Hiding in the Mirror: The Mysterious Allure of Extra Dimensions, from Plato to String Theory and Beyond

by Lawrence M. Krauss

Beginning well before Plato’s allegory of the cave and continuing to modern scientific breakthroughs from relativity to quantum mechanics, as well as to pop cultural icons like Twilight Zone and Star Trek, human beings have imagined, even longed for, alternate realities. Lawrence M. Krauss, one of the most gifted and engaging of writer-scientists today, examines why we have often believed that the answers to the great questions about existence lie in the possibility that we live in a universe more complex than we can see or otherwise sense. Drawing on work by scientists, mathematicians, artists, and writers—from Einstein to Picasso to C. S. Lewis—Hiding in the Mirror explores whether extra dimensions simply represent abstract speculation or hold the key to a deeper understanding of the universe. Krauss examines popular culture’s embrace— and misunderstanding—of topics such as black holes, life in another dimension, string theory, and some of the daring new theories that propose that large extra dimensions exist alongside our own. This is popular science writing at its best and most illuminating—witty, fascinating, and controversial.

Genres: Science, Physics, Nonfiction, Philosophy, History, Popular Science, Ebooks

276 pages, Hardcover

First published October 20, 2005

About the author

Lawrence Maxwell Krauss is a Canadian-American theoretical physicist and cosmologist who taught at Arizona State University (ASU), Yale University, and Case Western Reserve University. He founded ASU's Origins Project in 2008 to investigate fundamental questions about the universe and served as the project's director.
Krauss is an advocate for public understanding of science, public policy based on sound empirical data, scientific skepticism, and science education. An anti-theist, Krauss seeks to reduce the influence of what he regards as superstition and religious dogma in popular culture. Krauss is the author of several bestselling books, including The Physics of Star Trek (1995) and A Universe from Nothing (2012), and chaired the Bulletin of the Atomic Scientists Board of Sponsors.
Upon investigating allegations about sexual misconduct by Krauss, ASU determined that Krauss had violated university policy, and did not renew his Origins Project directorship for a third term in July 2018. Krauss retired as a professor at ASU in May 2019, at the end of the following academic year. He currently serves as president of The Origins Project Foundation. Krauss hosts The Origins Podcast with Lawrence Krauss and publishes a blog titled Critical Mass.

Reviews

[Paul Weiss · Rating 3 out of 5]

I’m still convinced that the anthropic principle is a meaningful cosmological outlook!

HIDING IN THE MIRROR is, first of all, a brief summary of the history and current status of physics' theoretical outlook at parallel universes, multiple dimensions, string theory, field theory and the manifestation of the forces - strong, weak, electromagnetism and gravity - we experience daily in the context of a visible three dimensional universe which might be described as a manifold embedded in a universe with a much larger but still undetermined number of dimensions. (Both the magnitude and the curvature of these dimensions is also far from locked down in these theories). Some very esoteric readers might also call it a primer on the subject but, even as a graduate of a university program in math and theoretical physics, I’m not sure that such a term has any meaningful application here. It’s pretty heady stuff and some of the reading is might tough sledding.

But, despite its difficulty, if you take your time you might be rewarded with some interesting insights. Consider, for example, this brief description of the Planck distance that conveys some idea of just how small it really is:

“Imagine you were looking at our galaxy through a distant telescope from another galaxy far, far away. Say your telescope could just barely resolve individual stars in the Milky Way, as the Hubble Space Telescope can in the nearby Andromeda galaxy, two million light years away. The problem of measuring extra dimensions on the Planck scale is for us, then, similar to the problem of trying to detect and probe individual atoms in that distant galaxy using your telescope!”

On multiple universes:

"… the principles [of inflationary theory] would in general imply that the entire visible universe is likely to be merely a part of an incredibly complicated “metaverse”of causally disconnected universes. Some of these may be collapsing, others expanding, some may only now be experiencing a big bang expansion … "

Interesting, enjoyable, informative but well beyond the difficulty level that might appeal to a casual reader of popular science.

Paul Weiss

[Bill · Rating 3 out of 5]

The spine of this bookhas been staring at me from my shelf for a while. I started it once, but found it all too easy to set aside. I think the problem is less with Krauss than with the subject matter: extra hidden dimensions in string theory and elsewhere. This area of study is still awaiting its Lincoln Barnett .

I took up the cudgels again owing to an inquiry from Scott Sigler. This time I finished it, though by end the game hardly seemed worth the candle. If you're looking for an incisive critique of string theory, you're better off with Lee Smolin's "The Trouble with Physics"; if you're trying to get the scoop on large extra dimensions (as I was for Scott), then Lisa Randall's "Warped Passages" would be the way to go.

Here one gets the sense that Krauss, who did such a masterful job of science popularization in "The Physics of Star Trek," has simply gotten tired of (to paraphrase Oscar Wilde's description of a fox hunt) explaining the inscrutable to the unedifiable.

