The Hidden Reality_ Parallel Universes and the Deep Laws of the Cosmos - Brian Greene [175]
*Ironically, an explanation for why magnetic monopoles have not been found (even though they are predicted by many approaches to unified theories) is that their population was diluted by the rapid expansion of space that takes place in inflationary cosmology. The suggestion now being made is that magnetic monopoles may themselves play a role in initiating future inflationary episodes.
*Another loophole arises from an incarnation of the measure problem from Chapter 7. If the number of real (nonvirtual) universes is infinite (if we’re part of, say, the Quilted Multiverse), then there will be an infinite collection of worlds like ours in which descendants run simulations, yielding an infinite number of simulated worlds. Even though it would still seem that the number of simulated worlds would vastly outnumber the real ones, we saw in Chapter 7 that comparing infinities is a treacherous business.
*A theory that allows for only a finite number of distinct states within a finite spatial volume (in accord, for example, with the entropy bounds discussed in the previous chapter) can still involve continuous quantities as part of its mathematical formalism. This is the case, for instance, with quantum mechanics: the probability wave’s value can vary continuously even when only finitely many different outcomes are possible.
*Borges allows for books with all possible character strings, without regard to meaning.
*When we discussed the Quilted Multiverse (Chapter 2), I stressed that quantum physics assures us that in any finite region of space there are only finitely many different ways in which matter can arrange itself. Nevertheless, the mathematical formalism of quantum mechanics involves features that are continuous and that hence can assume infinitely many values. These features are things we can’t directly observe (such as the height of a probability wave at a given point); it’s with respect to the distinct results that measurements can acquire that there are only finitely many possibilities.
*Max Tegmark has noted that the entirety of a simulation, run from start to finish, is itself a collection of mathematical relations. Thus, if one believes that all mathematics is real, so is this collection. In turn, from this perspective there’s no need to actually run any computer simulations since the mathematical relations each would produce are already real. Also, note that the focus on evolving a simulation forward in time, however intuitive, is overly restrictive. The computability of a universe should be evaluated by examining the computability of the mathematical relations that define its entire history, whether or not these relations describe the unfolding of the simulation through time.
CHAPTER 11
The Limits of Inquiry
Multiverses and the Future
Isaac Newton cracked the scientific enterprise wide open. He discovered that a few mathematical equations could describe the way things move, both here on earth and up in space. Considering the power and simplicity of his results, one could easily have imagined that Newton’s equations reflected eternal truths etched into the bedrock of the cosmos. But Newton himself didn’t think so. He believed that the universe was far more rich and mysterious than his laws implied; later in life he famously reflected, “I do not know what I may appear to the world, but to myself I seem to have only been a boy playing on the seashore, diverting myself in now and then finding a smoother pebble or prettier shell than