Ways of Thinking

I’m putting one more Richard Feynman clip up. This one struck me as particularly interesting, because it touches on a question I’ve often asked myself: what goes on in your head when do you mathematical calculations? I think I agree with Feynman’s suggestion that different people think in very different ways about the same kind of calculation or other activity.

There’s no doubt in my mind that I’ve become slower and slower at doing mathematics as I’ve got older, and probably less accurate too. I think that’s partly just age – and perhaps the cumulative effect of too much wine! – but it’s partly because I have so many other things to think about these days that it’s hard to spend long hours without interruption thinking about the same problem the way I could when I was a student or a postdoc.

In any case, although much of my research is mathematical, I’ve never really thought of myself as being in any sense a mathematical person. Many of my colleagues have much better technical skills in that regard than I’ve ever had. I was never particularly good at maths at school either. I was sufficiently competent at maths to do physics, of course, but I was much better at other things at that age. My best subject at O-level was Latin, for example, which possibly indicates that my brain prefers to work verbally (or perhaps symbolically) rather than, as no doubt many others’ do, geometrically or in some other abstract way.

Another strange thing is the role of vision in doing mathematics. I can’t do maths at all without writing things down on paper. I have to be able to see the equations to think about solving them. Amongst other things this makes it difficult when you’re working things out on a blackboard (or whiteboard); you have to write symbols so large that your field of view can’t take in a whole equation. I often have to step back up one of the aisles to get a good look at what I’m doing like that. Other physicists – notably Stephen Hawking – obviously manage without writing things down at all. I find it impossible to imagine having that ability.

But I endorse what Richard Feynman says at the beginning of the clip. It’s really all about being interested in the questions, which gives you the motivation to acquire the skills needed to find the answers. I think of it as being like music. If you’re drawn into the world of music, even if you’re talented you have to practice long for long hours before you can really play an instrument. Few can reach the level of Feynman (or a concert pianist) of course – I’m certainly not among either of those categories! – but I think physics is at least as much perspiration as inspiration.

In contrast to many of my colleagues I’m utterly hopeless at chess – and other games that require very sophisticated pattern-reading skills – but good at crosswords and word-puzzles. Maybe I’m in the wrong job?


3 Responses to “Ways of Thinking”

  1. I’ve been doing a lot of thinking recently about ‘physics lectures’ and what they’re good for and I keep coming back to this Feynman clip. In the physics community lecturing is a normative discourse (via Cath Ellis http://cathellis13.blogspot.com/2010/11/font-face-font-family-cambria-p.html ) and physicsts are often very defensive about it. But what do the ‘sage on the stage’ advocates assume about what is happening in students’ minds. I think we should find out.

  2. I remember when first considering physics at Uni I watched these clips:


    I thought they among were the clearest and most understandable material I’d seen on physics, and short-sightedly assumed that all physics lecturers must be equally gifted in the art. Unfortunately I didn’t find a lecturer as good as Fenyman, with the possible exception of Bowley at Nottingham who I remember liked to dance around and throw board-rubbers at sleepers. It kept us awake at 9am even though the material was tedious. I find powerpoint very difficult to learn from, and love the blackboard approach. It’s that much easier if you can write at the same speed as the lecturer, or at least dictate.

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