Hyperspace is a lively, fascinating, and highly readable account of state-of-the-art theoretical physics as of 1995. Arguably, the theories under discussion in this volume are outside the realm of science since they are at present, as they are likely to be into the far distant future, empirically unverifiable. Even so, as Kaku argues, science may yet uncover indirect evidence of wormholes, dimensions 5-10, and strings. Whether or not this proves true, one cannot help but be awed and delighted by the mere possibility that the universe -- fascinating already in its meager 4 dimensions -- is structured and functions in the ways MK describes. To see the mathematics of higher dimensions so neatly subsuming the laws of physics as we know them (electromagnetism, relativity, etc.), one cannot help but imagine that a beautiful and simple unified theory might indeed lie just round the bend. Hyperspace thrills with the excitement of that possibility. It is a terrific read.

The book is a good introduction to hypersapce,parallel universes, supergravity, string theory and every other physics theory difficult to understand for the lay person. Dr. Kaku interests the reader to a new world of possibilities.

Now almost 15 years old, this book is still an interesting read. An entertaining and well written introductory tour of superstrings and the quest for unification, with a little essential history of the evolution of physics and mathematics thrown in. (Mathematics is, after all, the language of physics, of which every modern student of physics is well aware.) It will take about the first 100 pages to get the experienced physics reader interested, and then it's a quick dash to the finish. Much of the text is on the speculative level, and there is a fair amount of redundancy. (Kaku repeats himself a lot, to the point of being periodically annoying.) One thing I found glaringly missing from the religious "logic" discussion was mention of either Rene Descartes or Blaise Pascal.

One amusing consequence of the "beauty" and "no empirical evidence" discussion concerning higher dimensional superstring theory is that these are precisely the arguments used by many theologists and lay religious adherents alike to justify the existence of God, as well as their faith. This suggests that modern (quantum) physics is in danger of becoming more religion then science, and its practitioners of becoming more a priesthood than a scientific community. But then this has happened before in physics - at least until the "test of time" transfigures faith into fact.

I gave the book 4 stars instead of 5 because of the redundancies, typos or misspellings that seem to occur every 20 pages or so.

good book. explains details in a way that laymen can comprehend. i never took any physics- but i was capable of understaning dr. kakus book. he is well spoken and well versed in the modern beliefs of theoretical science.

I really enjoyed this book when I was fresh out of high school. However, reflecting back on this work, it really is nothing more than a delightfully written book on a large collection of theories that have not been and probably cannot be verified through empirical observation. Sure, it might be amusing to hypothesize about parallel universes, superstrings, time machines and the like. Nevertheless, I do not see the utility in doing so until we have a compelling reason to believe that these things might exist.

I truly enjoyed this book. Except for some off-topic ramblings in the middle about the relationship of art to modern science, and some of the author's conceptual aids to help explain or express complex physical theories, I was thoroughly engrossed and mentally stimulated. Kaku has a respectable command of his subject and prose, even if, at times, there was some repetition. (In this type of book, repetition is a given.)

The book is virtually free of mathematics. Consequently, there are places the reader has to take Kaku's explanations and descriptions at face value. Having no math to back up theory isn't necessarily a bad thing, but it leaves even the expert word smith (and I consider Kaku to be one) at a disadvantage. On more than a few occasions I was unable to rap my brain around literal or diagrammatical attempts to explain principles and theories of math and physics. Of course, this might be my failing as a reader instead of Kaku's. It's possible I just didn't get it for the simple reason I didn't want to take the extra time for conceptualizing. (I was more anxious to get to his discussion of multi-dimensional space.)

As opposed to some of the other reviewers, I found the last two sections most enjoyable and enlightening. In the final two sections 'Wormholes' and 'Masters of Hyperspace', Kaku skillfully addresses multi-versus, traveling through time, the death of the cosmos; he encompasses divergent opinions and arguments from various perspectives (math, physics, cosmology, religion), comments on the difference between a God of Order and a God of Miracles, and concludes with a reasoned and hopeful statement about man's ability to solve the mysteries of nature.

I plan on reading more from this author.

-seabgb

The book is nicely organized and explains most of the popular theories till date in very basic layman terms which most anybody can understand and keeps you engrossed as you go along. There are also lots of quotes and reactions by all the great minds... Definitely a must read for anyone interested in all the work over 2 centuries by great physicists to understand and search for the unified theory to explain everything in the universe.

...with this book. The author does an excellent job of explaining the theories behind some of the most complex scientific theories to date through the use of analogies and examples. I picked up this book at the tender age of 15 and was riveted to it for weeks, unable to unglue my eyes. A great read for the casual scientific reader looking for someone to sit them down and explain the complexities of the universe.

