Is Music Really just Maths?

[Marty]

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.

Sorry. but the greatest achievements are not something that helps us understand the world, but language itself. How can there be a greater achievement than the ability to communicate internal thought? Obviously, just my opinion, but any equation that has been written or is yet to come would not be possible without language to communicate and explain it.

Maths is a conceptual tool, not a thing in itself (LEO and I agree on this, so it MUST be true...we've NEVER agreed before). It, like language, is a medium for expressing things that would otherwise be inexpressible. Does that even make it exist? No, not IMO, or in the opinions of a significant proportion of philosophers, past and present.

Music is pure human thought and emotion interpreted through sounds.

The day emotion becomes mathematical is the day man becomes a machine.

[Goalie]

You can describe music in mathematical terms.  You could also describe music as a second language, reading, physics, dynamics, history, and just about any other subject matter.  Music is everything, from vibrations to Italian, from reading to motion, you could say that "Music is Really Just Another Form of Communication" or "Music is a Way of Life."  Music encompasses everything, so to say that it is "just Math" is not talking about music.

[jim360]

The models in Physics, Chemistry, Biology and other Sciences are conceptual tools. Maths - isn't. A conceptual tool is something that helps you to think about the real world. But, as I gave an example of a couple of posts ago, the maths has often come before there was anything for it to be a conceptual tool for! Mathematics goes beyond conceptual tools because so much of it stands alone, studied simply because it exists. Let the rest of the world catch up with the mathematicians, who are so far ahead of it!

I could continue to come up with example after example of how this works. Fact is, though, that I will end now by saying that, in the end, music may be mathematical at its heart but, like everyone else here, I love music for what it means to me. And will always do so.

The day emotion becomes mathematical may have already happened - we just didn't realise it yet.

On the language issue, if anything that can hardly be called the greatest achievement because it fails to describe and explain the real world. That is why, even as long ago as 6,000 years, people realised that they needed to turn to mathematics.

[BFM_Edison]

The day emotion becomes mathematical is the day man becomes a machine.[/b][/color]

It either is or it isn't; it can't become mathematical.

Math is entirely a thing in and of itself. You need nothing outside of math for it to make sense as it is pure logic. I assure you people were doing addition in their head before language came about. Language is not necessary to develop mathematical ideas.

[BFM_SüprM@ñ]

I could say something so philosophical that it would completely distract everyone from the topic, but I'll see how far this continues. = )

[Marty]

I assure you people were doing addition in their head before language came about. Language is not necessary to develop mathematical ideas.

I'd like you to explain to me how people added in their heads without words to say 'one add one is', etc. Language HAS to come first because it is the only reliable way of structuring thought we know. It's actually quite interesting when you think that our brains have become so used to language that it is impossible for us to think without it in some form - language in its own way is limiting the brain. We have to hear our selves say something even though we already know what we're going to say.

Maths has often come before there was anything for it to be a conceptual tool for! Mathematics goes beyond conceptual tools because so much of it stands alone, studied simply because it exists....On the language issue, if anything that can hardly be called the greatest achievement because it fails to describe and explain the real world. That is why, even as long ago as 6,000 years, people realised that they needed to turn to mathematics.

But mathematics is dependant upon language. Language is, in its broadest sense, symbols and words representing some thoughts and concepts. the number '1' is a conceptual symbol that represents a single thing, be that real or imaginary. Similarly, 'x' for multiply is a symbol, etc. So mathematics is dependant upon language - maths is merely a branch of language.

Why I call mathematics 'conceptual' is not because it's necessarily trying to explain something, but because the numbers used don't actually exist (yes, three60, here we go again). You cannot show in terms of things that exist in a physical form things like 'multiply' or 'equals' - they are terms used to describe concepts that are common to the language of mathematics. concepts don't HAVE to be applied to the real, physical world - they are, for me, things that just don't exist in the real physical world. Like Language itself. Music exists - you can hear it, even if some people have a different opinion as to what counts as music or not. But it does exist in the physical world. Mathematics does not.

I could say something so philosophical that it would completely distract everyone from the topic, but I'll see how far this continues. = )

Please, say it!

[jim360]

I'm not sure about timescales here, but I know that a stick with regular etchings on it was found that is around 13,000 years old. Did this come before or after language? I don't know - but then, you can't say either.

But Maths a branch of language? Absolutely not. You can say "one", "un", "eins", "uno", "bat", or "two, "deux", "dos", zwei", "bi"... and all you mean is "one" or "two". The mathematical meaning of "one"? It's way beyond language.

And, again, "x" doesn't means "multiply by" any more than "=" means "equal to". We have assigned those symbols to mathematics, not mathematics to those symbols. The maths came first, you don't need language to describe it and what you do use is so ridiculously arbitray. Take "=" again. This means "equal to" for most people yet in computer codes "=" often means "assign this new value to this variable", while "x" just as often means "column vector" or "1xn matrix" or something.

