Vårt matematiska universum ePUB ¼ Vårt matematiska


Vårt matematiska universum [Reading] ➿ Vårt matematiska universum Author Max Tegmark – Thomashillier.co.uk »Fysiken är det yttersta intellektuella äventyret ett försök att förstå universums djupaste mysterier Fysik handlar inte om att ta något spännande och göra det tråkigt Tvärtom hjälper fys »Fysiken är det yttersta intellektuella äventyret ett försök att förstå universums djupaste mysterier Fysik handlar inte om att ta något spännande och göra det tråkigt Tvärtom hjälper fysiken oss att se klarare och får världen omkring oss att framstå i hela sin förunderliga skönhet«Max Tegmark tar i Vårt matematiska universum med oss på en svindlande resa i fysikens astronomins och matematikens fascinerande värld En av hypoteserna vi möter är att vår verklighet är en matematisk struktur Vårt matematiska PDF/EPUB or en annan att det existerar oändligt många parallella universum och därmed oändligt många duGenom att kombinera populärvetenskap och banbrytande forskning förklarar Tegmark på ett tillgängligt sätt sina teorier Han redogör också för överraskande framgångar och motgångar som format hans liv som forskare från uppväxten i en stockholmsförort till livet som kontroversiell professor i USADen här oavbrutet fängslande boken har mottagits med stort intresse och hyllats av några av världens mest framstående forskare och matematikerDet Max Tegmark skriver om påminner om science fiction när den är som bäst men verkligheten överträffar dikten Välkommen till Max Tegmarks universumMax Tegmark föddes och växte upp i Stockholm Han har kallats världens smartaste svensk och är idag professor i fysik vid MIT Massachusetts Institute of Technology i USA.

  • Hardcover
  • 498 pages
  • Vårt matematiska universum
  • Max Tegmark
  • Swedish
  • 03 March 2016
  • 9789187419270

