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Topic: Mathematics in music, Logical/creative< Next Oldest | Next Newest >
Sir Mustapha Offline




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Posted: Jan. 07 2008, 10:33

Quote (Alan D @ Jan. 04 2008, 17:16)
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true and false

Ah, now there I put up my hand and object. '1 and 0' are states, which in themselves are meaningless. 'True and False' are concepts, which we superimpose on the states to give them meaning.

Not really. "True" and "false" are values, just like 0 is a value and 3.14159... is a value. "True" and "false" don't have meanings, either; they're actually simply names, just like 0 and 1 are also names given to 0V and 5V in the transistors. "True" and "false" only become the concepts you speak of when you see them within a program, or among the data of a program, but that is already abstraction - and even only in certain cases. I'm going to look pompous for going into technobabble but please forgive me, but anyway, if you have a while(true) { ... } loop in a program, the "true" isn't even a concept exactly; it's a value, that keeps the loop running indefinitely. It's not "yes", or "positive". So, basically, any kind of "concept" you extract out of it is already an abstraction, but it is ENTIRELY the product of bits, and you can only abstract using some kind of external influence (i.e. the brain), because the computer itself doesn't do that.

So, yes, the abstraction is a subjective and completely human effort, but behind the layer of human interpretation, there's an inevitable, deterministic, measurable sequence of things going on. If we assume that happens in our brains too (in the form of immensely complex chains of communication between braincells), accepting that is not denying that those things result in an external, much bigger perception; it's merely an observation that may or may not lead to a bigger understanding about things. It's not a nihilistic "we're all a bunch of cells and this 'life' thing is just an illusion" statement; that is a mistake I think is made by those who abhor the idea of mathematics in music. In the very end, music is a bunch of sounds stringed together, but there are many layers above them, which are the point of music. Nobody makes music thinking of the frequencies and amplitude (okay, maybe Stockhausen did?); they do it without thinking, inevitably.

Also, I do not think that "pure science" can explain everything. Maybe it will, in a far future, when our supercomputers can finally discover the fundamental question of life, the universe and everything, but until then, we can't say. Studying the brain chemistry searching for the impact of a poem will yield near zero results, probably; to make yet another parallel to programming, it would not be possible to try to understand the whole working of my computer just by looking at the instructions the processor executes. We also need the abstraction in those cases.


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Alan D Offline




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Posted: Jan. 07 2008, 11:34

Quote (Sir Mustapha @ Jan. 07 2008, 15:33)
Not really. "True" and "false" are values, just like 0 is a value and 3.14159... is a value. "True" and "false" don't have meanings, either; they're actually simply names, just like 0 and 1 are also names given to 0V and 5V in the transistors.

Hmm... the problem that now arises is a linguistic one. If you're going to make them mean effectively the same as 0 and 1, then you're right - they are merely states. But I was using 'true' and 'false' as words expressing concepts, not states. Which brings us to:

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you can only abstract using some kind of external influence (i.e. the brain), because the computer itself doesn't do that.

Yes, that's exactly the point I was making. So we're now OK up to here, but then:

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If we assume that happens in our brains too (in the form of immensely complex chains of communication between braincells)

There I have to disagree, again, on two counts. First, it's an enormous assumption which requires a faith in the scientific process that I don't possess. Second, it fails the basic requirement for all scientific hypotheses: falsifiability. There's no experiment we can perform at present which could satisfactorily test the hypothesis. There might be at some time in the future, of course (though I'm sceptical whether we'll ever reach that point), but right now it's an untestable assumption.

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Also, I do not think that "pure science" can explain everything. Maybe it will, in a far future, when our supercomputers can finally discover the fundamental question of life, the universe and everything

It's that 'maybe it will' that worries me, and takes me back to a comment I made earlier: science doesn't 'explain' anything. The scientific method generates theoretical models (operating within strict limits) which make predictions, which can be tested, and the tests result in the models being rejected or modified, and so on. Every model is provisional, because we'll never know whether the next round of experiments will produce data that conflict with the model. We can't even say that our models are getting closer to 'the truth' (whatever that is): surely the primary illustration of that lies in the fact that Newton's Laws were thought inviolable for over 2 centuries, but their basic tenets are now known to be false.

Science is incredibly useful, and scientific models are often very elegant and beautiful; but no matter how long we go on pursuing scientific enquiry, we'll only ever possess good, predictive models. We'll never reach something we can call 'the truth'.

I ought to explain perhaps, Sir M, that I'm not in any way 'knocking' science. My degrees are both scientific ones, and I've spent most of my life in science. I think it's a hugely valuable (and often thrilling) activity, provided the nature of the process and its limitations are understood (which, usually, they aren't).
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Sir Mustapha Offline




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Posted: Jan. 07 2008, 13:50

Quote (Alan D @ Jan. 07 2008, 11:34)
I ought to explain perhaps, Sir M, that I'm not in any way 'knocking' science. My degrees are both scientific ones, and I've spent most of my life in science. I think it's a hugely valuable (and often thrilling) activity, provided the nature of the process and its limitations are understood (which, usually, they aren't).

No, I never thought you were knocking science; the conversation did start to go towards people who do so, in the first page, so it went from there. In that aspect, we're really not in opposition.

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There I have to disagree, again, on two counts. First, it's an enormous assumption which requires a faith in the scientific process that I don't possess. Second, it fails the basic requirement for all scientific hypotheses: falsifiability. There's no experiment we can perform at present which could satisfactorily test the hypothesis.


