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on 4 September 2016
This is a book of three parts. The first part focuses on cosmology and the modelling of our world and universe at a macroscopic level. The second part focuses on quantum theory and the modelling of our world a microscopic level. The third part focuses on reconciling the fundamental differences between quantum mechanics and relativity and the authors Mathematical Universe Hypothesis (MUH).

The first two parts are well written and very engaging. They give a good historical overview of the developments in thoughts, mathematics and physics leading up to and including relativity and quantum mechanics. The explanations are accessible and I found a good balance between lay descriptions and more technical detail. Tegmark interweaves scientific explanation with his own experience and career. There are a few autobiographical anecdotes, but these are short and do not interrupt the flow of the discussion.

There is an ulterior purpose to the first two parts – they set the scene for the third part in three important ways:
(i) They establish the great success of mathematics as the language of physics and the experimental confirmation that this approach has achieved.
(ii) The multiverse is a credible prediction of the underlying mathematics. As Tegmark states the multiverse is not a theory, it is an outcome of other theories.
(iii) Scientists whose theories are initially dismissed by the scientific establishment are often later rehabilitated. Tegmark makes no secret of his admiration for such people, most notably Hugh Everett, the originator of the many-worlds view of quantum wave functions. From a few searches, it seems that Tegmark's MUH falls into the category of dismissed by the establishment.

There is a strong emphasis on multiverse models in this book. At the cosmological level there are two possible versions. A Level I multiverse contains universes with the same fundamental physics as ours but different physical constants. Level II has universes with different physics too. At the quantum level we have the Level III multiverse which is essentially Everett's non collapse of the wave-function creating bifurcations – Schrödinger’s cat remains both dead and alive, just in different universes. The attraction of the Everett's multiverse solution is that it removes the dependency of the wave function collapse on observation, or the observer moment. Tegmark argues that all three multiverses contain an infinite number of universes although later he argues that the universe is finite – more on that later.

So, to the third part. Tegmark's basic premise is that the fundamental building block of the universe is mathematical structure. Essentially the physics that we perceive and investigate is the instantiation of mathematical structure. Rather than mathematics being the language we use to describe physics. As Tegmark states, mathematical structures are discovered not invented. The MUH is extended to allow all possible mathematical structures to be universes - this is his Level IV multiverse.

Part three of the book does not have the consistency of description and argumentation that the first two parts have – this may be because it is a new theory which is being developed and added to. It may be that it is an area that the mainstream has not yet adopted and therefore does have the self-consistency that consensus demands. I'm sure Tegmark would like to think of himself as another Everett. I certainly found it disjointed and got the impression that Tegmark was picking off criticisms of his approach. However, the third part did raise some interesting points.

Tegmark makes much of the deterministic nature of Schrödinger’s equation. So what we perceive as randomness is just the existence of almost identical universes within the multiverse. I was very much struck by the similarities with Laplace's 1814 demon which is the deterministic view that if someone (the Demon) knows the precise location and momentum of every atom in the universe, their past and future values for any given time are entailed; they can be calculated from the laws of classical mechanics. Heisenberg uncertainty tells us this is impossible. However, the infinite multiverse would suggest that all possible futures exist and the problem is no longer one of prediction but of knowing the universe to which we belong. Indeed, Tegmark argues that the initial conditions needed for such a calculation are simply a matter of knowing the universe in which we sit since all possible initial conditions exist within the multiverse. I found this, and other arguments, a little semantic – we still need a means of identifying the universe to which we belong.

This leads onto a discussion about external reality and what we perceive as reality which is mediated by our senses. There is some discussion about consciousness but Tegmark largely steers clear of the reductionist view that his MUH must surely entail. To quote Sheldon Cooper from the Big Bang Theory, "Excuse me, but a grand unified theory, insofar as it explains everything, will ipso facto explain neurobiology." I don’t see how the MUH hypothesis can admit anything but consciousness is a mathematical structure – albeit a highly complicated one. Our emotions would just be the firing of different neurons in response to external stimuli. Moreover, since everything that can happen in a Level IV multiverse does happen, there would be no free-will. Perhaps, more precisely, free-will would be an illusion because we cannot access the other universes where we make a different choice.

The explanation MUH almost immediately reminded of Plato's theory of Forms that non-physical forms represent the most accurate reality. Tegmark does reference Plato's realm of ideas (i.e. forms) but does not make much of it. Of course, in Plato's theory, the forms had substance and needed a Heaven as their repository. To paraphrase Laplace, Tegmark has no need to bring God into his hypothesis. However, he says little, if anything, on how the mathematical structures are held independently of their physical instantiation. He may not need a heaven or a god, but he needs something.

