Category Archives: maths

More fun with Triggertrap

I’ve added a couple of timelapses to Youtube this week, both made with Triggertrap here in Edinburgh.

The first is a capture of Bruce Munro’s Field of Light installation currently at St Andrew square. This was my first experiment with the ‘bulb ramping’ approach, of extending the shutter speed as the timelapse progresses to compensate for falling light as the sun sets. It’s a bit rough around the edges due to some technical limitations and having to guess at appropriate settings, but works reasonably well at compressing the hour around sunset into a minute. You can see Field of Light until April 27th.

The second is a collection of timelapses from the construction of a giant mathematical sculpture. Innovative Learning Week at the University of Edinburgh gives students and staff alike a chance to branch out from their usual lecture schedule and try something different, and this event organised by Julia Collins from the School of Mathematics was a UK first. Involving a team of 20 people, nearly 11,000 pieces of zometool, over six hours of construction time and several extra large pizzas, we were able to built a ‘giant 4D buckyball’, or more formally, a cantitruncated 600 cell. You should be able to go and see this at Summerhall until we need the pieces for something else – probably the Edinburgh Science Festival around Easter – and I’ll try to write more about the mathematics over on Modulo Errors in due course.

(For both videos, you may be better off viewing in full HD.)

Space-time manipulation (with buses)

I’ve been continuing my adventures in image manipulation with Matlab, taking the opportunity to play with a technique I’ve been interested in for a long time – ‘slit scan’ or ‘strip’ photography. A very brief (but rather maths-y) explanation of what’s going on in the clip above would be the following:

Let a video be defined by T frames each of dimension X-by-Y. Then the pixel value to be displayed at location x,y at time t is simply V(x,y,t) for some 3-dimensional array V; so the kth frame corresponds to the 2-d image Fk given by the plane T=k. But we may consider other planes to generate frames; by fixing a horizontal position X=k individual frames are images given by (t,y)=V(k,y,t) and iterating through these gives a new video V’(x,y,t)=V(t,y,x).

If that tells you everything you need to know, you can look at a couple more examples here and (more abstractly) here. Otherwise, read on for a fuller explanation!

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Gender shifts in US given names

About a month ago I read this excellent article on the fall from grace of the name ‘Hilary’. That alerted me to the fact that you can easily get US Social Security records on frequency of first names right back to the 1880s. Although Hilary focused on the raw numbers, I commented that I’d be interested in seeing the behaviour with respect to gender – specifically the tendency for ‘male’ names to become unisex or even predominantly ‘female’. Today I actually got around to crunching the data!

I found myself with 37,407 names that had been used for males, and 62,318 for females – so we immediately see that there’s a lot more diversity for female names. Of all these, 9800 are common to both genders – but only 8,564 have instances with both genders in the same year. Any such year I could use for a scatter plot of the proportion of males with a given name, out of all people with that name. So a value of 1 indicates a name was assigned only to males that year, with 0 showing that only females received it. Here’s the ratios for `Hilary’:

Proportion of male Hilarys.

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PhD Thesis

I have now submitted my PhD thesis for examination; hopefully the viva will be in April. Until then, I finally have the time for various projects and trips I’ve been planning, so there should be a bit more activity here. Coming up:

Should keep me busy!