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Post by speakertoanimals on Jan 26, 2011 2:58:49 GMT 1
Again, you are confusing proof in maths, with proof in physics. As I said before, physics doesn't prove, but disprove! And as I also said before, the question as to what geometry nature uses is a question in physics.
So, it can be disproved that nature uses Euclidean geometry, by just finding a triangle where angles do not sum to 180 degrees. Which is just by measuring space and finding it is not flat. We can't disprove that it uses exlusively Euclidean geometry, because as you say, we cannot show that the euclidean assumption doesn't break down at some unimaginably large length scale. Except that question isn't even academic, in that we already have good evidence that space is non-Euclidean -- and that can be proved, in a sense, by disproving that it is Euclidean -- as Gravity Probe B in orbit about the earth was sent up to measure (amongst other things), by directly measuring, if you like, whether the radius and circumference of its orbit agreed with the eucliudean assumption or not.
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Post by Progenitor A on Jan 26, 2011 9:10:16 GMT 1
You are interpreting Godel much too narrowly. If you look at the Pythagoras example then it can be seen that it is only true for triangles existing in 4 dimensional spacetime, not for more complex triangles that involve more than 4 dimensions. I think the point is, Abacus, that with Pythagerous theorem that works perfectly adequately for small lengths, yet there is no way whatsoever of proving that it works foe extremely large lengths (remember that the early mathematicians were practical people and were satisfied with theorems that produced results in their practical world - they were not seeking 'truths'- this is starkly illustrated by Carnyx's post on Pythagerous and root 2 - he and his followers regarded such things as literally 'magic' numbers). There is an assumption built into Pythagerous theorem that it applies to alll lengths - the fatal flaw of incompleteness because it simply cannot be proved that it applies to all lengths I must admit that my logic is based on the videos that you provided, I have not actually read Godel, but it seems that it is concerned with the incompleteness of mathematics (and hence, today, physics that is based almost entirely on maths) in that maths rest upon unproveable assumptions I can see intuitively the sense of that position, but I am worried (or delighted) that Godels theorem is a mathematical theorem and hence a paradox. As usual what we really need on this board are a mathematican and a physicist that speak English and have a flair for teaching, someone like that chap on your video.
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Post by abacus9900 on Jan 26, 2011 10:12:27 GMT 1
The fact still remains that Godel showed mathematics can never be completely predictive and therefore neither can science since science uses maths to describe and predict the universe. STA seems to have been underplaying this. And it's no good claiming that we can always turn to pure maths to remedy this because it is intrisically built into the nature of maths itself.
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Post by abacus9900 on Jan 26, 2011 10:26:27 GMT 1
I think the point is, Abacus, that with Pythagoras theorem that works perfectly adequately for small lengths, yet there is no way whatsoever of proving that it works foe extremely large lengths (remember that the early mathematicians were practical people and were satisfied with theorems that produced results in their practical world - they were not seeking 'truths'- this is starkly illustrated by Carnyx's post on Pythagerous and root 2 - he and his followers regarded such things as literally 'magic' numbers). There is an assumption built into Pythagerous theorem that it applies to alll lengths - the fatal flaw of incompleteness because it simply cannot be proved that it applies to all lengths I must admit that my logic is based on the videos that you provided, I have not actually read Godel, but it seems that it is concerned with the incompleteness of mathematics (and hence, today, physics that is based almost entirely on maths) in that maths rest upon unproveable assumptions naymissus, that bloody video was so misleading. The twit tried to make out that literally ANYTHING had to be taken on faith and was always just an assumption, which misrepresents what Godel meant. But, as you say, for straightforward mathematical ideas such as Pythagoras there is no problem with proof. I think the moral here is to beware of what you see on the net, although I still have not yet discovered a video that puts across Godel's central ideas without all the jargon. I understand that some mathematical ideas are not proveable because there's something in the logic that prevents their provability but it would be nice if someone who had a talent for communication (not STA of course) would make a video for the rest of us, but I have yet to discover one. Actually, the guy in the video, although wrong, was very good at putting things across.
