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19 of 20 people found the following review helpful
5.0 out of 5 stars A brilliant example of communication about science and humanity
Do you enjoy great detective puzzles? Do you like noticing small anomalies, and turning them into clues to an unexpected explanation? Do you like watching world-class scientists at work, piecing together insights to create new theories, and coping with disappointments when their theories appear to be disproved?

In the book “Our mathematical...
Published 10 months ago by David Wood

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22 of 34 people found the following review helpful
1.0 out of 5 stars Trillions upon trillions of William of Ockhams turning, all so slightly differently, in their graves
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...
Published 8 months ago by SteveT


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19 of 20 people found the following review helpful
5.0 out of 5 stars A brilliant example of communication about science and humanity, 30 Jan 2014
By 
David Wood - See all my reviews
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Do you enjoy great detective puzzles? Do you like noticing small anomalies, and turning them into clues to an unexpected explanation? Do you like watching world-class scientists at work, piecing together insights to create new theories, and coping with disappointments when their theories appear to be disproved?

In the book “Our mathematical universe”, the mysteries being addressed are some of the very biggest imaginable:
*) What is everything made out of?
*) Where does the universe come from? For example, what made the Big Bang go “bang”?
*) What gives science its authority to speak with so much confidence about matters such as the age and size of the universe?
*) Is it true that the constants of nature appear remarkably “fine-tuned” so as to allow the emergence of life – in a way suggesting a miracle?
*) What does modern physics (including quantum mechanics) have to teach us about mind and consciousness?
*) What are the chances of other intelligent life existing in our galaxy (or even elsewhere in our universe)?
*) What lies in the future of the human race?

The author, Max Tegmark, is a Swedish-born professor of physics at MIT. He’s made a host of significant contributions to the development of cosmology – some of which you can read about in the book. But in his book, he also shows himself in my view to be a first class philosopher and a first class communicator.

Indeed, this may be the best book on the philosophy of physics that I have ever read. It also has important implications for the future of humanity.

There are some very big ideas in the book. It gives reasons for believing that our universe exists alongside no fewer than four different types of parallel universes. The “level 4 multiverse” is probably one of the grandest conceptions in all of philosophy. (What’s more, I’m inclined to think it’s the correct description of reality. At its heart, despite its grandness, it’s actually a very simple theory, which is a big plus in its favour.)

Much of the time, the writing in the book is accessible to people with pre-university level knowledge of science. On occasion, the going gets harder, but readers should be able to skip over these sections. I recommend reading the book all the way through, since the last chapter contains many profound ideas.

I think you’ll like this book if:
*) You have a fondness for pure mathematics
*) You recognise that the scientific explanation of phenomenon can be every bit as uplifting as pre-scientific supernatural explanations
*) You are ready to marvel at the ingenuity of scientific investigators going all the way back to the ancient Greeks (including those who first measured the distance from the Earth to the Sun)
*) You are critical of “quantum woo woo” hand-waving that says that quantum mechanics proves that consciousness is somehow a non-local agent (and that minds will survive bodily death)
*) You want to find more about Hugh Everett, the physicist who first proposed that “the quantum wave function never collapses”
*) You have a hunch that there’s a good answer to the question “why is there something rather than nothing?”
*) You want to see scientists in action, when they are confronted by evidence that their favoured theories are disproved by experiment
*) You’re ready to laugh at the misadventures that a modern cosmologist experiences (including eminent professors falling asleep in the audience of his lectures)
*) You’re interested in the considered viewpoint of a leading scientist about matters of human existential risk, including nuclear wars and the technological singularity.

Even more than all these good reasons, I highlight this book as an example of what the world badly needs: clear, engaging advocacy of the methods of science and reason, as opposed to mysticism and obscurantism.
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3 of 3 people found the following review helpful
4.0 out of 5 stars The first part is great, the second part is less gripping, 19 July 2014
This review is from: Our Mathematical Universe: My Quest for the Ultimate Nature of Reality (Hardcover)
The first part of this book tells the story of long ago and of the very small in the manner of a detective story. Tegmark tells us what needs explaining - what we can all observe or what scientists cab on serve - and how successively strong theories have pushed our knowledge forward. Clearly the field has made great progress since I last reed about these things and I find it hard to praise this part of the book too strongly - it was a gripping read for someone who knows as little as I did and left me feeling I understood the Big Bang, inflation, quantum physics and so on - which I found quite remarkable.

