A new academic year

September has come around again, and with it a new influx of students into Edinburgh.  I like the sudden hustle and bustle of the university, even if all the lecturing staff seem completely stressed out at the moment!  Last week we had a couple of events to welcome the new postgraduates into the maths department.  On Tuesday was the departmental welcome party, where I got to meet the new staff and students for the first time.  I started chatting to an ex-number-theorist-turned-probability-student, and suddenly two hours had passed and the whole blackboard was covered in knots and other crazy symbols.  I love it when that happens!  I learnt a lot of stuff and also felt completely motivated about my own research again.

Watching someone enthusiastically talking about their work, clearly in complete thrall of the beauty of the subject, is something I will never get bored of.  And it’s something I hope to capture in the lecturers here at Edinburgh, by interviewing them and filming them talking about their research.  The ‘Outreach’ pages I wrote for the maths website are finally online, and I have a section called ‘Spotlight on research‘ where I will be posting these interviews.  So far I’ve only done one, and I haven’t yet got a video camera to film the interview, so I hope the written article will do the subject justice.

Speaking of videos, I thought that before I go ahead and try doing professional filming, I should at least try making and editing a little video at home.  My idea for a short clip was to document all the many sheepy items that we have in this flat, because there now seems to be quite a lot!  I persuaded Julia to help me out, and this is the result:

The most difficult thing was not in making the video but in editing it afterwards.  This version was put together by Windows Live Movie Maker, mainly because I haven’t yet found some decent open-source software to use.  It would have been nice to edit the audio separately from the video, which WLMM isn’t able to do.  Suggestions welcome!

Figure 8 knot musicThe final thing I want to mention from this week is my meeting with a young music student.  Harry came to see me on Friday morning, having just started his PhD and wanting ideas for a composition.  Topology is not a stranger to the music scene; composers like Bach, for example, made music containing a Möbius-strip-like structure.  Harry’s idea was to get the maths behind a knot into his music.

“How on earth do you encode the structure of a knot into a piece of music?”, was my immediate response.  Thinking about it for a bit, I thought that maybe you could encode some symmetries of a knot (such as mirror-symmetry or orientation-invariance) into the music.  Then I thought that maybe it would be easy to make music from a braid, since you’d just need a few interweaving melodies.  But when Harry came along, one of the first things he said was “If you just give me a matrix then I can turn that into a composition.”  Well, that was all the encouragement I needed! My thesis is very much built on the idea of making a matrix from a knot and using that to tell me about the knot’s 4-dimensional properties.

20 minutes later and Harry’s notebook was filled with my attempts at trying to explain Seifert surfaces, Seifert matrices and slice knots.  I mentioned to him how I was very impressed at his speed of understanding; he seemed to pick up concepts that other people (with more of a maths background!) would struggle with for hours.  Slightly bemused by my comment, Harry thought about it for a few seconds, and then said that it wasn’t so strange after all, because mathematicians and musicians think in the same way.  Both subjects are highly creative and abstract, involve writing down symbols and (at least in mine and Harry’s case) thinking of concepts in a very visual way.  When he composes music, he ‘sees’ it in the same way I can ‘see’ my 4-dimensional knots.

I hope that together Harry and I can do more to put music and maths together and to popularise both subjects.  I will let you know if more developments happen on the subject!

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3 responses to this post.

  1. Music and maths and creativity and knots and stuff… Hmmm…

    Percussion from tables of coefficients of polynomials?

    I remember a paper (will try to track it down, I know I have a copy) where the author had basically shown that every knot has a corresponding juggling pattern (however difficult it might be to actually execute the sequence of throws). I’m just wondering… Firstly, wouldn’t it be cool to have a catalogue of mp3s of knots? (“You’re mad, that totally sounds like $10_42$!” etc)

    Secondly, is there a way to bypass matrices derived from knots/surfaces in order to go straight to music?

    Third, can we distinguish mutants with music?

    Fourth (for now, so many intriguing questions are being thrown around in my head) are musical compositions derived from knots always invariant under Reidemeister moves? 🙂

    I really love the connections between maths and music here!

    Reply

  2. Posted by Stephen O'Neill on October 14, 2010 at 2:18 pm

    Is baldness recognised as a bona fide disease?

    Every day is a school day 🙂

    Reply

  3. Posted by Kizzy the Dog on October 15, 2010 at 1:34 pm

    Love the sheep video 🙂

    Reply

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