# If music is a manifestation of mathematics



## Vivaldi (Aug 26, 2012)

Then why do some people make strong musicians but poor mathematicians?


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## Ukko (Jun 4, 2010)

It doesn't go backwards. Same deal as halitosis not making good people.


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## GGluek (Dec 11, 2011)

Because you don't have to understand the mathematical underpinnings of music (or even be aware that they're there) to be able to play it (or compose it) well. I am really good at appreciating music, and was once really good at math -- but couldn't play it well to save my life. As Ukko says, but more mathematically, they're not commutative.


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## Manxfeeder (Oct 19, 2010)

Vivaldi said:


> Then why do some people make strong musicians but poor mathematicians?


I blame it on my teachers. My music teachers were inspiring. My math teachers just taught dry formulae. I wonder what an inspired math teacher could have brought me into.


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## aleazk (Sep 30, 2011)

No, music is not a manifestation of mathematics. Music is a thing by itself.
Mathematics and physics can help to understand some aspects of music, but that's a different thing.


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## Taggart (Feb 14, 2013)

aleazk said:


> No, music is not a manifestation of mathematics. Music is a thing by itself.
> Mathematics and physics can help to understand some aspects of music, but that's a different thing.


Absolutely! You can't do some sorts of physics without the mathematics to help you understand the underlying reality. So in some ways physics is simply an expression of an underlying mathematical reality. Music, however, uses a different language. Attempts such as Gödel, Escher, Bach ultimately fail because Music is more than structure and tones and dynamics. In a sense, however, Music is also an excellent demonstration of Gödel's incompleteness theorem but in a different sort of reality to the mathematical one.


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## Couac Addict (Oct 16, 2013)

Also, it's difficult to play when you need your fingers to add.


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## GreenMamba (Oct 14, 2012)

You can play a lot of music even if you only know how to count to four.


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## Weston (Jul 11, 2008)

I agree that music is not a manifestation of mathematics. A MIDI rendition with perfect tempo might be, but that is scarcely music. In the same way, a computer generated fractal landscape however realistic rarely equates to human guided visual art.


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## Sid James (Feb 7, 2009)

I think mathematics is an important aspect of music, however how a composer uses knowledge of numbers, proportions and formulae is up to him or her individually. Its in line with the aesthetics of the period and also with their personal artistic vision, what they're aiming to express and all those more fuzzy things. But at its highest levels, maths can also be experimental, not so much black and white as 1 + 1 and so on.

Take this recent article in Limelight magazine on Bach and what the relationships between mathematics and his music:
http://www.limelightmagazine.com.au/Article/356061,deconstructing-the-genius-of-bach.aspx

Of course you had others come after him and do their own thing with music. Bartok incorporated The Golden Mean ratio (Fibonacci sequence) into his Music for Strings, Percussion and Celesta. The article also mentions the likes of Xenakis and Varese, who did works linking music to things like architecture and the patterns found in nature.

The Viennese serialists wheree also interested in number patterns. Berg composed his Chamber Concerto with lots of three in it - from three themes, to three movements, to three lots of instruments all divisible by three (the solo pianist and violinist as well as the orchestra of 13 winds). The symbolism here was the piece's origins as a birthday tribute to his teacher Schoenberg, and the three themes represent him and his two students. Similarly, Webern composed his Concerto for 9 instruments as a palindrome, based on the Roman "Sator square."

An Australian contemporary composer who has done this is Ross Edwards, his violin concerto "Maninyas" was based on his study of patterns found in the Australian bush (his analysis of these after taping the sounds there, and using number patterns and sequences derived from that to use rhythmically in his music, for example).

Maths can be fun, its a vital aspect of our day to day lives, and music attests to these sorts of things. When we listen to music, we are listening to the end result of a number of considerations by the composer involved. How many musicians will play the piece? How many movements will there be? What will be done with themes or ideas as they go through the work? Will there be repetition or will it be more free and random? All these things are considered, but these are only the basics of course. The amazing thing is that the likes of Bach did music to such a high level without a computer.

Ultimately the piece has to not only work as patterns on paper but as music, which is audible and becomes reality when performed. It has to communicate the composer's vision. In the article, Christopher Hogwood talks about this in relation to serialism and the ever popular activity of row hunting: "If it helps a performer to trace the tone rows through a piece of Schoenberg, or reach an understanding of how the maths operates in the Goldbergs then, fine, analyse away. But those relationships will not be audible, and your audience is only interested in what is audible." Glenn Gould said the same thing, the music has to work as music, perfect mathematical patterns or formulas made into music don't necessarily make good music.

So yeah there are links between maths and music, but they aren't the same thing.


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## PetrB (Feb 28, 2012)

Vivaldi said:


> Then why do some people make strong musicians but poor mathematicians?


