Stressing and ignoring
Click on the link below to read William Boyd on 'Cabbages are not spheres'.
Click on the link to read the article ‘Cabbages are not spheres’ which is taken from a novel by William Boyd. Part of the conversation between the two characters, John and Hope, concerns how humans can look at one thing and see it in terms of something else.
Mark or make a note of any sentences or ideas which strike you as illustrating a mathematician's view of the world.
A key sentence comes towards the end of the excerpt.
The natural world is full of irregularity and random alteration, but in the antiseptic, dust-free, shadowless, brightly lit, abstract realm of the mathematicians they like their cabbages spherical, please.
The extract draws a distinction between the objects of the physical world around us and the ‘objects’ of mathematics: for instance, cones, spheres and straight lines. Yet for mathematics to be of use in solving problems in the physical world, it must also be possible to see these physical and mathematical objects as being the same thing under certain circumstances. Instead of stressing the differences, it can be important at times to ignore the differences; to be able to see cabbages as spheres, mountains as triangles, and rivers as flowing in straight lines. Thus particular features of the physical objects are stressed while others are ignored—with a cabbage, in some situations, its near spherical shape can be stressed while features like its colour, its stalk and its taste can be ignored. Seeing what to stress and what to ignore in particular circumstances is a key part of being a mathematician.
Another necessary component of developing a mathematical view of the world is being able to recognize mathematical ‘things’—shapes, curves, numbers, graphs, equations, and so on. Yet another element is developing a curious, questioning attitude towards the world around you. Why is that the way it is? Could it be different? If so, how? What if it were slightly different? Why isn't it different? What are the forces operating to make it the way it is? How can I describe the relationships I see?
Do people who study mathematics view the world and think about things any differently from other people? To find out whether there is a distinctively mathematical outlook on life, a member of the unit team noted down things that set off a train of thought which could be described (in a broad sense) as mathematical. You can hear the result in the audio clip on the next screen.