The mathematics is already there and all we have to do is discover it. Once we do, we attach labels randomly to what we found. There is no, NO, dependence on language. Because you can do maths equally well in Swahili, French, English, Mandarin. Indeed, language is more dependent on maths because every time a new mathematical area is made we have to either invent a new word for it (maths coming first again) or invent a new definition for a word (maths coming first again). Either way the maths comes first.

Language, similarly, isn't much of an achievement because it's arbitrary and doesn't take much work to start off really. Since, after all, every other animal has their own language. And how many of them can do maths, I wonder?

And since, as you say, language is limiting the brain, doesn't that suggest that once again language is just a block, holding us back, whereas maths is the exact opposite, moving us ahead in greater strides?

Someone who stopped studying maths before they left high school is in a bit of a problem really. The maths you are talking about is high-school maths. I just earlier showed you an example of something that, quite clearly, shows that maths doesn't just describe the physical world but also IS the truth of the physical world. There are hundreds and hundreds, thousands of such cases, where the mathematics is true before you even think of hlow this aplies to reality.

A simply stunning example of this, I think, is the fact that in 1926, two physicsists, Schrodinger and Heisenberg, decided that they would look at the world of the atom in two different ways. Schrodinger chose to think of it in terms of a physical model (waves) and Heisenberg decided to focus purely on the numbers and not even try to think of what it all meant physically. And they developed theories that explained what was going on. Both of them were right, but more importantly, both of their approaches, so radically different, led to the same answers. Again, the mathematics is true before you try to match it to the real world.

The fact is that whether you choose "1", "2", "3" or "sausages" to descibe the quantity of "1", that quantity exsists independent of what you call it. A bit like something called a "linear operator" that exists independent of what co-ordinates you choose to work with.

[Marty]

I couldn't disagree more. Mathematics is not part of the world - it is merely applicable, whether we know yet what to apply it to. And as I said, the meaning of "=" is still a concept in your mind, whether it is a simple "equals" or whatever.

In your argument that maths is independent of meaning in language, you appear to have missed that any symbol that 'means' something is a form of language. Language is not words. That's such an important point that I'll say it again.

LANGUAGE IS NOT WORDS

Words are simply a branch of language, much as maths, art, music and body gestures (eg a wave of the hand). They are all ways of communicating thought and emotion. Anything, anything which conveys the thoughts of one person to another person is a form of language.

At some points, the different branches of language cross over - eg. 1 and one. They are both linguistic concepts.

When I said that language is limiting thought, I really should have put words are limiting thought. I'm trying to escape from single-word thought, but it's almost impossible - it's like words are hard-wired into our mind.

As to which came first out of words and maths, it is estimated that words were in use 100'000 - 200'000 years ago. The oldest counting stick is believed to be around 35'000 years old. I believe that most archaeologists would therefore say words came first. However, as mentioned on the Wiki page of the Ishango Bone, it is believed this stick is more complex than just counting.

And I know that maths that you gave the example of shows maths is very much applicable to the real world. You have, however, yet to demonstrate why 'applicable' means 'is the basis of'. You seem to me to believe that the world is entirely mathematical - in other words, that the universe could eventually be expressed accurately through a single equation.

Once again, I hugely disagree. Not just because I don't like the idea - but also because I consider the randomness, the emotions and the thoughts of life and the universe in general to be far too complex and unpredictable to be expressed through mathematical laws. How could maths ever explain why (going, for a brief moment, back to music) a repeated semitone sounds so menacing? (Think 'Jaws', people) No-one can...certainly, not yet. It's too deeply routed in emotion, which is wholly un-mathematical. Emotion has no rules whatsoever - it changes from person to person, from second to second, depends on past circumstances, future expectations, and anything down to what colour socks you're wearing and the wind speed. Surely, no mathematical theory could ever reliably factor in everything which passes through the brain in a nanosecond which makes a chord sound pleasant, open or menacing.

[BFM_Edison]

Randomness is not a very strong argument at all, considering the fact that there are mathematical equations that represent quantum effects.

As far as words and counting sticks go, you're restricting the concept to outward manifestations, when the question is really coming down to thought manifestations. You also seem to be assuming that in order to use math, one has to consciously think of the mathematical problem, when math can be subconsciously, which completely circumvents the use of language. I don't need to consciously count that there are two objects in front of me in order to use both of my hands to pick them up. 2=2. It's done without the use of language as I pick them up. Math simply does not require language.

All that's needed to describe the Universe is the governing laws of the most fundamental constituents of the Universe, whether they be the particles of particle physics or the strings of string theory. Once you describe that, you have the fundamental equation(s) that describe all of the Universe. Whether they can be applied by humans to the extent that you seem to be thinking of is entirely irrelevant; those equation(s) express the Universe.