Related to Tegmark's view that the MUH makes each universe within a multiverse predictable, he discusses whether the each universe is actually infinite or finite. To me, if each universe has a finite number of particles each of which can undertake a finite number of quantum events then the multiverse must contain a finite number of universes. But mathematical structures are largely continuous. There are infinitely many real numbers between 1 and 2. The problem this creates is that if the MUH really leads to infinite precision numbers then there is no means of storing them in a universe with a finite number of particles – this was the initial counter to Laplace's demon before Heisenberg uncertainty came along. Tegmark quotes John Wheeler's assertion that quantum effects make any digits after the 35th decimal place meaningless. Tegmark quotes the way we do simulations as discrete representations of space as an example of granularity. However, I view this as an approximation to a continuous mathematical structure. To really make this case Tegmark needs a mathematical structure that is fundamentally discontinuous in its own right. In all of the discussion over infinite vs finite, I was surprised that Tegmark did not discuss the two transcendental numbers that are so central to the physical world: π and e. He does not even discuss whether π and e are truly fundamental. The multiverse is used as an answer to why the physical constants of nature are so finely tuned to lead to life. But surely, Tegmark's Level IV multiverse must allow the same considerations for mathematical constants.

I certainly found much of the third part interesting and thought provoking, but ultimately there is no evidential basis for the Level IV multiverse and, as yet, no testable predictions. For me, question of whether mathematics is a hugely successful way of modelling the physical world; or, a fundamental structure that constrains the physical world was unanswered.

The very last sections of the book stray into social and ethical commentary about topics as diverse as nuclear Armageddon, the quality of scientific debate in society and whether we are alone in the universe. These felt completely out of place and just express the author's views. I found myself skim reading them so I could get to the end of the book. I was actually struck by the inconsistency of this section with the MUH. Surely, in Tegmark's view, ethics are just a property of the mathematical structure we inhabit. In fact, the Level IV multiverse would contain all possible ethical frameworks and so one is no more valid that another. The problem is not of knowing which is the correct framework, it is knowing which universe we inhabit. I should emphasise that Tegmark does not make this claim, it is just what I see as the logical conclusion of his argument. I actually see this as a purely semantic difference: not knowing the correct ethical framework and not knowing which universe we inhabit are equivalent.

I'm rating the book a 4 based on the first two parts which were very engaging and informative. The third part had some interesting ideas but lacked consistency.
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on 21 August 2016
This stimulating book addresses two fundamental ontological questions "Why is the world as such but not otherwise?" "Why does the world exist at all?"
The fact that the Multiverse theory, which is purely speculative and neither verifiable nor falsifiable, still survives and not dismissed within the scientific community is a good start. Tegmark in this extraordinary book amplifies the Multiverse theory.
I think William of Ockham (and the infinite number of copies of himself in the Multiverse) would have approved because far from complicating things & multiplying entities the idea of Multiverse simplifies ontology to "Whatever is possible does actually exist" and so removes the problem of contingency. We nolonger have to ask the question "Why is the world as such but not otherwise?"
But Multiverse is not Tegmark's original idea. What is breathtakingly original is that Tegmark takes a huge leap and says "Reality IS a mathematical structure". Again William of Ockham would have approved because, if true, this reduces the duality of object and its description to a single identity. This is truly elegant. And removes the question of "Why does our material world exist at all? Who created it?" Because now the material world is reduced - from stars to rock to atoms to subatomic particles - to a mathematical structure which, being a mathematical structure and therefore non-material, and from the Platonist point of view, is neither created nor can be destroyed. It simply IS.
Furthermore, Tegmark's Multiverse cannot just be the totality of permutation of a number of objects, for whatever the number of objects the question of contingency remains "Why these objects but not others?" Tegmark's Multiverse must therefore be relational, not quantitative.
Indeed, Tegmark's use of the concept of infinity would have been problematic if he meant quantity. But let infinity be achieved within, say, the decimal expansion of 'pi', then one segment of 'pi' will encode & realize all the properties of one world, another segment will encode & realize all the properties of another world, and so on.
In this non-material and relational world, reality as well as the description of reality coincide, which is Tegmark's core idea.
And because the properties of mathematical relations are unchangeable, contingency has been removed.
There remains the problem of consciousness. What I don't quite follow in the book is when Tegmark introduces, within the overall mathematical structure, a self-aware substructure that has subjective perceptions. He does this in order to account for consciousness & self-awareness.
For me the overall thesis stands. I read this extraordinary book not as a science book as such but one that has speculatively removed the problems of contingency and the necessity of God. It uses scientific ideas to address philosophical problems.
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on 29 September 2015
This is a very interesting and thought-provoking book.
I have always thought the Everitt parallel-universe theory mad, and still do. Peter Schor's factorization algorithm
is often regarded as using the results of calculations done in parallel universes; but I remember no such idea in
Schor's paper. Different kinds of mathematics can make the same predictions about quantum theory. Do they
all correspond to reality?
And why should I believe our Max Tegmark when his counterparts in parallel universes are saying the opposite?
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on 26 March 2016
If you like the concept of a multiverse this has jam on it. Personally I find the concept difficult. It would be hard to disprove the theory. I stopped reading at a thought experiment of standing in front of a randomly fired gun: do you stop existing or move into another universe where the bullet just missed you? Schrodinger's cat++. (Maybe by then I had missed the point.)
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on 27 October 2014
An absolutely fantastic piece of writing. The first 2/3 or so focus on established theories and slightly more controversial theories, including multiverse levels I-IV. The last 1/3 focusses on his new idea for a mathematical universe.

