Infinities of Infinities

Her Majesty's Astronomer, Sir Martin Rees, wrote this article (link), “In the Matrix,” in May of 2003. However, the “matrix” Rees is talking about makes the Matrix of Neo-fame seem, well, rather simplistic.  He says that the equations which are the best candidates to explain the laws of our universe now appear to have more than one solution; in fact, they might have an infinite number of solutions – an infinite number of universes. And, each of those universes are likely to be infinite themselves – an infinity of infinities. Further, you could add more levels of  infinities (called Transfinite Numbers): “Indeed, there’s perhaps even a higher hierarchy of infinities: in addition to our universe being infinite, and there being an infinite number of possible laws of nature, we may want to incorporate the so-called many worlds theory of quantum mechanics.” (p. 2)

The quote that best describes the implications of infinity is the one about the monkeys writing Shakespeare (this one from Hitchhiker’s Guide to the Galaxy): “There’s an infinite number of monkeys outside who want to talk to us about this script for Hamlet they’ve worked out." Well, this theory about a transfinite number of universes produces this similar but more startling result: since there so many universes, then other universes would, by sheer statistics, have advanced life and those life-forms in some place in one of those infinitely infinite universes would be vastly more technologically advanced than we are, so they could have super-computers capable of creating infinite simulations of universes (i.e., infinity spawns infinity), and our universe, and us in it, could be one of these simulations. Rees states this idea: “…some universes will have immense potentiality for complexity… in some of those universes there will be the potential to simulate parts of themselves, and you may get sort of infinite regress, so we don’t know where reality stops and where the minds and ideas take over.” (p. 3) It’s like Matrix, but infinitely more complicated.