I can't believe I missed out on that. Maybe the hypothesis isn't entirely unfalsifiable, but yes, there's a big point that is also closely tied to the brain/computer parallel: the entire (classic) theory of computation is built on Church's hypothesis that the Turing machine can resolve every computable problem there is, and it's just a hypothesis that hasn't been proven for nearly a century; and it doesn't seem likely that it will be ever proved. So, the situation is that it's not possible (so far) to prove it is correct, and it's more likely to prove it wrong, if anyone shows a machine more powerful than Turing's. But all observations so far indicate that Church's hypothesis is correct; after all, all our computers are Turing-equivalent, and the stunning thing is that there is no evidence saying that the human brain has more computational power than a Turing machine. Mind you: I'm talking about being able or not to resolve problems, not in terms of speed or memory. Our computers have strengths our brains don't possess and vice-versa, but those are performance constraints. We are all able to do everything a computer does, albeit millions of times slower; and the question is whether a computer can perfectly emulate the human mind. Nothing says it can't, so the effort is in saying it can.

So do please take my words with a pinch of salt, because I'm talking entirely in assumptions. At least I'm not entirely invalidated: after all, assuming we do discover that there is "something else" in the human mind, something we hadn't seen before, probably science will have to rethink some of its concepts, we'll have to adapt to new facts, but we can still carry on. If there's something that completely defy human reasoning and logic... maybe that'd be pretty cool in a way. But we haven't reached that point, and goodness knows what lies ahead.


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Check out http://ferniecanto.com.br for all my music, including my latest albums: Don't Stay in the City, Making Amends and Builders of Worlds.
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Alan D Offline




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Posted: Jan. 07 2008, 16:03

Quote (Sir Mustapha @ Jan. 07 2008, 18:50)
If there's something that completely defy human reasoning and logic... maybe that'd be pretty cool in a way. But we haven't reached that point

I think that in the search for 'truth', almost everything of importance to us defies human reasoning and logic, and always has done. The reason why the scientific method is so successful is that it excludes so much from consideration. That's what Whitehead meant when he said that the exactness of science is a fake. There is this vast range of phenomena, and science says, OK, I can deal with a,b and c, but x,y, and z are not measurable things so I'll leave them out of my model. And that's fine as far as it goes, except for the fact that x,y and z include the most important things in typical human lives. (Love, faith, hope, friendship, trust, gratitude, awe, inspiration, generosity etc - the list is endless).

But so often the limitations are forgotten when the models are applied. On a crude level, just as an example, the scientist who examines the human brain and pronounces that he finds electrochemical activity but no evidence of a soul, is merely enacting a self-fulfilling prophecy. The conditions of his experiment prevent him from finding anything except electrochemical activity. His electrochemical findings may be excellent for medical research, but they're useless to the philosopher. (I'm not arguing for the existence of a soul - whatever that may be; just arguing for the irrelevance of scientific statements for or against the existence of such a thing.)

Human beings have one great advantage over the Turing machine. We're self-aware; we have subjective experience; we have inside information; we know what it's like to be human, and can test that inner experience against the pronouncements of science. That's where the problems arise.
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Sir Mustapha Offline




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Posted: Jan. 07 2008, 17:40

Quote (Alan D @ Jan. 07 2008, 16:03)
But so often the limitations are forgotten when the models are applied. On a crude level, just as an example, the scientist who examines the human brain and pronounces that he finds electrochemical activity but no evidence of a soul, is merely enacting a self-fulfilling prophecy. The conditions of his experiment prevent him from finding anything except electrochemical activity. His electrochemical findings may be excellent for medical research, but they're useless to the philosopher. (I'm not arguing for the existence of a soul - whatever that may be; just arguing for the irrelevance of scientific statements for or against the existence of such a thing.)

You've hit a good spot there. Using those methods to prove the non-existence of such thing is definitely threading on dangerous waters.

Quote
Human beings have one great advantage over the Turing machine. We're self-aware; we have subjective experience; we have inside information; we know what it's like to be human, and can test that inner experience against the pronouncements of science. That's where the problems arise.


Totally excellent observation. To me, that area of "artificial intelligence" is, in one hand, a little scary, but also totally fascinating. I have the impression that, no matter how many advances people make in that area, there will always be something there to be discovered. Maybe I'll bite the dust when they recreate the human brain in a computer, but still, if they do that, what happens? Game over? Where do we go now? Mysteries are the source of life for science. If all mysteries disappear, where does all the fun go?


--------------
Check out http://ferniecanto.com.br for all my music, including my latest albums: Don't Stay in the City, Making Amends and Builders of Worlds.
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Alan D Offline




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Posted: Jan. 08 2008, 04:21

Quote (Sir Mustapha @ Jan. 07 2008, 22:40)
Maybe I'll bite the dust when they recreate the human brain in a computer, but still, if they do that, what happens? Game over? Where do we go now? Mysteries are the source of life for science. If all mysteries disappear, where does all the fun go?

I don't think we have much to fear from the findings of science - only from the faulty philosophical conclusions people draw from them. The mystery will always be there.

I mean, how about this: the universe begins as a point in space/time which proceeds to grow. Stars and galaxies are born, go through their cycles, and die, manufacturing more complex elements that infiltrate the remaining space. More stars are born, and planets are built from those complex elements on which life can develop. This goes on, and on, for 14 billion years to bring us to this point, right at the cutting edge of the universe's evolution, here and now, where two people at opposite ends of the Earth are discussing, on a Mike Oldfield message board, the philosophical implications of their own intellectual activities.

I mean, it doesn't get more mysterious (or more fun) than that. Like it or not, we're responsible for what the universe does next.
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Danny_1985 Offline




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Posted: Jan. 13 2008, 14:54

Music and sound is a derivative of maths, the whole equal temperement and the tuning system was made up using mathematics and numbers.
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The Big BellEnd Offline




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Posted: Jan. 13 2008, 15:39

so what came first the music or the math, I mean I,m really struggling with the mental picture of primative man working out the calculus before stretching the hide over the drum and giving it a good old bang.

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