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Post by speakertoanimals on Nov 10, 2010 19:02:29 GMT 1
Utter nonsense, and yet another misunderstood Godel.............
What Godel said has nothing to do with what we actually measure, which is what it is. Our theory then trys to predict what we have measured. None of which is anything to do with Godel!
What Godel said, basically, is there are things which are true within a given axiomatic system, but unprovable within that system. Should we care trying to make predictions from our physical theories? Not really, because what we want from a physical theory is just:
If I put these numbers in (encoding my experimental set-up), what number do I get out (representing the predicted measurement). Or in the quantum case, we don't get a single number, but a probability diostribution over the various possible values, but the principle remains the same.
So, what do we want our physical theory to do? Given an input, produce an output. That's it, that is the prediction.
Godels theorem doesn't mean that a defined mathematical procedure such as the one above doesn't give a output, or won't give the same output if you repeat the computation.
The only possible worry (nothing to do with misprepresented measurements, which just sounds as if you have no idea what godel is about...........) is that given a theory of physics, we won't necessarily be able to show that that theory predicts everything within existing rules, but others dispute this.
But it isn't doesn't effect the validity and testability of what it DOES predict, just says (possibly) that no finite set of physics axioms can predict EVERYTHING, and be shown to be able to do that. It can be read as meaning not that there isn't a theory of everything, but that even if we had it, we couldn't prove it was the theory of everything.
None of which has ANYTHING to do with misprepresenting measurements, or saying that the theory can't predict what has been measured, and be thrown out on the basis of getting the wrong answer.
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Post by abacus9900 on Nov 10, 2010 20:26:48 GMT 1
Utter nonsense, and yet another misunderstood Godel............. What Godel said has nothing to do with what we actually measure, which is what it is. Our theory then trys to predict what we have measured. None of which is anything to do with Godel! What Godel said, basically, is there are things which are true within a given axiomatic system, but unprovable within that system. Should we care trying to make predictions from our physical theories? Not really, because what we want from a physical theory is just: If I put these numbers in (encoding my experimental set-up), what number do I get out (representing the predicted measurement). Or in the quantum case, we don't get a single number, but a probability diostribution over the various possible values, but the principle remains the same. So, what do we want our physical theory to do? Given an input, produce an output. That's it, that is the prediction. Godels theorem doesn't mean that a defined mathematical procedure such as the one above doesn't give a output, or won't give the same output if you repeat the computation. The only possible worry (nothing to do with misprepresented measurements, which just sounds as if you have no idea what godel is about...........) is that given a theory of physics, we won't necessarily be able to show that that theory predicts everything within existing rules, but others dispute this. But it isn't doesn't effect the validity and testability of what it DOES predict, just says (possibly) that no finite set of physics axioms can predict EVERYTHING, and be shown to be able to do that. It can be read as meaning not that there isn't a theory of everything, but that even if we had it, we couldn't prove it was the theory of everything. None of which has ANYTHING to do with misprepresenting measurements, or saying that the theory can't predict what has been measured, and be thrown out on the basis of getting the wrong answer. Yes, but all you are really saying, in a nutshell, is that we can only know stuff based on what we know. In other words, the maths we use to test predictions do work but work within a limited context thus preventing us from further insights. How can we ever hope to understand the universe fully (if that is possible) when our conceptual tools are limited by our number system?
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Post by speakertoanimals on Nov 10, 2010 20:38:20 GMT 1
Eh? This is one of the most ludicrous statements you've made so far!
It isn't the limitations of our number system -- just that being able to include basic arithmetic is a requirement of the formal system used in the proof of Godels theorems. It isn't saying that our aritmetic is shot!
And it would be totally bloody daft to think anything other than -- what we can know is limited by what we know. So, before Newton discovered the calculus, before cartan discovered cartesian coordinates, some problems were a bit hairy. Hence sometimes what physics we can do is limited by what maths tools we have, and in the case of string theory, the maths has had to run to keep up with what physics considerations needed.
But how you think there can be ANY alternative is beyind me! Our physics is limited by our presebtr knowledge of maths, BUT that doesn't mean that if physics perceives a lack in a certain area, that someone can't go off and try to discover the relevant maths.
Yes, there is probably a limit to what maths a human brain (ANY human brain, even the most brilliant, one in a century type of genius) can comprehend, and we just have to hope that that will be enough. But what else you think we could do if it wasn't, is again, beyond me!
If the real theory of everything is beyond human comprehension, then that is it. Nothing else we can do except try and design artificial minds who can perhaps design even more sophisticated ones, and take artificial intelligence into realms where human intelligence cannot go.
No, that wasn't what I was saying, you are confusing OUR personal limits, with what is mathematically possible. SO, Godel says that certain things cannot be shown, not because we are too daft, but because of the way he described the process of mathematical reasoning in his proof. Basically, he was talking about maths as a purely mechanical process, and as many people pointed out, that is not the way human mathematicians do maths anyway.
Its not a human limit, in that sense, but an absolute limit. Not what we know or do not know (as regards maths), but what is ever knowable or provable.
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Post by Progenitor A on Nov 10, 2010 21:27:40 GMT 1
And it would be totally bloody daft to think anything other than -- what we can know is limited by what we know. This is contradicted by history. What we know now would have been inconceivable in the 16C. So, before Newton discovered the calculus, before cartan discovered cartesian coordinates, You must mean Descartes But how you think there can be ANY alternative is beyind me! Our physics is limited by our presebtr knowledge of maths, BUT that doesn't mean that if physics perceives a lack in a certain area, that someone can't go off and try to discover the relevant maths. More rubbish English making gibberish of whatever it is you are trying to say
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Post by abacus9900 on Nov 11, 2010 11:00:52 GMT 1
No, it is not the human way, thank you for finally realizing this point. You do seem to be coming round to the idea (albeit kicking and screaming) that maths is not 'out there' just waiting for humankind to stumble on it, no, we have to invent it through our consciousness by interacting with the environment and participating in the positive feedback process that underlies all scientific progress, so that here again, we're 'inventing' reality at every turn. You really have to get away from the positivist idea that we and non-we are separate and independent from the rest of reality because this is a terrible denial of the plain fact that we are an active participant in the formation of it and that it is a truism to say that the universe is simply a reflection of the way we perceive it. Never forget that human beings invented mathematics, therefore, it will always be subject to the way they relate to it at any given time.