He's also gotten tired of writing -- or at least of reading over what he's written, or he wouldn't leave in place such boners as (p. 53) "In physics, as in horeshoes, being merely close is not good enough." What makes this gaffe particularly egregious is that he subsequently gets it right ("close is *only* useful in horseshoes and hand grenades," p. 160), and then back-references the place where he got it wrong.

[Chiara · Rating 4 out of 5]

I was kind of let down by this book. When I started reading it (that was yesterday) I was very excited about exploring the parallel universes subject - which fascinates me deeply - from many interestingly unexpected angles. So I was ready to be carried away by new literary and philosophical insights linked to alternate realities but, as it turned out, that is not quite what I got. This essay was written by a physicist and it is about the discoverings in physics in the last two centuries. Krauss does that quite well, I have to say, - his writing is way better than Greene's in my opinion - but doesn't illustrate - as it set out to - "the Mysterious Allure of Extra Dimensions from Plato to String Theory and Beyond". To Krauss' credit, I might have given too much importance to that "and Beyond". In that case: my fault.

[Aleksandar Janjic · Rating 2 out of 5]

Моје раније мишљење да скоро све научнопопуларне књиге личе једна на другу као два јајета и да кад прочитате једну као да сте прочитали и остале није баш претјерано пољуљано овим остварењем Лоренса Крауса. Те књиге се можда у теорији баве (бар донекле) различитим темама, али окрени-обрни, на крају ћеш завршит читајући по петстохиљадити пут о Њутну, Ајнштајну, Мајклсон-Морлијевом експерименту, Пензијасу и Вилсону (који су, додуше, из потпуно непознатих разлога ипак одсутни из ове књиге, тј. споменути су, ако се не варам, само онако успут као "два научника која су открила то-и-то"), елементарним честицама, теорији струна, разноразним нагађањима и шпекулацијама о стварном броју просторних димензија и томе слично. Вјероватно су те ствари неопходне кад је физика у питању, али брате зар баш мора да постоји ОВОЛИКО књига које рециклирају те исте теме? Као и већина људи, нисам више тако млад као прије двадесетак година и стварно бих морао да направим неку селекцију у својој листи књига за читање.

О чему се у овој књизи ради, осим о стварима које сте прочитали већ милион пута, можете донекле да наслутите из поднаслова, али само донекле, јер ово "alternate realities" заправо се односи на евентуално постојање више од три просторне димензије. Читава књига је заправо о томе и колико тачно о тој теми може да се закључи на основу наших тренутних теорија у физици (одговор: скоро ништа, бар колико сам ја укапирао). Лоренс Краус је прилично добар писац, међутим ова књига ме једноставно није "зграбила". Спомиње он на разним мјестима разне класике што филма што телевизије што књижевности, укључујући наравно и оне научнофантастичне, али ми те његове референце често изгледају исфорсирано и нисам стекао утисак да је он онакав одушевљени гик као рецимо Мичио Каку, који је вјероватно прочитао и погледао све што је направљено у историји научне фантастике у умјетности. Већи проблем је било праћење свега овога јер многи појмови су објашњени превише штуро или чак никако, а то се односи и на неке кључне појмове, који су, је ли, кључни за разумијевање свега осталог. Ово као да је научнопопуларна књига намијењена широј публици, а заправо је намијењена физичарима. Да не гријешим душу, може врло лако бити и да је до мене и да сам једноставно глуп/недовољно пажљив да све упратим.

Оно што ми се свидјело је Краусова скепса према теорији струна, чије поријекло је јасно из његовог излагања у овој књизи и, иако о физици немам благог појма, имам утисак да бих дијелио његово мишљење да се којим случајем тиме бавим. Оно што ми се НИЈЕ свидјело, поред оног генералног утиска да књига није тако фасцинантна као рецимо Атом, јесте неколико изјава у којима Краус показује фрапантно незнање о неким темама о којима би интелектуалац било којег типа морао да зна (нарочито ако ће већ да пише књигу у којој се те ствари спомињу). Прво, једна врло ситна ситница која заправо и није проблем, али морам да цјепидлачим. Краус на једном мјесту спомиње да Еуклидов пети постулат каже да у равни кроз сваку тачку ван неке праве може да се провуче тачно једна права која је паралелна датој правој. Ово је свакако свима нама познато тврђење из школе и оно јесте еквивалентно петом постулату, али то НИЈЕ пети постулат. Пети постулат заправо гласи овако, пазите добро: Ако су дате двије праве и трећа која сијече те двије, прве двије праве се сијеку са оне стране треће праве на којој она са прве двије праве гради углове чији је збир мањи од два права угла. Љепота овог постулата управо јесте у томе што је срочен на тако бизаран начин, што је вијековима математичаре нагонило на мисао да то заправо уопште није постулат него теорема (тј. да може да се докаже из осталих постулата) и онда су се они јадни трудили цирка хиљаду и по година док Лобачевски и остали нису направили нееуклидску геометрију (што нико О ТОМЕ не напише књигу???). Једна од омиљених ствари у математици ми је пакосни Еуклидов смијех из гроба којим је сасвим сигурно реаговао на ове јалове покушаје. Не мош се зезат са Еуклидом!

