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Originally posted by ZeuZZ
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 Einsteinedit on 8-7-2012 by ZeuZZ because: (no reason given)
If travel is searching,
And home what's been found...
I'm not stopping.
The question is, how is it that Kurt Gödel can believe that God is not malicious? That it’s all understandable? Because Gödel is the man who has proved that some things cannot be proven logically and rationally. So surely God must be malicious? The way he gets out of it is that Gödel, like Einstein, believes deeply in Intuition - That we can know things outside of logic, maths and computation; because we just intuit them. And they both believed this, because they both felt it. They have both had their moments of intuition, moments of sudden conceptual realisation that were by far more than just chance.
Originally posted by dxdydz
reply to post by Americanist
I had to look that up. And I understand the definition of what a Cantor set is and that is uncountable.
So extending it into 3-dimensions seems logical.
The Menger Sponge something I've never heard of but can totally understand it in terms of surface area and volume and as an extension to the Cantor set.
Thanks for posting this!
Hence Arithmetic is the source of that preestablished harmony between reality and language that we can not not believe after almost four centuries of astonishing achievements, but we must even say that, neither tendentially, syntactic representation can thoroughly mirror reality, become someway iconic. And this because it is marked in its basic principles with a preestablished disharmony, that is even its hidden evolutive principle. It plays the role of source of never ending paradoxes well recognizable ever since the beginning of formal thinking. Negation, truth and being ground an antinomical argument, from the “negative judgement paradox” (impossibility of asserting falsity), through the “liar paradox” (contradictory nature of self-asserting falsity), to set-theoretical paradoxes and to Gödel's and Tarski's limitative theorems.
According to my notes, Gödel’s response went as follows: It should be possible to form a complete theory of human behavior, i.e., to predict from the hereditary and environmental givens what a person will do. However, if a mischievous person learns of this theory, he can act in a way so as to negate it. Hence I conclude that such a theory exists, but that no mischievous person will learn of it. In the same way, time travel is possible, but no person will ever manage to kill his past self. Gödel laughed his laugh then, and concluded, The a priori is greatly neglected. Logic is very powerful. Apropos of the free will question, on another occasion he said: There is no contradiction between free will and knowing in advance precisely what one will do. If one knows oneself completely then this is the situation. One does not deliberately do the opposite of what one wants.581
Originally posted by Moduli
Originally posted by ZeuZZ
can you show me where we have ever in situ measured something with an infinite value?
Yes, all of the things I said. E.g., the conductivity of a superconductor is measured to be equal to infinity.
Originally posted by Tormund
Originally posted by Moduli
Originally posted by ZeuZZ
can you show me where we have ever in situ measured something with an infinite value?
Yes, all of the things I said. E.g., the conductivity of a superconductor is measured to be equal to infinity.
No it is not. It is utterly incorrect thinking. What you are doing here is entering in absurd philosophical domain that should be kept away from science. (EDIT:) To prove that you don't have a clue what you are talking about and that it has nothing to do with infinity, we can talk about conductivity and resistance in percentage. In your case, resistance is 0%, but conductivity is 100% and it cannot be any greater. When resistance is maximal or 100%, it would be a really stupid idea to think about it as infinite. Because it is finite (at least in this case). But, when we are talking about infinite distance, for example, we cannot give the percentage, get it? It would be absurd.edit on 9-7-2012 by Tormund because: To clarify more...
Originally posted by chr0naut
reply to post by Virtruvian
Perhaps, by reduction, we could approach an understanding of Pi raised to the power of Pi.
Pi equals a number slightly bigger than three. More accurately, approximately 3.1415926535897932384626433832795
Therefore Pi ^ Pi = 36.462159607207911770990826022692
Not sure what you are getting at, doesn't equal infinity.edit on 8/7/2012 by chr0naut because: (no reason given)
Originally posted by Vitruvian
Originally posted by Tormund
Originally posted by Moduli
Originally posted by ZeuZZ
can you show me where we have ever in situ measured something with an infinite value?
Yes, all of the things I said. E.g., the conductivity of a superconductor is measured to be equal to infinity.
No it is not. It is utterly incorrect thinking. What you are doing here is entering in absurd philosophical domain that should be kept away from science.
Therefore the conductivity can be thought of as infinite: a superconductor.