Am I a crank?
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From: schoenfeld.one on 31 Aug 2006 07:48 Lester Zick wrote: > 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. Definitions can be false too (i.e. "Let x be an even odd"). > >In physics, a hypothesis is never true only verified xor false. > > In physics a hypothesis is either contradictory or not. > > ~v~~
From: Jesse F. Hughes on 31 Aug 2006 09:58 schoenfeld.one(a)gmail.com writes: > Definitions can be false too (i.e. "Let x be an even odd"). That is not what one usually means when he says "mathematical definition". A mathematical definition is a stipulation that a particular phrase means such-and-such. Like: A /group/ is a set S together with a distinguished element e and an operation *:S x S -> S such that blah blah blah But what you're doing is different. You are specifying that a variable should be interpreted as a certain kind of number, namely an even odd. Even though there is no such thing as an even odd, however, this is not false. How could it be false? It's an imperative, telling the reader to do something (namely, assume that x names an even odd). If I tell you to find integers a, b such that a/b = sqrt(2), I haven't said something false. I've given you a command that is impossible to fulfill, but it isn't false. Imperatives don't have truth values. I'm not sure that "Let x be an even odd," is impossible to do in the same sense that finding a rational equal to sqrt(2) is impossible. I think that this imperative just means: Assume that x satisfies certain conditions. And as far as I can see, I can assume impossible facts willy nilly. -- Jesse F. Hughes Jesse: Quincy, you should trust me more. Quincy (age 4): Baba, I never trust you. And I've got good reasons.
From: fernando revilla on 31 Aug 2006 05:59 schoenfeld.one(a)gmail.com wrote: > Definitions can be false too (i.e. "Let x be an even > odd" That is not a definition. See ( 7 is an even and 7 is odd ) --> ( All the elephants are yellow ) it is a proposition, by the way, a true proposition. Fernando.
From: Chris Smith on 31 Aug 2006 10:58 skialps10(a)yahoo.com <skialps10(a)yahoo.com> wrote: > I like mathematics and play with it in my spare time, perhaps > excessively. I would like to prove something as yet unproved, but doubt > I ever really will. I just read an article about mathematical cranks > and began questioning myself. > > I know its a very odd question and perhaps awkward, but I'm really > curious to have feedback. Ooh, I've been looking for an opportunity to quote this, from a thread on a different newsgroup a while back. Marshall wrote: So it's not sufficient to say "I don't think I'm a crank, therefore I'm not a crank" because *everyone* thinks that. One has to test against external markers. One test would be to go in to a newsgroup on a topic one was familiar with. If one is quite shy and doesn't say much, one is probably not a crank. But perhaps one posts a lot. Are one's ideas greeted with a mix of agreement and disagreement? That would be normal. Are one's ideas greeted with universal derision? Does one then hypothesize that all the posters there are in cahoots against you? That would be a sign that one was a crank. Hope that helps, -- Chris Smith
From: Phil Carmody on 31 Aug 2006 11:47
schoenfeld.one(a)gmail.com writes: > Definitions can be false too (i.e. "Let x be an even odd"). Nonsense. It appears you are unaware of the use of the word 'vacuous' in mathematics. Probably due to the matching state of your brain cavity. I'm sure I've plonked you before, are you a morpher as well as a nutcase? Phil -- "Home taping is killing big business profits. We left this side blank so you can help." -- Dead Kennedys, written upon the B-side of tapes of /In God We Trust, Inc./. |