Друге двије грешке су много озбиљније природе (ово прво заправо и не можемо да назовемо грешком, можда прије ситном непрецизношћу). "His (мисли се на Ајнштајна) discovery that we are living in a possibly curved three-dimensional space had an immediate popular impact that might be akin to the revelation in Renaissance Europe that the earth wasn't flat. In a single moment, everything changed, and Einstein's fame would soon rival that of Columbus." Само прекуцавање ових реченица у мени је изазвало толику непријатност да сам то једва успио да дотјерам до краја. Имамо једног врло образованог човјека, универзитетског професора и једног од најпознатијих данашњих популаризатора науке, који без трунке блама пише да се стварни облик Земље открио тек у Ренесанси и да је Колумбо на неки начин за то заслужан. И да од свих тих других, такође несумњиво вансеријски образованих и интелигентних, људи којима је Краус дао да прочитају рукопис прије слања у штампу апсолутно ниједан не каже "Чуј, Лоренсе, драг си ми веома, али бриши ово и немој више никад ништа слично да ставиш на папир, смијаће ти се људи!" Ово вам је за наук, дјецо, да су чак и еминентни научници и писци и те како подложни предрасудама.

Други "блундер" је... па, можда чак и гори од овог са равном Земљом. Краус на неколико мјеста говори о бесконачним редовима (то вам је просто збир бесконачно много бројева - нпр. 1+2+3+... и тако у недоглед) и проблемима који се с њима појављују. Ту нема ништа спорно, али Краус уопште не спомиње разлику између конвергентних и дивергентних редова и не каже да се проблеми о којима говори јављају само код ових других (наиме, дивергентних). Ако је ово само малецка непрецизност, о��о што слиједи је много горе. Он каже да је код бесконачних редова могуће, чак и ако су сви чланови позитивни, да збир буде мањи од сваког појединачног члана (хинт: није) и онда као "примјер" наводи "чињеницу" да је сума реда који сам споменуо малоприје, наиме, 1+2+3+... једнака -1/12. Ако вам изгледа потпуно сумануто да саберете бесконачно много природних бројева и добијете разломак који је при том још и негативан, онда сте потпуно у праву. Јесте сумануто и није тачно. Ово је примјер дивергентног реда, а то су они који у збиру не дају коначан број него или плус или минус бесконачно или збир уопште не постоји (нпр. 1-1+1-1+1-...+1-....). Краус спомиње некакве "одговарајуће математичке алате" којима се ова једнакост наводно покаже, али такви алати наравно не постоје. Истина, број -1/12 јесте, бар колико сам чуо, из неких разлога битан физичарима, али то НИЈЕ, понављам, НИЈЕ, збир свих природних бројева. Математика зна бити тешка, али није бесмислена и контрадикторна. Ето.

Да у посљедњем пасусу будем мало мање строг - наведене мане на страну, ако сте пажљивији читалац од мене и ако нисте читали много научнопопуларних књига (нпр. ако су вас потпуно мимоишли Мичио Каку и Стивен Хокинг), слободно на ову моју оцјену додајте још једну звјездицу и сматрајте књигу препорученом за читање. На крају крајева, тужна је чињеница што сам је оцијенио истом оцјеном као Еуклидов прозор, који је скоро потпуна бламажа у сваком погледу и недостојан било каквог поређења. Морам да порадим на својим критеријумима оцјењивања...

[BlackOxford · Rating 2 out of 5]

Scientific Validity Is Not Truth or Reality

Within this brief summary of physics over the past two centuries Krauss has a great deal to say about truth and reality and the way the first is established by the second in science. He puts it this way: “[T]he central question becomes: To what extent do our imaginings reflect our own predilections, and to what extent might they actually mirror reality?” This metaphor of a ‘mirror’ is one that has been casually used for centuries. It has also be roundly critiqued as misleading and problematic for the concepts of both truth and reality (See: https://www.goodreads.com/book/show/3...). Krauss’s book and particularly his criteria for determining the truth of recent scientific theories demonstrates the issues which he seems unaware of.

As background to my interpretation of the book, for example: the physical theory of gravity formulated by Isaac Newton allowed us to successfully land human beings on the Moon and bring them back safely. Does this mean that Newton’s theory is true? No, it is not. More recent theories in physics claim that gravity is not a force as Newton conceived it but rather a distortion in space-time caused by massive objects. Gravity as such is therefore not even a ‘thing’.

