Is Music Really just Maths?

[BFM_Edison]

Your analogies are fairly faulty, Octane.

Thanks for the input, Edison. 

They're not analogous is what I'm saying ;p

[Daigoro]

Once again, great thread.

"Every year more and more objects turn out to be explicable using maths"

I would agree, but the percentage of objects currently 100% explicable using maths is still near zero. (Aspects of pretty well anything are explicable using maths, but only aspects. In fact, take any 4 minute piece of live music and provide a full formula which expresses it: not doable. Note, a sampled waveform doesn't count as it only approximates the piece, it doesn't fully express it).

Neither "explicable" nor "expressible" is the same as "is".

P.S. As you've explained it, the cochlea might be doing a Fourier transform. I see on the InterWebs that FT is generic for *any* transformation "from one complex-valued function of a real variable into another". At the cochlea I guess that's the old standby "time domain" to "frequency domain" (waveform to series of pulses). If we use the generic form of FT, I suppose the brain might be doing several of them, not that anyone would be fully understanding them anytime soon.

Regarding the idea that ultimately everything *is* maths, I suppose one could claim that everything *is* physics (not just Newtonian of course!). I personally wouldn't claim that, "one" could claim that.  :-)

[conrad96]

i hate math but i love music...oh no im contradicting myself! help me!!!!!!

[jim360]

Neither "explicable" nor "expressible" is the same as "is".

Regarding the idea that ultimately everything *is* maths, I suppose one could claim that everything *is* physics (not just Newtonian of course!). I personally wouldn't claim that, "one" could claim that.  :-)

Well, yes, that's right. I guess it's a question of whether the maths is just a model or the real truth. A question that has been debated right back since the time of the Ancient Greeks and Plato's "forms".

[BFM_SüprM@ñ]

In order to determine whether or not "music is maths" we must first define music. There is no solid definition of music, for it is left up to one's perception. So.... how can we say that music is maths when music is constantly changing?

Yes, sound waves can be expressed mathematically, and a series of sound waves can be expressed mathematically, and then combining those series of sound waves being expressed mathematically can show the number of formulas used to make a song. It would take a lot of formulas to do so, but it's possible.

And really, numbers are like time or any other word out there, labels we've created in attempts to organize and explain the world we live in. = )

[Racr]

I have four simple words for you, Three60:

STOP.
WITH.
THE.
MATH.

[Glêññ Z]

its all math and sciance! 


sciancceeee i like sciance

[Marty]

As I'm the one that actually started this debate on Vent with three60, I feel I might as well post something.

As has been said many, many times in this thread, explicable and expressible are not the same as 'is'. An elephant can be quite actually expressed through pen and paper to show what's happening, where, and why. At no point does that piece of paper become an elephant. Leastways, I hope not...

As for the Cochlea performing Fourier transforms, as much as the ear might be doing maths, the brain isn't. The brain is comparing the input sounds to sounds stored in its memory and interpreting the sounds based on those. So in that sense, maths drops out of the window - our emotional response to music is largely based on our previous emotional responses to things since the day we were born - bird song, voices, sirens, crying, etc.

Similarly, while you can express an insect's colours through maths, the reason that is beautiful is based upon our emotional response - again, maths drops out of the window. Look at a painting of Caravaggio's and you are interpreting it emotionally. The composition, colour differences and lighting can all be expressed through maths, but the emotion is based upon experience.

In conclusion, unless maths becomes so hyper-advanced that language becomes superfluous and all emotions can be expressed through maths, music, art and language will all transcend maths. And if maths does become that advanced, I hope I'm not alive to see it, because it'd take all the fun out of life.

[jim360]

Well, you see, you've said it's all down to the emotional aspect. While there is truth in this, what is emotion? Isn't it just a series of stored data? And, in the long run, if this were true, could it not then be interpreted mathematically?

