We are asked to fill the front rows so we move. We are asked to participate in conversation so we try. Short introduction: Who? Why? What? (John Mason to educate us holds a lecture on thinking mathematically.) Then he walks to the middle fires up his Mac and soon we stare at the blue screen filled with circles, numbers and colour. The lecture is called Thinking Mathematically. So the circles – at least for me – bring up memories of Maths and stick figures (And stick figures make me - like a dog of Pavlov - to associate with a giant in the playground. Hence the goblins in the header.) Of course they should mean numbers and addition and powers and laws but that’s why we have this lecture. Not to train our strictly meant mathematical knowledge but to make us better understand what we already should now.
We are sorting colourful objects, putting them in bags and then generating functions like wings of angels
All this to learn something most people would think impossible to learn. But we do, and we like it.
After all this is what maths about. Understanding what you already know to make something entirely new and astonishing. Or help someone else make it.
1 comment:
This was a fascinating workshop in many ways.
I was particularly struck by the opening exercise, in which John showed us how each of us was interpreting a visual layout in different ways - this resonates (and perhaps contradicts) the discussion between Mark Haddon and Marcus du Sautoy at the Royal Society this week, which suggested that (crudely) the artist doesn't want to prescribe the audience's response whereas the scientist/expositor wants everyone in the audience to be thinking in the same way.
And I was forced to confront one of my own most cherished beliefs. As a child, when I was shown the paradoxical geometric proof that all triangles are isosceles, my response was to abandon diagrams as a mathematical tool. Maths is about proof and pictures mislead, so there is no place for diagrams in maths (sorry, Euclid). Since then I have never done maths visually. I know that if you cut a section through a cube you get a perfect hexagon, but I don't know that geometrically: I recognise the words now but I have no idea how it really works. John's talk led me to wonder whether perhaps there is a place for pictures in mathematics after all.
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