Einsteins last years with Godel were ignored for 50 years, UNTIL NOW! We still stand at the frontier

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.

TETRA50.......... thank you for your insight.......StudIed chemistry and physics in a junior college setting, but no real serious math education here either - art, philosophy, and theology, but with strong interest in science and physics.

When I first saw the equations come across the 'screen' I wasn't sure if they were to be divided, multiplied, added to or subtracted from. All I was sure of was that they were to be understood as interacting with one another in a way that would lead to a solution. The "message" I heard was something like........these equations in combination will lead to solving the mystery of unification.

Your mention of the Moebius loop and its definite relation to 'Infinity' did occur to me often while ruminating on the equations. I thought it noteworthy that you immediately thought "division" rather than ....???

It did also occur to me that Einstein did incoprorate into E=MC 2 the notion of Pi.

An "image" of the "speed of light" also seemed to dominate my thoughts on the two equations and their manner of interaction, and seemed very important as a means of calculation that would eventually lead to a resolution of the unsolved problem of unification, which to my personal understanding of the entire event was the whole point of their appearance at the end of the vision.

I guess it can be safely said that Pi - in and of itself - is essentially INFINITE and it also occurs to me that so might be Einstein's famous equation as regards the "infinite" universe.

reply to post by ZeuZZ


ok i am no mathematician so this thread is beyond me but this caught my eye...


Its a flaw is science give misinterpretation of data significant meaning, You might say, indeed, it has a infinite height, but 0 width. So it doesn't even exist at all. ?

I would say it does and you are describing the 1 of the extra dimensions that modern science theorizes we have 11 of?

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.)

I will quote from above thread,,too try and build a better understanding;
for myself, and hopefully others.

quote
"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."
unquote

At the "become infinite" moment in time, yes speed of light time.,,Higgs-Bosun is created.
And from our perspective in time,, dependent on the ,location of that perspective, on the Spiraling Wave, of existence.
Mass,,and the creation their of.comes into reality.
At different perspectives mind you,, for each unto thier own,, perspective.

This has been a very interesting read. I have enjoyed it very much.

I am no great mathematician or scientist, but I do feel that I have a very logical, scientific, and dare I say inquisitive mind. So, here is my 2 cents...

Math and science has attempted (infinitely) to understand or explain the concept of God, a higher being, all knowing, all seeing, and yes...INFINITE. Our little minds can not grasp all the mysteries of our universe or universes, and will never be able to. Any "theorem" starts with accepted "facts" and builds from there. But what if the facts are actually fallacies? What then?

Big Bang started from (insert your "fact" here). Where did that come from?
Well, it came from X. Where did X come from?
And so on, and so on, to infinity and beyond.

When you get so caught up in these exercises and forget to live, it's time to stop and go look at a beautiful sunset, or smell a flower, or hold someone's hand. We are only human after all.

Smile!

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.

The op was concise readers digest version, more a light narrative in the context of a far deeper subject, I largely agree with what you have just said. Maybe I should sum up Godels theorem more succinctly for clarification:

Godel's incompleteness proof involves constructing statements that are well-formed within the system in question, and cannot be proven true within the system, but can be proven true via analysis outside the system. Mere undecidable statements (that cannot be proven true or false at all) are far easier to construct and do not render a formal system incomplete.

The theorem is obvious. And it's quite obviously un-impeachable in it's brilliance, profundity and simplicity. Irrespective of it's deeper meaning relating to the matrix of maths and logic science is precariously predicated on.

Godel took Occams Razor and sharpened it with the power of his mind.

Which is really what this thread is getting at, the power of the mind and consciousness over any mathematical, logical system and resulting physical science; Einstein seemed to realize this in his later years even as the scientific community ran off and made 'mainstream' the science truths and mathematical absolutes he himself was deeply uneasy with.

Talk about a mind F*&#

reply to post by ZeuZZ
Wow, after watching that I couldn't get to sleep,and from that this is what I got.
Is it possible that we need two infinities, one numerical and one spacial, so numerically it's calculable but spatially, everything all ready exists, there for none can be added or divided externally to spacial infinite because outside spacial infinity does not exist.
another thought was say if I was to calculate infinity plus one I could only insert one because infinity has no start or end. is this true?

all so would some one be able to explain to me why infinity is so useful to mathematicians? if its a short cut, I find ironic that the biggest thing ever is a shortcut.

