Originally posted by XanthosNZBy the way, I like the way you used the word cannibalize. Not sure how it applies but it sounded smart. Double talk usually does that for some reason. I guess numbers eat those of its own kind. Or maybe mathematicians do or something like that. Anyway I was hoping you would be able to do a better job of explaining it. But cool, man...far out, I will leave it to the hippies. You can have your thread.
Who is to say what pure maths physics or engineering will at some point cannibalize to describe real life situations?
An example you may understand, complex numbers were once purely mathematical. Nowadays you use them in plenty of real world problems. What if back when someone said, "Let's define sqrt(-1) as i." you were around to say, "Why? What's the ...[text shortened]... you really don't want to discuss the Hodge Conjecture then get the hell out of my thread.
Peace
Originally posted by cashthetrashIt's actually a pretty good metaphor -- cryptography cannibalised parts of number theory, for example, and finance cannibalised statistics. The reverse also occurs: fluid mechanics vomited vector calculus and signal processing vomited information theory, for example.
By the way, I like the way you used the word cannibalize. Not sure how it applies but it sounded smart. Double talk usually does that for some reason. I guess numbers eat those of its own kind. Or maybe mathematicians do or something like that. Anyway I was hoping you would be able to do a better job of explaining it. But cool, man...far out, I will leave it to the hippies. You can have your thread.
Peace
Originally posted by royalchickenYes, thanks I can understand that it all sounds rather nauseating.
It's actually a pretty good metaphor -- cryptography cannibalised parts of number theory, for example, and finance cannibalised statistics. The reverse also occurs: fluid mechanics vomited vector calculus and signal processing vomited information theory, for example.
Originally posted by royalchickenJust because Py was (as you say) and idol-worshipper, doesn't mean he didn't hit on something fundamentally true.
Pythagoras took this to mystical extremes. It's sort of incongruous for a chair-sitter to be quoting an idol-worshipper.
Excellent tongue-in-cheek, though, via the use of a mathematical term.
Originally posted by FreakyKBHOnce one of Pythagoras' students hit on something fundamentally true, so Pythagoras drowned him. The fundamentally true thing was the existence of irrational numbers, something which Pythagoras' own famous theorem guarantees if every rational square is to be constructible. Not only was he an idol-worshipper, then, he was also a purveyor of contradictions for no good reason at all (he was also a very important contributor to mathematics).
Just because Py was (as you say) and idol-worshipper, doesn't mean he didn't hit on something fundamentally true.
Excellent tongue-in-cheek, though, via the use of a mathematical term.
'All is number.'
The diagonal of a 1x1 square has a length, which is part of 'all'.
This length is an irrational number.
Irrational numbers do not exist (are not part of 'all'😉.
Thus there exists a number which is not part of all (namely, the square root of two) and a part of all which is not a number (namely, the length of the diagonal of a 1x1 square).
Thus Pythagoras' views are incompatible; to believe that 'all is number' while acknowledging Pythagoras' theorem and not believing in irrational numbers entails a contradiction.
Originally posted by fiestaAre you saying he is one of the ends of the pony? Which one if so?
way to go xanthos....I am with you all the way here..and to all you non-believers,he's not just a great mathematician,theorist and bsc degree person thingy he's also a great artist look what he did to my photo when he was going through the "my little pony" phase...
http://img.photobucket.com/albums/v694/XanthosNZ/fiestapony.jpg
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Originally posted by shrewnumbers are an agreement ...
All numbers are imaginary
they are only what we decide them to be ...
it takes imagination to make that decision ...
numbers are a creation ... an imaginary creation ...
they can be a representation of a real thing ... that is when i find them fascinating ... i would like to know what hodges conjecture represents ... what it might mean ... i believe the path to this is ...
why the hell did hodge make this conjecture? why did it seem sensible? surely calculations can verify its likey field of applicability ... what is that? .. and where is left in the dark that it might break down?