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Post by Ben on May 6, 2006 14:53:29 GMT 1
but mathematics has predicted things that haven't been experienced yet, and thus it doesn't 'explain the world', since it has nothing to explain. indeed, lots of important scientific discoveries have been found because maths has said "these should exist", and indeed they have. Plus, since Mathematics' axioms are based upon logic, they are completely abstract of the universe. Logic is the only thing Nihilists can be sure of, and thus is the only thing that you could construct an infallible system for the universe from. Apart from the natural numbers, all else follows from that idea. Hence there is no discipline that could overrule maths, since it would require the same ideas as maths to begin. Mathematics is and isn't man-made. Certain fields of maths were originally created to deal with daily life (counting, equations, etc etc), but throughout the years, they have been proven to be independent of real life, and so sit up there with all other abstract concepts. There are many different ways to explain the world, but they all have to give the same answer, right? 2x=4 is the same as 4x=8. They're different but they reduce to the same answer. Newton's law of motion is equivalent to Hamilton's Equations of motion, and they both describe the same thing, despite being completely different.
The point is, however you describe the universe, you have to the get the SAME answer. Since the universe could never be objective, since everything relies upon your standpoint and frame of reference, any discipline that describes the universe has to be correct for every situation and person that observes it. Maths fits that bill because it's independent of the universe. To quote a famous mathematician,G.H. Hardy: "317 is a prime, not because we think so, or because our minds are shaped in one way rather than another, but because it is so, because mathematical reality is built that way"
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Post by dozyjulia on May 8, 2006 1:00:22 GMT 1
*yawn*
nothing to do with your post. i'm just really tired. honest.
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Post by Chris on May 8, 2006 1:17:43 GMT 1
Good post by Ben. *Julia smells* Nothing to do with your post, it's just that you really do! I'm so witty I make myself cry...
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Post by dozyjulia on May 8, 2006 1:23:13 GMT 1
CHRIS HAS SEX WITH MATHS
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Post by Ben on May 8, 2006 1:31:59 GMT 1
you know maths wins this.
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mcv
When I Argue I See Shapes
Posts: 630
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Post by mcv on May 8, 2006 1:36:05 GMT 1
you know maths wins this. *cough*lies*cough*
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Post by dozyjulia on May 8, 2006 1:38:05 GMT 1
that's rubbish. Maths is fantastic, and if you don't believe me, i'll show you the scars to prove it. EDIT: Ben manipulated my post! I would never have written this in a gazillion years, 'kyou
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Post by Chris on May 8, 2006 2:01:20 GMT 1
SHUT IT WITH THIS MATHS SHIT!!!
I did not have sexual relations with that area of knowledge.
Did have a quicky with Business and Management, though: it was well dissappointing.
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elaine
When I Argue I See Shapes
Mitsy the Magnificent
Posts: 605
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Post by elaine on May 8, 2006 12:43:55 GMT 1
"abstract concepts" - ?
I think this discussion is getting a bit off the rail, but I put forward:
- you cannot think without language, or a notion of symbols, a type of order, right? - maths is just such an example of that language/symbol/order - these are all human constructs. because without us, there would be no "maths" as we know it. there may be the principles, and things may work the same, but nevertheless, we constructed maths to order these things for us to imagine in our heads.
My point is, that, if you think about it, everything is an abstract concept. Language is, words are, meanings are. and maths too, is. but these abstract concepts are still constructed by us, and are not universal. you have to have human contact to be able to understand and use them.
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Post by Ben on May 8, 2006 13:07:05 GMT 1
yes, they are abstract ideas given concrete meaning by the necessity to name objects for survival. however, mathematics still exists without humanity. supernovae still happen, primes are still distributed according to the n/log n, and so on. just because we define things as we do, doesn't prevent them being true. order happens without an ordering system. I know that sounds absurd, but look at it this way: Prime numbers are co-prime to all other numbers in every base. If we were born with 3 fingers on each hand, then every prime number would still be prime. It would have a different name. 10 would be prime in base 3, but it is independent of humanity, is what i'm saying.
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elaine
When I Argue I See Shapes
Mitsy the Magnificent
Posts: 605
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Post by elaine on May 8, 2006 13:33:15 GMT 1
ok, maybe i didnt explain myself properly. I didn't mean that things that maths describes, wouldn't happen. I meant that Maths, as the discipline, as the language that EXPLAINS these phenomena in our lives, is manmade. Without humans, maths (the language) wouldn't exist becuase it is a human construct.
