"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?
Cooking something for two hours at 350 degrees isn't equivalent to cooking something at 700 degrees for one hour.
Caledonian has made a great analogy for the point that is being made on either side. May I over-work it?
They are not equivalent, but there is some length of time at 350 degrees that will burn as badly as 700 degrees. In 3^^^3 seconds, your lasagna will be ... okay, entropy will have consumed your lasagna by then, but it turns into a cloud of smoke at some point.
Correct me if I am wrong here, but I don't think there is any length of time at 75 or 100 degrees that will burn as badly as one hour at 700 degrees. It just will not cook at all. Your food will sit there and rot, rather than burning.
There must be some minimum temperature at which various things can burn. Given enough time at that temperature, it is the equivalent of just setting it on fire. Below that temperature, it is qualitatively different. You do not get bronze no matter how long you leave copper and tin at room temperature.
(Or maybe I am wrong there. Maybe a couple of molecules will move properly at room temperature over a few centures, so the whole mass becomes bronze in less than 3^^^3 seconds. I assume that anything physically possible will happen at some point in 3^^^3 seconds.)
Are there any SPECKS advocates who say we should pick two people tortured for 49.5 years rather than one for 50 years? If there is any degree of summation possible, 3^^^3 will get us there.
But, SPECKS can reply, there can be levels across with summation is not possible. If lasagna physically cannot burn at 75 degrees, even letting it "cook" for 33^^^^33 seconds, then it will never be as badly burned as one hour at 700 degrees.
"Did I say 75?" TORTURE replies. "I meant whatever the minimum possible is for lasagna to burn, plus 1/3^^3 degrees." SPECKS must grant victory in that case, but wins at 2/3^^3 degrees lower.
Which just returns the whole thing back to the primordial question-begging on either side, whether specks can ever sum to torture. If any number of beings needing to blink ever adds to 10 seconds of torture, TORTURE is in a very strong position, unless you are again arguing that 10 seconds of TORTURE is like 75 degrees, and there is some magic penny somewhere.
(Am I completely wrong? Aren't physics and chemistry full of magic pennies like escape velocities and temperatures needed for physical reactions?)
TORTURE must argue that yes, it is the sort of thing that adds. SPECKS must argue that it is like asking how many blades of grades you must add to get a battleship. "Mu."