I'd also recommend The Elegant Universe: Superstrings, Hidden Dimensions, and the Quest for the Ultimate Theory

A must have primer in the physics world. His writing is easy to follow even through some heavy duty stuff.

In this painless, friendly, math-devoid dissertation, Michio Kaku attempts to explain the existence of "higher dimensions". These are
abstract concepts and may be hard to accept.

The day will come when mankind will comprehend, utilize, and exploit the means to slip through hyperspace. Whether this road to hyperspace was
mapped out by Dr. Kaku is sheer speculation for now. Neophytes take note: this book is a good start.

I'm not a scientist (I'm a classicist) and didn't even enjoy science in school at all. In fact until writers like Michael Behe, Heinz Pagels and Michio Kaku came along science was totally unapproachable for me. For a writer to take such incredibly complex information and present it, not only clearly and understandibly, but also enjoyably, one has to be uniquely gifted. Kaku and Behe can do this and remain my favorites. It's been years since I read this and to this day I can't forget it. So, here's my point. If you, like me, long to understand fascinating ideas that have always seemed incomprehensible, let Michio Kaku help you out. Get this one.

Even though this book is over ten years old, it has paved the way to understanding a little bit more about this universe, prallel universes, ten dimensions and even time warps. Shades of Star Trek and Star Wars!
It's wonderful! Kaku stretches the mind and for a lay person an easy read.
Kaku gives a greater insight into quantum physics without the long equations. I recommend it. Bettye Johnson, award-winning author, Secrets of the Magdalene Scrolls.

This book has been around for more than a decade now, and while some of the material within is a bit dated, the general principles are very accessible through Kaku's writing style. I'd still highly recommend this book as a good introduction to string theory for the layman.

Once you finish Hyperspace, then I would recommend Brian Greene's The Fabric of the Cosmos: Space, Time, and the Texture of Reality and after that Lisa Randall's Warped Passages: Unraveling the Mysteries of the Universe's Hidden Dimensions. Of course, The Elegant Universe is a good intro as well, but your can rent the DVD.

No matter which other books you choose to read, Michio Kaku's Hyperspace is a necessity, because he mentions things you won't hear elsewhere.

Wow, this book was just plain fun to read. Better yet, it was not dumbed down in any way, yet it was completely understandable. This world of cutting-edge physics is not just interesting, but also important. It really makes one wonder what is possible if we can ever solve these last mysteries of physics. I particularly thought he explained higher dimensions well. It's a very difficult idea for us 3 dimensional beings to wrap our heads around, but he manages to give a thorough and convincing explaination. You won't regret buying this book, you'll blow right through it and be telling all your friends about the crazy things you learned about hyperspace.

Once again, Dr Kaku has produced an informative yet accessible book on modern physics. Although this isn't up to date on the latest developments in strings and M theory, the reader isn't likely to be looking for the latest technical findings and conjecture. If what you're seeking is an interesting and absorbing account of this intriguing but untested field, then this is probably the first book you should read on the subject. What makes string theory so fascinating is that it is following the same sequence as previous breakthroughs in physics: a concept is thought out, found to be mathematically consistent, a model is developed, and finally, testing confirms the model. String theory (M theory) has progresssed to the model stage, but we currently lack the technical means to test that model. But the fact that the numbers are in agreement makes it look promising.

Don't be concerned about the math, though. The book mentions some mathematicians and their contributions, but the reader isn't required to get out his pocket calculator to follow along. The book is 99% fact and science, in popular form, and about 1% interesting speculation on what the model implies, if it's accurate. And those implications are stunning: parallel universes, possibly infinite in number, with every conceivable permutation of reality, and many more beyond our comprehension.

When the author wrote this book string theory was very "hot"... it has since cooled a lot.
The main problem is that string theory is a limiting "scale".
Physically and geometrically that seems to be just wrong.
This book is somewhat better than the run of the mill Popularization or
"dumbing down of physics", because he is faithful to history and names specific equations
( mostly without giving them) like the modular functions of Ramanujan.
I think the author could learn something about this kind of writing from Robert Kanigel ( biographer for Ramanujan).
This author appears to be a pathological string field theory and superstring physicist in combo of 10 and 26 dimensions.
But he by being faithful to his materials gives even more advanced readers Google searchable names and important papers.
And unlike the Nobel prize winner Steven Weinberg , this author hasn't lost either hope or faith in the future or faith in humanity
to solve impossible problems. The book has a sense of history and a likable tone of writing.

