I read Max Tegmark’s book “The Mathematical Universe” in which he describes his career in science in a autobiographical way while exploring cosmology and the wider story of how we came to believe the universe is how it is. In depth microwave-background radiation analysis, the mapping of it matching the models pretty well, validating cosmological inflation.

Cosmological Inflation is the theory that keeps on giving he reckons, not only in that it’s predictions keep on being met, but also in that inflation never stops. Not everywhere. One of it’s predictions is therefore that our ‘big bang’ isn’t the beginning of the universe, but merely the time when inflation stopped in our cosmic backwater, while it continues in the some other parts of the universe. An infinite number of parallel bubble universes growing over an infinitely increasing range of space.

And the multiverses don’t stop there. That’s just the level one multiverse. For he reckons not only does the evidence support a theory which suggests there exists space and matter beyond the edge of our visible universe, but also that there exist universes in which the ‘constants’ of nature vary wildly. The level 2 multiverse contains universes with all possible ranges of values of these constants, and inflation looks like it creates those too. The main argument for this seems to be anthropic reasoning on the finely tuned nature of those constants, alongside the fact Inflation allows it. Vary those constants only a little and the universe can’t support life. If the 100+ digit accuracy of their values isn’t an unbelievably astronomical coincidence then *all* the values they can take on exist, somewhere in that forever-inflating universe, and we must unsurprisingly find ourself in the space where they support life.

The multiverses keep on coming, with the Schroedinger equation from Quantum Physics describing the evolution or our universe’s wave-function. The Schroedinger equation works well, it’s accurate, it’s verified in experiments and allows us to build cool toys. But the Schroedinger equation has no term for wave-function collapse. Schroedinger’s kitten IS both alive and dead, in the level 3 multiverse. Observation, interaction, consciousness, *nothing* makes it collapse and each version of us *seeing* only one of the worlds is the expected result if you follow the equation to it’s logical conclusion.

So far pretty easy to agree with really. He keeps throwing around the word ‘infinite’ like it doesn’t bother him at all but those infinities do bother me. I don’t mind the universe being *unbounded* in size and growing for ever. That’s fine, coz you never get to ‘forever’, it never actually achieves infinite size. But literal infinities are uncomputable in the information-theory sense. A literally infinite universe causes many difficulties which a merely unbounded one doesn’t suffer. Have it as big as you like, but not impossibly big! But other than this I’m agreeing with him so far.

He hasn’t stopped yet though, the level 4 multiverse is still to come.

What is the deepest level of reality, he wonders? The Theory Of Everything? Well of course it would be an equation, or set of equations, which describe how everything in the multiverse acts. If these equations captures the entirety of the multiverse, then the multiverse has no properties other than those described by the equation. If it *did* have properties outside those described by the equation(s), the equation(s) wouldn’t be that Theory Of Everything. So at the bottom level, the universe is built out of mathematical objects he reckons.

He loses me a bit here. Sounds like classic model/territory confusion, no? That a universe can be modelled by math doesn’t mean it IS math. I mean math can model pretty much anything, it’s damned useful like that.

But he presses on, if a mathematical universe exists, then why would it just be *this* mathematical universe that exists? Why not all of them? Every possible mathematical structure existing in a platonic sense.

Now I *am* a bit of a mathematical Platonist. I think that the real numbers, for instance, aren’t a human invention but an actual thing that was there to be discovered. I *do* think that the integers ‘exist’ in some sense. And if the integers, the mandelbrot set, imaginary numbers etc. all ‘exist’ in that sense then why would the Theory Of Everything equations not ‘exist’ in the same sense? And just as it’s true that 1+1=2 however you write it, or even if you don’t, then the consequences of the Theory Of Everything will be true however you write it, or even if you don’t. And one of the consequences of the Theory Of Everything is of course self-aware observers observing the universe that the theory models. IE: People, seeing a universe like we see.

So maybe we *are* all living inside a mathematical structure. It does feel like that would hint at some answers to the ‘why is there something rather than nothing’ type questions, and if true it would indeed imply a level 4 multiverse, that being the platonic realm in which the counting numbers live.

He also addresses that uncomputability question here in the final chapters, conceding that literally infinite universes may be mathematically undefined, and that thus they may not be in the Level 4 multiverse. Our universe can be unbounded, but not infinite if this is true.

So am I convinced about these multiverses? Yeah, well, surely everyone agrees that there’s space and matter beyond our cosmological horizon, so level 1 is surely true. Inflation suggests Level 2 is possible, and the fine-tuning of the constants does indeed need explaining somehow, and Level 2 multiverse does that neatly. So a ‘probably’ to level 2 I guess. Level 3 I already believed before I started reading, the idea of waveform collapse is a joke, invented merely because physicists refused to take their own theorys seriously. It’s unphysical, undefined, and violates many otherwise well defined physical laws. If Quantum Mechanics is true, and it seems it is, then there are level-3 multiverses.

And level 4? Is the universe made out of math?

To that I can only say ‘maybe’, I’ve revised my estimate of the probability that that’s true upwards over the last few weeks reading this book anyway.

Good stuff. Tegmark is cool.