Because, *TA DA!!!* _Music is *not* a manifestation of mathematics_ ~ we will leave that comfortable supposition delusion / rationale -- which to this date has yet to be remotely proven -- to the mathematicians, and other intellectuals who nonetheless have wildly insupportable airhead notions about what music is 'other than music.'


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## Ukko (Jun 4, 2010)

Has a nerve been pinged here? Careful, _Vivaldi_, troublemakers go into a special file in Moderator Country.

There seem to be special cases of, ah, bidirectional music, e.g. the computer generated stuff. In that realm the computer is probably not a 'strong musician' though.


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## Forte (Jul 26, 2013)

Taggart said:


> Attempts such as Gödel, Escher, Bach ultimately fail because Music is more than structure and tones and dynamics. In a sense, however, Music is also an excellent demonstration of Gödel's incompleteness theorem but in a different sort of reality to the mathematical one.


Except that was not what _Gödel, Escher, Bach_ was trying to convey. Music _itself_ was not used as the example, much like art was not used as the example - it was specifically what Bach did with it and what Escher did with it that were _similar_ to what Gödel had done. They were *not* meant to be representations of the incompleteness theorem in art, either - all three were more like representations of self-referential systems and certain concepts related to artificial intelligence and used to help illustrate the thesis (or theses, depending on how you interpret the book).

In other words, analogies are in the end, of course just for the purpose of explanation, even Gödel's mathematics.

I think Sid James brings up a fascinating point, where even though music and math need not be related, sometimes it's the synthesis that makes the music effective. Does the use of a permutation matrix in a Bach fugue mean that music is "a manifestation of mathematics"? No, it just means that it is possible to use mathematical methods to construct the ideas of a piece of music. It can add something notable to the composition, but the composition does not _absolutely_ require it.

But back to discussion of the OP's post, even if mathematics was a part of music, and it seems to have been established that it does not need be, that does not imply music is part of mathematics and therefore there is no reason to assume that good musicians should be good mathematicians.


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## Aramis (Mar 1, 2009)

Is bellbottom manifestation of Byzantine Buddha


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## Stargazer (Nov 9, 2011)

When you're playing (or composing) music, you aren't exactly calculating the wave interference patterns, amplitudes, and frequencies. Well, I guess you are in a roundabout way when composing but using a completely different system from that used in math. And when you're performing the numerical stepwise integration of a differential equation, you aren't exactly thinking of notes and sounds.


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## science (Oct 14, 2010)

I've recently changed my mind on this. Music is no more mathematical than anything else is. Just about anything can be portrayed as being mathematical…. 

We can say that certain simple ratios make pretty harmonies, but with equal tempering (what we use in current mainstream western music), I believe we only play the octave exactly at that ratio. If we change the tempering so that the fifth is justly intoned, then we'll have to mess something else up somewhere. There is no way to make a justly intoned tempering (~using those famous ratios) that works in every key across several octaves. The pretty math breaks down any way you do it. 

Of course if we analyze any scale we have to use numbers (half-step, whole-step, etc.), but that's just counting. It's like saying bookshelves are mathematical because any particular section of shelf has a discrete number of books. Yes, it's true, but it's trivial, not insightful. 

Also, anything other than a computer generated sound isn't going to make a perfect sine wave. The reason a violin sounds like a violin or a trumpet sounds like a trumpet is because they don't make perfect sine waves. If they did, the sound would be much less interesting and pleasing to us. 

Besides, even though simple harmonies and rhythms can be broken down to simple mathematics, in practice musicians in every single tradition break those all the time. They'll attack the note a touch early or late, they'll attack it just a bit sharp or flat and slide on to it, or slide off it. Whether we're conscious of it or not, these techniques add a lot of the interest in music. 

Anyway, other than simple harmonies and rhythms--which , what else is mathematical about music? There's nothing mathematical about a composer's decision to give an oboe a solo rather than a clarinet, or vice versa; nothing mathematical about passing a melody from the strings to the winds or whatever, nothing mathematical about the decision to give a passage of a mass to a soprano or a tenor. 

There is nothing like a mathematical formula for a good melody. We can identify tendencies and patterns (usually a good melody moves in small intervals, any large interval in one direction is usually followed by small intervals moving the opposite way, etc.) but it's child's play to find beloved melodies that break all those rules - and more to the point, following them does not guarantee a pretty melody. Calculators can't create nice melodies. There is no algorithm. Because aside from a few simple rhythms and harmonies, music isn't actually mathematics in any meaningful way. 

The most mathematical thing at that level is complex counterpoint. But I've taken music theory classes and written counterpoint and I sucked at it - not because I couldn't follow the rules (although, truth is, that's not easy either) but because even when I managed to follow the rules I just couldn't make anything sound very good. Someone like J. S. Bach did what he did not only with his mathematical mind but with a great set of "inner ears" and an amazing creative talent. (In this sense even mathematics isn't purely mathematics - the difference between Euler and me isn't just that he could figure things out better than I can, but that he could express it all with creative and beautiful equations.) 