Maths is a description of the behaviour we see around us, and it works very well indeed to explain and describe and predict things that we see and understand to be true. (It is still a little bit inaccurate though, my friend told me about Penrose, how he himself proves that geometry is inaccurate to the width of a hydrogen atom, ie: angles of a triangle dont add up to exactly 180 degrees).
This shows that maths, like man, is imperfect. It is not an absolute, or a universal concept. It is something that we have grown up with, have come to incorporate without realising, or without choice into our way of thinking.
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Post by Ben on May 8, 2006 19:13:55 GMT 1
I'd like to see the article on which the Penrose thing is based. "my friend" is a bit of a dubious source for a sweeping statement such as "maths is inaccurate" to come from. In Euclidean geometry, on paper, angles always add up to 180 degrees. They have to. Else the contour is not closed. If you are taking an intersection and move it away by even a fraction, they are no longer touching. Hence even the width of a hydrogen atom (which is about 1*10^-15 IIRC) would throw it off by a huge amount, especially if the shape was big. Think about it; if you set off on a journey on a bearing of 170 degrees and walk for thousands of miles, and somebody else stands from the spot you left and walks at 171 degrees for the same distance, you won't be in the same spot.
I honestly don't believe the Penrose thing is true. Perhaps in reality, then yes there's always going to be quantum uncertainty, and so nothing can be truly measured (hence Heisbenburg's uncertainty principle), but in Mathematics, everything is correct. There's no such thing as a perfect circle in existence, yet nature STRIVES to be mathematical. Objects tend to be spherical since it minimises energy, which is a fundamental principle of the universe.
I agree that us coming along and calling this that and the other certain things means that Mathematics as a discipline is man-made, but mathematics could also be argued to be us. Our very fibres are held together by mathematical equations, and hence we don't need to discover maths, since every action, reaction, emotion, electrical pulse, etc etc is mathematics.
Basically, i'm just arguing that mathematics *is* perfect since it IS the universe. Because we're taught mathematics, people tend to assume that it's about doing sums and this that and the other, but it's really not; without the rules that are mathematical (since mathematics is axiomatic), the universe would not exist.
Maths does not have 'exceptions' to its rules. Everything else does. Even Philosophy has the 'get out of jail free' card known as God. And english has a million counter examples to its rules. Axioms are the only way to build a system, and algorithms are the only way to implement. And both of those are mathematical concepts.
i'm tired, and i should be working..
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Post by Chris on May 8, 2006 19:50:56 GMT 1
The God=getoutofjail thing, and the way you argue your point aside, that was a pretty well-written post.
Anyway, the Universe exists independently of maths, the fact that we percieve it to be a governing force is merely that: a perception. The universe exists because it does (sans divine intervention), and humans look at things that are abstruse to the point of incomprehensibility, and try to understand: they attempt to divine from that some way of understanding why the universe doesn't just disappear into the general mélange (ELLIOT!!! LOOK WHAT I DID!!! hee...) of whatever-the-hell-it-is-that-it-is... They just are.
To say that maths governs it is like saying a painting of a horse governs the horse's existense. Hence, Maths is an art!
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elaine
When I Argue I See Shapes
Mitsy the Magnificent
Posts: 605
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Post by elaine on May 9, 2006 0:21:55 GMT 1
The Penrose book is called "the emperor's new mind", and i apologise for the "my friend" thing. It's just that I'm not a mathematician beyond a-level, and I sometimes need some collective inspiration.
but i still stand by the geometry thing. it is inaccurate by the width of a hydrogen atom.
so, i guess we are not in agreement about whether the universe would exist without maths or not. I dont pretend to know, but I see maths as just another one of those absolutes which anti-religious people seem so afraid of. In that case, I sort of unsubscribe from anything concrete and universal, which leaves me in a bit of a hopeless position.
But I still dont know, and am not sure.
I think the crux of my argument would be to say that maths, like religion, seems to exhibit the same signs of a man-made construct, developed through perceptions that are intended to fit certain observations, to realise and give meaning and understanding to the universe and our lives within it. Who knows if its right/accurate/reliable?
People who say they do, may be right, but they may also be wrong. How can we judge right/wrong, or true/false (in the logic sense of maths)...
