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All That Jazz: Uncovering the Similarities Between Music and Math

February 1, 2010

What do music and math have in common? More than most people think, according to Lehman Mathematics and Computer Science Professor Rob Schneiderman.

9 Minutes 12 Seconds

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This is Christina Dumitrescu, a student at Lehman College. What do music and math have in common? More than most people think, according to Lehman Mathematics and Computer Science Professor Rob Schneiderman.

In this podcast, the former professional jazz musician explores the similarities and differences between math and music, and talks about his ongoing research in a field of math known as low-dimensional topology.




I was a professional musician for a number of years before I even got interested in mathematics. I played piano mainly. And most of the music I've played my whole life is what's called jazz which is a broad term, takes in a lot of kinds, a lot of styles of music. And, you know, I appreciate lots of kinds of music. And I still play and perform occasionally.


In the beginning, I didn't consciously think about connections between mathematics and music. And over the years, I've started to realize lots of ways that they could be related. Although, its very elusive and lots of ways where it seems like they're not related.

One of the amazing things about music is that musicians can pick up instruments, start making sounds. And it seems like they're telling a story or even something way deeper. When they're making sounds and combining tones that don't directly refer to anything that you may be aware of. Yet, it can have deep meaning.


And in mathematics, a similar phenomena happens where mathematicians study these constructions that are quite abstract and complicated and don't necessarily correspond directly to applications in the physical world. Yet, they have lots of deep meaning especially to the mathematicians.

The other side of the coin is that both music and mathematics have lots of applications. So usually when people listen to music there's images, words, maybe dance, ceremony associated to the music. And similarly with mathematics, most people experience mathematics through applications such as to the physical world or even just measuring and quantifying aspects of life rather than the abstract development that the mathematician experiences. So both music and mathematics are full of patterns as is the world in general.

And when you try to specifically nail down mathematical content in the patterns that you find in music, you almost always fail. So lots of people, they s-- they hear lots of patterns. They try to make sense out of them in music using mathematics.


But for me analyzing music is almost missing the point. You can use musical analysis to create music if you're a musician. But you always do it in a creative way. So you-- whenever you're analyzing things and trying and experimenting with sound, you're doing it with your ear guiding the way not the rules or the logic the way you perceive as mathematics. So I think in a way this is how music and mathematics are different.

Science and art in general are mixtures of culture and objectivity. So some things are deeply affected by the cultural point of view. But other things seem to transcend culture.

So you see that in music and math a lot, that you can appreciate music from other cultures. And the same mathematical theorems and theories are gonna be true no matter where you are on the planet. But there's a really nice analogy between improvised music and the discovery of mathematics.



Most people might not realize that when mathematicians are looking for new theories and trying to prove new theorems that they often work in combinations of two or even more mathematicians that get together and ask some questions, throw out ideas, you know, trade taking the lead. And you never really know what's gonna happen. And a lot of times there's surprising detours that you take. And you never know whether you're actually gonna prove what you wanted to prove in the beginning.

And this is very similar to, for instance, jazz improvisation where players get together. They have enough common musical language to get going. And they don't really know exactly where the song is gonna take them or the performance is gonna take them. And they have to spontaneously exchange ideas, take turns leading, accompanying, know when to lead-- leave space.

And it's-- it's a really strong analogy. And I think it could be-- powerfully applied to other aspects of education in general because if you can learn to develop the spontaneous generation of constructive ideas, you could apply that to anything.



Well, one of the great examples of an abstract, sort of, pure mathematical theory that in the modern world became very applied is the study of numbers, just the-- the set of prime numbers is still a mysterious object, mathematical object, that's being studied. And, you know, this has been going on for thousands of years. But recently, it's-- shown up as a tool in encryption for the internet. So these originally pure, abstract problems in mathematics that seemed like just for the, you know, pleasure of the thinker turned out to have this valuable application in this modern digital world of encrypting transactions over the internet.

My main area of specialty is topology. And that's the study roughly of the shape of spaces. So geom-- it's related to geometry which is more rigid in studies on spaces that have distance and curvature. And in topology, it's more of-- a fluid notion of what space is. And in particular, you can have spaces in any number of dimensions.

And it's an interesting fact that spaces and dimensions five and higher are actually easier to understand in a certain way than spaces and dimensions three and four. So what I concentrate on is the hard stuff. It's called low dimensional topology. And we study three and four-dimensional spaces.


Topology is-- it's connected to the r-- real world in many ways. But it's also fairly abstract. So physics, in particular, you know, uses topology and geometry. But on the other hand, many of the objects that topologists study are-- are very wild objects.

And they may be infinite dimensional. And if you can imagine taking 12 dimensional spheres and tying them in knots in some 14 dimensional space, then, you know, that's the kind of thing that is fascinating to topologists and may not have a direct application to the real world. Although, on the other hand, sometimes we find connections after the fact. So after mathematical theory is developed, sometimes you'll find unexpected applications.

For the second half of the year 2010, I'll be visiting researcher at the Max Planck Institute in Bonn, Germany. And I'll be able to concentrate on my research. And I'll be collaborating with-- a couple of other mathematicians in particular on a project we've been working on for some years.


And, for me, that's a chance to think intensely, concentrate and develop ideas to the point where they're-- they'll be-- appear in journals and give talks and-- and have more time to talk with graduate students and other mathematicians. So that's the kind of, you know, intense concentration and research that sort of rejuvenates you.



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