But we certainly experience something which we call gravity. Does this mean that we simply don’t have the natural sensory apparatus necessary to detect its real character. Also no, because we have been able to enhance our sensory faculties through technology. This allows us to confirm and precisely measure the distortions in space-time correlated with our experience of gravity.

With our newer relativistic theories we have been able to predict and confirm the movements of large galactic structures. Does this mean that we have been able to ‘approach reality’ more closely? No. Newtonian physics is not a ‘special case’ of relativity physics even if it gives the same suggestions for getting people to the moon. The two are contrary views of reality, with very different ontological concepts. The entire history of physics is one of successive ‘breakthroughs’ the effects of which are to rubbish everything previously thought to be taken for granted about reality. As some physicists put it therefore: Even space-time is ultimately doomed. It doesn’t exist except as a very useful fiction.

I am not primarily suggesting this has anything essential to do with our natural perceptual limits (although there is a good argument that this is the case). I am claiming that it is a consequence of ideas and concepts that are derived from reflection* on this experience, not from experience itself. These ideas and concepts are literally imagined. Krauss points to imagination as the essentially human attribute: “[I]magination almost defines what it means to be human.” And he’s correct. But imagination requires language in order to formulate and communicate, even to communicate the concept of imagination. And there’s the rub.

Krauss goes off the rails when he claims that through science, as a disciplined form of imagination, “… we gain new insights into our own standing in the universe.” This we certainly do not do, unless it is to recognise that “our standing” is entirely uncertain. That is, we know nothing more about the reality of the universe, including our place in it, than we as a species have ever known before, which is precisely nothing.

Surely we are able to do things we have never done before because of the knowledge we have accumulated and shared about ‘how the world works.’ But we can only use that phrase in the strictly pragmatic sense that our knowledge has permitted us to achieve a result based on the behaviour of the universe as it responds to us, not because we know anything about what it is. And part of that knowledge of behaviour is that we have produced innumerable desirable results - like travel to the Moon - using knowledge which we have subsequently learned to be wrong about what is actually ‘there.’. In other words, our ideas and theoretical concepts may useful whether they are true or not and whether or not they conform with something called reality.

Krauss feels that “If we couldn’t imagine the world as it might be, it is possible that the world of our experience would become intolerable.” This seems dangerously close to the religious belief that we need the concept of God to make the world bearable. In any case, the epistemological value of that sentiment is zero. It is a kind of whistling in the ontological dark. By ignoring our own incapacity to definitively match our scientific ideas and concepts, indeed any kind of language, with what is not-language, we repress the knowledge that we cannot control the universe, not even by naming it (See: https://www.goodreads.com/review/show... And https://www.goodreads.com/review/show... And https://www.goodreads.com/review/show... ).

Krauss makes frequent reference to religion as a sort of parallel inquiry into reality. But what he doesn’t seem to realise is that theologians have long recognised the basic principle that fundamental reality, that is what they call God, is beyond any description, that no theory of God’s existence is even remotely correct. So unless scientists wish to call their findings some sort of divine revelation which is fixed in dogmatic formulae that can’t be challenged, they are forced to accept this basic principle. Reality is beyond language. No matter what we are able to accomplish through language, we get no closer to the world it purports to represent.

In fact it seems as if the more we know, for example about quantum physics and general relativity, the less coherent our language about the world becomes. Reality is very likely something beyond our experience given our perceptual limitations and the overwhelming power of our reflective ability. But whatever reality is, it is certainly beyond our capability to express it other than that single word’ reality.’. Krauss’s suggestion that there are “hidden realities” to be discovered through science is therefore highly misleading. There may be many more theories of the world in our future, but none of these will correspond to a reality. Like God, whatever we think reality is, He/It is not that.

Krauss is correct in one specific observation. Science, like art, discloses new ways of viewing the world. But to claim that these new ways are about reality or even an approximation of reality is unsustainable by the standards of science itself. What science creates may be useful, exciting, inspiring. But ultimately it is another form of poetry. Like the best of poetry, science is useful, exciting, or inspiring when it points to something beyond itself that cannot be described by science. Like the best of theology, science is most robust when it recognises that truth, like God, is a fictional ideal which motivates inquiry but can never be reached.

Krauss’s potted history of scientific achievements is really a story about overcoming the prejudices and false presumptions developed largely by previous science. Science, although it is empirical, is never about experience; it is about coherence of the scientific, especially the mathematical, language du jour, and through the things that may be accomplished with that language. It is through incoherence that science progresses in the drive to eliminate it. But there will always be such incoherence, just as there will always be another poem to write (or read).

This is one implication of Gödel’s Incompleteness Theorem in mathematics, perhaps the most significant scientific finding of the 20th century. But this scientific finding, because it implies an infinity of future ‘horizons’ for inquiry, is, it seems to me, far from “intolerable.” It is as inspiring as the knowledge that there are infinite number of poems to be penned or paintings created. Krauss implicitly recognises this himself when he writes, “ultimately the driving force behind all human inquiry is the satisfaction of the quest itself.” This may be the fundamental human instinct correlated with our reflective capability. If so it acts as both a spur and an end point, an end point which is being defined while it is simultaneously pursued.

