Understanding mathematics indirectly

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Do you think it's possible to gain insight into the nature of mathematics (albeit indirectly) via mastery of say, music, art, language, etc...?

yes, there is much math directed towards understanding patterns in reality

For example, referencing the mathematician John Nash, we saw in the movie , 'The Beautiful Mind' in which he watched bird patterns and tried to think of algorithms that described their pattern of behavior
http://en.wikipedia.org/wiki/John_Forbes_Nash,_Jr.

music, art, language may contain hidden patterns, and understanding the relationships of the parts and how a pattern is formed is math - even if no math notation is used

When I was around 14 in 1969 I ran to my desk to write a spoof of the dueling partisan politcal pundits you would see on TV back then.

Pundit A says "the president is in trouble because of high unemployment".

Then Pundit B says "but the rate of unemployment is going down."

Pundit A: "But recent reports show that the RATE at which unemployment is going down is...going down!"

Pundit B: "But the rate at which the descrease in the decrease in the decrease in unemployment is decreasing is...DECREASING".

And so on..

I stood up to read it aloud to see how it would sound. And I ended up laughing my hat off hardily.

This caused my dad to come up stairs from the basement and yell at me for talking to myself ( which being aspie I guess I was guilty of alot back then).

So- it was both a good moment and bad moment in my growing up.

But - in addition to penning a funny piece of comedy that day- I realized decades later that I had- ALSO inadvertently invented something else: that being the whole field of Fractal Geometry! Thats basically what the piece was illustrating.

So standup comedy can lead to mathematical insights!

Haha, excellent naturalplastic. Do I also see some little echoes of Calculus there? Rates of rates and all that.

Actually, I find it that music is filled with math. Try turning the twelve tones into ordered numbers (say C maps to 0, C#/Db maps to 1 and so on till B which should map to 11) and you'll find it that hard operations such as transposition to other keys become matters of adding the number of tones you want to shift it by to all the numbers representing the notes in a piece.
Chords are nothing but vectors in a n-dimensional vector space (where n=number of maximum tones used in a given context).

When we compose music, we are unawarely doing a lot of maths. As Leibniz put it once, "Music is a hidden arithmetic exercise of the soul, which does not know that it is counting."

Probably not a surprise that some studies have found it that children who were exposed to musical education have improved results in Mathematical fields.

I would suggest reading A Mathematician's Lament by Paul Lockehart Ph.D.
http://www.maa.org/external_archive/dev ... 03_08.html

It is primarily a criticism of the current math curriculum (which he calls a "third rate bastardization,") but he also manages to explain visually how math works.

I might also suggest you pick up a copy of Euclid's Geometry, which is almost entirely visual.

You see, Math is the "art of expression" it can express many things that apply directly to our world, but it is nothing more than symbolic logic that we use to describe, or express, a concept. Much of math is entirely fantastical, as it doesn't need to correlate to reality.

Last edited by Protogenoi on 31 Aug 2014, 7:49 pm, edited 1 time in total.

No. At most a motivation to study mathematics. But how much of, say, first year mathematics will you understand through musical notes or (laically) observing bird patterns? Yeah, 0%.

Actually if what we are talking about is the "nature of Mathematics, stressing «albeit indirectly»" rather than "Mathematics" itself, I would dare propose musical notes, board games and puzzles, but also a lot of things which do not involve mathematics directly but can be thought of and made clear in a mathematical way, can help you have some intuition behind your mathematical thought. In this sense it gives you a fair deal of the idea of what the nature of the field of Mathematics is.

But I fully agree with 1024, given a more careful thought. To believe you can come up with mathematical knowledge merely based on that intuition, is a belief that leads to an impossibility. In fact, I would also dare say that whilst one can learn a lot of the nature of mathematics by looking at things around us and seeking a mathematical model of these things by creating new concepts, definitions, etc.; one will have very much difficulty learning the formalism and logical rigor that coherent Mathematics requires. You can learn that a mapping of musical notes to the naturals exists, for instance, and define operations within it. But without a certain ability of abstraction, that is, to dispense all intuition in favor of a mechanistic, logic based approach, how will you arrive at conclusions of the hidden theorems that your definitions in that theory/model/field imply?

I speak as an amateur mathematician, but I have spent hours and even days trying to understand or arrive at proofs for theorems myself, and only now (after 2 years of dedication in self-teaching efforts) am I managing to clearly define problems, theorems and understanding a familiar field's theorems at first sight.

More importantly, I think a great part of the nature of Mathematics besides its intuition and formalism comes also from the fact that, to a certain extent, it is built collectively. This makes it both a fascinating but also frustrating field. Whereas it's fascinating to see the work of many influential Mathematicians still being continuously expanded by people all over the world, it's also becoming so immense and some fields are so specific in their language and notation, that it becomes really hard to keep up with it.

This last point means, that even if you arrive at the intuition of Mathematics and at its formalism, you still have to face a multitude of people who might have the same ideas as you, and that is competition. At the same time, you have a multitude of people who have different perspectives on the same topic, and so, you can learn a lot from them. And of course, the more people you have, the more conjectures and hypothesis are generated, and the more you have to work on.

Music is based on mathematics. The pythagorean and equal temperemant systems rely on precise calculation. Jazz musicians also rely on hierarchies of harmonies modes tonalities etc. Any professional musician will have mathematical principles embedded in their consciousness even without formal training.

As a maths teacher (yes, we call it maths in the colonies), I dislike the methods taught in high school. They work ok for some, but for many the method doesn't address the why. I teach students several methods and whys, with explanations, and encourage them to use what makes sense to them.

In year 10, I got 20% for maths and thought I was a dummy at it. After completing high school I worked for 3 years and then went to college to study engineering. In college, I came top of the class in maths, with calculus being my best skill. I attribute this to relevance, which tells me it's not only method, but engagement that counts. I would not be surprised to find many adults have chosen a career path that excludes maths, when they might actually find it stimulating. Just because high school maths was awful, doesn't mean adult maths will be the same.

As for the OP question, I'm told that if you're good at music, your brain will also be good at maths, but high school maths often gives people the wrong impression about our abilities.