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unicate my thoughts as well as you...
Though, I still don't understand what you mean by "Until Now."
Cantor originally had hoped that at its deepest level mathematics would rest on certainties, which, for him, were the mind of God. But instead, he had uncovered uncertainties. Which Turing and Godel then proved would never go away; they were an inescapable part of the very foundations of maths and logic. The almost religious belief that there was a perfect logic, which governed a world of certainties had unsurprisingly unravelled itself.
I'll make a declarative statement...infinity is a truth. And qualify it with the simple notion that
you can always add one to the sum, or that you can always divide a sum by one half. That is
proof of a mathematical infinity....but I could be wrong
Originally posted by ZeuZZ
Just to bite at this, infinity is not a truth, more a concept used in mathematical theory [...] In the real world of science it bears absolutely no relation to anything the scientific method has ever discovered, or likely ever will. We have never found a ruler of infinite length, a star of infinite mass, a singularity of infinite density, or for that matter, science has never even discovered a singularity.
Originally posted by ZeuZZ
System of Truth
Science? Truth? Those two words dont even do together. Science does not give you truth, it merely gives you internal self consistency that you can extensively cross reference and interdisciplinary test, but it will never, and should never claim to, give you truth.
Science evolves.
It doesn't declare truth, then stop.
It never mentions absolutes like that, if its real science.
Originally posted by Moduli
Ok, the craziness here has gone far enough. Allow me to shoot down your childish misunderstandings.
Originally posted by ZeuZZ
Just to bite at this, infinity is not a truth, more a concept used in mathematical theory [...] In the real world of science it bears absolutely no relation to anything the scientific method has ever discovered, or likely ever will. We have never found a ruler of infinite length, a star of infinite mass, a singularity of infinite density, or for that matter, science has never even discovered a singularity.
Hate to tell you (heck, who am I kidding, love to tell you) this is nonsense. Infinity is a perfectly concrete, reasonable concept that is totally understood and accepted by all competent scientists and mathematicians.
Saying infinity is something weird is the same as saying the interval
0 < x < 1
means something's "wrong" with the number one, because no point in this interval can ever get to 1, because they're all less than 1. Indeed, the intervals
0 < x < 1
and
0 < x < infinity
are identical in all of their properties! They are homeomorphic.
And infinities show up in plenty of every-day calculations.
I think you are confusing the extremely sparse field of phase transitions which can be applied to all sorts of fields of science? from acoustics to the EM spectra. Maybe you are referring to graphical paradoxes of representing infinities that were not measured but were of limit to the scale and algorithm in a specific case?
For example, in phase transitions (such as between liquid and solid water) certain functions that describe them, or their derivatives, become infinite. Not "big" or "approximately" infinite, honest-to-god infinite. This is what a phase transition means. It's why the different phases are so distinct.
can you show me where we have ever in situ measured something with an infinite value?edit on 7-7-2012 by ZeuZZ because: (no reason given)
Originally posted by ZeuZZ
can you show me where we have ever in situ measured something with an infinite value?