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.

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## About isomorphismes

Argonaut: someone engaged in a dangerous but potentially rewarding adventure.