10 thoughts on “Vårt matematiska universum

  1. Manny Manny says:

    Aaargh No Make it stopThat's my girlfriend who's just been unwise enough to let me read her a paragraph of this book But our guest K a local nuclear physicist is tolerant Well she smiles it doesn't sound so bad A bit exciting a bit populistic Blah blah blah On the other hand she isn't a native speaker of EnglishOkay let's start by getting the bad news out of the way Max Tegmark's chatty informal slightly manic style is on the irritating side and if you know some physics it may also give you the impression that you're not going to learn anything from Our Mathematical Universe Unless you're working at the cutting edge of the subject that impression is almost certainly false When I briefly explained the content to K I soon found that it wasn't just a uestion of a few interesting details that she hadn't previously come across Isolated like most working scientists in her own specialty the dating of rocks using radioactive isotopes she hadn't even heard that a major paradigm shift was under way in the theoretical basis of her field I hope I managed to convince her that the book was well worth looking at Yes the style is annoying at first but after a couple of chapters I stopped noticing it I was in the bar I'd had a few beers and my new buddy Max Mad Max he'd said with an ironic smile was telling me about his research life in the charmed inner circle of theoretical physics and his ideas about the ultimate nature of reality Every now and then I managed to get a word in edgeways and complain about some of the outrageous claims Max had evidently heard it all before and deftly batted back my objections I wasn't exactly convinced but he made it sound a whole lot plausible than I'd expected Max's central idea is the Multiverse where he has been one of a small number of people who's played an evangelical role More or less considered as science fiction fifteen years ago it's now almost respectable; it's astonishing how uickly the change has happened Max has a cunning scheme in which the Multiverse is presented in four increasingly bolder versions from Level I to Level IV I'd seen a fair amount of his material already particularly in Brian Greene's The Hidden Reality but Max's presentation is much better He's worked directly on several of the key ideas and his hands on experience makes the stories considerably believable He starts off with Level I which at first sounds innocuousWhat is there in the universe? he asks A naive answer might be that it's everything we can see through our telescopes But even a moment's thought will prompt some revision Sometimes there are things in the way clouds of dust and gas along the galactic plane for example Surely there's something behind those clouds Well then the universe consists of all the things we can see plus all the similar things we can infer must also be thereBut what are those other things? Objects getting in the way is just one problem There are also things that are very distant so distant that light from them hasn't had time to reach us yet How far away could these other objects be? That's a complicated uestion which has to do with the structure of space Max has done a lot of work with the Cosmic Background Radiation the light from the Big Bang to see what it can tell us about that structure It was fascinating to see him uickly sketching graphs on paper napkins explaining how he'd analyzed the data and what the results told us One key finding as I'd heard before is that space turns out to be flat That means it goes on forever so there are infinitely many galaxies over the horizon of visibility In that infinite expanse every possible history has played out including histories arbitrarily close to our own It's sort of Nietzsche's Eternal Recurrence but in space instead of time At some unfathomable distance he makes a rough estimate there are doppelgangers of Max and me sitting in the same bar and having the same conversation An extremely weird conclusion but oddly enough it seems to follow from entirely reasonable premisesAnd this is only Level I So why is the universe flat? asks Max rhetorically Inflation? I say as I order another round I've seen many explanations of inflation but it's hard to decide how seriously I should take them Max knows all the ins and out and argues both sides of the case He collects some beer mats and arranges peanuts on them to demonstrate a simple argument due to his buddy Alexander Vilenkin that shows why inflation has to be eternal If it happened at all it or less had to generate an infinite number of Level I multiverses all with different physical laws; that's Level II But did it happen? I ask What's the evidence? Max scribbles down pictures of the power spectrum from the CBR and explains how they fit the inflation scenario while ruling out a bunch of other theories He really has that talent for showing you what the mathematics means in intuitive terms I have to admit it the case looks better than I'd realizedLevel III is the uantum multiverse everything that can happen does happen I've read several books about this and am or less convinced already but Max's version of it is very nice He describes how he invented the uantum suicide thought experiment and tells me about some clever details that I should have thought of but hadn't It's even weirder than I'd realized And now we need to proceed to Level IV before closing time But surely we should get some beer first? I mumble something about how I've maybe had enough but Max isn't taking no for an answer Du sa nåt om att du bott in Sverige? he says and before I know what's happened there's a bottle of akvavit on the table between us He pours out a couple of generous glassesLevel IV it turns out makes all the others look modest in comparison Think about the fundamental particles urges Max We can see that they are entirely specified by their mathematical properties So what's the simplest explanation? Reality just is mathematical structure Every mathematical structure specifies a reality But what breathes fire into the euations? I ask Nothing does says Max Skål I empty my glass which is magically full again a moment later The room seems to be revolving slowly It's uh interesting I say But surely there's no way to investigate the idea empirically? Maybe replies Max and sketches out yet another graph this time showing constraints on the Higgs VEV His explanation is fiendishly clever unless that's just the effect of the akvavit But surely there are problems with all this? I say weakly ashamed that I can't immediately come up with half a dozen objections Max suddenly looks thoughtful and almost sober The measure problem is very serious he says It's a crisis in physics He and his identical twin who's just appeared next to him proceed to explain it I nod every now and then and try to put my hand over my glass but he's too uick for meThe next morning I have no memory at all of how I got back to my hotel room though I dimly recall Max saying something about the dangers of nuclear war meteorites and evil AI entities Or was that a dream? I do at any rate have a pile of paper napkins covered in illegible scrawls and smelling strongly of akvavitRead this book It's fun

  2. Emma Sea Emma Sea says:

    I have three things I'd like to say about this book1 I accidentally left it behind at a cafe When I went back it was gone Imagine my surprise when I discovered some nice person had found the book and returned it to the library for me Thank you kind human2 Tegmark writes fantastically Wisely he doesn't try to make the reader cough me cough follow his maths but instead offers URLs for papers offering the mathematical proofs for the concepts he discusses as additional reading for those so inclined Tegmark walks us through the information gradually and interspersing the heavy concepts with light personal anecdotes His analogies are so clear and this makes the book gripping understandable and illuminating3 Tegmark's writing is in fact so clear that I had a moment of the most exuisite understanding while reading it I was lying in bed and I started crying because for a split second I had an clear conceptualization of the beauty of the mathematical universe and it was vast and overwhelming and fucking gorgeous I was weeping with a sublime bliss It was a very special moment I doubt I'll ever have another like it and I'm ok with that I feel privileged to have had that glimpseRecommended