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Post by speakertoanimals on Nov 11, 2010 13:47:35 GMT 1
No I don't -- I said elsewhere I'm basically a platonist as regards maths.
But even if you say it is invented, just because our representation of reality may be biased ebcause it is OUR maths, doesn't mean that there isn't an external reality out there, to which our representation refers, that is independent of us, even though our representation isn't.
nonsense. And boring nonsense at that...............
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Post by nickcosmosonde on Nov 13, 2010 23:02:34 GMT 1
I'm definitely on your side on this one StA, as far as Godel and maths goes...Though a lot of what you say on this thread seems to contradict what you've said on the Schrodinger thread.
As for Abacus, you confuse me as much here as you do there. Are you saying, for example, just to try to pin you down a little, that we have somehow arbitrailt decided, "invented", that 137 is a prime number? Or have we discovered it? Is it dependent in some way on our perceptual or conceptual or socio-cultural apparatus, or was it always thus, in this or any other universe?
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Post by nickcosmosonde on Nov 13, 2010 23:51:04 GMT 1
I don't understand what you mean by "ideas" here.
Well, this certainly was not Schrodinger's understanding of the matter. You're conflating Schrodinger and the Copenhagen Interpretation here, I think. And then introducing this "idea" idea, which, speaking personally, you need to unpack and expicate before I can begin to understand what it is you're saying.
Huh??
Who says we're "non-material"?
I think I know what you're getting at. You're going back to an 18th century pre-Kantian world, at least, where Cartesian dualism was the widespread accepted conceptual understanding of the relation between the mind and the world. I think...? And you're presenting a Humean critique and eneding up in Berkleyian idealism. I think...? Everything is mind - "ideas"? Or...what is it that you understand by "material world" and "matter"? You say it's all at bottom "energy", and this you seem to equate with "ideas". Thus, all is "ideas". Do ideas exist in the brain? Does therefore all energy exist in the brain? Your brain, perhaps?
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Post by Progenitor A on Nov 15, 2010 8:50:52 GMT 1
I'm definitely on your side on this one StA, as far as Godel and maths goes...Though a lot of what you say on this thread seems to contradict what you've said on the Schrodinger thread. As for Abacus, you confuse me as much here as you do there. Are you saying, for example, just to try to pin you down a little, that we have somehow arbitrailt decided, "invented", that 137 is a prime number? Or have we discovered it? Is it dependent in some way on our perceptual or conceptual or socio-cultural apparatus, or was it always thus, in this or any other universe? We have quite definitely (almost quite definitely) arbitrarily decided that 137 is a prime number. Mathematics is basically tautological . In this case we have defined what is meant by a prime number and hey presto some numbers fit the arbitrary rules we have made. I suppose that it could equally well be argued that primary number were pragmatically 'discovered' in that one number was found to have the characteristic of being integer-result dividable by itself (hence creating its own rule), and then the search was on for others that shared that characteristic. However the 'rule' is a construction of the mind (although I suppose that by subtracting various numbers of pebbles from a larger number of pebbles the rule could equally well have been 'discovered'), but the definition of a primary number is a construct of the mind - a rule searching for a compliant subject.
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Post by abacus9900 on Nov 15, 2010 12:41:13 GMT 1
Yes, there is an external reality but it is our relationship with it that is of crucial importance here and that relationship expresses itself, among other things, in the form of maths.
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Post by abacus9900 on Nov 15, 2010 12:58:46 GMT 1
What we discover when we do maths is our inner mental workings which is based on the way our species has interacted with its environment in the past in order to survive, so there is nothing 'mysterious' or 'magical' about maths. Mathematics is all to do with organizing things into sets to make things manageable and to suggest that it somehow already exists 'out there' to be stumbled upon by us is plain nonsense. The discovery of prime numbers or any other mathematical patterns is simply an extension of set building.
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Post by abacus9900 on Nov 15, 2010 13:01:50 GMT 1
Mathematics does. The fact is, when we examine matter at the maximum focus we can only describe events mathematically, not in any material sense.
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Post by nickcosmosonde on Nov 16, 2010 12:40:38 GMT 1
The "rules" are not arbitrary though, are they? We may define it, but having done so there are numbers that fit the class we've defined and those that don't.
The definition has to made by the mind. But what is defined was, is, and always will be the case.
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Post by nickcosmosonde on Nov 16, 2010 12:42:49 GMT 1
Hang on. You've just argued elsewhere that reality is entirely made up of ideas, and here that ideas do not exist outside of a mind. What then is this "external reality" of which you speak?
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Post by nickcosmosonde on Nov 16, 2010 12:49:41 GMT 1
I don't think so, and I can't see how this definition of maths could possibly be evidenced. There's nothing magical about it, I grant you, but it's not about our inner mental workings either.
Well, if it is it's "plain nonsense" that is ascribed to with a great deal of thought and expertise by the majority of mathematicians.
That's a theory that was once believed in by a number of mathematical theoreticians - metamathematicians if you like - but failed to be realised. Sets are a large element of maths, but marks and ratios come first, logically speaking. The program to define ratios by means of sets didn't work and remains at most a hopeful hypothesis.
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