So here's what I think happens. Not very many people try to write counterpoint and even fewer have to sit through someone playing the crap they've written; not very many people try to orchestrate a famous work and have to sit through a band playing the crap they've written. But except for a few geniuses, nearly everyone has reached what they experience as the limit of their mathematical ability, generally before finishing high school. So a lot of people feel like music is basically easy and that mathematics is basically hard, so we emphasize the mathematical aspects of music in order to glorify our heroes like Bach, or in order to add some mystical intrigue to the whole field. But at that level it's ideology and propaganda rather than pure science. 

So the overlap between mathematical talent and musical talent is random - there are people talented at both, at neither, at one, or at the other, and other than some basic intelligence (like being able to understand the circle of fifths or quickly transpose from one key to another) or other personality traits (creativity, willingness to take risks, ambition, diligence, perseverance) being useful in both, there's no other particularly deep relationship.


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## ArtMusic (Jan 5, 2013)

Vivaldi said:


> Then why do some people make strong musicians but poor mathematicians?


I'm not very good at math. I don't understand differential calculus very well.

Neither was Beethoven, apparently who had difficulty adding up his grocery bill total.


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## Taggart (Feb 14, 2013)

ArtMusic said:


> I'm not very good at math. I don't understand differential calculus very well.
> 
> Neither was Beethoven, apparently who had difficulty adding up his grocery bill total.


Considering the amount he reputedly drank, he probably saw everything twice!


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## millionrainbows (Jun 23, 2012)

ArtMusic said:


> I'm not very good at math. I don't understand differential calculus very well.
> 
> Neither was Beethoven, apparently who had difficulty adding up his grocery bill total.


All you need to know about calculus is that it trys to predict "change through time," like, where will that artillery shell hit? That's all it's good for in these times.


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## starry (Jun 2, 2009)

science said:


> Music is no more mathematical than anything else is. Just about anything can be portrayed as being mathematical….


Well yeh, isn't that the whole idea of mathematics? It's meant to underpin the physics of the world.


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## Taggart (Feb 14, 2013)

starry said:


> Well yeh, isn't that the whole idea of mathematics? It's meant to underpin the physics of the world.


Nope. Mathematics is one of the basic ideals in the Platonic sense. Physics is merely a practical example of the mathematical ideal. Music incorporates some mathematical concepts but is a different ideal form.


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## PetrB (Feb 28, 2012)

Aramis said:


> Is bellbottom manifestation of Byzantine Buddha


The rules for Zoo and State / National Parks should apply here:

Do not feed the animals.


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## Blancrocher (Jul 6, 2013)

Taggart said:


> Nope. Mathematics is one of the basic ideals in the Platonic sense. Physics is merely a practical example of the mathematical ideal. Music incorporates some mathematical concepts but is a different ideal form.


Roger Penrose writes very eloquently about the relationships between mathematics and physics. In his view, anyways, all of physical reality can be described by mathematics, but only a very small part of mathematics is necessary for the purpose. His discussion of "three worlds and three mysteries" is quite profound (though his Platonism has frequently been criticized).


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## Crassus (Nov 4, 2013)

You don't need to "calculate" things consciously, the system becomes ingrained to your mind once you memorize the notes and their values.


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## dgee (Sep 26, 2013)

Crassus said:


> You don't need to "calculate" things consciously, the system becomes ingrained to your mind once you memorize the notes and their values.


Have you played much contemporary music? Or Stravinsky? Or even doing slow triplets in (say) Mahler with rubato? You need to calculate consciously if you want to play with others or sound rhythmical by yourself. Not that this has anything to do with mathematics


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## aleazk (Sep 30, 2011)

