In the end Max Tegmark‘s Our Mathematical Universe: My Quest for the Ultimate Nature of Reality has proved to be something of a disappointment – somewhere along the way the science got lost and was replaced by a lot of metaphysical speculation.
I haven’t quite finished it yet – so I’ll do a fuller review when I do (and there were good bits too), but what I want to take issue with here is his case (or, perhaps more accurately, the cases he quotes with approval) against the idea that we live in some sort of great computer simulation.
I am not arguing in favour of such a view of our universe – but it certainly has its strengths – if you think computer power will keep on growing then it is pretty difficult, if we apply the basic “Copernican” principal that we are nothing special, to avoid the conclusion that we are in such a universe.
Tegmark uses two major arguments against this idea that I want to take issue with.
The first, I think, is not an argument against it at all – namely that we are more likely to be a simulation within a simulation if we accept this basic thought. Well, maybe – but this is completely untestable/falsifiable and so beyond science. (In contrast the basic idea that we are in a simulated universe is testable – for instance if we find that our universe has a “precision limit” that would be a strong pointer.)
The second is the degree of complexity of simulating a many worlds quantum multiverse. But, of course, the simulator does not need to actually “run” all those other quantum worlds at all – because it’s not a physical reality, merely a simulation. All it has to do is leave the signs (eg the traces of superposition we can detect) in our environment that such alternate universes exist, but once “decoherence” takes place those alternate universes go straight to your garbage collection routines. So too for more anything much beyond the solar system – all the simulation has to do is provide us with the signals – it doesn’t have to actually, for instance, “run” a supernova explosion in a distant galaxy.