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Post by abacus9900 on Jan 26, 2011 10:49:03 GMT 1
Which is what I have been saying for ages! So, we either have to turn to some idea already existing in maths to cover novel situations or invent some new maths like Newton and Leibniz did in the form of calculus. But, again, I have to remind you that maths is just another analogy that science uses in order to make sense of physical reality, it is not reality in itself. This is why maths has to be tailored to new phenomena in order to organize it. It doesn't mean the maths is already existing within the phenomena under question - you need people for that.
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Post by Progenitor A on Jan 26, 2011 10:55:08 GMT 1
I think the point is, Abacus, that with Pythagoras theorem that works perfectly adequately for small lengths, yet there is no way whatsoever of proving that it works foe extremely large lengths (remember that the early mathematicians were practical people and were satisfied with theorems that produced results in their practical world - they were not seeking 'truths'- this is starkly illustrated by Carnyx's post on Pythagerous and root 2 - he and his followers regarded such things as literally 'magic' numbers). There is an assumption built into Pythagerous theorem that it applies to alll lengths - the fatal flaw of incompleteness because it simply cannot be proved that it applies to all lengths I must admit that my logic is based on the videos that you provided, I have not actually read Godel, but it seems that it is concerned with the incompleteness of mathematics (and hence, today, physics that is based almost entirely on maths) in that maths rest upon unproveable assumptions naymissus, that bloody video was so misleading. The twit tried to make out that literally ANYTHING had to be taken on faith and was always just an assumption, which misrepresents what Godel meant. But, as you say, for straightforward mathematical ideas such as Pythagoras there is no problem with proof. I think the moral here is to beware of what you see on the net, although I still have not yet discovered a video that puts across Godel's central ideas without all the jargon. I understand that some mathematical ideas are not proveable because there's something in the logic that prevents their provability but it would be nice if someone who had a talent for communication (not STA of course) would make a video for the rest of us, but I have yet to discover one. Actually, the guy in the video, although wrong, was very good at putting things across. Well I'm glad that you have some scepticism about the video; I honestly do not think it matters if the video was not entirely accurate (simplifications invariably sacrifice accuracy).What mattered to me was that I could follow it and think logically about what he was saying - that to me is the essence of learning for understanding. (I am afraid that STA digs deeper and deeper holes for madness. On the 'information' thread she mind-bogglingly states (repeatedly) that a binary store (e.g a computer 20GB memory store) filled with 0's (empty) contains as much information as if it is filled 20,000, 000,000 encoded bytes of data! She further claims that Shannon suports her in this idiocy! Even worse than her calculus explanation - at least that contained correct results even if the explanation was unbelievably stupid.)
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Post by abacus9900 on Jan 26, 2011 12:13:37 GMT 1
I think what may be happening here is that she tends to confuse ideas by straying from the point. In science or indeed maths there are always different ways of looking at things but you must always make clear the context within which you are speaking. She doesn't.
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Post by carnyx on Jan 26, 2011 12:30:31 GMT 1
Abacus
Exactly ...
And the consequences are profound.
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Post by abacus9900 on Jan 26, 2011 12:44:31 GMT 1
STA doesn't seem to think so. She calls it all bollocks!!
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Post by speakertoanimals on Jan 26, 2011 12:58:56 GMT 1
Absolute and utter RUBBISH! Total bollocks! And you can't even spell Pythagoras.................................. IF geometry is Euclidean (the five axioms hold). then Pythagoras holds for all lengths, by definition. Especially since geometry itself has no innate length scale. So, it doesn't matter if you call the length of one side of your triangle 6 flodgets, or 1 wibble, as long as you define all other lengths in the same units. Whereas non-Euclidean geometry (like geometry on the surface of a sphere), DOES have a length scale (the circumference of the sphere), which tells you how far you move from approximately Euclidean as the size of the triangles increases. As I keep saying, whether or not Euclidean geometry holds in the universe, just says WHAT the associated length scale (or the lower limit on the length scale is), for non-Euclidean geometry. We cannot prove in science that it IS Euclidean, just that if non-Euclidean, the length scale/curvature is above/below some defined limit. So, for instance, measurements on the CMB indicate that the curvature of our universe is ALMOST flat, just as the associated limit on the size is very, very large (possibly infinite). the comments on here are becomi9ng so ludicrous that I'm not sure what is more likely -- that posters really are this dense, or that they would really spend this much effort posting nonsense that they knew was nonsense just in an attempt to wind me up. I can't be THAT important surely....................... As I said elsewhere, Shannons original paper: www.math.harvard.edu/~ctm/home/text/others/shannon/entropy/entropy.pdfMaths at Harvard, so I presume they know a little bit about the subject. Page 1 of the paper: That is, if we are considering binary strings of N bits, the total number is 2^N, hence the information content of ANY one string (N 0's, say), is defined to be - log(p), where p = 1/2^N. Which hence gives the information content of a string of zeros as the SAME as any other bit string of the same length. Perhaps someone would care to explain WHY what SHannon says above DOES NOT mean this? In which case, someone ability to comprehend english is in severe doubt.