So Krauss’s unsupportable presumptions about reality and scientific validity lead him to curious conclusions. For example, he says “It is also simply disingenuous to claim that there is any definitive evidence that any of the ideas associated with string theory yet bear a clear connection to reality,” ‘Who cares?’ must be the only reasonable response. Newtonian gravity never had any connection with reality. Einsteinian space-time doesn’t either. Yet both were useful and, for their time, scientifically valid. In many ways string theory is the most coherent version of physical laws we have. Yet we have known from its inception that it is wrong. And it may not be considered ‘useful’ for decades or centuries - like many other scientific and mathematical advances - until one day it is. But it’s correspondence with reality will no be the deciding factor.

Perhaps scientists and their boosters might benefit from a slightly wider reading list. Just sayin’.

*Reflection is the old fashioned term for what is now coming to be called ‘metacognition.’ Being old fashioned I tend to use the former term. But metacognition also has a useful connotation which is important: suffering. Part of this suffering is the necessity of intellectual advance through unlearning what we thought we knew. This is a painful process and we tend therefore to resist it in proportion to the potential advance.

[S. · Rating 2 out of 5]

I actually didn't finished it, I've just given up, something I rarely do.

The problem with this book is that it pretends to be something it's not. I picked it up based on a summary that led me to believe this was a discussion of how the theme of parallel dimensions have been used in science fiction and fantasy literature for many years, with a bit of explanation of the physics behind the concept and why the authors of said literature have misunderstood the underlying physics. I expected it to be written in terms a layperson could understand.

Instead, it's an in-depth discussion of the history of the physics behind alternate dimensions, with very, very little discussion of literature at all. The non-science discussion is basically limited to an introduction in which the author explains how The Twilight Zone inspired him to become a physicists, and a few chapter-opening quotes (though most chapter-opening quotes are from physicists). Much of the discussion involves mathematical concepts that are indecipherable to someone like me, who considers math to be a particularly incomprehensible foreign language. When the author describes these concepts as metaphors, I understand the concepts better. However, Krauss does this far less than I expected.

Someone with a better background in math and/or physics and an interest in dimensions in space time would probably enjoy it better than I did.

[Filip Ligmajer · Rating 3 out of 5]

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These are the luxuries of art and literature: to create imaginary worlds that cause us to reconsider our place within our own world. Science has comparable impact. It, too, unveils different sorts of hidden worlds, but ones that we hope might also actually exist and, most importantly, can be measured. Nevertheless, the net result is the same: In the end we gain new insights into our own standing in the universe.

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In 1856, while still in studying in Cambridge, Maxwell wrote a lengthy paper entitled “On Faraday’s Lines of Force,” in which he attempted to put Faraday’s idea on a solid mathematical footing. This was the first step in his attempts to determine and formulate the laws of electrodynamics in a mathematically consistent fashion, which would culminate in his Treatise on Electricity and Magnetism (1873). By the time his work was completed, he had taken the geometric crutch of Faraday—the electric and magnetic lines of force, and the “fields” they represented—and turned them into entities as real as you or I.

[Audioreader · Rating 2 out of 5]

I received a free copy of this book at the 2005 Canadian Undergraduate Physics Conference, handed to me directly by Lawrence Krauss. I found it more boring than any of the other popular level physics books I had read before...I just couldn't get into it.

This shouldn't reflect on Lawrence Krauss, who I think is a great guy and I respect his work both in and out of physics. I'm planning to try his latest book "A Universe from Nothing"

[Michael Norwitz · Rating 4 out of 5]

Well-written account of the history of multi-dimensionality in the history of the sciences. I was engaged by the book although (as someone obsessed with alternate realities in fiction) it is NOT as literarily oriented as the cover makes it seem.

[Boštjan · Rating 5 out of 5]

The author fascinates with history of science, cultural references, and the book also doubles as his memoir.
He reminds readers about the hidden realities that our forefathers have been wondering about, like Plato's allegory of the cave, or Alice in Wonderland etc.
Groundbreaking scientific discoveries of Faraday, Maxwell and Einstein are well explained, too.

Krauss has a gift for demystify profoundly complex ideas (such as electromagnetism, relativity, quantum mechanics, string theory) without dumbing them down. I felt like I was sitting with a brilliant, patient, and wonderfully witty friend who was guiding me through the most exciting ideas at the frontiers of physics.
I liked reading about his honest and balanced assessment of string theory, especially because the next two books I read were a sharp critique by Lee Smolin.

Hiding in the Mirror is a thrilling, enlightening, and deeply human journey. It didn't just teach me about physics; it made me feel the awe and wonder that drives scientists to ask these profound questions in the first place. I cannot recommend it highly enough.