I definitely do not share all this "platonization" of mathematics. For me, mathematics is just a thing we humans invented in order to study things, using logic, in a more systematic and clear way. So, mathematics is just a refinement of ordinary logical and analytical thinking for me.
Mathematics consists only of two things: i) definitions; ii) theorems. You define things and then you prove theorems about those things using logic. Theorems' thesis are just relations between those definitions.
For example, you can define the set of real numbers axiomatically and then using those axioms you can prove that, say, the zero element is unique.
In physics, we start with the assumption that physical reality is comprehensible using logic. This means that, in physical reality, there exist a number of basic concepts, with associated rules and properties about these concepts, so that every observed phenomena can be naturally explained and understood as a consequence of the properties of these concepts. So, as we can see, mathematics doesn't have any role in the basic metaphysical assumption we use in physics about the physical reality.
We only need these basic concepts and logic in order to analyse the implications of the properties of these concepts. And that's basically what people in physics do.
Now, mathematics is relevant when these concepts begin to become more and more complex. So, it's necessary to eliminate all the superfluous wording and to isolate in a precise way the basic concept (i.e., to make an abstraction of it), so that we can study its properties in a systematic and clear way. Then, we start to use mathematics instead of ordinary language. This is because mathematics is designed specifically for this kind of tasks. In fact, a lot of the main concepts in modern mathematics (like vector spaces, differentiable manifolds, etc.) were invented as an attempt to abstract some basic properties of some physical objects. And some others, like differential calculus, in order to have tools for studying the properties of these mathematical concepts.
For me, it's not a mystery at all why mathematics is useful in physics: when things become complex, a refined and precise way of logical thinking is necessary, and that's what mathematics is.
And that's why mathematics is also useful in many other disciplines when a certain degree of precision and clarity in the logical process is needed. It can be economics, biology, anthropology, or music.
For example, integral serialism is defined through a set of very precise rules. So, it's not a surprise then that certain level of abstract logical thinking is needed in order to manipulate those rules properly. That's an example of mathematics in music.
Another example can be the harmonic series mentioned before. But that's more complex, since it also involves physics, and psychoacoustics. The fact that the basic triad is constructed using some of those partials is not evidence of any "cosmic" connection between music and mathematics. Instead, it's just a consequence of some basic physics and the fact that those partials are the most easier to perceive to the ear.
The real mystery of physical reality is: why it's comprehensible to us and by using logic?. Mathematics has little to do with this metaphysical question.
The real mystery of music and art is: what is human emotion, what triggers it?, why two people can connect their emotions through art?.


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## starry (Jun 2, 2009)

aleazk said:


> The real mystery of physical reality is: why it's comprehensible to us and by using logic?. Mathematics has little to do with this metaphysical question.
> The real mystery of music and art is: what is human emotion, what triggers it?, why two people can connect their emotions through art?.


Yeh I was thinking of the more concrete aspect of mathematics, perhaps it just relates to how our brain functions and perceives particular patterns.

As I said before I think there is far more agreement on music and the effect of it than some may think, that's why a forum and discussion is even possible. I'd rather not talk about things as 'emotion' though as that leads to quite simplistic approaches from some people. Maybe listener 'response' is a better term, as it can embrace the complexity of how our minds interact with things (emotionally, intellectually).


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## tdc (Jan 17, 2011)

aleazk said:


> The real mystery of physical reality is: why it's comprehensible to us and by using logic?. Mathematics has little to do with this metaphysical question.
> .


But maybe it is comprehensible to us by using logic, _because it is logically ordered_. Perhaps mathematics is one of the key ways we can understand this order. Numbers seem to be a game that nature plays (ie- the Fibonacci sequence, the degrees of a circle etc.). Not just a human construct. Vortex based mathematics is a branch of math dealing with these fascinating topics.


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## trazom (Apr 13, 2009)

What does "mathematically perfect" mean regarding Bach's music? Does his compositional process fit some sort of algorithm?


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## Blake (Nov 6, 2013)

Mathematics is a tool of understanding form.

Music is a tool of expressing the formless.


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## tdc (Jan 17, 2011)

trazom said:


> What does "mathematically perfect" mean regarding Bach's music? Does his compositional process fit some sort of algorithm?


I don't know if Bach's music was "mathematically perfect" but I consider him to have been very adept at incorporating sacred geometry into his works. In some ways I think of him as the Leonardo Da Vinci of music.


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## PetrB (Feb 28, 2012)

tdc said:


> I don't know if Bach's music was "mathematically perfect" but I consider him to have been very adept at incorporating sacred geometry into his works. In some ways I think of him as the Leonardo Da Vinci of music.


Somehow, "Sacred" and "Geometry" don't quite sound together as "Mathematics."


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## tdc (Jan 17, 2011)

PetrB said:


> Somehow, "Sacred" and "Geometry" don't quite sound together as "Mathematics."


Mathematics is a broad term, encompassing many things including geometry. I often wonder why "sacred geometry" isn't a major part of the curriculum in schools. Don't you think it would be a worthy topic to learn about? You don't think it is related to math? The Fibonacci sequence is found everywhere in nature, it is found across the world in music, art and architecture of the great masters. Yet I guess this didn't seem like a topic of much importance for the masses to learn about.


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## aleazk (Sep 30, 2011)

tdc said:


> But maybe it is comprehensible to us by using logic, _because it is logically ordered_. Perhaps mathematics is one of the key ways we can understand this order. Numbers seem to be a game that nature plays (ie- the Fibonacci sequence, the degrees of a circle etc.). Not just a human construct. Vortex based mathematics is a branch of math dealing with these fascinating topics.


Well, yes, but that's tautological... of course that if it is comprehensible to us by using logic, then it must be logically ordered... that's exactly what "comprehensible to us by using logic" means. The question is precisely, why it's logically ordered?.
Again, yes, mathematics is helpful for understanding reality, but that's because reality is logically ordered and mathematics is a device for dealing with logically ordered things.

