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Originally posted by tetra50
reply to post by Vitruvian
no mathematician, and limited in intelligence, but just wanted to say that what struck me about your lower "equation," appears to express that trying ti divide Pi evenly equates to a Mobius Twist, and therefore goes back to the beginning repeatedly, only to repeat again, in an effort to divide without remainder, which is currently not possible, supposedly, at least with the processors we have available to us and their ability to extrapolate the equation infinitely.
Originally posted by Stunspot
The problem with your post's ideas is that you've only half-understood Godel's Theorem. What it shows is that for any reasonably powerful symbol manipulation system, there will always be statements that are unprovable but true OR that there are statements that are both provably true and false. That is, you must have either incompleteness or inconsistency. Godel makes no claims about which condition is likely to obtain for a given system. Most prefer to think about the former, but the later is just as reasonable.
Beneath the surface of the world are the rules of science, but beneath them, there is a far deeper set of rules, a matrix of pure mathematics, that explains the nature of the rules of science, and how it is we can understand them in the first place.
Modern materialistic science has a shadow constantly whispering doubts of it's veracity into it's ear. The shadow is comprised not of material substance, but words; the words of Godels incompleteness theorem and the logic they illuminate. The theorem is obvious, almost intuitive. It's un-impeachable in it's brilliance, profundity and simplicity.
Godel took Occams Razor and sharpened it with the power of his mind.
"To see a world in a grain of sand, And a heaven in a wild flower, Hold infinity in the palm of your hand, And eternity in an hour."- William Blake.
Originally posted by Stunspot
reply to post by ZeuZZ
Again, I feel the need to stress that I'm not talking about undecidable statements, but rather statements that are provably true and provably false at the same time. It should be known as his Incompleteness/Inconsistency theorem.
As far as mathematics undergridding physics, that's a pretty big assumption. While few would deny that mathematical relationships seem isomorphic to the universe, isomorphism is not identity. Math is the product of mind, not nature.
He realised that there’s a way in which in order to understand something you have to look very hard at it but you also have to be able to sort of move away from it and kind of see it in a kind of wholistic context, and the person who stares too hard can often can lose that sense of context.
Originally posted by Stunspot
The problem with your post's ideas is that you've only half-understood Godel's Theorem. What it shows is that for any reasonably powerful symbol manipulation system, there will always be statements that are unprovable but true OR that there are statements that are both provably true and false. That is, you must have either incompleteness or inconsistency. Godel makes no claims about which condition is likely to obtain for a given system. Most prefer to think about the former, but the later is just as reasonable.
And as useful and important as his theorem is, it only applies to systems where the categories of "True" and "False" are well-defined and diametrically opposed. That does not seem to be the case in the universe. Every quantum interaction epitomizes the concept "both provably true and false at the same time". On the macro scale, one need only look at relativity to find numerous trivial examples where both A and NOT-A obtain at the same time (especially relevant in the case when observing events outside your causal domain). Or, as my Philosophy of Physics professor used to put it: "Reality is NON TRANSITIVE!".
As to the computability of Mind, I would submit that there is significant evidence pointing to the brain having fundamentally quantum characteristics, from synaptic entanglement, to the microtubual's role in memory propogation, even to the basic nature and behavior of thought. If the mind is ultimately the result of quantum computation, then it is, at its core, inconsistent, with ambiguously valued theorems.
Remember, Logic is bigger than Aristotle. Good post though. (Coulda used some editing, though. I mean, come on. It's "auditory" -- of or relating to the ear.)
Science's weirdest realm may be responsible for photosynthesis, our sense of smell, and even consciousness itself.
Godel took Occams Razor and sharpened it with the power of his mind.
So Cantor proved using a set of axioms that you can take an infinite set and create a larger infinite set so the new infinite set has more elements than the original. Pretty mind blowing.
Originally posted by Americanist
reply to post by ZeuZZ
Godel took Occams Razor and sharpened it with the power of his mind.
I invite you to take an in-depth look into the definitions for both image and frontier as they apply to mathematics.