer the "actual" question. There's absolutely no reason to > >believe that we can do better than a heuristic argument in many cases. " Except that 1) in many cases we _can_ do better. 2) many perfectly plausible statements, supported by all kinds of heuristics, turn out to be wrong." Ironically this is a good heuristic argument that we can do better than a heuristic argument in many cases! Thus we should ordinarily try, which contrary to Petry's claim that mathematicians turn a blind eye to heuristics, leads to minutely careful evaluation of them. Heuristic arguments good; formal proofs better. Empty rhetoric and hand waving, still cheaply priced (but questionable values). --c
From: Lester Zick on 30 Aug 2006 13:51 On Wed, 30 Aug 2006 09:10:10 +0200, Han de Bruijn <Han.deBruijn(a)DTO.TUDelft.NL> wrote: >Lester Zick wrote: > >> Actually an interesting prespective. Certainly mathematical axioms if >> not theorems are empirically established. > >Axioms are implicit definitions. Which are empirically established and not demonstrated. ~v~~
From: Lester Zick on 30 Aug 2006 13:53 On Tue, 29 Aug 2006 18:03:17 -0400, "Jesse F. Hughes" <jesse(a)phiwumbda.org> wrote: >John Schutkeker <jschutkeker(a)sbcglobal.net.nospam> writes: > >> Jeremy Boden <jeremy(a)jboden.demon.co.uk> wrote in >> news:1156865725.8346.5.camel(a)localhost.localdomain: >> >>> Unfortunately mathematics is not an experimental science. >> >> I disagree. > >Fair enough. > >*Fortunately* mathematics is not an experimental science. And yet unfortunately mathematical axioms are empirically established. ~v~~
From: Lester Zick on 30 Aug 2006 13:55 On 30 Aug 2006 02:43:00 -0700, schoenfeld.one(a)gmail.com wrote: > >Proginoskes wrote: >> 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). > >Hello Crackpot. Crackpot=disagreer. Quite mathematical. ~v~~
From: Lester Zick on 30 Aug 2006 13:58
On 30 Aug 2006 05:01:52 -0700, schoenfeld.one(a)gmail.com wrote: > >Han de Bruijn wrote: >> schoenfeld.one(a)gmail.com wrote: >> >> > Then there is no experiementation. Mathematics is not an experimental >> > science, it is not even a science. The principle of falsifiability does >> > not apply. >> >> Any even number > 2 is the sum of two prime numbers. Now suppose that I >> find just _one_ huge number for which this (well-known) conjecture does >> _not_ hold. By mere number crunching. Isn't that an application of the >> "principle of falsifiability" to mathematics? > >Falsifiability does not _need_ to apply in mathematics. In math, >statements can be true without their being a proof of it being true. >Likewise, they can be false. Except apparently for definitions. >In physics, a hypothesis is never true only verified xor false. In physics a hypothesis is either contradictory or not. ~v~~ |