[David Zubl · Rating 3 out of 5]

Don't be deceived by the blurbs on the back cover and inside pages... this book is not for the faint-of-heart! I enjoy reading books on science, and don't mind giving my brain a moderate workout, but much of this book was beyond me.

I don't mean that as a criticism; it says more about me than about the book. I did finish it, but will admit to reading really quickly over many of the middle chapters.

What I took away from this book is an appreciation for the intricacies of physics, and for the imagination and determination of scientists who spend years (and careers) exploring avenues of thought that may or may not lead to meaningful results. Without this hard, complicated work, we would have a much more limited understanding of the universe.

Reading this book was a humbling experience for me... though I will say that I now know what "compactification" of extra dimensions means! (Now if I could just find a way to work that into casual conversation...)

[Voyt · Rating 3 out of 5]

Induction or deduction?
POSTED BY ME AT AMAZON 2005
Science is said to proceed on two legs, one of the theory, and the other of observation and experiment. What Lawrence Krauss conveys in a very gallant and respectful way is, that we have too much of induction going on in today's modern cosmology physics. He praises all involved scientists, but at the same time is gently dubious about strings.
Blame Kaluza for this, blame his theory of "extra dimension" for huge cohort of math-tweaking physicists trying to convince science and general population about Braneworlds and large number of other string related theories apparently solving so called "hierarchy problem".
The book is complete, I read it with pleasure. I will direct criticism to chapters 13 and 14 where text is less coherent. Second drawback: book "cries out" for just one drawing representing scale of different forces and their unification. Overall: decent read and good summary of strings/branes. It altered my opinion about it.
Many particles (supersymmetry) or many dimensions (strings)? - be your judge. But how possibly can we believe that our reality is based on theories ruled by weird mathematics of AB=-AB? I will not buy it now lightly, not since I have completed reading "Hiding in the Mirror".

[Randall Scalise · Rating 3 out of 5]

Page 49: "The term general here refers to the fact that special relativity applied to observers in constant relative motion. What general relativity did was to extend these considerations to accelerating observers."

This is not correct. Special relativity can handle accelerations perfectly well. In SR, the spacetime is flat; in general relativity, the spacetime is curved. Gravity is the curvature.

Page 72: "It was, after all, in 1900 that Lord Kelvin uttered his famous remark that all laws of physics had already been discovered and all that remained were more and more precise measurements."

Kelvin never said this. In fact, he said the opposite.
https://www.bbvaopenmind.com/en/scien...

Page 132: "When considered using appropriate mathematical tools developed to handle infinite series, the sum of the series 1 + 2 + 3 + 4 + 5 + . . . can be shown to not equal infinity, but rather −1⁄12!"

Complete bullshit. https://www.youtube.com/watch?v=YuIIj...

[Amedeo Balbi · Rating 4 out of 5]

Ne parlo qui: http://www.keplero.org/2008/11/dietro...

[So Hakim · Rating 3 out of 5]

Sometimes I feel that some -- repeat, some -- popular physics writers forget that they write for people without physics background. Well, that applies to this book.

Don't get me wrong, I like Lawrence Krauss; his "Physics of Star Trek" was good. Unfortunately in this one he seemed to miss what made that book enjoyable: more diagrams, more analogy, and less name-checking obscure scientific figures.

I mean, readers familiar with physics know about Kaluza, Yang-Mills, and the likes. They also, at least supposedly, have idea about supergravity, supersymmetry, spin, meson, etc. The problem with this book is not that the terms were not explained -- they WERE -- but slogging through the pages, less-accustomed readers will start to wonder: "Uh, what does meson mean again...?"

You have the idea.

It gets slightly worse with how many physicists' and mathematicians' name dropped like confetti. Here's an example I take randomly (from page 169):

"But even before all of this—indeed, within a few years of the first GUT proposal and of Wess and Zumino’s elucidation of the possibility of supersymmetry in our four-dimensional universe—there was another reason proposed for considering a supersymmetric universe, but this time not in four dimensions, but rather in eleven dimensions. As I keep stressing, the development of GUTs set the stage for far more ambitious theoretical speculations about nature. Once scientists were seriously willing to consider scales a million billion times smaller than current experiments could directly measure, why not consider scales a billion-billion times smaller? This scale is the Planck scale, where as I have mentioned one must come face to face with the problems of trying to unite gravity and quantum mechanics. Thus it was that from 1974 onward, a growing legion of physicists began to turn their attentions to this otherwise esoteric legacy of Einstein."

So, yeah...

I would give 3 stars because of neat chronological exposition, also, for explaining context behind the scene of discoveries. Seriously though: it could have been better.

[Jim Razinha · Rating 5 out of 5]

Five stars, because I love this stuff...and he does an amazing job of simplifying very complex concepts. Well, that is until he got to D-branes and M-theory...kind of lost me there for a bit.