When the author wrote this book string theory was very "hot"... it has since cooled a lot.
The main problem is that string theory is a limiting "scale".
Physically and geometrically that seems to be just wrong.
This book is somewhat better than the run of the mill Popularization or
"dumbing down of physics", because he is faithful to history and names specific equations
( mostly without giving them) like the modular functions of Ramanujan.
I think the author could learn something about this kind of writing from Robert Kanigel ( biographer for Ramanujan).
This author appears to be a pathological string field theory and superstring physicist in combo of 10 and 26 dimensions.
But he by being faithful to his materials gives even more advanced readers Google searchable names and important papers.
And unlike the Nobel prize winner Steven Weinberg , this author hasn't lost either hope or faith in the future or faith in humanity
to solve impossible problems. The book has a sense of history and a likable tone of writing.

A good book for understand higher dimensions with examples, dates and works of famous mathematicians and physicists.

A good book for understand higher dimensions with examples, dates and works of famous mathematicians and physicists.

I say great airplane book because I fly internationally a lot and this book is ALWAYS in my carry-on. Even though I've read it probably 30 times through, I never skip chapters, it still is a great read each time. I'm trying to do the "physics by osmosis" method of learning.

I say great airplane book because I fly internationally a lot and this book is ALWAYS in my carry-on. Even though I've read it probably 30 times through, I never skip chapters, it still is a great read each time. I'm trying to do the "physics by osmosis" method of learning.

Humankind dreams control time and space. This holistic superstring plain mathematical theory aproaches reality in this amazing book.
Easy to read at once. Sometimes very interesting few times boring I recomend give your time to this book.

Kaku attacks some very difficult subjects in Hyperspace. Subjects usually reserved for theoretical physicist and mathematicians. Kaku not only adeptly conveys these supremely difficult subjects in a way that the average reader can understand, but also takes the reader on a well organized and engaging journey through the theory of everything. If you have ever wondered if time travel will ever be possible, if other dimensions exist, or if humans will ever live on other planets in other galaxies then this book is for you. It will give you the theoretical physicist's point of view on these mysterious subjects. This book is supremely informative and wonderfully entertaining. I gave it 4 1/2 stars instead of five, because of the last Chapter which was contrived and superfluous.

The book is a bit outdated, as to be expected, and does not include M theory, the theoretical, incomplete theory unifying the many string theories. The book used too many technical terms without explaining them in depth. As the pages went on these terms built up until I was pretty lost. I just figured it was due to the complexity of the subject but then I research it online and find a very short webpage that described things wonderfully.

I attended Kaku's lecture on Hyperspace in 1995 when he came to the Science Museum to launch his book. The lecture and the book were mesmerising. The book is worth reading again and again. I just finished reading it a few weeks ago and thought it worthwhile to make a brief comment.

Kaku diligently takes the layman through the odyssey of time and space and explains complicated theories in simple terms. Did you know that all of us have heard about the theory of Hyperspace? Read Alice in Wonderland, read Hyperspace, and then read Alice in Wonderland again.

The concept of multi-dimensions to a 3D audience has been simply explained by Kaku and, like Richard Dawkins, makes the reader feel intelligent! What used to belong in the realm of science fiction is now being accepted as a plausible theory on the evolution and end of our universe. It is a shame that we won't live long enough to see if Superstring/Hyperspace theories are proven to be true or not!

I do like Kaku's debate into various philosophers and their ideas about the universe and their concepts of God. I also liked his slight digression into the classifications of possible intergalactic civilisations into 3 types depending on the advancement of technologies and management of their solar resources. These are worthwhile digressions which support the main body of the book, which is a multidimensional universe.

If you are a Star Trek fan or interested in Astronomy or you are just plain interested in our universe, this book is for you. I can't wait to get hold of Kaku's newer books!

I don't know about you, but Michio Kaku is freaking me out. It's this new theory of parallel worlds. Imagine: infinite universes out there, many of them with near identical copies of you. They say every possible outcome in your life will occur in another universe.

So, you're a dismal failure who never achieved anything. Don't fret. In a parallel universe, you might be drinking expensive champagne on your yacht and talking shop with Donald Trump.

So, your wife ran off with your brother and took the truck and the dog to boot. Take heart. One universe over, the shrew is serving you drinks and vacuuming floors in your palatial estate. Your dog watches over your fleet of trucks and your brother is in prison.

So, the Red Sox finally win a World Series after 86 years of heartbreak. It's been year after year of thwarted hopes, for as long as you can remember. But somewhere in the multiverse, the Sox have won so many championships, it's sickening.

Every possible outcome. Those horrible mistakes you made here never happened there. You ate right, exercised and took vitamins every day in some other universe. You are buff and not ashamed to take your shirt off on the beach in another dimension.

The multiverse has its privileges. And it is scientists who claim it as fact, not tabloid writers drunk on cheap wine. To account for errors in the math of quantum physics, some say the existence of multiple universes is the only possible solution.

Before you go scoffing and stuffing this review into the bird cage, think about the possibilities. You can eat ice cream all you want because in another universe, you do ab crunches every day. You can tell your boss off right now because in the other world, you are independently wealthy.

