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

Originally posted by Moduli
As for Godel's theorem, you (and tons of other people) have it all wrong, too. It's an interesting theorem, but it doesn't mean what you say it means. All it says is that certain kinds of mathematical frameworks aren't strong enough to prove statements larger than they are, and that some statements about all possible combinations of statements in the framework are stronger than the framework, and thus can't be proven within it. Neither of these results are surprising. (What's interesting is the details; exactly what kinds of frameworks can and can't do this (e.g., the Peano axioms do not satisfy this, and can be proven, where ZFC cannot), and what impact this has on current results (very little), etc.)

At any rate, Godel's theorem has no impact on science whatsoever, because of the kinds of questions they're interested in answering v.s. the kind mathematicians like to answer.

Allow me to point out that the only thing infinite in this thread is your arrogance and your ignorance:

"There are mathematicians who say that what Gödel did is just irrelevant to their working lives as mathematicians, that they never have to think about incompleteness, or even know what exactly it is, in doing mathematical work. So you can do your mathematics and stay out of the meta-discussion. This is probably a pretty common attitude among mathematicians. And in some sense it's a natural attitude. When you're working within the discipline you're doing what can be done within that discipline. The fish doesn't have to be an expert on the nature of water.
That's true in other field, too, say in physics. Physicists who disagree radically on the interpretation of physical theories—some thinking they're descriptive of an objective physical reality, others thinking theories are just instruments for predictions—can collaborate qua physicists, can employ the same physical theories to get out scientific results, whether theoretical or applied. Your day-to-day work as a physicist isn't necessarily going to be changed one way or the other because of your meta-view of what physics is; and your day-to-day life as a mathematician isn't necessarily going to be changed by your meta-view of what mathematics is. You don't even have to have a meta-view. Gödel's theorems only matter if you're interested in those meta- questions and to be a mathematician you don't necessarily have to be interested in those questions."
-Rebecca Goldstein, www.edge.org...

Please, by all means, continue to carry on in an entirely different mode of thinking from that being discussed by everyone else here, and ignore the vast and fertile ground of Philosophy while playing around in the dust of your myopia, like the low level technician you seem so proud to be.

How dare you insult others because of your inability to acknowledge that there may be more facets to an idea than you are aware of. How dare you. You should be ashamed, knocking people down for trying to learn something. You've steered them right off course into your own playpen of an opinion and then bullied them. Are you proud of yourself now?

For the rest of you, here are some places to continue!
en.wikipedia.org...
www.philosophypages.com...
www.edge.org...

The OP raises some beautiful thoughts! Don't listen to people who right off the bat try and make you feel stupid for not being versed in something so INFINITELY deep and wide!

reply to post by ZeuZZ


What a great post!

All my life I have had a problem with mathematics, I think the main reason was, I was expected to accept numerical facts without having had it explained fully, how numbers could describe the unknowable or reduce a multiverse into an equation. My intuition always told me that there was something fundamentally flawed in the logic founded upon our limited perceptions of our Universe. Within infinity there has to be the probability that 1+1=3 if that is not a probability, then it is not infinity and so the paradox is born.

As you so beautifully put it your precis

And so, as then, we still desperately want to cling to belief in certainty. It makes us feel safe. At the end of this journey the question, I think we are left with, is actually the same as it was in Cantor and Boltzmann’s time. Are we grown up enough to live with uncertainties? Or will we repeat the mistakes of the twentieth century and pledge blind allegiance to yet another certainty?

You have put it in a nutshell for me, Science will never be able to feel comfortable in it's certainties because the logic behind logic is flawed in an infinite universe.

That is why I and many like me, feel comfortable in the certainty of our immortality through our intuitive knowledge, never proven nor required to be for us to feel secure.

reply to post by ZeuZZ


ZeuZZ
Thanks for the enlightening post(s).............While reading it I was reminded of something that came to me several years ago by way of an extraordinary religious experience, and I thought I would share the very last portion of it here - it might be relevant and it might not. I had to present it as an image file.

"But flaws in the materialistic paradigm of science have appeared in recent years.
These flaws have grown to a gaping rent, torn across the whole fabric of the materialistic conception of reality.
Strained by the conflicts between Einstein and Bohr over the ultimate meaning of quantum mchanics (developing in the Einstein-Podolsky-Rosen paradox), subjected to further stress in Bell's theorem, and finally ripped through in recent tests by Aspect France, the whole cloth of the materialistic picture of reality must now be rejected."
Transcribed from "the physics of consciousness", by Dr. Evan Harris Walker. circa 2000.