  3. BlackOxford BlackOxford says:

    The Mind of GodIt starts with Plato this idea that the universe is a mathematical expression populated by objects which are often imperfect copies of abstract ‘forms’ the most perfect of which are numbers which in turn interact according to strict rules of geometry and aesthetic necessity More importantly it was Plato who suggested that things are not what they seem What we are able to perceive are distorted manifestations of eternal truths which are permanently beyond our grasp leaving open therefore the meaning of what we glibly call reality In a sense he was the first post modernist in pointing out that reality isn’t even verifiable much less obvious through our observation and experienceHence the general preference of ‘hard’ scientists like physicists for Aristotle rather than Plato Aristotelians like to rely on their senses; they crave observational data facts They look down on Platonists including mathematicians just as Freudians look down on Jungians and for the same reason They simply can’t abide the idea that eternal laws could generate facts whether those laws are of the Collective Unconscious or the Eternal Forms For science facts precede laws both logically and ontologically Facts are real Laws are inferred regularities evolving theories As such they can only be considered as expedient hypotheses So the conflict of fact and law has been fought for two and a half millennia with no victory for either side in sight Tegmark‘s book is a chronicle of a recent skirmish in which the Platonic standard is held high Tegmark is a bit coy but he puts forth the historical Platonist party line clearly as “a crazy sounding belief of mine that our physical world not only is described by mathematics but that it is mathematics making us self aware parts of a giant mathematical object our physical world not only is described by mathematics but that it is mathematics a mathematical structure to be precise”This particular battle is part of a much larger war in a sense a cosmic war called metaphysics Metaphysics is the discipline of thinking about ‘what’s really there’ The main difficulty in the metaphysical war from an intellectual point of view is the same as in any other war namely that the cause one is fighting for justifies its own arguments Each side has an implicit criterion of validity which uelle surprise produces precisely the results to show success by that criterion and failure by the opposing view All wars in metaphysics are therefore ‘just’ for both sidesTo oversimplify but not by much mathematicians really appreciate patterns They search for them constantly and revel in the thought that they are already there waiting to be discovered While scientists are also attuned to patterns however they know that scientific progress is most often generated not by taking patterns at face value but by concentrating on the apparent exceptions to patterns which are the source of new theoretical patterns The standards of evidence in the two disciplines are very different So for the scientist the weirdness of uantum physics and black holes is a spur to create a new theory to confront a resistant universe with observational challenges For the mathematician the challenge is to coax out the already existing pattern within the structure of his mathematical representations and techniues One man’s Mede is another man’s Persian to coin a phrase Each considers the other to be somewhat Gnostic in their reliance on esoteric knowledge and their distinctive forms of mistrust of the universe the scientific hesitation about generalization and the mathematical disdain for the particularIt makes no sense trying to reconcile the two views because as an observant philosopher might point out each already contains a presumption about what reality is and these presumptions are validated by there very use not by their results which are fundamentally incomparable This incomparability is not rational; it is aesthetic that is pre rational The aesthetic is the foundation upon which each constructs his own edifice of ReasonThe bottom line then is that while Our Mathematical Universe is an entertaining as well as informative read its real value is probably to confirm the views already held by the Platonist choir It is only likely to irritate the Aristotelians who already think that mathematics has ruined real science by its entirely abstract reasoning To the latter Tegmark will not seem merely “crazy sounding” but crazy tout courtIt turns out that Plato was correct than even he could have thought according to the latest science For a rather wonderful tale of the Platonic view of mathematics see

  4. ☘Misericordia☘ ~ The Serendipity Aegis ~ ⚡ϟ⚡ϟ⚡⛈ ✺❂❤❣ ☘Misericordia☘ ~ The Serendipity Aegis ~ ⚡ϟ⚡ϟ⚡⛈ ✺❂❤❣ says:

