Monday 2 September 2019

Infinity

Murder Bound, ix.

Yamamura:

"'Math isn't a science, it's the most mystical of the arts. When they start telling me that some kinds of infinity are bigger than others, I get off the boat.'" (p. 81)

See:

Infinity Comes In Different Sizes

Mathematics is not a science because it is not empirical.

I lack mathematical aptitude so I had to work at understanding the proof that there is no highest prime number but then I got it unlike someone I knew on Facebook who dismissed the proof as "gobbledegook" because he did not understand it.

I have not followed the argument in the above linked article but then I have not worked at trying to understand it yet. But surely it is straightforward that an infinite straight line is smaller than an infinite plane which is smaller than an infinite volume?

Isaac Asimov recounted an incident when he proved that not only mathematicians but everyone uses "mystical" language. He asked someone who had accused mathematicians of "mysticism" because they talked about unreal numbers to hand him half a stick of chalk. When the guy broke his stick of chalk in two and handed one of the pieces to Asimov, the latter pointed out that he had been given one piece of chalk.

1 comment:

Sean M. Brooks said...

Kaor, Paul!

I recall the interest Dominic Flandry took in how the Sea People of Starkad (in ENSIGN FLANDRY) had developed mathematics. If my memory is correct, the Sea People had trouble with the concept of "zero."

And trying to make sense of an infinite line, an infinite plane, or an infinite volume risks hurting my head! (Smiles)

But I think I can somewhat grasp the idea of an infinite line extending in both directions with no end or stop.

Sean