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Post by speakertoanimals on Jan 26, 2011 13:09:40 GMT 1
And we seem to have descended into madness , with people claiming that Godels says NOTHING can be proved (including GOdels theorem itself), which is just piffle of the highest order. A total inability to understand (or even LEARN), what the basic terms such as axiom, theorem, theory, proof, or paradox actually mean.
A few key quotes about Godel:
and so on. In summmary, MOST of what non-specialists say about Godels theorems is just plain WRONG. And what we have on here is not even wrong, it's just totally lunatic....................
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Post by abacus9900 on Jan 26, 2011 13:19:03 GMT 1
The trouble is, when you talk about 'all lengths' you must include ludicrously long lengths that exceed the size of our universe. Now, how can you actually prove that lengths behave the same once beyond our universe? You cannot, of course, which is why such axioms are not proveable in all cases, only in a limited set. You have to make it clear what you are mean otherwise you are in danger of being parochial.
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Post by speakertoanimals on Jan 26, 2011 13:31:33 GMT 1
Is this not exactlyn what I said? Except you KEEP confusing proof in maths (Pythagoras is true for ANY length as long as the geometry is Euclidean), with proof that the geometry of the universe is Euclidean.
Anyway, even if the universe is flat on the largest scales, the upper limit given by the size of the universe isn't a FUNDAMENTAL problem, in that since it is expanding, we just have to wait long enough, until it is big enough.
But we can still mae meaningful physical predictions, such that if it is EUclidean now on longest scales, it will remain so even when the scales get larger as the universe expands.
WHY can't you make the simple distinction between maths and physics, WHY do you keep muddying the water and writing as if they are the same? ARe you really that stupid, or just stupid enough to pretend to be that stupid?
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Post by Progenitor A on Jan 26, 2011 13:35:53 GMT 1
The trouble is, when you talk about 'all lengths' you must include ludicrously long lengths that exceed the size of our universe. Now, how can you actually prove that lengths behave the same once beyond our universe? You cannot, of course, which is why such axioms are not proveable in all cases, only in a limited set. You have to make it clear what you are mean otherwise you are in danger of being parochial. I am afraid you are banging your head against a very stupid brick wall Abacus. See above where she suports her orignal stance that an empty memory store has as much information content as one full of encoded data. This is so incredibly stupid that it is not worth arguing with. Also see her usual tactic of including irrelevant quotes that have no bearing to her imbecilic argument. This person is an anti-scientist If anyone wants a logical discussion of information theory wuth Shannons analysis of an empty information set I will happily join in but STA is beyond the pale.
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Post by speakertoanimals on Jan 26, 2011 13:47:40 GMT 1
Irrelevant? The very paper and the very lines where shannon defines information content? And you seriously think ANYONE is going to be fooled by your claim that this is irrelevant to a question involving information content?
I see that you haven't actually attempted to SHOW that it is irrelevant, just hope that if you keep slinging the mud, others will be so wowwed by your intellectual brilliance that they won't bother to read it and judge for themselves. Thankfully, not everyone is a stupid as you (apart from abacus, if he even is a separate entity).
The problem is not that you're so stupid that it isn't worth arguing with you, the problem is that you're either so stupid that it is worth posting against you to try and stop others being fooled by your drivel, or so vindictive, that you know it is drivel but post it anyway.
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