Two things: I urge you to abandon the idea that mathematics="numbers". Second, you may got it in the wrong order. It's not that mathematics is in some "cosmic" relation with nature, that nature "chose" mathematics as her "language". The fact that physical reality is describable using mathematics is a consequence of what I said in the first paragraph.

I consider the "mystification" of mathematics as philosophically repugnant, a kind of magical thinking.
Metaphysically speaking, I prefer to accept as a mystery the question about the logical order of reality instead of the "mystification" of mathematics, which is a very problematic concept. In the latter, a lot of things have to be accepted; like accepting that mathematics is a thing by its own, with its own reality, and that physical reality is just some kind of image of this mathematical reality. As I said, metaphysically speaking, that's not exactly the most economical thing to do in terms of conceptual clarity.
Anyway, that's my own view, based on my own experience with mathematics. You can take it or leave it. Some people find it disappointing because it does not have that aura of mystery that surrounds mathematics for them. Of course, I don't have any problem with that, on the contrary.


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## Sid James (Feb 7, 2009)

tdc said:


> I don't know if Bach's music was "mathematically perfect" but I consider him to have been very adept at incorporating sacred geometry into his works. In some ways I think of him as the Leonardo Da Vinci of music.


I was thinking of Leonardo da Vinci after my initial post. In any case, Renaissance art and architecture did have a focus on developing a perfect sense of proportion. In terms of music I think there are parallels there with what Giovanni Gabrieli was doing at Venice, working with the specific acoustic of that space. All that stuff about positioning of brass and choirs at different points in the church, to get those acoustic multi-directional/antiphonal effects. Its like building a stereo system before that kind of thing even came near to being invented.

Another thing is that not all composers where lousy at mathematics. The non musical variety I mean. Xenakis was trained in architecture and engineering, so was no slouch in maths. Elliott Carter was trained in both English and mathematics.

Xenakis' electronic works also dealt with music in vast spaces, just as Gabrieli's did centuries before. One that I've got on cd is Le Legende de'er, composed for the opening of the Centre Georges Pompidou in Paris and premiered at that event. The shapes of the building informed his work, and like Gabrielli his music was often designed for a particular acoustic. There is a science to all this, its not just what a composer wants but what he can do with the limitations and possibilities of the space involved.



tdc said:


> Mathematics is a broad term, encompassing many things including geometry. ...


Basically I think the debate here is how we see maths. How broadly or narrowly we see it. Is it limited to pure or theorectical maths or does it extend to practical uses of maths in the real world? Does it include only more directly related professions like accounting or others like engineering or architecture, or even others like music or visual art? What about our daily lives? The simple things like budgeting, making estimates in terms of time it takes to travel to a place or cook a meal, or even things like the spatial skills involved in many sports (or indeed, driving).

I myself see mathematics as including many things, not only the things we strictly think of as maths related. The other thing is that pure maths in its higher forms can be very experimental, but I am no expert in that. In any case what you're looking at now, the computer screen, involved researched by those in a branch of mathematics, computer science. The person credited with inventing the first computer was Charles Babbage, and he was not only a mathematician but also had interests in other areas including philosophy and engineering. That was back in the 19th century before everything became specialised and put in neat little boxes.


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## science (Oct 14, 2010)

aleazk said:


> Well, yes, but that's tautological... of course that if it is comprehensible to us by using logic, then it must be logically ordered... that's exactly what "comprehensible to us by using logic" means. The question is precisely, why it's logically ordered?.
> Again, yes, mathematics is helpful for understanding reality, but that's because reality is logically ordered and mathematics is a device for dealing with logically ordered things.
> 
> Two things: I urge you to abandon the idea that mathematics="numbers". Second, you may got it in the wrong order. It's not that mathematics is in some "cosmic" relation with nature, that nature "chose" mathematics as her "language". The fact that physical reality is describable using mathematics is a consequence of what I said in the first paragraph.
> ...


The root question seems to be something like, "Why is there order rather than complete chaos?" If there's any order, it'll have patterns, so mathematics will be able to say something about it eventually. But why is there order at all? That I don't know.

On the other hand, if there were chaos - we wouldn't be around to answer the question, but even so, it would be a valid question, why is there chaos? It's like the "why is there something rather than nothing" question - why would there be nothing rather than something? Maybe questions like this are just tricks the human mind plays on itself because it's able to think of nonsense - "What would a square circle look like?" But maybe sometimes they can lead to interesting ideas anyway: "What if an unstoppable force met an immoveable object?"

They would go through each other. Obviously. Like, duh.


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## PetrB (Feb 28, 2012)

tdc said:


> Mathematics is a broad term, encompassing many things including geometry. I often wonder why "sacred geometry" isn't a major part of the curriculum in schools. Don't you think it would be a worthy topic to learn about? You don't think it is related to math? The Fibonacci sequence is found everywhere in nature, it is found across the world in music, art and architecture of the great masters. Yet I guess this didn't seem like a topic of much importance for the masses to learn about.