    An unexpectedly deep perusal of the mathematial nature of this baffling world we find ourselces in Well written and rich in ideas to ponder on to me an electron colliding with a positron and turning into a Z boson feels about as intuitive as two colliding cars turning into a cruise ship On microscopic scales particles schizophrenically appear in two places at once leading to the uantum conundrums mentioned above On astronomically large scales —surprise—weirdness strikes again if you intuitively understand all aspects of black holes I think you’re in a minority of one and should immediately put down this book and publish your findings before someone scoops you on the Nobel Prize for uantum gravitycwe’ll explore the fascinating relations between computation mathematics physics and mind and explore a crazysounding belief of mine that our physical world not only is described by mathematics but that it is mathematics making us self aware parts of a giant mathematical object We’ll see that this leads to a new and ultimate collection of parallel universes so vast and exotic that all the above mentioned bizarreness pales in comparison forcing us to relinuish many of our most deeply ingrained notions of reality сI wanted to do my small part to make our planet a better place and felt that the main problem wasn’t that we lacked technical solutions but that we didn’t properly use the technology we had I figured that the best way to affect people’s behavior was through their wallets and was intrigued by the idea of creating economic incentives that aligned individual egoism with the common good Alas I soon grew disillusioned concluding that economics was largely a form of intellectual prostitution where you got rewarded for saying what the powers that be wanted to hear Whatever a politician wanted to do he or she could find an economist as advisor who had argued for doing precisely that Franklin D Roosevelt wanted to increase government spending so he listened to John Maynard Keynes whereas Ronald Reagan wanted to decrease government spending so he listened to Milton FriedmancAlthough the book wasn’t really about physics dwelling on topics such as how to pick locks and how to pick up women I could read between the lines that this guy just loved physics Which really intrigued me cphysics is the ultimate intellectual adventure the uest to understand the deepest mysteries of our Universe Physics doesn’t take something fascinating and make it boring Rather it helps us see clearly adding to the beauty and wonder of the world around us When I bike to work in the fall I see beauty in the trees tinged with red orange and gold But seeing these trees through the lens of physics reveals even beauty captured by the Feynman uote that opens this chapter And the deeper I look the elegance I glimpse the trees ultimately come from stars and studying their building blocks suggests their existence in parallel universescI love uestions Especially big ones I feel so fortunate to be able to spend much of my time tackling interesting uestions That I can call this activity work and make a living from it is just luck beyond my wildest expectationsc There’s no better guarantee of failure than convincing yourself that success is impossibleand therefore never even trying с Read as Макс Тегмарк Наша математическая вселенная В поисках фундаментальной природы реальности

