Max Tegmark |

*one of my favourite posts from two years ago...*

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Our Mathematical Universe by physicist Max Tegmark is a popular science book in which he unpacks his theory of the level 1,2,3 and 4 multiverses and then in the last third explains his theory of the mathematical universe. I understood the multiverse idea (the first 3 multiverses anyway) but I didn't really get his concept of the mathematical universe (he's either saying that all the laws of physics depend upon fundamental mathematical concepts which isn't very interesting, or he's saying that everything in the universe (suns, planets, you, me, our conscious minds,) is mathematics itself, i.e. we are living in a platonic universe of numbers that only thinks it's a physical universe - this is a very interesting concept indeed but seems completely crazy to me.) I don't have the competence to judge the last third of the book but I do want to talk about the multiverse idea which is fascinating.

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The level 1 multiverse is very easy to understand. All Tegmark is saying here is that space is infinite and beyond the visible light boundary of our universe there must be other shit out there. Indeed there must be entire universes out there. This is the cool part: since space is infinite and the different way atoms in a universe can assemble themselves is huge, but, crucially, finite, then there must, logically, be universes out there with an exact replica of you reading this and me typing this. Indeed there are an infinite number of universes out there with exact replicas of you and me, and an infinite number of universes where we are slightly different, or you became President or we both swam the Hellespont or I ended up playing rugby for Ireland (I still believe this cd actually happen). Infinity is a very powerful concept and creates some surprising results. Like I say, cool stuff.

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The level 2 multiverse is also easy to comprehend. In the expansion phase of our universe just after the Big Bang a 'baby universe' was formed that became our universe, an infinite number of these formed, some with completely different laws of physics than our own, but sentient entities like you and me could only exist in one like ours, the Goldilocks one where gravity, Plancks constant, the electro-magnetic force etc. balance perfectly. But again because an infinite number of these multiverses formed there are other yous and mes out there in slightly different physical realities.

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The level 3 multiverse is a trickier beast to grasp. Tegmark and what he claims are "an increasing number of quantum physicists" are beginning to reject the Copenhagen interpretation of quantum physics that has been the dominant interpretation of quantum physics since the 1920's. If you remember the infamous "double slit experiment" from high school you'll recall that when an electron is fired through a piece of metal with a double slit in it sometimes the election acts like a wave and sometimes like a particle. No understands why this is so and it is deeply mysterious to this day. The Copenhagen interpretation basically says that the electron both goes through one slit and does not go through the same slit at the same time. When the election is "observed" by a conscious entity or by a machine (like a camera) its probability wave collapses and it picks one slit to travel down. This has lead to the Schrodingers Cat paradox wherein a cat is both dead and alive at the same time until it has been "observed" - a thought experiment meant to ridicule the Copenhagen Interpretation itself, which I think it did. One alternative to the Copenhagen Interpretation is the Many Worlds Theory. Here there is no need for dead-alive cats, because when the cat experiment is done 2 worlds are created, one in which the cat is dead and another in which it is alive. When you open the cat's box you don't collapse the cat's probability wave you just find out which universe you are in. Similarly when the quantum double slit experiment is carried out, many worlds are created full of scientists carrying out the same experiment. This, some people say, (smart people like David Deutsch) is how quantum computers work - an infinite number of computers exist in an infinite number of many worlds. I know this sounds crazy but I found this part of Tegmark's book very convincing and I now think that the Many Worlds interpretation of quantum physics invented by Hugh Everett is more logical than the Copenhagen Interpretation. Which would mean, if Tegmark, Everett, Deutsch etc. are correct, there is an infinite number of yous and mes existing in what is called Hilbert Space who can interact with one another at a quantum level. If you want to interact with another you in Hilbert space you can do so, here.

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The level 4 multiverse is the multiverse of Platonic mathematics that I didn't really understand. You can read Tegmark's short explanation of it on his MIT website here. Like I say, I didn't follow this in the book or on the website.

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I would like to offer an an alternate level 4 multiverse that exists temporally rather than physically. Consider Paul Steinhardt and Neil Turok's idea that the universe goes through an infinite number of big bangs, expansions, heat deaths, brane collapses and big bangs...(This is not mentioned in Tegmark's book but I just thought I'd throw it in here. If this is true then not only have I typed this sentence before and you've read it before, but we've all done this infinitely many times in the past, which I for one find depressing. (As did Nietzsche when he thought about the similar notion of eternal recurrence.)) Another possible Level 4 or maybe Level 5 multiverse is Nick Bostrom's idea that we are probably all living in a simulated universe anyway, which he proves from 2 assumptions and then a statistical argument.

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Scott Aaronson |

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Max Tegmark's book really gave me food for thought. I didn't get all of it, but I enjoyed reading it and I would recommend it for any of you who have ever, Douglas Adams fashion, wondered about the big questions of life, the universe and everything. It got good reviews in the Guardian and The New York Times among many other papers. The best take down I've read of Tegmark's thesis was done by Scott Aaronson on his vastly entertaining and informative computational science blog Shtetl-Optimized.(Tegmark himself gets sucked into the really rather geekily clever comment thread.)