Also, from the same source;

"But where science, all of it, failed most has been in its inability to cope with the question of mind---the question of the nature of consciousness---the doorway to the quantum mind."

Fascinating read, OP. One of my favorite subjects.

reply to post by ZeuZZ


Hey awesome post.
I would have to conclude from this post that the human mind is a logical machine.
Just from the fact that these fellas all found problems that they couldn't prove and sent their brains into seemingly non-terminating computation until they went mad.

Luckily after a few beers my brain wanders from such problems otherwise I'd go mad too.

reply to post by ZeuZZ



Thank you for your posting. Very informative. I enjoyed reading it !

I'm still not understanding this part

"Einsteins last years with Godel were ignored for 50 years, UNTIL NOW!..."

Has science taken up the cause, or is your personal attention with this post the beginning
of the new frontier in scientific thought...?

And this answer...is this condescension?...an obvious example of the concept of *a moment* in time?
....or just a side-step shuffle?

Sorry guess that is a bit dated now. I mean until NOW. actually wrong, NOW seems more likely. No, Now.

I watched the vid...nothing there that isn't there in my posited proof of infinity---you can always
add one unit to something (in one direction) or cut the unit in half (in the other).
One plus infinity is infinity, half of infinity is infinity...etc.

Infinity is uncomprehensive and unquantifiable. This is where genius goes mad in attempting to define
that which has no boundary....My over-riding point is that we don't know much and what we think
we know could be wrong---That's a terrible platform from which to launch discussion or experiment
because qualifying every statement with "I think," or "probably", or "perhaps" is seen as too timid
as to be taken seriously...but I prefer the courage that it takes to say you don't for sure, over the
arrogance of saying that you do.....

As most men reach the truth... they find themselves facing the very thing that led them to want to forget in the first place.

Wonderful thread.

Namaste.

That's quite a good read OP. Thanks for that!
Limbo

There's a book called The Mystery of the Aleph: Mathematics, the Kabbalah, and the Search for Infinity , which is about Georg (not George) Cantor and about Kurt Gödel to a fair extent, but even more so about the twists and turns that mathematics takes on the way to finding the Ein Sof.

Isn't that really the point, after all? I've always thought so.

Is it not encouraging that the two conditions, Autism and Synesthesia, are being viewed by many in a different light now as these conditions are getting explored in more depth? I have always been of the opinion that perhaps they can even be gifts rather that afflictions if used to their best advantage, with the full acceptance that we do not all have to be the same and fit into the "accepted" social straight-jacket.

reply to post by KenArten


A poster above you brought up another view that rejects the assumption that a statement must be true or false, and provides the mathematics, supposedly, where any equation can have four conclusions. I mention it, because, I find it comparable, in a way to what you say above, here, about the "social straighjacket," great term, btw. Do we have to be either sane or insane?

Anyway, everyone, comments here have been as interesting as the OP, which is so thought provoking.

This is the type of post I love and hate all at the same time. While the subject matter is incredible to contemplate and discuss. There are an infinite possibility of subjects that can spin off of this thread and yes I am totally having fun here with the subject. There is never any real conclusions or definite resolutions. Only in my mind the fact that the amount of things that we do not understand is ever growing. The fact that thinking about this subject drove great minds into insanity. Shows how foolish we are to push ourselves to try and understand them now, but truly thinking people will do just that. Most my friends and family in real life do not understand why things like this cause me to loose sleep at night. It is my drive to never stop learning and to pushing myself to a greater understanding of the great multiverse in which we live in today. I hate forcing myself to shut my brain off when it is growing the seeds of knowledge planted by these ideas. This is where I imagine we are mostly all alike here in this forum. I applaude the OP for bringing this subject up, and once again pushing me to open my mind to the thinking of the great minds of our past. Thank you!

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.

reply to post by ZeuZZ


This is a strange and enigmatic thread, but lovely…for ATS and for me, who generally reads ATS with a sense of humor. A lovely thread because it injects a cold, fresh breeze of non-absoluteness into what I feel is the usual ATS menu of crank opinions and conspiracy
povs. Enjoyable reading - nice historical picture. Thanks.

Props for posting all that. But I wonder why.

Isn't it completely wasted here where most people who read it aren't even competent to tell if it is more meaningful that the rest of the nonsense posted on this forum? They have no ability to distinguish it from the other pseudoscientific gobbledigook that happens to have tickled their fantasy.

