Oct 30, 2007

608 comments

"What's the worst that can happen?" goes the optimistic saying. It's probably a bad question to ask anyone with a creative imagination. Let's consider the problem on an individual level: it's not really the *worst* that can happen, but would nonetheless be fairly bad, if you were horribly tortured for a number of years. This is one of the worse things that can *realistically* happen to one person in today's world.

What's the *least* bad, bad thing that can happen? Well, suppose a dust speck floated into your eye and irritated it just a little, for a fraction of a second, barely enough to make you notice before you blink and wipe away the dust speck.

For our next ingredient, we need a large number. Let's use 3^^^3, written in Knuth's up-arrow notation:

- 3^3 = 27.
- 3^^3 = (3^(3^3)) = 3^27 = 7625597484987.
- 3^^^3 = (3^^(3^^3)) = 3^^7625597484987 = (3^(3^(3^(... 7625597484987 times ...)))).

3^^^3 is an exponential tower of 3s which is 7,625,597,484,987 layers tall. You start with 1; raise 3 to the power of 1 to get 3; raise 3 to the power of 3 to get 27; raise 3 to the power of 27 to get 7625597484987; raise 3 to the power of 7625597484987 to get a number much larger than the number of atoms in the universe, but which could still be *written down* in base 10, on 100 square kilometers of paper; then raise 3 to *that* power; and continue until you've exponentiated 7625597484987 times. That's 3^^^3. It's the smallest simple inconceivably huge number I know.

Now here's the moral dilemma. If neither event is going to happen to you personally, but you still had to choose one or the other:

Would you prefer that one person be horribly tortured for fifty years without hope or rest, or that 3^^^3 people get dust specks in their eyes?

I think the answer is obvious. How about you?