## A few lectures

A few lectures from Gresham College:

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An interesting lecture on symmetry patterns and symmetry breaking. A lot of the discussion of the relevant principles takes animal skin patterns and -movement patterns as the starting point for the analysis, leading to interesting quotes/observations like these: “Theorem: A spotted animal can have a striped tail, but a striped animal cannot have a spotted tail”, and “…but it can’t result in a horse, because a horse is not spherically symmetric”.

He also talks about e.g. snowflakes and sand dunes and this does not feel like a theoretical lecture at all – he’s sort of employing an applied maths approach to this topic which I like. Despite the fact that it’s basically a mathematics lecture it’s quite easy to follow and I enjoyed watching it.

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He takes a long time to get started and he doesn’t actually ever say much about the non-Euclidian stuff (he never even explicitly distinguishes hyperbolic geometry from elliptic geometry using those terms). He’s also not completely precise in his language during the entire lecture; at one point he emphasizes the fact that three specific choices used in a proof were ‘mutually exclusive’ as though that was what was the key, even though what’s actually critical is that they were also collectively exhaustive – a point he fails to mention (and I’d assume it would be easy for a viewer not reasonably well-versed in mathematics to mix up these distinctions if they were not already familiar with the concepts). But maybe you’ll find it interesting anyway. It wasn’t a particularly bad lecture, I’d just expected a little more. I know where to go look if one wants a more complete picture of the things briefly touched upon in this lecture and I’ve looked at that stuff before, but I’m certainly not going to read Penrose again any time soon – that stuff’s way too much work considering the benefits of knowing that stuff in details (if I’m even theoretically able to obtain knowledge of the details – some of that stuff is *really hard*).

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I took a class on mathematical thinking this past semester and we went through a few models of mathematics as well as fundamental ideas. What happens in the class is that we’re given new problems each week and we’re supposed to figure out the idea behind the problem and find the solution. One of the key basic ideas that was mentioned and given great emphasis was symmetry. It has been tremendously useful in thinking about problems. The other basic ideas (that were stressed as much as symmetry was) were that of projection/ reflection, maximum and minimum, and homotopy. I thought it was amazing that so much could be done if one started from these concepts.

Comment by Nia | December 11, 2013 |

I think in mathematics it’s very often the case that you can get very far, indeed much further than you’d think, with just a few simple ideas. Sometimes you need to pull some ugly stuff out of the hat to get anywhere, true, but simple ideas can often be used to analyze problems which may well be far from simple. And the more tools you know, the easier it gets to find at least one tool which you may be able to use to apply to any given problem.

Comment by US | December 12, 2013 |