[jim360]

Ultimately, Marty, the big weakness in your argument is that you have several times resorted to "surely".

Surely, no mathematical theory could ever reliably factor in everything which passes through the brain in a nanosecond which makes a chord sound pleasant, open or menacing.

Why surely? Surely it is impossible to explain the rainbow, or the path of an arrow, or why the orbit of Mercury isn't quite in accordance with Newtonian Mechanics, or why the electron does not decay from its orbit when it should radiate away all its energy in nanoseconds, or why there was more mattter than antimatter in the universe? Yet, for the most part, all these questions have been answered. "Surely" is a non-argument when we are making progress very rapidly. And, furthermore, any theory that explains, or tries to explain, something like that as its starting point isn't a mathematical theory but a physical one. When you are a mathematician, the real world is irrelevant initially, and you just focus purely on the problem and its numbers.

As for "mathematics is not part of the world" - I again refer you to the Fourier Transform. I did not try to explain the result of diffraction mathematically, I merely solved an equation and performed an experiment and found that the results were exactly the same. Does that not show that mathematics isn't an explanation but the truth, not an application but what is actually going on? If not, why not?

I'll happily concede the point about which came first, words or maths, if expert opinion is that words probably came first. Having said that it's still true that maths arises because of the failure of language. Mathemactics, it is said, is "the langauge of the universe", so since I agree with this statement I'll again accept that maths is a language.

Once again, I hugely disagree. Not just because I don't like the idea - but also because I consider the randomness, the emotions and the thoughts of life and the universe in general to be far too complex and unpredictable to be expressed through mathematical laws.

Take a look at the double pendulum equation some day and you'll see Edison's point. Randomness is often easy to express mathematically. That's what Chaos Theory and Probability Theory are all about, as well as Statistical Mechanics and Thermodynamics. All of these explain, quantify and deal with randomness.

I don't believe that the universe can be explained in a single equation, but rather a set of equations. In fact, for what it's worth, we've already come fairly close to a unifying equation that, while not quite perfect or complete, is capable of explaining most things in the universe. Sadly I can't remember it but it's an action that contains Electromagnetic Theory, Relativity and Quantum Theory and take the form of an integral over space and time.

Finally, bear in mind that human beings are (probably) not much more than a set of interesting biochemical reactions. Which, one day, could be explained since, after all, that's what chemistry and biology are all about.

[Marty]

You still have not explained to me why 'gives the same result' is 'is the same thing as'. To use a very simple sum to explain my point:

2 x 2 = 4
1 + 3 = 4

Is, therefore, 2 x 2 the same thing as 1 + 3? Mathematically, they achieve the same result, but the process, reasoning and actions are quite dissimilar.

Ultimately, Marty, the big weakness in your argument is that you have several times resorted to "surely". Surely it is impossible to explain the rainbow, or the path of an arrow, or why the orbit of Mercury isn't quite in accordance with Newtonian Mechanics, or why the electron does not decay from its orbit when it should radiate away all its energy in nanoseconds, or why there was more mattter than antimatter in the universe? Yet, for the most part, all these questions have been answered. "Surely" is a non-argument when we are making progress very rapidly.

All these examples aren't based upon consciousness, which is so much more complicated than Quantum Physics or a Unified Field Theory. We are, to be blunt, talking about the 'soul'. It is not a physical thing, nor a set of stored responses, nor anything else that we can relate to - again, certainly not yet.

As for man being an interesting set of biochemical reactions...hmm. Even if you can come up with a way of saying 'this is how the thought process works' can you explain in terms of biochemical reactions why certain people will choose course A over course B? Tricky one, that. Again, that question will probably take centuries or millennia more to solve - if there is a 'solution'.

You also seem to be assuming that in order to use math, one has to consciously think of the mathematical problem, when math can be subconsciously, which completely circumvents the use of [words]. I don't need to consciously count that there are two objects in front of me in order to use both of my hands to pick them up. 2=2. It's done without the use of language as I pick them up. Math simply does not require [words].

I disagree. The reaching out of both arms is not thinking, even subconsciously, in a counting way. The brain is saying 'left arm pick up object X, right arm pick up object Y' in a set of electrical nerve impulses. Just because that requires two movements doesn't mean that's subconscious maths - you might as well argue that raising your eyebrows (requiring some 30-ish muscles) is doing maths - but it's simply sending signals that cause muscles to move. Just because it needs multiple processes doesn't make it maths.

Oh, and just as an aside - haven't we moved a wee bit away from the topic question?