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between the bars
Can't Get No Satisfaction
I wish I was as cool as Simon
im way cooler than simon
Posts: 18
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Post by between the bars on May 9, 2006 8:56:07 GMT 1
ooh this is so exciting! philosophy, yay!!!!! But geomatry isnt inaccurate by the width of the hydrogen atom. Its never inaccurate. Eculidian geometry is the study of e.g. a perfect triangle on a flat surface. Its not an empirical science. It's never 'wrong' as long as it stays within its own axioms (e.g. shortest point between two lines is a straight line). Now in situations where those axioms are untrue, eg. real space, it turns out that its predictions are wrong. But thats not really the same thing as innaccurate. It cant be inaccurate by the width of a hydrogen atom because it isnt the study of physical things. Sure we draw triangles at high school, but they're just a mental aid. No triangle's angles are ever going to add up to exactly 180 degrees, because of physical imperfections. But thats ok cause thats not the triangles we're studying in geometry. We study something like the platonic form of a triangle, or if that offends your ontology an imaginary 'perfect' circle. You can have universals without appeal to God or higher order. Easily. I think the crux of my argument would be to say that maths, like religion, seems to exhibit the same signs of a man-made construct, developed through perceptions that are intended to fit certain observations, to realise and give meaning and understanding to the universe and our lives within it. Who knows if its right/accurate/reliable? People who say they do, may be right, but they may also be wrong. How can we judge right/wrong, or true/false (in the logic sense of maths)... But see just cause maths is devopled by observations doesnt mean that it isnt uncovering some higher truth. Your final point looks a lot like extreme realativism. I really hope that you dont mean that all ethical and philosophical stances are equal. Cause if you do, then you're saying that what you're saying is as valid and right as what ben is saying. Thus its self defeating. But yay for this whole thread. katie x Frege on why logic isnt devolped through perceptions; "But what if beings were even found whose laws of thought flatly contradicted ours and therefore frequently led to contary results even in practice? The psychological logican could only acknowledge the fact and say simply: those laws hold for them, these laws hold for us. I should say: we here have a hitherto unknown kind of madness ... One could scarely falsify the sense of the word "true" more mischievously than by including in it a reference to the subjects who judge"
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Post by Ben on May 9, 2006 12:52:31 GMT 1
nice
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Post by Chris on May 9, 2006 13:11:27 GMT 1
but i still stand by the geometry thing. it is inaccurate by the width of a hydrogen atom. The geometry thing is right for euclidian geometry (i.e. Geometry on a surface), but there are different types to that. I'm sure Ben could elucidate on it far further than I, but there were developments in the 18th century on different types of geometry where, indeed, the angles of a triangle can add up to less or even more than 180 degrees.
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Post by Tom on May 9, 2006 13:18:01 GMT 1
true. if you draw i triangle from the north pole, to the equator, a quarter of the way around the equator, then back up to the north pole, you have a triangle where all of the angles are 90 degrees.
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Post by Chris on May 9, 2006 13:29:06 GMT 1
Which adds up to 270!! ;D ;D ;D ;D ;D ;D ;D ;D ;D ;D ;D
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Post by Ben on May 9, 2006 14:01:52 GMT 1
Indeed, and it's a form of Hyperbolic Geometry, where there is a different Axiom to Euclidean geometry. These are the 5 axioms of Euclidean:
1. To draw a straight line from any point to any other. 2. To produce a finite straight line continuously in a straight line. 3. To describe a circle with any centre and distance. 4. That all right angles are equal to each other. 5. That, if a straight line falling on two straight lines make the interior angles on the same side less than two right angles, if produced indefinitely, meet on that side on which are the angles less than the two right angles.
In fact, all but the 5th one are pretty much self-contained. The 5th one was introduced by Euclid to prove that the angles of a triangle add up to 180deg. Anyway, Non-euclidean has this odd property:
All straight lines which in a plane go out from a point can, with reference to a given straight line in the same plane, be divided into two classes - into cutting and non-cutting. The boundary lines of the one and the other class of those lines will be called parallel to the given line.
which pretty much translates into:
There exist two lines parallel to a given line through a given point not on the line.
I've not actually done any work on it, but it's quite interesting. Indeed, if you want a more intuitive way of thinking of it, see the above example.