_What on earth is "Sacred" about it_ is my question, and possibly my problem. It is "just math" like music is "just music," ~ no more, no less.


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## starry (Jun 2, 2009)

I was about to bring up the subject of chaos, and though it was brought up I want another angle on it. Everything tends towards chaos (entropy), it's us and our minds that want to create and find the order in things. So I still wonder how much it is the minds of living things that give priority to patterns of order even if in the overall scheme of things they may not be that important.


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## tdc (Jan 17, 2011)

aleazk said:


> I consider the "mystification" of mathematics as philosophically repugnant, a kind of magical thinking.
> Metaphysically speaking, I prefer to accept as a mystery the question about the logical order of reality instead of the "mystification" of mathematics, which is a very problematic concept. In the latter, a lot of things have to be accepted; like accepting that mathematics is a thing by its own, with its own reality, and that physical reality is just some kind of image of this mathematical reality. As I said, metaphysically speaking, that's not exactly the most economical thing to do in terms of conceptual clarity.
> Anyway, that's my own view, based on my own experience with mathematics. You can take it or leave it. Some people find it disappointing because it does not have that aura of mystery that surrounds mathematics for them. Of course, I don't have any problem with that, on the contrary.


I'm not sure that the "mystification" of math is what we are really debating here. It comes across as more along the lines of an origin issue to me where you are seeing math as a human construct, and I am looking at it as not just a human construct but more as something that can also be seen to be sewn into the fabric of the universe. So, yes I think math is to some extent a human construct but certain concepts were always there waiting to be discovered (or rediscovered).

Fundamentally, if we go down to the roots of this I think what we are basically talking about is whether or not one thinks there is an intelligent design and creator/architect of this reality. I do think there is and I'm guessing you either don't think that or you think the question is unanswerable. There does seem to be sufficient evidence of ancient cultures that were more advanced technologically speaking than we are. Yet a lot of scientists seem to have this idea that we are at the cutting edge of technology right now. I think it is possible we are just catching up to where some civilizations in the past were. A lot of our technology is very dirty and destroys our planet, I see this as repugnant and a sign we are not living in balance with our surroundings and natural laws. I see this as evidence we are not very advanced. I think advanced means working with natural laws and living in balance with ones surroundings, not killing ourselves and the planet.

Ultimately what will occur here if we keep debating this is you will think I am arguing under false pretenses because I believe that clean free energy devices exist and/or can be produced eliminating the need for "dirty" technology. I think one can connect certain dots and see these technologies must exist. If you don't think this is necessarily possible or exists right now than I will believe you are arguing under false pretenses. I don't think either of us can prove this point here.

I know I'm straying a little off topic but coming back to math the fact we are talking about this abstract topic and trying to understand it shows there is "mystery" surrounding it already. Therefore it is already "mystified". This is not a point that I think we are debating - I think it is a given.



PetrB said:


> _What on earth is "Sacred" about it_ is my question, and possibly my problem. It is "just math" like music is "just music," ~ no more, no less.


For me the term "sacred" is not problematic because "sacred" geometry ties into the intelligent design of the universe. I see life as sacred therefore I have no problem with the term. I would rather live in a society that honors life and sees it as sacred (not dogmatic about religion - but truly seeing *all life* and in fact everything as sacred) than a society that sees things as chaotic and meaningless. I think if one contemplates the moral implications of both of these two philosophies it isn't hard to see which one is more destructive.


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## Taggart (Feb 14, 2013)

aleazk said:


> Well, yes, but that's tautological... of course that if it is comprehensible to us by using logic, then it must be logically ordered... that's exactly what "comprehensible to us by using logic" means. The question is precisely, why it's logically ordered?.
> Again, yes, mathematics is helpful for understanding reality, but that's because reality is logically ordered and mathematics is a device for dealing with logically ordered things.
> 
> Two things: I urge you to abandon the idea that mathematics="numbers". Second, you may got it in the wrong order. It's not that mathematics is in some "cosmic" relation with nature, that nature "chose" mathematics as her "language". The fact that physical reality is describable using mathematics is a consequence of what I said in the first paragraph.
> ...


OK Let's have a look at a fairly major area of Math that overlaps with music - the Riemann hypothesis. This is, essentially, a conjecture about the prime numbers. Since it involves a sine function (eventually) this can be reduced (by Fourier analysis) to what some people have described as the "music of the primes." So far, so simple. We're looking at work that was done in the 19th century - Riemann and Fourier, the 18th Century - Euler and way back beyond that.

Switch to the late 20th Century and people looking at atomic spectra and chaos at the quantum level saw that there was a connection to the Riemann Hypothesis. This is not surprising, because one of the approaches to solving the Riemann Hypothesis was the Hilbert-Pólya conjecture which runs into spectral theory which has substantial links to vibrations and sound. We're going round and round - maths to music to maths to physics to maths - and all the time we are learning both about maths and about physics.