  5. David Katzman David Katzman says:

    Before I begin a brief word about physics from a ninjaThis is a book of speculative physics At the same time it is a mostly lucid walkthrough of the latest theories in physics It's important to distinguish between theories and speculation Theories are directly testable Results of the theories are repeatable Special and General Relativity are examples of theories that have been demonstrated over and over again A result is calculated from the theory an experiment is performedthe results match Where the speculative part of the book comes in to play is where Tegmark attempts to project what he sees as the natural outcome the logical result of these theories or the real world ramifications That is to say if the mathematical theories are accurate representations of the real world then what must this real world look like? Really He describes these hypotheses as predictions of theoriesAs an overview of the current state of physics this is highly digestible It's exciting to get a window into the latest thinking in cosmology and subatomic space I'm going to focus on his speculations According to Tegmark the latest theories result in their being a possibility of four different types of multiverses At the core of these propositions are two contentious suppositionsInflationThe Schrodinger EuationI think most of us have heard that the universe is expanding although I think few of us can really envision what this means Space is getting largerlike a balloon However inflation is different Imagine taking an object and then duplicating it Duplicate it exponential times Then duplicate each of those duplicates exponential times This is inflation and apparently the hypothesis that inflation occurred immediately after the Big Bang explains several big puzzles of cosmology At least for now Such as why the background radiation is evenly distributed throughout the universe With inflation you get your matter for nothing and the matter comes from Energy EMC2 being converted And inflation can propagate faster than the speed of light Not all scientist are in agreement; inflation is still a hypothesis but Tegmark points out that it neatly answers many conundrums I did see this article recently about a discovery that could be inflationA lot of could bes More on inflation in a bitThe Schrodinger Euation is the mathematical formula that captures the state of a uantum particle What it has always shown is a range of probabilities and never a defined location When a particle is captured it is always found in one of the positions defined by the Schrodinger Euation and the probability of finding it in any given position can be calculated with this formula before you locate it The Schrodinger Euation has been demonstrated to be accurate over and over again through experimentationThe mind bending issue arises because physicists haven't been able to explain why the euation collapses when a particle is observed That is before observation a particle exists only in a state of probability it does not have an exact position or velocity But the moment it is observed it assumes instantly a location You've likely have heard of the Schrodinger Cat thought experiment the cat being both alive and dead until observed that demonstrates the absurdity and mind bending nature of this result If not here's a description of itHow is it that the act of observation or measurement causes the uantum particle to assume a state? The common solution called the Copenhagan Interpretation simple says it does but not why Observation closes the loop end of story What is the mechanism that causes an interaction with a probability sphere to collapse into actuality? There are now uite a few other interpretations Such as that it never collapses only seems to Tegmark sees the most coherent solution to this to be the Everett Many World's Interpretation More on that in a bitAs a result of both the concept of inflation and the difficulty in explaining how the Schrodinger Euation relates to reality Tegmark suggests that there are four possible conditions that may describe the universes But all are preceded by the idea that if inflation is correct then space must be infinite This an important assumption and one that there is really zero proof of but it makes for interesting conceptual thinking These are his Universe LevelsONE Given space as infinite there are infinitely many universe islands like our own That would mean there are infinite beings just like us but different in some small or large aspects These beings are beyond the distance that light could even travel to us since the Big Bang In some universes our duplicates don't exist at all In others our species doesn't exist or our planet In others everything exists exactly as it does except your eyes are purple He claims this is the natural outcome of having infinite space along with fairly similar starting conditions This reminds me a lot of Nietzche's Eternal Recurrence hypothesisTWO Same as one except that in these universe islands the laws or constants of physics might be different He uses the fine tuning argument as some justification for this view More on fine tuning in a bit Andeach universe island may have had its own Big Bang momentTHREE Multiverse timeTegmark's preferred explanation of the Schrodinger Euation is that at each moment in time when a particle can exist in different states the universe splits into a uniue universe for each potential state All states occur and then due to decoherence they separate and cannot interact with each other There is no state vectoreuation collapseall states occur and split us into multiple universes These universe all exist simultaneously doesn't really mean anything because all time exists at the same time in an infinite Hilbert Space The Hilbert Space is basically the uber universe All time and space as an unmoving objectFOUR The Universe is a mathematical object This is his pet preferred hypothesis My interpretation of it is something like this Particles can be fully described mathematically The universe can be thought of as a collection of particles in a particular arrangement Therefore the universe is much like a computer program an arrangement of numbers The matrix An individual life form is a complex mathematical object traveling within this mathematical universe Kind of like a parenthesis in a larger formula Universe being 1 being 2 etc He essentially says that consciousness and free will is an illusion and is merely the sensation of experiencing the split into multiverses I'm given the impression that he believes in Levels 2 3 and 4 combined And here's where it gets really weird abstractabstruseabsurd he suggests that all that exists is math A sort of reverse Platonism Somehow when mathematical formulas are complex enough they become self aware and perceive the mathematical universe as a reality Even basic mathematical systems exist in their own universe albeit one not complex enough for life He gives the example of how videos are constructed from ones and zeros but give us the impression that they are real images The universe is kind of like that A self contained mathematical formula that simulates reality Although he actually doesn't believe in the simulated universe hypothesis it seems to me to be the same thing Math formulas take on a life of their own Jeff Noon wrote a book called Nymphomation that was about math formulas coming to life as I recallUnfortunately although Tegmark presents this model he really can't explain it It is certainly intriguing and unanswered what reality is and how we perceive it as suchand how we could if we do have free will However it is even harder to explain how an abstract structure a computationally valid mathematical formula could somehow form a reality Math is pure abstraction So how could an abstraction perceive? How could an abstraction create a form? Saying something is emergent doesn't explain it it's just saying that you can't explain itThe universe may be imaginary but it sure damn feels real How could a mathematical formula feel real? How could math develop the ability to feel His hypothesis doesn't really explain anything He says the theory doesn't need to explain consciousnessthat's someone else's jobOne justification he has for level 2 universe is the fine tuning argument I'm no mathematician and Tegmark is one of the top in the world apparently So I say this with humbleness that I may be wrongbut I see a profound gulf in one simple area It is a misunderstanding of the relationship between probability and real life If something has actually happened ie exists then the probability of it happening is 100% There is no probability Before it occurs there is a probability Therefore when the so called fine tuning argument is used as a factor to sell a theory my back gets up The fine tuning argument states that some constants are so finely tuned to support life that either God tuned them Tegmark doesn't say this but creationists door there is a significant theory missing to explain why the uantities are such as they are so specifically For example if dark energy was minimally less dense then the universe would have flown apart already If dark energy was slightly denser then it would have collapsed Of course dark energy hasn't even been proven to exist yetalthoughthere was this recently Tegmark believes all these constants will be justified mathematically at some point Lot of belief there But regardless of why the constants are in the state they are they are There is no chance or probability that they could be anything else So regardless of how you explain them there is no proof that they could anything other than what they are which means the probability of them being what they are is 1 It's not amazing that the odds turned up life Life is The constants are It wasn't god who made them nature did I'm not saying we won't necessarily learn which will explain why some values are what they are I'm saying that the fine tuning argument falls apart because probability is not relevant to the outcome There are no other statesIn the end this book is both lucid and whimsical It's uite entertaining and rather farfetched at the same time After I had completed most of this review I went and read a few professional reviews on the NYTimes website The Guardian etc All of these reviewers find the multiverse theory to still be bunk and unprovable andor the mathematical universe idea to be absurd So take it all with a grain of salt Still a fun read

