Max Tegmark. Our Mathematical Universe: My Quest for the Utimate Nature of Reality. Allen Lane, 2014.

Back in his native Sweden, the then high school student Max Tegmark came within a whisker of being smashed to bits by a 40 ton lorry at a crossroads. This experience, quoted at the beginning of this book, is perhaps the nucleus around which this book is constructed, the inspiration for his visions of grand multiverses and their implications for matters of life and death. He presents these ideas interwoven with aspects of autobiography in the current work.

Linking cosmic inflation (link HERE) with quantum mechanics, Tegmark takes us through a hierarchy of multiverses, each one more bizarre than the other

Level 1: Distant regions of our own universe or inflation bubble, far beyond the observation horizon. This might be infinity large, or just be humungously large. If it is large enough it will eventually, at a mammoth distance, include other copies of earth and ourselves. If it is truly infinite, logically it will contain an infinite number of copies of each of us (as well as an infinite number of alternate earths, such as those in which the novelist David Copperfield wrote a novel about a character called Charles Dickens. Some regions will be very odd indeed, but they will all be governed by the same laws of physics.
Level 2: Separate bubble universes within the same inflation event, separated by inflationary space and therefore unreachable even by magic faster than light technologies. Here the fundamental laws of physics apply, but their practical expression might be different (the velocity of light might be much higher or lower, or there are more dimensions.
Level 3: The alternate histories envisaged by the 'many worlds' and similar interpretations of quantum mechanics
Level 4: Defined by Tegmark as the set of all mathematical structures, where almost anything that is logically possible occurs. Perhaps they can be thought of as completely separate inflation events, generating their own nests of Types1-3 multiverse.
I wonder if that could be the end, Tegmark argues that at the deepest level everything is mathematics, but that raises the question of whence came mathematics, or indeed logic. Is maths not perhaps just the way human beings look at the universe? Or if not, is there a Level V multiverse in which there are multiverses not based on mathematics (or anything remotely like anything human beings could begin to imagine).
The quantum version of multiverse, led Tegmark to speculate about quantum immortality. If you are sentenced to death, get yourself executed by an instantaneous vapouriser linked to a quantum process. You never experience your own death, because there will always be realities in which the process does not work, and they will eventually give up and set you free. Of course everyone else will know you died, and from now on all the people you interact with will be zombies, or so it would seem.
Quantum events can affect the whole of reality, perhaps the most dramatic example is to assume that it is quantum events which eventually lead cells to become cancerous. Then it was a quantum event that led to the cancer in the throat of Crown Prince Frederick of Germany and Prussia and hence to his death 99 days after having inheriting the throne. If he had lived, he might well have transformed Germany into a moderate constitutional monarchy, and thus no First World War, no Russian Revolution, no Hitler, no Holocaust, no Second World War, no nuclear weapons. Thus quantum events could generate completely separate histories.
In the end of the vision of infinities of infinity rather appal Tegmark and he starts to argue that there is no such thing as infinity (but that leads to the problem of what is the largest number). Perhaps he means nothing in the physical world is infinite (but then there must logically be a multiverse in which there are infinities).
Tegmark goes on to some of the really big questions, such as the nature of consciousness, which he suggests is “how information feels when it is processed in certain complex ways”. I wonder should we then equate information with mathematics and envisage that infomaths, and thence physics and consciousness, is assembled upwards from something a lot lot simpler. Perhaps there is no bottom line and metaphorically speaking it is turtles all the way down without end.
In the final section of the book Tegmark comes down to earth, argues that it is probable that human beings are the only technological species in the galaxy and that life itself may be rare, and therefore our world and humanity is of great cosmic significance and it is our duty to protect the planet from environmental degradation, cosmic accident and nuclear war.
This is an interesting and challenging book, but by no means an easy read, and the sections on the mathematic basis of reality is particularly hard going to the non-specialist. More information can be found on Tegmark’s own website http://space.mit.edu/home/tegmark/mathematical.html -- Peter Rogerson

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