It is not difficult to read and he explains concepts thoroughly. In most places (whilst I don't want to spoil) Tegmark's arguments follow logically and his idea is certainly very, very interesting indeed.

I've enjoyed reading this book more than any other this year and was compelled to share my 5* review - as I so rarely am..!

Enjoy a new angle of looking at cosmology!
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on 6 March 2014
If you can believe that in millions of universes everyone in those universes has superglued a banana to their head and have rushed outside shouting "OINK OINK BOINK" whilst in a equal number of different universes they have rushed outside, also suitably attired with banana, but shouting "OINK OINK HOINK" then multiverse theory is for you. My criticism is of multiverses as per Everett et al, not the possibility of areas of space time outside our own.

It seems to me that multiverses, like God, have been invented to answer two so called fundamental questions - of Origin, why does something rather than nothing exist and of tuning, why are the constants of reality just right for life. Multiverses reduce Origin to a commonplace happening at all places and times, fine tuning is explained away by positing there is a infinite variety of tuning and it is merely contingent we live in a Universe with this tuning. You could in fact say pseudo scientists need to invent multiverses in order to stop God jumping into a perceived logical hole.
Both God and multiverses involve infinite regress, a infinity of multiverses and the who created God? God2? regress.

There is however a much simpler solution involving no regress whatever. If one keenly applies Ockhams razor then one just accepts Reality as a given, THE given in fact. This given is the object of scientific investigation. There is no why. Science and maths can describe how but "why?" is not a meaningful scientific question. It is an expression of most of humankinds psychological need to feel there is a "higher meaning" to life.

As for Mr T's Vision of ultimate reality as mathematical !! Well, it is neither scientific or philosophically sound.

To say reality IS mathematical is none sense. There is no formal identity. Dr Johnson, in a similar context, never kicked an equation. (Although interestingly Bishop B was claiming the Real was virtual whilst Mr T is claiming the virtual is real ). Maths is a human activity not something Reality does.

To say that if something can be described mathematically then it itself is mathematical is meaningless, it is a simple conceptual category error, a nonsensical pseudo tautology.If something is described by its colour as green it does not mean its nature is "greenness".

Being mathematical is not an attribute of Reality. Attributes of Reality are atoms, forces, stars etc.
Even "being able to be modelled mathematically" is not a attribute of Reality, it is a function of mathematics.

If one is speaking in a ordinary day to day discourse it is however perfectly feasible to say, as a METAPHOR or simile, that reality is mathematical. E.g both reality and maths are ordered having constituent parts which follow rules, elementary particles are equivalent to numbers, fundamental forces are equivalent to axioms etc. But that usage is purely metaphorical and cannot be used in a scientific discourse as a basis for theory building. In a similar way in day to day discourse it can be used as a reasonable circumlocution For the long winded "reality can be described mathematically".

The Universe exhibits observable order. ( the hows whys and degrees of order etc are not pertinent to the question at hand). The point is the universe exhibits order, what kind of order is irrelevant to the current question. It is also pertinent that there are very few ways of a system being ordered compared to a infinity of ways of it being disordered, entropy. There are a limited number of models needed to model reality, not a infinite number.

Mathematics, devised by sentient intelligences,uses axioms and rules to elaborate models/systems. Mathematics has a infinite toolset to construct these models so it can in theory, as Bertrand Russell has mathematically (sic) shown, MODEL ANY AND EVERY ORDERLY SYSTEM.