  6. Manuel Antão Manuel Antão says:

    If you're into stuff like this you can read the full reviewThe Stages of Truth Our Mathematical Universe My uest for the Ultimate Nature of Reality by Max TegmarkForget about Tegmark’s 4 levels The stages of truth I can remember are• Old Greeks saying We only see a faint reflection of reality ie we have observation and that's flawed• Old Chinese saying All we have is observation Reality is observation and observation is a function of the human form which is a most interesting thing They state that sense is inherently limited by our being Excellent• Descartes saying to know stuff you must have doubt Knowledge is developed by doubt which means testing the scientific method Which he didn't invent but put on a logical footing And also founding it all on I think therefore I exist• Karl Popper saying that the essential property of what's knowable is what can be tested uestioned This continues from Descartes and uite a few in between including Kant obviously who's really cool but illegible

  7. Tara Tara says:

    This book covers uite a bit of material topics ranging from astronomy cosmology and uantum physics to far precarious stuff such as the level IV multiverse and the “Mathematical Universe Hypothesis” which Tegmark champions rather emphatically In the beginning of the book page 13 he includes a helpful diagram that clearly states which chapters are considered “mainstream” “controversial” and even “extremely controversial” He’s very upfront about which parts of his book fall into which category so I don’t believe we should fault him overmuch for being too speculative I mean in order for science to work for it to explore radical new territory and discover eually radical new truths radical new hypotheses are absolutely essential Even or perhaps especially the ones that seem a little bananas As Tegmark points out it is “amusing how strong the conformist herd mentality is among many physicists given that we all pay lip service to thinking outside the box and challenging authority” After all we don’t want to be like Mac on It’s Always Sunny in Philadelphia best show ever slam science for barking up the wrong tree sometimes and end up hating all the “stupid science bitches” now do we?

