Actually, I think he's abusing the word infinite by assuming that it's all inclusive.
From his article, here is how he calculates the odds for someone's twin, not only existing in a parallel Hubble volume, but appearing in an infinite number of them.
One way to do the calculation is to ask how many protons could be packed into a Hubble volume at that temperature. The answer is 10^118 protons. Each of those particles may or may not, in fact, be present, which makes for 2 to the 10^118 possible arrangements of protons. A box containing that many Hubble volumes exhausts all the possibilities. If you round off the numbers, such a box is about 10 to the 10^118 meters across. Beyond that box, universes--including ours--must repeat. Roughly the same number could be derived by using thermodynamic or quantum-gravitational estimates of the total information content of the universe.This shortcut may work for the early universe, but I don't see how it could work for a time when humans have already evolved. It looks like he's incorrectly assuming that a human can appear anywhere in the Hubble volume, but instead it must appear on the surface of a habitable planet. Not only that, but it must be on a planet where the quantum states of my parents appeared, and their parents, and so on all the way back to the primordial ooze. And then he goes on to make the following conclusion:
Your nearest doppelgänger is most likely to be much closer than these numbers suggest, given the processes of planet formation and biological evolution that tip the odds in your favor.It seems to me that such required physical processes would greatly decrease the odds of my twin appearing in another Hubble volume.
(Some of you may object to the lack of electrons and neutrons. We can assume that for every proton, an electron is "along for the ride", and combine each proton with its electron to form a neutron, wherever the nuclear equation of state demands it. Alles klar, Herr Kommisar?)
As it turns out, however, not every IHV is physically allowed. In those 210^118 IHVs, almost all of them will be a uniformly dense mass of nuclear matter. In the reality, we can disregard them.
In the tiny subset of IHVs where the density is as low as we observe it to be in our Hubble volume, which we'll denote "Low-density Hubble Volumes" (LHVs), almost all of those will be a rarefied gas of protons. These we can disregard also, because in the real world gravity will collapse the gas into condensed objects.
In the tiny subset of LHVs where the matter is collapsed into dense objects, which we will call "Condensed Hubble Volumes" (CHVs), almost all of them will be unvariegated piles of homogeneous crap. In the real world, the condensed matter will be formed into galaxies, stars and planets, so we can disregard almost all CHVs. We'll call this subset "Proper Hubble Volumes" (PHVs).
To recap: the number of IHVs >>> # of LHVs >>> # of CHVs >>> # PHVs (where ">>>" means "gigantically greater than"). Tegmark's distance calculation reaches past all the IHVs, but that's a gigantic overestimate, because in reality you'll only find PHVs out there, and the PHVs happen to be the ones that contain the right conditions for making guys like you and planets like ours. Nature has already done almost all of the winnowing out of that ensemble of 210^118 possibilities. All of the absurd ones are gone, so you don't have to "reach past" them.