In the second part of the book Tegmark turns more philosophical. He sets out the view first that all properties of the world are mathematical properties. And the view that every mathematical possibility is a reality in some possible universe. I was left thinking this might be true or then again it might not. What I also felt was that there are very serious philosophical implications of the interpretation of quantum physics that Tegmark argues for - persuasively. If all the things that might happen to me do happen to me - in some world - and the question is simply 'what world am I in?' This might seem to raise some quite serious philosophical issues about the nature of the self. Not issues that grip Tegmark though...indexicals - I, here and now and so on - seem particularly worth thinking about further. I also wonder whether theories like natural selection through evolution hood is some of Tegmark's possible worlds but not others....

So I felt the first part of the book was great but the second part is less interesting...
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1 of 1 people found the following review helpful
5.0 out of 5 stars Top Rate, 4 Sep 2014
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This review is from: Our Mathematical Universe: My Quest for the Ultimate Nature of Reality (Hardcover)
The first part is an excellent summary of cosmology and quantum physics that's the most readable and informative I've read to date.Or maybe that's an effect of having read too many books in the same genre. Either way the author makes light work of issues other authors struggle with, and each chapter concludes with a helpful brief outline to ease the process.
The second part of the book deals with more esoteric subject matters,which is more challenging for the lay reader and requires more abstract imaginative processing to comprehend.
Overall I found the book is readable and I rarely counted the pages or became over taxed intellectually,which to me, is the sign of an excellent author.
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1 of 1 people found the following review helpful
5.0 out of 5 stars An outstanding and interesting read - could it reshape the way we look at reality?, 27 Oct 2014
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This review is from: Our Mathematical Universe: My Quest for the Ultimate Nature of Reality (Hardcover)
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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8 of 10 people found the following review helpful
5.0 out of 5 stars Prepare to meet your maker - Mathematics., 23 Mar 2014
By 
Shane (Northern Ireland) - See all my reviews
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This review is from: Our Mathematical Universe: My Quest for the Ultimate Nature of Reality (Hardcover)
If Max Tegmark is correct (and I have to say I think he *is*), we inhabit a universe that is just one of several hierarchies of multiverse that exist by virtue of the fact that they are mathematical structures. Not simply "describable" by mathematics, but that they fundamentally *are* maths. It's a conclusion that a lot of people have reacted against, and some of the implications are mind-boggling, but Max outlines his reasoning with wit and clarity in this very enjoyable romp between the physics of the Very Big to the Very Small and back to us humans. What is the meaning of Life? What *gives* meaning to the Universe? The ultimate answer is *us*, self-aware substructures within a larger mathematical entity, apparently evolving as the Schroedinger wavefunction through infinite-dimensioned Hilbert space, seeding clones at every quantum decoherence point, generating vast (infinite) numbers of parallel universes that are themselves part of this grander mathematical multiverse.

Max writes in an accessible and engaging style - it is clear that he is enjoying himself in coming up with his ideas (they seem to usually strike him when he's riding a bike (unlike a huge truck in Stockholm when he was a kid, fortunately for the Max in this universe) or walking in a park with one of his colleagues - in some ways these little biographical details add to the charm, and allow parallels to be drawn to the incredible writing of Richard Feynman.

That said, you can tell that Max knows this is an uphill struggle - many of his ideas strike deeply at some of the core notions we have as humans. Could there really be an infinite number of "yous" within *this* contiguous spacetime, not to mention within an infinite number of parallel spinoffs of this universe, each with the same subjective feeling that they are unique? These are not concepts that Max tosses out to deal with tricky problems - they are a fundamental prediction of certain formulations of physics. I have to say that I have not read a better description of cosmic inflation than Max presents here - I thought I had run the gamut of popular science descriptions, but this book makes several aspects much clearer, and provokes the reader to think on a wider level about the implications, and how we might test them.

The final chapter is a gem - what are the major existential threats facing humanity, and what should we be doing about them? As far as we can tell, we are alone in the Universe. He's a bit pessimistic here, in thinking that other civilisations are unlikely, and I very much hope that he is wrong (or do I?), but even so, there are multiple hazards that we will need to avoid if we are going to fulfil the role that we seem compelled to adopt - WE are what gives the universe meaning, so WE need to protect ourselves, our planet, our science. Whether it's dodging asteroids, or avoiding hostile artificial intelligence take-over, we would do well to plan ahead. Increasing scientific literacy is critical - this will drive both research and the intelligent use of new information as it arises. In the end, this is the only way we can hope to avoid a possible Great Cosmic Filter - if it lies ahead of our current technological state, it could well be the reason why we have not found other alien civilisations yet.

