Conceiving of ∞ as a mathematician is simple. You start counting, and don’t stop.

That’s all.

(`$i++`

for programmers)

Which is why ∞ seems very small to the mind of a mathematician.

With projective geometry you can map ℝ to a circle, in which case there is a point-sized hole at the top where you can put ∞ (or −∞, or both).

Same thing with the Riemann Sphere.

So to them ∞ is very reachable. It’s just a tiny point.

**Graham’s Number**

It takes much more mental effort to conceive of Graham’s Number than ∞. It took me several hours just to begin to conceive Graham’s number the first time I tried.

Graham’s Number is basically a continuation of the above, recursed many times. Maybe I’ll do a write-up another time but really you can just look at Wikipedia or Mathworld. It’s absolutely mind-blowing.

**Bigger**

Here’s what’s weird. Infinity is obviously bigger than Graham’s Number. But Graham’s Number takes up more mental space. Weird, right?

**EDIT:** Maybe ∞ takes up less mental space than `g64`

because its minimal algorithmic description is shorter.

### Like this:

Like Loading...

*Related*

Tags: ℝ, ∞, education, generalised number, generalised numbers, Georg Cantor, Giuseppe Peano, imagination, infinity, iuseppe Peano, math, mathematics, maths, mental space, number, projective geometry, real numbers, science

This entry was posted on November 23, 2010 at 2:30 pm and is filed under Uncategorized. You can follow any responses to this entry through the RSS 2.0 feed.
You can leave a response, or trackback from your own site.

## Leave a Reply