So it is no surprise that it can model reality. If reality was ordered in a different way mathematics would still be able to model it. ALL orderly systems conform to mathmatically modelling - in fact that could be a definition of "order". You cannot thus visualise a orderly system/universe which does not conform to mathematical modeling.

So The effectiveness of maths in modelling reality is not a random accident, nor does it imply in any way that what is being described mathematically must be itself be mathematical ( whatever that is supposed to mean), nor does it imply anything suggestive of any more deeper "correlation" or hidden truths about the Universe and Maths etc. It is simply a example of the great explanatory power of maths. It is what Maths , a human construct, does.

I have a accurate map of Hackney, when I go to Hackney I am not amazed the topography of Hackney agrees with the map, nor do I think Hackney has a mapematical nature, nor do I think is is mere luck Hackney is mappable, nor do I think that if the topography of Hackney was different it would be unmappable, nor do I think there is any hidden correlation between map making and the topography of Hackney, nor do I think Hackney is in itself a map, nor do I think "out there" in different mapverses there are infinite slightly different maps of this Hackney and it is just because i am a human in this mapverse that I happen to have the correct map

Mr T's "theory" of MUH is not any kind of science it is just a example of circular speculative thinking exactly akin to medieval speculations as to how many angels can dance on the head of a pin.

Personally as I do not concede it is a scientific theory I do not think it can be proved or disproved. However if I remember correctly, as i have dekindled the book in disgust, Mr T in a token Popperian gesture posits that his theory can be falsified if it can be shown that there are aspects of reality that cannot be modelled mathematically.

Well, as far as I am aware, there are chaotic systems that you could argue Maths cannot model effectively, if at all e.g., in describing turbulent flows or the laminar to turbulent transition from first principles and the chaotic nature of fluid dynamics in general. Also I know of no mathematical modelling of consciousness, the appreciation of a Bach fugue, the experience of a sunset etc. Thus according to Mr T's own posited test of his theory it is not valid.

Finally, if we were to convene the court of poetic justice and summon a Mr Godol as witness he would testify that any mathematical system , in a formal logical sense, is incomplete and cannot fully and adequately prove or describe ITSELF (sic). This, aside from showing Mr T's falsebility criteria is in fact invalid and thus again showing his theory not to be scientific, also amusingly implies that if Reality itself was a mathematical structure then Mr T would never be able to fully prove it.

My cat, Salem, in one of those infinite multiverses is at this moment exclaiming, " Hah! Since it cannot be proved to be true, and Mr T has not proved it to be true, then it must be true." Such is the logic of multiverses.
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on 19 April 2015
Tegmark takes a mathematical approach without being too mathematical. He posits the notion that earth supports conscious life, which is a mathematics aware that it is information emergent from mathematics. Its as if consciousness is an equation with both sides mathematically defined in such a way that exchanges between sides cannot go unnoticed. Whenever information passes from one side of the equation to another, the result is instantaneous self awareness in order for the mathematical structures to reconcile and be in balance. Consciousness is the eternal imbalance of two sides of a set of equations containing 32 fixed parameters, but simply capable of nonlinear adjustment. The sets of equations, Tegmark describes by their various degrees of universality of information. Being permanently in disequilibrium, we have the driving force of consciousness at many levels and subject to many different systems ...
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on 21 April 2014
After having read this book, I am convinced that the universe can be described by mathematics - but that I was already before. However, the book did not convince me that our world IS mathematics, as Tegmark says. Tegmark's argument is winding, with several alternatives and turns, which in my mind towards the end just leaves the reader confused.
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on 15 June 2015
The major and detracting issue with the book is the quality of the figures which are needed to understand the text. The paperback version has black and white diagrams which are hard to read due to quality of the printing, I was about to buy the hardback for decent figures but read the review that said they were black and white too. Whilst its a great read I wouldn't recomend it unless they sorted it out. If they did then it would be a great science for the layman book.
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on 15 March 2014
A long and remarkable book that is the Grand Tour of the author's quest for the (answer to) The Ultimate Question, you know the one (and yes, Douglas Adams' book makes many cameo appearances). The material is sometimes complex but delivered in such a witty and engaging style that, like a great novel, I found myself dragged into the "just one more chapter" effect.

This is the first account I've read of the multiple universe idea that made any kind of sense. Yes, yes, it does sound daft, but it turns out to have a very respectable theoretical foundation, and on the credit side it make sense of paradoxes like Schrodingers cat. I'm told that many physicists object to this kind of thing, which sounds good. Maybe because, if there are other universes out there, with other natural laws, then it rather downgrades their efforts to understand "the whole thing" by observing our own universe.
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