Tag Archives: Noam Chomsky

Multiplicity of Mathematics

I continue with the recent posts about mathematics, which so far have been as follows.

  1. What Mathematics Is”: As distinct from the natural sciences, mathematics is the science whose findings are proved by deduction. I say this myself, and I find it at least implicit in an address by Euphemia Lofton Haynes.

  2. More of What It Is”: Some mathematicians do not distinguish mathematics from physics.

  3. Knottedness”: Topologically speaking, there is a sphere whose outside is not that of a sphere. The example is Alexander’s Horned Sphere, but it cannot actually be physically constructed.

  4. Why It Works”: Why there can be such a thing as the horned sphere.

When I first drafted the first post above, I said a lot more than I eventually posted. I saved it for later, and later is starting to come now.

Continue reading

On reading too much into words

First let it be noted that nothing I say here will have any effect on hostilities in the so-called Holy Land or anywhere else. I have no need here to take any particular line; no reader should assume that I do or do not elsewhere follow any particular line.

I do wish to promote clear thought. I should like to think that my friends and colleagues have a similar wish, especially when they are academics like me.  Of course, what counts as clear thought may vary. I am a mathematician, professionally; I work in the mathematics department of a university. Certain modes of thought are therefore habitual with me; they may not be habitual in other departments, not to mention other walks of life. I may adopt my modes of thought at the expense of others.

I feel compelled to say such things, having been shocked to find that what I say here may be at all controversial. Continue reading