  8. WarpDrive WarpDrive says:

    This is a complex and very interesting book addressing many important uestions about the fundamental nature of reality The author adopts and convincingly explains a particular version of mathematical Neo Platonism stating that reality is essentially nothing but mathematical structures His position might be classified as a form of mathematical “monism” as it essentially denies ontological reality to anything except mathematical objects From a philosophical perspective the author can be allocated to what is termed Ontological Structural Realism whose main statement crudely expressed is the claim that there are no ‘things’ as such and that “structure” is all there is This approach has proved uite attractive to a few philosophers of physics philosophers of mathematics such as Stewart Shapiro and physicists and I personally find it uite compelling my Neo Platonism was at least until I finished reading this book of the Heisenberg or Roger Penrose flavour – the latter famously positing the existence of three worlds – the world of conscious perception the physical world and the Platonic world of mathematical forms interconnected in a complex fashionThe author starts his argument by observing in a convincing way that the very fabric of our physical world appears to be fully describable in a mathematical way Look at space itself for example whose only intrinsic properties are mathematical such as dimensionality curvature and topology; and this eually applies to the “stuff” our physical world is made of – the only intrinsic properties of elementary particles are mathematical charge spin and lepton number for exampleI think that the author here is correct and I must add that this debunks the myth of the Kantian “thing in itself” das Ding an sich this mysterious “essence” which Kant confusingly opposed to the phenomenological behaviour of the object The most fundamental entity in classical uantum mechanics the wave function can be considered after all a mathematical object which lives in the infinite dimensional place called Hilbert space Fields can be considered mathematical objects or at least spatially defined clusters of information Just as a side note I would have expected the author to also explore the concept of entropy which is a fundamental emergent phenomenon ultimately driving the time arrow evolution of the Universe and which again is nothing but a “mathematical”statistical concept based on the measure of the number of specific ways in which a system may be arranged commonly understood as a measure of “disorder” This would have further confirmed his theory I tend to share the author's views here the I have studied uantum mechanics and relativity the I have started to feel that the deeper you dig the this physical “stuff” starts looking like an illusion as its fundamental core nature appears to be nothing but information and structure “mathematics” if you wish After all particles are excitations of the corresponding uantum fields which are not “physical” in the traditional meaning of the term or they can be defined in modern particle physics as elements of an irreducible representation of the corresponding symmetry group And after all what does the word “physical” mean ? Is it what it can be perceived by our limited sensory organs ? Well I think that this old fashioned concept of physical world has been made obsolete for uite some time Moreover the author compellingly and beautifully explains that we DISCOVER such structures fully describing reality we do NOT invent them – all we invent is the NOTATION for describing such structures A structure is defined as a set of abstract entities with a set of relations between them whereby the only properties of these entities are those embodied by the relations between them and it is clear to the author from the latest developments in science in the last 90 years that the properties of nature stem not from properties of its ultimate building blocks but from the RELATIONS between such building blocks and I find myself in substantial agreement with this viewThe author after discussing the point that the fundamental properties of reality appear to be mathematical addresses the relationship between such mathematical structures describing reality and reality itself What is such relationship ? Is such relationship an isomorphism or is it an identity? In other words is mathematics the language of nature or IS IT nature itself ? Here the author thesis is that if two structures are “euivalent” where euivalence is defined as the existence of a one to one relationship between the two structures preserving all relations they are the same and they describe the one and the same thing The author's conclusion is “this means that if some mathematical euations completely describe both our external physical reality and a mathematical structure then our external physical reality and the mathematical structure are one and the same” Here the author disappointingly does not really develop this crucial point in any satisfactory detail he refers to the work a master thesis done by a certain Marius Cohen page 280 of the book and this is all we have Not enough and I was left profoundly dissatisfied here I will try and retrieve Marius Cohen's work but that such a crucial point was not developed in detail remain a weakness of this book in my opinion But overall his points are very compelling beautifully addressed and explained and fascinating – a real intellectual challenge to our everyday perspective of realityThere is so much to discuss here in relation to this book I feel I could write a book on this book as there are so many different interesting themes and fascinating points discussed by the authorJust as an example the author beautifully highlights how fundamental the property of “symmetry” is in the characterisation of mathematical structures and of reality Also the author addresses the issues raised by the concept of “infinity” and by incompleteness as raised by Godel elaborating as a response to such issues his initial “Mathematic Universe Hypothesis” into a Computable Universe Hypothesis CUH which posits that all COMPUTABLE mathematical structures exist Fascinating I must sayWhere I disagree with him however is in his own enthusiasm for the Multiverse interpretation of uantum Mechanics Level III Multiverse in his book I found his treatment of this specific issue uite weak and the author also makes the mistake unfortunately still common of interpreting Bell's ineuality experimental results as ruling out hidden variables – this is not correct – what has been ruled out is the existence of hidden LOCAL variables so alternative interpretations in particular the de Broglie Bohm theory which I personally find uite attractive and which elegantly tries to address the measurement problem are still not ruled out I realize though that this particular interpretation sits in a minority position and many do not agree with it at allOverall it is a great book challenging rich and fascinating It even explores with fascinating insights hard problems such as the nature of consciousness the issue of the potential future singularity and our place and our meaning in the Universe To finish I would have loved a uantitative treatment of some of the items discussed in the book at least in areas such as uantum mechanics and symmetry but I guess this is part of the current commercially driven trend of dumbing down the maths in order to enlarge the potential audience and therefore the potential customer base this is together with the couple of other shortcomings I highlighted above why I could not give this otherwise great book a full 5 star rating