The idea of accepting Mathematics as the base reality and physics as a form is similar to the allegory of the cave where the prisoners stared at the shadows on a wall and tried to understand what reality they represented. I think it does lead to considerable clarity of thought and allows us to consider what is real and what is not. No "mystification" or deification of mathematics. No assumption that Nature speaks in math. No assumption that reality is logically ordered. I accept chaos and indeterminacy because I accept that I am mortal and finite. I recognise that Heisenberg's uncertainty is the flip side of Godel's. But I also believe that Godel's theories take priority and that Heisenberg's indeterminacy is the shadow of the mathematical reality.

This is also a matter of (metaphysical) taste and I doubt that we will ever reach a satisfactory conclusion.


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## aleazk (Sep 30, 2011)

Taggart said:


> This is also a matter of (metaphysical) taste and I doubt that we will ever reach a satisfactory conclusion.


At the end, yes, you are right in that.
Views are founded in some things that have to be accepted beforehand.

In my view, my beforehand accepted supposition is that reality is logically ordered. Then, I see the fact that some aspects of reality can be modeled using mathematics as a consequence of my supposition and my definition of mathematics as a kind of language which is particularly useful when logical thinking is needed.

On the other hand, in the platonic (_à la_ Penrose) view, they prefer to accept mathematics as a given thing, and their beforehand accepted supposition is that physical reality is just a reflex of mathematical reality. In that way, they see the fact that reality is comprehensible using mathematics as a consequence of this supposition.

The two views are not equivalent. Their beforehand accepted suppositions are quite different. But, at the end, they both explain the observed phenomena. And since there's no way now for determining which one is the correct one, different people will accept one or the other according to their own taste and ideas. In fact, that's basically what I said in the last paragraph of my previous comment.

Your view seems to offer a third position. Something like "we don't know what reality is", the only thing we know is that we have a thing called mathematics that has proven to be useful for studying it, but we don't know exactly why and also we refuse to answer what mathematics is. At least that's how I interpret the third paragraph of your comment. If this is not your view, please correct me.
I would call it the "agnostic" position.

Certainly it is a valid position, and to some extent I prefer that position to the platonic one.


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## aleazk (Sep 30, 2011)

tdc said:


> I'm not sure that the "mystification" of math is what we are really debating here. It comes across as more along the lines of an origin issue to me where you are seeing math as a human construct, and I am looking at it as not just a human construct but more as something that can also be seen to be sewn into the fabric of the universe. So, yes I think math is to some extent a human construct but certain concepts were always there waiting to be discovered (or rediscovered).


Well, maybe mystification was not the most accurate word (I was trying to speak about seeing mathematics as something fundamental in the metaphysical sense when I used the word). 
Yes, what you say is basically what we are discussing, and definitely we don't agree.



tdc said:


> Fundamentally, if we go down to the roots of this I think what we are basically talking about is whether or not one thinks there is an intelligent design and creator/architect of this reality. I do think there is and I'm guessing you either don't think that or you think the question is unanswerable.


Yes, I think the question is more or less unanswerable (but if I have to answer in a completely sincere way, I would say I'm an atheist). And definitely my beliefs on this respect influence my views about the topic we are discussing.



tdc said:


> There does seem to be sufficient evidence of ancient cultures that were more advanced technologically speaking than we are. Yet a lot of scientists seem to have this idea that we are at the cutting edge of technology right now. I think it is possible we are just catching up to where some civilizations in the past were. A lot of our technology is very dirty and destroys our planet, I see this as repugnant and a sign we are not living in balance with our surroundings and natural laws. I see this as evidence we are not very advanced. I think advanced means working with natural laws and living in balance with ones surroundings, not killing ourselves and the planet.
> 
> Ultimately what will occur here if we keep debating this is you will think I am arguing under false pretenses because I believe that clean free energy devices exist and/or can be produced eliminating the need for "dirty" technology. I think one can connect certain dots and see these technologies must exist. If you don't think this is necessarily possible or exists right now than I will believe you are arguing under false pretenses. I don't think either of us can prove this point here.


We can discuss this in other forum, since it would imply off topic debates.



tdc said:


> I know I'm straying a little off topic but coming back to math the fact we are talking about this abstract topic and trying to understand it shows there is "mystery" surrounding it already. Therefore it is already "mystified". This is not a point that I think we are debating - I think it is a given.


haha, well, certainly it's mysterious in one way or another. I'm not denying that, since in my own point of view, there still is the mystery of the logical nature of reality.


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## Blake (Nov 6, 2013)

PetrB said:


> _What on earth is "Sacred" about it_ is my question, and possibly my problem. It is "just math" like music is "just music," ~ no more, no less.