Oh, and he gets five stars for saying things like

I will also attempt to present a "fair and balanced" treatment of string theory (in a "non-Fox News" sense)

and on Hubble's initial estimation of the age of the universe being only 2 billion years (he revised it)

This was embarrassing, because the earth was, and is, known to be older than that, except by school boards in Ohio, Georgia, and Kansas perhaps.

and in the same vein on Euclidean vs non-Euclidean geometry...

As any European high school student could tell you, the sum of the angles inside this triangle is 180 degrees.

This is a wonderfully composed progression of physics history from Plato to string theory and Krauss was in my reading extremely fair and balanced in his discussions of the various incarnations of string theory. Easy to read, not focused on the math. I think it takes someone extremely comfortable with the subject to simplify it for the masses. He did well.

My two nit-picks, for all the accolades I can gush:
1) Krauss opens with a Twilight Zone quote and a snippet from an episode that dealt with another dimension...and he got the title wrong (three times in the text, so it was not just a typo). It was "Little Girl Lost", but he called it "Little Lost Girl".
2) He misquotes a line from his favorite movie (The Adventures of Buckaroo Banzai across the Eighth Dimension) - he said "Wherever you go, there you are." but it really was "...no matter where you go, there you are"

Why is that important? If Glenn Beck or Bill O'Reilly misquoted, I'd shrug it off because I expect that from them, but I expect that Krauss's editor didn't bother checking because he was Krauss.

Still, I very highly recommend this book for anyone interested in the subject who doesn't want to mess with tensors and other such math.

[Paul Weimer]

A non fiction book pimped heavily by Ira Flatow on NPR, Hiding in the Mirror is an overview of cutting edge cosmology and particle physics by Lawrence Krauss.[return][return]The full title of the book is: Hiding in the Mirror: The Quest for Alternate Realities, from Plato to String Theory (by way of Alicein Wonderland, Einstein, and The Twilight Zone)[return][return]In reality, Plato, Alice, Einstein and the Twilight Zone are hooks for Krauss to investigate and discuss higher dimensions, string theory, particle physics, cosmology and a host of related subjects and digressions underneath that umbrella.[return][return]Starting with a memory of a Twilight Zone episode ("Little Girl Lost"), Krauss explores the ideas of extra dimensions, eventually getting into particle physics, quantum gravity, and string theory. Having written about and clearly being a big fan of Star Trek, Krauss is tuned into popular culture and uses examples from science fiction as vehicles for discussing some very tricky subjects. He's not a devotee at the church of String Theory, and so his view of it is somewhat more skeptical than other books I've read on the subject (eg, Brian Greene's work). [return][return]Krauss does a good job at balancing the material. Its difficult to make these esoteric subjects accessible to everyone, and perhaps only someone like Carl Sagan could have done much better. Equations are at a bare minimum in the book. I did take away a better knowledge of some of the corners of particle physics. Since reading this, I picked up the latest Scientific American, and a discussion of some particulars of bosons in an article made me think "Aha! Krauss discussed *that*!"[return][return]I think its a good primer on these subjects for intelligent readers who want to know more about some very tricky subjects.

[Graham Crawford · Rating 2 out of 5]

This is a very problematic book. At best it's a call for science to remain true to its experimental roots and not slip into a faith based religion of mathematics. At worst it's a bitter (name dropping) rant at the current crop of young (post 1984) physicists who have eclipsed the careers of the good old boys who work with particles and heavy lifting machinery.

No-one - let alone me, can say who is correct yet, but I can certainly comment on how successful the writing in this book is. It suffers from not really knowing who it's audience is for. Sometimes he's writing for String theorists, trying to convince his (mostly younger) colleagues they are too enthusiastic. Other sections seem to be aimed at a more popular audience, but lack the clear exposition other books in this field have. He is certainly not an educator - often leaving out important steps in his examples because he makes huge assumptions about his readers' knowledge. Diagrams are often unclear, and many analogies are murky.

The best of this book is the roughly chronological history of the theories that bit the dust, and how many of these were subsequently dusted off in new contexts several decades later. However his skepticism about String theory paints most of the current possibilities in the same colour as the red herrings of the past, so it can be confusing to follow which of the competing models was/is accepted and/or promising Science.