  9. David David says:

    The first half of this book is a review of modern physics on the macro and micro scales The second half of this book is a discussion of the author's speculation that the universe is a mathematical structure Max Tegmark is uite clear he is not saying that the universe is described by mathematics but that the universe is mathematics He calls this the Mathematical Universe Hypothesis or MUH for shortTegmark asserts that this idea is a testable falsifiable hypothesis I did not find the experimental test but perhaps I simply missed it To be perfectly frank I don't even understand his reasoningThe last chapter of the book switches gears entirely and discusses the existential threats to human survival Things like asteroid collisions eventual expansion of the sun and so on Then the book describes the two most immediate threats to human existence The first is a nuclear war And the second is are you sitting down for this? the singularity where artificial intelligence takes over the worldI didn't read this book I listened to the audiobook read by Rob Shapiro He did an excellent job giving the narration an aura of authenticity It's just too bad that the content of the book is not as good as the narration

  10. Gendou Gendou says:

    The thesis of this book is nothing but a giant exercise in circular reasoningMax Tegmark calls his idea the Mathematical Universe Hypothesis that the external physical reality described by the Theory of Everything is a mathematical structure He starts off by I kid you not assuming that the external physical reality is a mathematical structureThis radical idea that reality is made of math is embodied in the title of the book but nowhere within the pages is there any logical argument in for the idea It's merely assumedThis assumption is necessary to apply the rule of isomorphism to the external physical reality and the Theory of Everything an undertaking which is supposed to provide support for the Mathematical Universe Hypothesis But you can't start out assuming the thing you're trying to proveMad Max as he's known in the physics community has the gall to let this glaring logical error stand uncorrected On his Facebook page I asked him about this circular reasoning and he dodged the uestion but admitted the starting assumptionIt's infuriating that someone can publish a book claiming the universe is made of math and have no argument inside the book to support this outrageous claim This isn't speculative It's unscientificAside from his own pet theory he presents an out of date picture of the Everett's Many Worlds interpretation as thought it were a uniue theory from other interpretations of uantum mechanics This is wrongThere's also a whole chapter full of bogus Anthropic arguments like uantum suicide etc Max has got to be the sloppiest thinker who's eyes I've ever had the displeasure of being forced to see the world throughThe first half of the book does contain some half way decent introduction to cosmology but you're better off reading a real author like Stephen Hawking or even Brian GreeneSee also

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