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Our mathematical universeMax TegmarkWhy I looked at this bookI've heard about Tegmark's ideas that, at a fundamental level, the universe can be thought of as a mathematical system. It's an intriguing idea, but it isn't easy to see exactly what it is supposed to mean. Hence I decided I needed to read this book.First impressionsThe book starts off by looking at some of the fundamental questions we ask ourselves. Where does everything come from? What is reality, and is there more to it than meets the eye? Physics is telling us that the answer to the second questions is Yes! Should we be surprised about this? Tegmark writes in a lively, fast moving style, and it promises to be an entertaining read.Main reviewThe book continues by going through the list of questions that Tegmark has posed for himself. Soon we're into modern cosmology, looking at where different structures in our universe came from. Then there's the microwave background, and Tegmark explains how studying this has greatly helped us to understand the beginning of the universe. This leads on to cosmological inflation, which implies our universe is much bigger than what we can see. This means that there will be many parts very similar to the one we live in, and so many near copies of you and me. This is the Level 1 multiverse, and for the rest of the book Tegmark describes the different multiverse levels he has identified. Level 2 is based on eternal inflation  the idea of a constantly inflating system, from which universes like ours are continually being created. The level 3 multiverse is the well know 'Many worlds' of quantum theory. Eventually we get on to Level 4, the main idea of the book. This says that universes don't have to be based on the mathematical structures underlying our universe, other mathematical structures will do just as well.My first objection to this was what I call the 'dash for infinity', that is adopting infinite mathematical systems as descriptions of physics just for the sake of it when there doesn't seem to be any physical justification for it. Here I was in for a bit of surprise: Tegmark doesn't trust infinities either, and explains that his ideas are based on finite systems. There's another big problem I see with Tegmark's idea though. He shows that anything can be encoded as a mathematical systems, and as I see it this means that 'anything goes'. There exists a universe consisting just of the events of Alice in Wonderland. If the universe is based on mathematics it is the symmetry, and indeed the beauty of the mathematical system which is important. I felt that Tegmark didn't properly address this issue, although it does seem to get some attention is his somewhat more technical paper: The Mathematical Universe In the last part of the book Tegmark moves away from his ideas on what threats are facing humanity. He identifies unfriendly A.I. singularity as a leading one. He estimates the probability of this at about 1% and suggests that we should therefore spend about 1% of GDP on preparing for the possibility. I'm not convinced about this reasoning  it seems a bit too much like Pascal's wager. In fact I felt the last chapter was rather out of place, yes it discusses important issues, but it squeezes them in to one chapter when they really need a whole book.