Is this an easy introduction to a complex subject? Is it a sales pitch for a radical reformulation of what we think of as "reality"? Is it Max's musings through the worlds of physics and ethics? It's all of the above and more. In at least *some* universes it is destined to become a classic, and those are the universes that are most likely to retain intelligent life. Probably.
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2 of 3 people found the following review helpful
5.0 out of 5 stars Mathematics is everything, 22 Jun 2014
This review is from: Our Mathematical Universe: My Quest for the Ultimate Nature of Reality (Hardcover)
Max communicates his ideas and past research into various areas of mathematics and physics enthusiastically, which form the basis of this book. His look back at past work during his career nicely fit in with the way in which the book helps build a bigger picture of our universe and reality. Some quite mind-boggling ideas are explored which may require a pause in reading and further reflection on what he is conveying at times but with a gradual understanding of the concepts he outlines as the book progresses, these concepts come together nicely towards the end.

A enjoyable read and one which I would recommend.
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2 of 3 people found the following review helpful
5.0 out of 5 stars Nice and not heavy but could have gone into a bit more mathematical problems., 26 Feb 2014
By 
Michael Hambro (Norway) - See all my reviews
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This review is from: Our Mathematical Universe: My Quest for the Ultimate Nature of Reality (Hardcover)
Excellent book, but I would like something with a bit more chewable math. The various nice ideas need a math basis to illustrate where theory today is working.
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1 of 2 people found the following review helpful
4.0 out of 5 stars Mind blowing, 6 Jun 2014
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He explains some of the most advanced ideas on the edge of physicists' understanding of the world we live in. And, amazingly, manages to do it in words that are comprehensible and interesting to non-scientists. The physics is leavened with some material about his own personal journey and about his colleagues.

Most amazing though is the conclusion he presents: That the history of the universe - or more accurately, the set of all possible histories of all the possible universes - is a pattern that arises naturally from mathematics, in the same way that those famous pictures of Mandelbrot and Julia sets have infinite complexities all arising from a simple formula.

At present many physicists are sceptical of this model. But they tend to be the older ones! I have a feeling that in 20 or 30 years' time, the view that Tegmark and others are developing will be pretty much the standard. That's the way physical theories develop.
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3 of 5 people found the following review helpful
5.0 out of 5 stars Four kinds of multiverse, 29 Mar 2014
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If you thought our universe was big, wait until you see the size of the four multiverses it's part of!

Tegmark's book is an entertaining and informative read. It takes you through a lot of the ideas behind cosmology (on the large scale) and quantum physics (on the small scale). Despite the title of the book, this is done in a very non-mathematical way and constitutes an easy read for the layman. Well, I say "easy" but by that I mean it's not throwing differential equations at you all the time; some of the concepts - even expressed in plain English - can be difficult to imagine.

It's quite "current" in that a lot of the latest theories about inflation are covered and it's interesting that since the publication of this book we've just discovered further supporting evidence of inflation in the cosmic microwave background. Inflation is still by no means certain but it's the theory that best fits the evidence we have at the moment. Most cosmologists would probably favour some form of inflation these days.

Multiverses are a different matter. There are good reasons to think that they follow naturally as a result of some theories of cosmology and quantum mechanics, but proof will be hard to come by. Either way, inflation accounts for multiverses I & II. Multiverse III comes by way of quantum mechanics, Hilbert space and the collapse (or to be more precise the lack of collapse) of a the quantum wave function. Tegmark does as good a job as anyone at explaining these multiverses in plain English.

Multiverses I, II & III have been out there in science for a while and they are becoming serious propositions for 'reality' these days, if not what you might call "fully mainstream". Where Tegmark goes further is with multiverse IV, which contains purely mathematical - but no less real - universes. This is where the title of the book comes from and, whilst such ideas have existed in various forms since Plato, Tegmark champions the mathematical universe as his personal tour de force.

Tegmark writes well. It is very difficult to transfer some of the concepts in this book to the layman because they seem so "foreign" to us, but Tegmark does a stirling job. You don't have to believe it all but Tegmark is a real scientist and he presents real scientific theories with proper peer-reviewed papers behind them, even if it sounds more like science fiction sometimes. That doesn't mean that they're all correct, merely that they are consistent and stand up to scientific scrutiny. It's up to the experimentalists to devise ways to prove or disprove these theories.

Recommended.
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22 of 34 people found the following review helpful
1.0 out of 5 stars Trillions upon trillions of William of Ockhams turning, all so slightly differently, in their graves, 6 Mar 2014
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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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