A recent study of human brainwaves showed that (given limited choice - brain science is still in its infancy) it is possible to predict what box someone is going to choose out of two boxes 6 seconds before the choice is actually made. To be fair, this "prediction" was only made five weeks later but nevertheless, without prior knowledge of the event the professor in question knew what box the subjects would pick, based solely on their brainwaves. This is relevant because it suggests that there is more to our brain than we would like to think.

Another related topic: suppose, without making any physical assumptions, that you were curious to know what the Fourier transform of:

f(x) = 1 for |x|<1 and 0 elsewhere.

Well, you do the maths and it turns out that it is sin(k)/k. Just for the fun of it we'll square this so that it's only positive.

You get this (roughly):



Now, just for laughs, let's shine laser light through a small hole onto a screen and plot intensity against distance from point on the screen in line with the light source and the hole. Oh, my goodness, how incredible! You get just that same curve.



And this was without even thinking about anything physical. Yet, there you have it, the maths tells you what shape you get before you even know there's an experiment that uses it.

This happens agian and again in mathematics. The results are there before there is even any known physical use for them. Group theory, Combinatorics, Set Theory, Calculus, Matrix Algebra... you name it, there is a physical application for it that was only found years, even decades later.

Mathematics is the fundamental truth of the universe. Within the bounds it has set itself (Godel's Incompleteness theorem, that roughly states that the only way you can know everything is if some of it is wrong) it can tell you everything you need to know. We'll never quite get there, I hope so too. But it can.

[OBOLeader]

As I'm the one that actually started this debate on Vent with three60, I feel I might as well post something.

As has been said many, many times in this thread, explicable and expressible are not the same as 'is'. An elephant can be quite actually expressed through pen and paper to show what's happening, where, and why. At no point does that piece of paper become an elephant. Leastways, I hope not...

As for the Cochlea performing Fourier transforms, as much as the ear might be doing maths, the brain isn't. The brain is comparing the input sounds to sounds stored in its memory and interpreting the sounds based on those. So in that sense, maths drops out of the window - our emotional response to music is largely based on our previous emotional responses to things since the day we were born - bird song, voices, sirens, crying, etc.

Similarly, while you can express an insect's colours through maths, the reason that is beautiful is based upon our emotional response - again, maths drops out of the window. Look at a painting of Caravaggio's and you are interpreting it emotionally. The composition, colour differences and lighting can all be expressed through maths, but the emotion is based upon experience.

In conclusion, unless maths becomes so hyper-advanced that language becomes superfluous and all emotions can be expressed through maths, music, art and language will all transcend maths. And if maths does become that advanced, I hope I'm not alive to see it, because it'd take all the fun out of life.

LOl half of what is said, i have no idea wat u mean..

But i play a instrument, and while u do need to use numbers, what is music without emotion? Would Ozzy be as good? WOuld the honas brothers still suck? Yea they would, but thats not the point... the point is that while there is no end to numbers, not everything can be expressed in math.

Well, you see, you've said it's all down to the emotional aspect. While there is truth in this, what is emotion? Isn't it just a series of stored data? And, in the long run, if this were true, could it not then be interpreted mathematically?

A recent study of human brainwaves showed that (given limited choice - brain science is still in its infancy) it is possible to predict what box someone is going to choose out of two boxes 6 seconds before the choice is actually made. To be fair, this "prediction" was only made five weeks later but nevertheless, without prior knowledge of the event the professor in question knew what box the subjects would pick, based solely on their brainwaves. This is relevant because it suggests that there is more to our brain than we would like to think.

Another related topic: suppose, without making any physical assumptions, that you were curious to know what the Fourier transform of:

f(x) = 1 for |x|<1 and 0 elsewhere.

Well, you do the maths and it turns out that it is sin(k)/k. Just for the fun of it we'll square this so that it's only positive.

You get this (roughly):



Now, just for laughs, let's shine laser light through a small hole onto a screen and plot intensity against distance from point on the screen in line with the light source and the hole. Oh, my goodness, how incredible! You get just that same curve.



