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#2 Re: Euler Avenue » Strange things about Xeno's Paradox » 2007-03-20 16:10:00
the universe cant be continuous, or else we run into this paradox, where any division of distance can be reduced to .000...1. obviously a paradox. therefore, space must be discrete, which is the only other logical logical possibility. a sort of proof by contradiction of the discreteness of the universe. as mentioned before, the plank length is the discrete unit of space, just like the quanta is the discrete unit of energy...which was discovered by max planck. this in itself leads to interesting physical conclusions, but also mathematical ones. yay!
The bolded part is a logic fallacy known as a False Dilemma. You are forcing me to choose between X and Y, when in reality other choices such as Z exist.
A more accurate statement is "which is the only other possibility, that I can think of".
Perhaps movement is discrete and space is continuous. Perhaps space is continuous but acts with very weird properties on the small scale. Actually, we already know the 2nd is true.
The list goes on...
ah...you have got me thinking again. in fact, when i wrote that i almost put in the "that i can think of" part. 
of course, "those strange properties" that is, quantum physics (i think thats what you mean) dont mean the universe is continuous do they? i mean, the discrete space theory of the plank length is accepted, right?
#3 Re: Introductions » Meesa New Heah » 2007-03-20 11:59:14
haha. not quite. i meant, 'me new here' which was an admittedly lame jar-jar binks impersonation (note spelling!)
as for my conjecture, even if you dont count the number 2 as prime, its false, because it all breaks down at 12/17. 
oh well. we cant all be fermats.
as for my username, it refers to the shimura-taniyama conjecture which states that all elliptic curves can be related to modular functions on the complex plane. this conjecture, once proved, gives way to the proof of fermats last theorem, because fermats last theorem states that there is no solution to x^n+y^n=z^n where n>2. this is an elliptic equation on three dimensions, and the curve its solution would give cannot be modularized. therefore, if all true elliptic curves can be modularized, but fermats curve cannot, then fermats theorem has no solution. (my favorite piece of mathematics).
#4 Re: Euler Avenue » Strange things about Xeno's Paradox » 2007-03-19 16:08:57
o wait, i totally got it.
the universe cant be continuous, or else we run into this paradox, where any division of distance can be reduced to .000...1. obviously a paradox. therefore, space must be discrete, which is the only other logical logical possibility. a sort of proof by contradiction of the discreteness of the universe. as mentioned before, the plank length is the discrete unit of space, just like the quanta is the discrete unit of energy...which was discovered by max planck. this in itself leads to interesting physical conclusions, but also mathematical ones. yay!
#5 Re: Euler Avenue » Strange things about Xeno's Paradox » 2007-03-19 15:53:30
hmm...i think that what zeno was referring to is that all change can be reduced to .0000...on to infinity...1. since the limit of this is zero, we can never move, hence the paradox. the problem with this is that all change cant in fact be reduced to .0000...1. which of course, leads us to the nature of the continuity of change. this leads us on to continuous functions on the complex plane, i think...or maybe im just a freshman who knows nothing.
#6 Introductions » Meesa New Heah » 2007-03-19 15:36:43
- elliptic=modular
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ello everyone.
my name is aaron, and i like
1: math
2. jazz
3. number theory and topology, to get specific on the first one
4. physics
5. biology
6. philosophy
7. literature
so... i joined this site because i had an idea, and tried it out, and it seems to work. the conjecture is:
I/(second prime after I)=a repeating decimal
where I is any integer.
i've tried this out and it seems to work. if there isnt already a proof or disproof of it, this would be an awesome contribution to number theory, so nobody steal it! of course, im sure its false, but its worth putting out there.
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