I don't believe either of these arguments, and the reason can be summed up in two words: Quantum Mechanics.

To answer Bostrom: If one were to simulate a universe, Quantum Mechanics would be a very bizarre foundation to choose. It is notoriously difficult to simulate and does not add anything essential (that I am aware of) to a simulation. Instead one would just write a normal program, as done for video games or cellular automata (e.g. the "Game of Life"). Hence, our universe does not (so far) look at all like a generic instance of computer simulation.

And to answer Tegmark: Mathematical objects are clear-cut and well-defined. If we lived in a generic math object, then we should not experience any problems with definitions or consistency. However, the so-called "measurement problem" of Quantum Mechanics is exactly such a problem, as I described in my earlier post "The Problem with Quantum Mechanics" (Feb. 2010). Indeed, if the current framework of QM proves to be fundamental, then our universe exists at the very edge of what can be described by mathematics. It cannot be axiomatized (because there is no way to fully define what a measurement is) and it is definitely not the sort of universe one would expect to see if universes were chosen at random from the full set of math objects.

In my earlier post I conclude this way: "For some reason, our universe chooses to exist at the very boundary of conceivability. Perhaps it is a joke of some kind, or perhaps for some reason this is the only kind of existence that is really possible." The Tegmarkian or Bostromian hypotheses seem, at first, equally abstruse or difficult to conceive, but in fact, in comparison to the actual universe we observe, both of these possibilities are just

*too simple*.