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I did this calculation, which was relatively simple. You take, first of all, the observed density of matter in the universe, which is roughly one hydrogen atom per cubic meter. The universe is about thirteen billion years old, and using the fact that there are pi times 10[7] (10 to the 7) seconds in a year, you can calculate the total energy that's available in the whole universe. Remembering that there's a certain amount of energy, you then divide by Planck's Constant — which tells you how many ops per second can be performed — and multiply by the age of the universe, and you get the total number of elementary logical operations that could have been performed since the universe began. You get a number that's around 10[120] (10 to the 120). It's a little bigger — 10[122] (10 to the 122) or something like that — but within astrophysical units, where if you're within a factor of one hundred, you feel that you're okay; The other way you can calculate it is by calculating how it progresses as time goes on. The universe has evolved up to now, but how long could it go? One way to figure this out is to take the phenomenological observation of how much energy there is, but another is to assume, in a Guthian fashion, that the universe is at its critical density. Then there's a simple formula for the critical density of the universe in terms of its age; G, the gravitational constant; and the speed of light. You plug that into this formula, assuming the universe is at critical density, and you find that the total number of ops that could have been performed in the universe over time (T) since the universe began is actually the age of the universe divided by the Planck scale — the time at which quantum gravity becomes important — quantity squared. That is, it's the age of the universe squared, divided by the Planck length, quantity squared. This is really just taking the energy divided by h-bar, and plugging in a formula for the critical density, and that's the answer you get. This is just a big number. It's reminiscent of other famous big numbers that are bandied about by numerologists. These large numbers are, of course, associated with all sorts of terrible crank science. For instance, there's the famous Eddington Dirac number, which is 10[40] (10 to the 40). It's the ratio between the size of the universe and the classical size of the electron, and also the ratio between the electromagnetic force of, say, the hydrogen atom, and the gravitational force on the hydrogen atom. Dirac went down the garden path to try to make a theory in which this large number had to be what it was. The number that I've come up with is suspiciously reminiscent of (10[40])[3] (10 to the 40, quantity cubed). This number, 10[120], (10 to the 120) is normally regarded as a coincidence, but in fact it's not a coincidence that the number of ops that could have been performed since the universe began is this number cubed, because it actually turns out to be the first one squared times the other one. So whether these two numbers are the same could be a coincidence, but the fact that this one is equal to them cubed is not. Having calculated the number of elementary logical operations that could have been performed since the universe began, I went and calculated the number of bits, which is a similar, standard sort of calculation. Say that we took all of this beautiful matter around us on lovely Eastover Farm, and vaporized it into a fireball of radiation. This would be the maximum entropy state, and would enable it to store the largest possible amount of information. You can easily calculate how many bits could be stored by the amount of matter that we have in the universe right now, and the answer turns out to be 10[90] (10 to the 90). This is necessary, just by standard cosmological calculations — it's (10[120])[3/4] (10 to the 120, quantity to the 3/4 power). We can store 10[90] (10 to the 90) bits in matter, and if one believes in somewhat speculative theories about quantum gravity such as holography — in which the amount of information that can be stored in a volume is bounded by the area of the volume divided by the Planck Scale squared — and if you assume that somehow information can be stored mysteriously on unknown gravitational degrees of freedom, then again you get 10[120] (10 to the 120). This is because, of course, the age of the universe squared divided by the Planck length squared is equal to the size of the universe squared divided by the Planck length. So the age of the universe squared, divided by the Planck time squared is equal to the size of the universe divided by the Planck length, quantity squared. So we can do 10[120] (10 to the 120) ops on 10[90] (10 to the 90) bits. |