[jim360]

Just recently there has been a major breakthrough in meteorological studies that is likely to be a huge step on to explaining, at long last, the weather. Not in a series of complicated numbers where chaos reigns and entering the wrong digit in the 13th decimal place leads to a hurricane in Texas, but in an equation. Specifically, the mathematics of multifractal fields has been applied to one aspect of weather, and with a combination of power laws (say, a system that depends on x, y, z, w, v, u, t and s is described by A*s²t³u²v^2.5w^1.3x²y⁴z) it is possible to observe fractal behaviour at almost all levels of the weather system (from 1km scales to 10,000km scales, I believe). In the long run this is a first step on the road to "solving" one of those most complicated of systems.

This is relevant because it shows that even the most complicated systems obey simple mathematical laws. And you know what? It's beautiful. Far better than Caravaggio in my opinion.

Which is perhaps the nub of the argument - do you think mathematics is beautiful? Since it can be, maybe the beauty we see in the world around is merely a new face of the beauty of mathematics. All I'm saying is that music is yet another way in which the beauty of mathematics shows itself.

High-School maths, on the other hand, is an ugly beast, a series of totally disjoint topics and techniques for solving mundane problems like, "How much money will I spend on this shopping trip?" or, "How high is that building?". Small wonder so few kids enjoy the subject, as they never get a chance to see what it truly is. Even people like Edison and myself, who have studied maths at higher levels, have only just started to glimpse the beauty of mathematics - where everything is connected to everything else and there is no part of mathematics that stands truly alone, where simplicity and clarity reign supreme.

I can't prove to you that "is the same thing as" is the truth of the world. I have given the biggest and simplest example I can think of where a mathematical problem standing seemingly alone suddenly becomes the truth in the real world. I can't express that any more clearly - the hole in the card performs a Fourier Transform on the incoming wave. That is the truth. It is the same thing.

And no, 2x2 and 1+3 aren't the same thing, or even, strictly, the same result. One of the 4's is a member of the group (R, +) and the other a member of the group (R, *) (although they may be the same member in the Field R but in that case + and * are essential to define 4 so the two operations aren't separate).

Admittedly that last paragraph wasn't a good illustration of "beauty" in maths but it does make the point that you can't use High-School maths in this discussion. "4" means slightly different things depending on whether you are working in Natural numbers, Real Numbers, Rational numbers, Complex numbers, or any other system of numbers.

[Marty]

As much as I appreciate the beauty of something incredibly complex becoming represented through a simple(ish) equation - to pick a very famous example, E = mc². I don't find the actual equation beautiful, but I do love the idea of something incredibly complex becoming so simple in that way.

Which is perhaps the nub of the argument - do you think mathematics is beautiful? Since it can be, maybe the beauty we see in the world around is merely a new face of the beauty of mathematics. All I'm saying is that music is yet another way in which the beauty of mathematics shows itself.

As you already conceded, mathematics is merely a branch of language. Perhaps the most promising one in terms of its potential to solve problems, but still - a branch. Mathematics does not lead to music (another branch of language), but merely has crossover points in which both are 'beautiful' - personally I prefer the music. Just because they cross over does not make music come from maths. The strings on a guitar are represented through maths, but the interpretation of the sounds is an area of language (as yet) untouched by maths.

[Spood]

It actually depends on what form of music you are talking about, there can be the sounds, and the 'practical' side of music, and then there can be the theory and the writing of music. Sure, the way you get the sounds can result in mathematical ways, but music theory doesn't involve maths does it? Eg. Learning about 'British Rock 'n' Roll, does NOT have anything to do with maths... LOL...

BUT.
In music, you need to count   hehe.
And, also, in writing music, you don't exactly need to be a mathematician to write music. But, my music teacher told me, she could have been a maths teacher, which is true.
♪♫♪♫♪♫♪♫ - does not involve maths... Except maybe using a ruler.

Another point, you can't 'feel' maths... you can 'feel' music though. And the ways you can express maths are totally different to music. Eg2. Maths cannot make me cry, but a piece of music may be able to, it depends on the way its played. Maths, cannot be played...

I haven't really read much of the above posts, so I'm probably repeating something, sorry if I am  

-Spfd
Oh, and
E=F♭ (Musician's Theory Of Relativity)

[jim360]

It's been said (mainly in jest, I think) that ♪♫♪♫♪♫♪♫ is a representation of a roughly linear relationship between the position on the stave and the frequency of the note in logarithmic space. But even for me, the preson who's been arguning that music is maths, that's just far too cold and useless - but then that's the point that the lecturer was making in this case. Of course, the various labelling and symbols used to represent their notes also represent their duration and volume.

My final point, as mentioned by Daigoro, is that there is a large crossover between good mathematicians and good musicians (think Brian May, for example, who also has a PhD in Astrophysics), which suggests (though doesn't prove) that there is a fundamental link between the two.

Maths can make me cry - though mainly when I fail at it . But I've looked at certain parts of maths and felt something. It is possible.