Then there is the individual who pretends to understand it and claims very loudly that you don't know what you are talking about, citing the use of infinity in mathematics as used by physicists. (The example of infinite conductivity of a superconductor made me laugh pretty hard. I guess by ohms law you get infinite current if you apply a voltage, do you?)

Well done for knowing your stuff and posting a fine essay. But I wonder what your real purpose was.

We were led down a mental rabbit hole, and einstein was playing his part.

Is infinity divided by infinity one or infinity, both, neither or each and everything in between.

We are being tricked, on every level.
Everything mainstream is designed to bamboozle the masses.
It is a most massive conspiracy.

Originally posted by XtraTL
Then there is the individual who pretends to understand it and claims very loudly that you don't know what you are talking about, citing the use of infinity in mathematics as used by physicists. (The example of infinite conductivity of a superconductor made me laugh pretty hard. I guess by ohms law you get infinite current if you apply a voltage, do you?)

Ohm's law only applies to resistors, genius. A superconductor is not a resistor, that's the whole point of it. Also, again, I'm a professional physicist, so I do know what I'm talking about.

Originally posted by OutonaLimb
Is infinity divided by infinity one or infinity, both, neither or each and everything in between.

None of the above. To determine what infinity divided by infinity is, you have to refer back to the definitions of infinity and division.

Typically, a/b is defined to be the value c such that b*c = a. This works in mathematical number systems called "fields" (so long as b is not zero) and sometimes works in "rings" (for so-called "invertible" elements).

Actually, if you are working in the ordinary real numbers or complex numbers, infinity is not actually a number and so the statement infinity/infinity has no meaning.

Even if you don't care about the fact that infinity isn't a number, you can see that infinity/infinity has no meaning because there is not a unique number c such that c*infinity = infinity. Clearly any positive number will do. So c is not well-defined. Therefore we say infinity/infinity is "undefined".

To show that this is no more mysterious than the every day real world we are used to dealing with, consider the question, "what type of rock is a dog". You can ask the question, but when you have a clear understanding and conception of the definition of a dog and of a rock, you see that the question itself is just nonsense.

Originally posted by Moduli
I'm a professional physicist, so I do know what I'm talking about.

And I'm a professional mathematician.

The ironic thing is that us mathematicians do not call a proof what you physicists call a proof. And the crux of the matter is usually that you ignored singularities in your equations. There are entire fields of physics which persisted for forty years without being placed on a rigorous mathematical footing for precisely this reason.

It's hilarious to me that physicists are the ones that ignore the lack of physicality in the quantities appearing in physics equations.

Just because you define a quantity to be the inverse of another, doesn't mean that if the one drops to zero then the other having an infinite value has some physical meaning.

Not being a physicist, I am going to assume that when applying Ohm's Law to a superconductor (E = rho J), that making the resistivity rho zero prevents you from setting up anything but a zero electric field in the superconductor.

Thus, your infinite conductivity 1/rho, has no physical meaning. It's a mathematical quantity, not a physical one!

Originally posted by XtraTL

Originally posted by OutonaLimb
Is infinity divided by infinity one or infinity, both, neither or each and everything in between.

None of the above. To determine what infinity divided by infinity is, you have to refer back to the definitions of infinity and division.

Typically, a/b is defined to be the value c such that b*c = a. This works in mathematical number systems called "fields" (so long as b is not zero) and sometimes works in "rings" (for so-called "invertible" elements).

Actually, if you are working in the ordinary real numbers or complex numbers, infinity is not actually a number and so the statement infinity/infinity has no meaning.

Even if you don't care about the fact that infinity isn't a number, you can see that infinity/infinity has no meaning because there is not a unique number c such that c*infinity = infinity. Clearly any positive number will do. So c is not well-defined. Therefore we say infinity/infinity is "undefined".

To show that this is no more mysterious than the every day real world we are used to dealing with, consider the question, "what type of rock is a dog". You can ask the question, but when you have a clear understanding and conception of the definition of a dog and of a rock, you see that the question itself is just nonsense.

edit on 8-7-2012 by XtraTL because: correction

edit on 8-7-2012 by XtraTL because: (no reason given)

In complex mathematical equations, aren't infinities cancelled out?
How can this be if infinity/infitity is undefined?

To answer your question: 'What type of rock is a dog?'.... A RockWeiler?