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lavalamp comments on The Apparent Reality of Physics - Less Wrong
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I was going to say, it {can be calculated}-exists, but it does not {is extant in the territory}-exist. It certainly has a value, but we will never know what it is. No concrete instance of that information will ever be formed, at least not in this universe. (Barring new phyisics allowing vastly more computation!)
Thanks, I think that's the clearest thing you've said so far.
I think my own concept of "exist" has an implicit parameter of "in the universe" or "in the territory", so it breaks down when applied to the uni/multiverse itself (what could the multiverse possibly exist in?). Much like "what was before the big bang" is not actually a meaningful question because "before" is a time-ish word and whatever it is that we call time didn't exist before the big bang.
But then, how do you determine whether information exists-in-the-universe at all? Does the number 2 exist-in-the-universe? (I can pick up 2 pebbles, so I'm guessing 'yes'.) Does the number 3^^^3 exist-in-the-universe? Does the number N = total count of particles in the universe exist-in-the-universe? (I'm guessing 'yes', because it's represented by the universe.) Does N+1 exist-in-the-universe? (After all, I can consider {particles in the universe} union {{particles in the universe}}, with cardinality N+1) If you allow encodings other than unary, let N = largest number which can be represented using all the particles in the universe. But I can coherently talk about N+1, because I don't need to know the value of a number to do arithmetic on it (if N is even, then N+1 is odd, even though I can't represent the value of N+1). Does the set of natural numbers exist-in-the-universe? If so, I can induct - and therefore, by induction on induction itself, I claim I can perform transfinite induction (aka 'scary dots') in which case the first uncountable ordinal exists-in-the-universe, which is something I'd quite like to conclude.
So where does it stop being a heap?