(take it easy on me, long time browser but first time to partaker in discussion)

www.facebook.com...

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.

I wrote this up again under my facebook group with that at the start, join if you want

www.facebook.com...

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.

I'd like everyone to keep in mind that Cantor's infinities were related to cardinal numbers.

from wiki:
In mathematics, cardinal numbers, or cardinals for short, are a generalization of the natural numbers used to measure the cardinality (size) of sets.

and chew on this from wiki:
In elementary set theory, Cantor's theorem states that, for any set A, the set of all subsets of A (the power set of A) has a strictly greater cardinality than A itself. For finite sets, Cantor's theorem can be seen to be true by a much simpler proof than that given below, since in addition to subsets of A with just one member, there are others as well, and since n < 2n for all natural numbers n. But the theorem is true of infinite sets as well. In particular, the power set of a countably infinite set is uncountably infinite.

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 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.

I like this post, and agree with it, especially the bolded.

Personally I would add at the end, "and nature is the product of consciousness".

I don't think we are actually disagreeing about much ...

There is something to be said about a wholistic universal approach (strong gaia hypothesis) vs. reductionism approach (quantum consciousness [Penrose]) though. The key being emergent properties we observe in all of nature. Biology is an emergent property of chemistry, which is in turn an emergent property of physics. From a reductionistic standpoint, if we knew the state of all the subatomic particles in a system we should be able to tell which gazelle the lion will eat. However, such a notion is laughably absurd--you simply cannot know the nature of the system by pure reductionistic methods. You have to accept that there's a lower limit to the units in the system, a basic component that cannot be split.

In terms of isomorphism not being identity, I'm not entirely sure what you mean by this. You've got to look at the organism's position in morphospace as a whole--meaning that the organism, not the trait, is the "pixel" of evolution, as it were.

It may work out what the wholistic 'strong theory of gaia' universal approach to consciousness manifests via quantum processes anyway ... which sort of brings you back in a logical loop of the reductionist approach being an emergent property of the wholistic one.

Which is another paradox in its self

Unless.

Everything is alive

Wow I just found this great link talking about Godel's Incompleteness theorem in almost laymen terms.
www.math.grinnell.edu...

Basically if you have a system of axioms F and different models that successfully use them, then you can create statements that are true in one model but false in the other models of F. Therefore F is inconsistent.

Two models that successfully use F are the rational numbers and real numbers in this link.

One example given is using the axioms of F you can say a*a = 2 in the real numbers. Whereby a = square root of 2. But in the rational numbers there is no solution and that statement is false. The real numbers and rational numbers are both models of F but the statement a*a = 2 is true in one model and false in the other! So it can NOT be proven the statement is True or False in F.

reply to post by ZeuZZ


Great writing, I especially felt this:

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.

How I have been there, so many times...I am at the brink of madness on some days...I know what Cantor went through, it's the same persecution that Nikola Tesla went through (and much of the same self demise).

We should stop staring at the dot, eventually we will forget there is a whole universe set up around it and that has infinitely more amazing secrets to share with us.

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.)

Is Quantum Mechanics Controlling Your Thoughts?

discovermagazine.com...

Science's weirdest realm may be responsible for photosynthesis, our sense of smell, and even consciousness itself.

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.

reply to post by dxdydz

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.

This is demonstrated by the menger sponge in iterations.

reply to post by ZeuZZ


I also have read most of Douglas Hofstadter's books and your post resonated beautifully with "Goedel, Escher, Bach: an Eternal Golden Braid".

Thank you, it is this quality of post that draws me to ATS.

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.

Now that was an invitation to a place I could happily spend the rest of my days.

Thanks for showing you comprehended my point

Thanks for the invite, I'll be on the frontier shortly, after I've got a few more people to join along

"Any intelligent fool can make things bigger and more complex... It takes a touch of genius --- and a lot of courage to move in the opposite direction." - Albert Einstein