His mantra that Science should not be emotional or enthusiastic about things might make a good researcher, but it makes for a very dry book. That said - I'm still looking forward to his new Post Cern/Higgs book - where he presumably puts the boot into those sloppy stringers once again. :-)

[Maurizio Codogno · Rating 4 out of 5]

Come dice il mio amico Fabio (beh, è vero che anche lui come me è un matematico...), il tempo di validità di un articolo con un nuova teoria in fisica teorica è leggermente inferiore a una settimana. D'accordo, esagera un po'; ma è vero che nell'unico secolo sono state proposte decine di teorie più o meno simili tra loro e sempre piuttosto esoteriche. In questo libro Krauss, noto per aver scritto La fisica di Star Trek, usa come filo conduttore le proposte di aggiungere dimensioni (spaziali) addizionali per far quadrare i conti nelle teorie di unificazione delle forze fondamentali. L'autore la prende molto alla lontana, con Faraday e la sua nozione di campo che a detta sua è stato il primo esempio di una teoria che dà come esistente qualcosa che in effetti non c'è, e continua con un racconto scritto in modo appassionante di come le varie teorie sono sorte, messe nel dimenticatoio, riciclate perché come per il maiale non si butta mai via nulla. Non garantisco che, nonostante l'ottima traduzione, alla fine uno abbia capito come funzionino le varie teorie delle stringhe; ma quello mi sa sia un problema della fisica e non nostro.

[Rose · Rating 4 out of 5]

I liked this book a lot, but it is very specific in subject material and the reader will probably not enjoy it unless they have at least some basic knowledge of quantum mechanics, particle physics, and string theory.

All in all, the author did make the book easy to understand for the most part from the point of view of someone who does not have the mathematics background for this stuff, but there were parts of the book that did completely lose me. It wasn't too bad, but I can see where it would be frustrating for some readers.

Essentially, the author takes us through a history of our obsession with finding alternate realities/dimensions/etc. in the scientific realm and the discoveries in physics and math that have led us to where we are today when thinking about complex quantum physics and why the universe ticks. It isn't too long of a read, but again the subject material may go over the head of the layperson. It went over my head quite a few times.

[JS Found · Rating 3 out of 5]

I'll have to read this book again; I failed with it. I'm not scientifically minded and I haven't practiced reading other physics books to understand better what's going on in that world. After the best explanation of relativity I've read, I got lost in the explanation of particle forces and of string theory. The book isn't--what you may infer from the cover--a look at science in pop culture, but a primer on 20th century particle physics. There are a few chapters on representations of other dimensions in art, but it's mainly a tutorial on why some scientists believe there are other dimensions that exist outside our four dimensional universe. But to get there, Krauss has to explain hard--for me--topics like gauges, quark confinement, the hierarchy problem, and so on. I wouldn't trust my own review. Read it and see if you understand it.

[David Olmsted · Rating 5 out of 5]

This book first published in 2005 is a balanced, clearly written history of the allure of extra spatial dimensions in both science and literature. The main goal of this book is to show how these extra spatial dimensions are ultimately used in string theory which is claimed by its promoters to be the ultimate theory of physics able to unify all the forces of nature. This author is justifiably more skeptical of string theory than other book authors on the subject because the theory has yet to produce any testable predictions.

I did especially enjoy chapter 7 entitled "From Flatland to Picasso" which described the history of multiple dimensions outside of science starting in the late 1800's.

[Scott · Rating 4 out of 5]

Not a light read but amazingly fascinating

For those of us not physicists or mathematicians, the concepts in this book are challenging but also enlightening. To understand the very nature of the universe and everything in between, is the very foundation of a species that explores its own existence and truths.

I thoroughly enjoyed reading this book, albeit at times the challenge of truly comprehending all the content was above where I need to be. People may be afraid to try to read complex theories but it is important we all do comprehend the discovery that is the essence of who we are and where we are going.

If you are up for that challenge, then you have to read this book.

[Jason · Rating 3 out of 5]

The first few chapters were slow going, but the middle chunk was great. A good overview of just what the title says, the allure of extra dimensions. The last few chapters spoke about string theory, and Krauss and I share a more skeptical nature of the validity of string theory, but was still a decent read.

A few typos throughout, and some parts I had to slog through, but if you're looking for a fair summary of the background of how science has explored extra dimensions, this seems a good place to start

[David · Rating 4 out of 5]

I love Dr. Krauss - exactly as engaging in person as he is in writing. You want to have a beer with this guy, which is my standard for trust and humaneness of approach. In my voluminous free time, I want to check off his other books too (Physics of Star Trek, anyone!?)

[Dave Peticolas · Rating 4 out of 5]

Excellent. A physicist examines the history of our fascination with extra spatial dimensions in religion, philosophy, popular culture, and science. Most of the emphasis is on science and, in particular, string theories.

[Greg Berghorn · Rating 3 out of 5]

Hyperspace concepts (hidden dimensions beyond 3D) have always fascinated me.

[Tom Lobur · Rating 4 out of 5]

Hiding in the Mirror gets a little dense for my limited abilities in the latter chapters. Still a good book, though.

[Melissa Banaszak]

This is a book that is very good if you are interested in String Theory,Alternate plains-Black Holes,etc.
It is NOT light reading-but is VERY interesting.

[Morgan Storey · Rating 5 out of 5]

Excellent book on cosmology and quantum dynamics