I'm not sure, but it does sound beautiful. Don't ya' think?

It's okay to spice things up with imagination every once in a while.


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## jamallax89 (May 20, 2013)

I think that music is not a manifestation of mathematics.


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## Blancrocher (Jul 6, 2013)

aleazk said:


> Yes, I think the question is more or less unanswerable (but if I have to answer in a completely sincere way, I would say I'm an atheist). And definitely my beliefs on this respect influence my views about the topic we are discussing.


Interestingly, it's also the case that Roger Penrose was an atheist. I don't doubt that a disproportionate number of mathematical Platonists are religious by comparison with mathematicians in general (let alone physicists! :lol, but there is no _necessary_ connection in my opinion. It probably comes down mostly to differences in temperament, as Taggart suggested earlier.

Interesting conversation, by the way. I'm trying--unsuccessfully--to get up to speed on some of these issues on Wikipedia!


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## LordBlackudder (Nov 13, 2010)

but it isn't a manifestation of mathematics. so there is no argument.

i don't think tribal africans playing a drum immediately make good accountants.


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## aleazk (Sep 30, 2011)

Blancrocher said:


> Interestingly, it's also the case that Roger Penrose was an atheist. I don't doubt that a disproportionate number of mathematical Platonists are religious by comparison with mathematicians in general (let alone physicists! :lol, but there is no _necessary_ connection in my opinion. It probably comes down mostly to differences in temperament, as Taggart suggested earlier.
> 
> Interesting conversation, by the way. I'm trying--unsuccessfully--to get up to speed on some of these issues on Wikipedia!


haha, well, Penrose is definitely one of the most clever persons out there. His contributions to, particularly, general relativity are overwhelming. He owns the theory.

Nevertheless, he also has quite peculiar philosophical ideas. Particularly regarding to quantum mechanics.

This was said by Hawking as an introduction in a joint presentation he made with Penrose about their discoveries:



> I think Roger and I pretty much agree on the classical work. However, we differ in our approach to quantum gravity and indeed to quantum theory itself. Although I'm regarded as a dangerous radical by particle physicists for proposing that there may be loss of quantum coherence I'm defitely a conservative compared to Roger.


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## millionrainbows (Jun 23, 2012)

The Greeks considered music as part of The Quadrivium, along with Geometry, Astronomy, and Arithmetic. In the modern era, this is rarely questioned, except by those souls who wish to discedit modern music, or keep music "poetic" and emotional(with tightly closed eyes and both fingers crossed). "Music is pure emotion" seems to be their mantra.


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## Taggart (Feb 14, 2013)

millionrainbows said:


> The Greeks considered music as part of The Quadrivium, along with Geometry, Astronomy, and Arithmetic. In the modern era, this is rarely questioned, except by those souls who wish to discedit modern music, or keep music "poetic" and emotional(with tightly closed eyes and both fingers crossed). "Music is pure emotion" seems to be their mantra.


Hmm. We seem to approaching a paradox. The Quadrivium derived from Plato's Republic naturally includes a healthy dose of idealism. As Proclus remarked in his "A commentary on the first book of Euclid's Elements":



> The Pythagoreans considered all mathematical science to be divided into four parts: one half they marked off as concerned with quantity, the other half with magnitude; and each of these they posited as twofold. A quantity can be considered in regard to its character by itself or in its relation to another quantity, magnitudes as either stationary or in motion. Arithmetic, then, studies quantities as such, music the relations between quantities, geometry magnitude at rest, spherics [astronomy] magnitude inherently moving


I am sure there are those among us who enjoy modern music who would be repelled by this rampant Platonism.


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## science (Oct 14, 2010)

millionrainbows said:


> The Greeks considered music as part of The Quadrivium, along with Geometry, Astronomy, and Arithmetic. In the modern era, this is rarely questioned, except by those souls who wish to discedit modern music, or keep music "poetic" and emotional(with tightly closed eyes and both fingers crossed). "Music is pure emotion" seems to be their mantra.


Well, I question that, and I neither seek to discredit modern music nor have any notion whatever ever that music is pure anything, even pure music, let alone pure emotion.

What the heck is going on in this discussion?


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## Blake (Nov 6, 2013)

science said:


> What the heck is going on in this discussion?


Roaming the twisting labyrinths of the mind.


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## Taggart (Feb 14, 2013)

Vesuvius said:


> Roaming the twisting labyrinths of the mind.


Listening to the music of the spheres.


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## Guest (Nov 7, 2013)

I'm tempted to ask the OP to return and elaborate, or offer his own comment. But I don't think Vivaldi can be a real member, as s/he never engages in conversation here...

S/he may just be an aberrant manifestation of our collective consciousness.

As for the question, no need to wax philosophical (Platonic or otherwise). Music and maths are connected manifestations of our capacity to reason and create. The fact that you can use maths to analyse musical constructions does not mean one is dependent on the other.


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