And this was without even thinking about anything physical. Yet, there you have it, the maths tells you what shape you get before you even know there's an experiment that uses it.

This happens agian and again in mathematics. The results are there before there is even any known physical use for them. Group theory, Combinatorics, Set Theory, Calculus, Matrix Algebra... you name it, there is a physical application for it that was only found years, even decades later.

Mathematics is the fundamental truth of the universe. Within the bounds it has set itself (Godel's Incompleteness theorem, that roughly states that the only way you can know everything is if some of it is wrong) it can tell you everything you need to know. We'll never quite get there, I hope so too. But it can.

Where did u get that? Emotion is something that cant be expressed in numbers. Emotion is... memories. Your brain is limitless on what is can store, and how much it can store. There will never be perfect math. Math is not perfection, but a way of explaining things that SUPPOSDLY cant be explained anyway else. And can ya dumb it down for people who are just statrtin algebra?

 

[jim360]

The fact that barely four hundred years ago, people could have easily said the same thing about the stars that shine, or why arrows fall, or why the Sun rises, shows that just because you can't express emotion numerically now doesn't mean that it cannot be expressed that way in future.

I'm not entirely sure what you mean though, about maths being about explaining things that supposedly can't be explained any other way. What other way is there? Maths is the universal language that describes everything you can see in the universe today. And what it can't describe at the moment it may well be able to in the future. It takes a brave man to say "never" to that question.

As for the explaining what I said for people who are new to maths... it's kind of hard - there's a loong way to go between algebra and what I just wrote down. But if you like I can try by PM.

[Miser]

I'm not sure I would want music to be maths. From what you just said jim it will undoubtedly be expressed as maths at some point. But how can we take music as maths when our own "instruments" to measure it aren't perfect. Our ears may be complex but far from perfect. And even when someone takes the time to find the exact math involved in our hearing, the distortion between our own judgment and what the calculator spits out, whats do we do then? Do we take music's history, all the efforts and sacrifices people have made to expand the subject, and compress it into a mathematical equation. Quickly followed by a formula for our entire existence?

At what point will someone pick up a flute or a guitar and a calculator? And at this point, does that mean that everything in life will be easy as typing a formula into a calculator, deciding which notes in succession would make the best song? I don't think it will ever happen because music is based on the human mind. Tell me when a person can make a formula that predicts what that individual is thinking at all times and I'll believe you.

[jim360]

What's so horrific about mathematical equations that makes people saddened by the thought? Some of the greatest achievements in the world, indeed THE greatest achievements in my opinion, are those in maths and physics - such as the Invention (or discovery) of Calculus, the four equations of Electromagnetics, the Theories of Relativity, Quantum Electrodynamics, the Internet and World Wide Web.

[Miser]

It's not math itself that frightens me it's the loss of ways to express things. Yes, i know, mapping the universe with a calculator allows us to express it.

But would you rather type some numbers into a computer that then generates music or would you rather hold a violin in your hands and find which notes you like, which ones you don't?

What is the appeal of an acoustic guitar player when we already have computer systems that can emulate it almost exactly?

So the statement I'm making is not that music won't be expressed in maths but why would we want it to be?

[jim360]

At this point it's a good idea for me to mention something called "The Three-Body Problem". It's pretty much what it sounds like - what happens when you consider three different objects? What forces to they exert on each other? And - the killer - what happens next? Where do they go?

The answer is that you can't answer this exactly. This means, basically, that in any situation where you have more than two objects, you can't precict what they're going to do except in certain very special cases. You can only ever get an approximate answer by simulating the problem or solving it numerically (that is, in specific cases rather than in general).

So, even if there were a time when you could say, "Yes, I finally have an equation that describes music," it probably won't be "solvable". There will still be some mystery left.

As a final aside, don't forget that part of making great music is also the acoustics of the room in which it's played. And how do they optimise this? Yup... maths.