Basically, think of a triangle with 270degrees as a 'triangle' on a sphere. Instead of working on a flat sheet of paper, imagine drawing on a sphere, and that's how non-euclidean geometry works. It's really interesting, because it has a lot of interesting consequences for space, since nobody knows for sure what space is in terms of geometry (since we don't live on a rubber sheet, do we?). Perhaps hyperbolic geometry describes space better?
I wish i knew more about it, but i'm lazy and busy and can't be bothered reading up on it.
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Post by Tom on May 9, 2006 14:17:51 GMT 1
if space-time is indeed warped, like general relativity seems to suggest, then surely we wouldnt be looking at Euclidian geometry for the universe.
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elaine
When I Argue I See Shapes
Mitsy the Magnificent
Posts: 605
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Post by elaine on May 9, 2006 15:16:11 GMT 1
I don't want to dampen spirits, but if we turn away from Maths for one second, and go back to the original argument. Which was about how our perception is just that, our own personal individual conception of the world around us, the way it seems to fit together and the way we can relate ourselves to it.
Logic, yes, is part of that perception. I don't think that means it's any less useful or necessary for us to live or make sense of our living. Maths is logical up to the point of the method which we have created it for. But a complete belief, an almost "faith" in logic and maths, can exclude other things. Just as the complete and utter faith in judaism excludes the fact that jesus was the son of god.
I do think we can create universals, but it doesnt mean everyone subscribes to them automatically. its only that they are needed for us to make sense of ourselves.
This perception with which we see the world etc. IS personal individual and unique. It is the quality of consciousness that is unable to define itself. And I think it is therefore the act of the individual to make sense of things in their own way.
"But see just cause maths is devopled by observations doesnt mean that it isnt uncovering some higher truth." yes, i didnt say that. i was comparing it to religion though, in that search for higher truth. the origin of this argument was the fact that maths is sound and religion is not. But i was trying to argue that both, perhaps are not, or that both perhaps are.
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Post by Ben on May 9, 2006 16:50:31 GMT 1
i always love that way that forums never get to the point
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elaine
When I Argue I See Shapes
Mitsy the Magnificent
Posts: 605
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Post by elaine on May 9, 2006 19:30:20 GMT 1
I have such a bad way of saying things.
Anyway, Indie Schmindie: I watched "Waking Life". and i thought it was ace! really well shot, and well done. and pretty interesting discussions. i want to watch more of linklater.sounds good.
anyway, i didnt take too much away from it, in terms of philosophical arguments, but i've been reading up a bit more about phenomenological approaches. and have you ever read Schumacher? Guide to the Perplexed? Very good book. well it talks about the order of beings, and how each are only equipped to comprehend things that are at or below their level of adequate comprehension. hard to explain right now, but its worth a look. basically, it says that scientists put their faith in science, shutting off the possibilities of things that are outside perception/observation/measurability and therefore cannot hope to comprehend other things.
just a thought
ps: did you go to Arna's Children last night? really really good documentary about Israel/Palestine again. But this time, less analysis and more on-the-ground footage. i really recommend it
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indie_schmindie
Part of My Generation
"blue jeans and moonbeams"
Posts: 369
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Post by indie_schmindie on May 9, 2006 20:25:30 GMT 1
"it says that scientists put their faith in science, shutting off the possibilities of things that are outside perception/observation/measurability and therefore cannot hope to comprehend other things." - but there are religious scientists - and not only those who promote creationism - in the world so i'd disagree with that being a universal comment
waking life is definitely worth watching several times... i've even made notes on it to try and fit together all the different arguments... i love the idea that you may be able to live on a your dreams after death, it even makes a scant realist like myself begin to believe a little spirituality... i don't see this idea as the same as a heaven, though
"I see maths as just another one of those absolutes which anti-religious people seem so afraid of" - i would disagree with this, though i'm not entirely sure what you mean by it.... for me, maths is created within human boundaries and is tangible, provable through trial and error and is always looking for ways to tighten its argument... faith is, to me, a collection of unjustified beliefs which have no way of being proven since they rely on the unknown/unreachable areas of human perception.... going back to nietzsche, maths fits with real life, faith is the distraction from real life
yes, i did see arna's children - are you going to go to that demo/protest malarky on saturday? as ever, the monday documentary was definitely worth a look... i was right at the back though so i had a task and a half trying to see the subtitles.... you know i've probably seen you there and not even realised it, seeing as my only available perception of you is an ice-skating cartoon character....
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