Cultures of the image and cultures of the word

Upvote:5

I think Weinberg is wrong when asserting the struggle between the word and the image. I thin this paper by Atiyah may be informative regarding image-word interplay. Here's a relevant quote from it:

"Let me try to explain my own view of the difference between geometry and algebra. Geometry is, of course, about space, of that there is no question. If I look out at the audience in this room I can see a lot; in one single second or microsecond I can take in a vast amount of information, and that is of course not an accident.

Our brains have been constructed in such a way that they are extremely concerned with vision. Vision, I understand from friends who work in neurophysiology, uses up something like 80 or 90 percent of the cortex of the brain. There are about 17 different centres in the brain, each of which is specialised in a different part of the process of vision: some parts are concerned with vertical, some parts with horizontal, some parts with colour, or perspective, and finally some parts are concerned with meaning and interpretation. Understanding, and making sense of, the world that we see is a very important part of our evolution. Therefore, spatial intuition or spatial perception is an enormously powerful tool, and that is why geometry is actually such a powerful part of mathematics—not only for things that are obviously geometrical, but even for things that are not. We try to put them into geometrical form because that enables us to use our intuition.

[...]

Algebra, on the other hand (and you may not have thought about it like this), is concerned essentially with time. Whatever kind of algebra you are doing, a sequence of operations is performed one after the other and ‘one after the other’ means you have got to have time. In a static universe you cannot imagine algebra, but geometry is essentially static. I can just sit here and see, and nothing may change, but I can still see. Algebra, however, is concerned with time, because you have operations which are performed sequentially and, when I say ‘algebra’, I do not just mean modern algebra. Any algorithm, any process for calculation, is a sequence of steps performed one after the other; the modern computer makes that quite clear. The modern computer takes its information in a stream of zeros and ones, and it gives the answer.

Algebra is concerned with manipulation in time and geometry is concerned with space. These are two orthogonal aspects of the world, and they represent two different points of view in mathematics. Thus the argument or dialogue between mathematicians in the past about the relative importance of geometry and algebra represents something very, very fundamental.

Of course it does not pay to think of this as an argument in which one side loses and the other side wins. I like to think of this in the form of an analogy: ‘Should you just be an algebraist or a geometer?’ is like saying ‘Would you rather be deaf or blind?’ If you are blind, you do not see space: if you are deaf, you do not hear, and hearing takes place in time. On the whole, we prefer to have both faculties."

I would like to add to the above quote that IMO there's a certain amount on interplay between the word (which is similar to time-bound algebra because it describes the World as a sequence of words), and the image (which is similar to space-bound geometry for obvious reasons). Following Atiyah's analogy, taking a side in the alleged struggle between them is like making a choice between being deaf and being blind; most people, as he put it, would "prefer to have both faculties."

More post

Search Posts

Related post