Personally, I feel liberated. I'm going out to buy a boat and some cool cars because I can probably afford it one or two dimensions over. If that money-grubbing Mark LaFlamme in the next universe isn't good for a loan, who is?

Really, man, it's time to relax. String theory dictates that our time here is really not that important. We're just an insignificant speck in an infinitesimal bubble in the froth of a sea of universes. Stop hollering and worrying all the time. Chill out and let some other you do all the heavy lifting. This applies especially to politicians and city leaders.

Few scientists can write with the clarity and enthusiasm that Kaku achieves every time. Read him or watch in on countless science specials on TV, and you start thinking about these possibilities in a real world way. Kaku is a brilliant man and one who loves to share his knowledge and theories. Kaku may be formulating the theory of everything this very moment.

I'm getting carried away. I know I am. People who don't absolutely love books like "Hyperspace" back slowly away from me when I start talking about the multiverse. My wife doesn't allow words like singularity or participatory anthropic principal around the house. Not in this world, anyway.

I don't know about you, but Michio Kaku is freaking me out. It's this new theory of parallel worlds that's getting so much attention. Imagine: infinite universes out there, many of them with near identical copies of you. They say every possible outcome in your life will occur in another universe.

So, you're a dismal failure who never achieved anything. Don't fret. In a parallel universe, you might be drinking expensive champagne on your yacht and talking shop with Donald Trump.

So, your wife ran off with your brother and took the truck and the dog to boot. Take heart. One universe over, the shrew is serving you drinks and vacuuming floors in your palatial estate. Your dog watches over your fleet of trucks and your brother is in prison.

So, the Red Sox finally win a World Series after 86 years of heartbreak. It's been year after year of thwarted hopes, for as long as you can remember. But somewhere in the multiverse, the Sox have won so many championships, it's sickening.

Every possible outcome. Those horrible mistakes you made here never happened there. You ate right, exercised and took vitamins every day in some other universe. You are buff and not ashamed to take your shirt off on the beach in another dimension.

The multiverse has its privileges. And it is scientists who claim it as fact, not tabloid writers drunk on cheap wine. To account for errors in the math of quantum physics, some say the existence of multiple universes is the only possible solution.

Before you go scoffing and stuffing this review into the bird cage, think about the possibilities. You can eat ice cream all you want because in another universe, you do ab crunches every day. You can tell your boss off right now because in the other world, you are independently wealthy.

Personally, I feel liberated. I'm going out to buy a boat and some cool cars because I can probably afford it one or two dimensions over. If that money-grubbing Mark LaFlamme in the next universe isn't good for a loan, who is?

Really, man, it's time to relax. String theory dictates that our time here is really not that important. We're just an insignificant speck in an infinitesimal bubble in the froth of a sea of universes. Stop hollering and worrying all the time. Chill out and let some other you do all the heavy lifting. This applies especially to politicians and city leaders.

Few scientists can write with the clarity and enthusiasm that Kaku achieves every time. Read him or watch in on countless science specials on TV, and you start thinking about these possibilities in a real world way. Kaku is a brilliant man and one who loves to share his knowledge and theories. Kaku may be formulating the theory of everything this very moment.

I'm getting carried away. I know I am. People who don't absolutely love books like "Hyperspace" back slowly away from me when I start talking about the multiverse. My wife doesn't allow words like singularity or participatory anthropic principal around the house. Not in this world, anyway.

Wow.

This book is just plain amazing. After seeing Professor Kaku on a television show call "Parallel Worlds" two years ago, I was immediately intrigued. But now that I have read Professor Kaku's book, I'm hooked!

The concepts and sheer amount of material in this book is mind boggling. But what is still so amazing to me is how Professor Kaku brings some of hte wildest ideas in Physics down to earth so a lay-person like me can understand it with no problem. Of course, it is good to have some basic knowledge about physics before you go diving into this book, but only the extremely basic stuff.

Wormholes, Time travel, Multi-dimesional spaces, it's all here, and best of all, it's all crytal clear! Professor Kaku takes the almost mind boggling idea that all matter in the universe is made from vibrating strings that are 10^-32 mm long. He also discuses the possibility of traveling through a black hole and going beack in time to "fulfill" an event (as physics shows one cannot change the events of the past, only eleborate on them). Another brilliant trait of this book is Professor Kaku's ability to make every key idea into an easily understandible anicdote. What Professor Kaku does in this book is explain the ideas first in a scientific sense, then "laymanizes" the same ideas through a story or real-world example.

Besides that this book is purely science, it is just plain facinating. Professor Kaku "shows" what it would be like to enter the 4th demension as a 3-D being. He also discusses the idea of other deminsions in our universe, and what strange happenings would occur there. One instance is what would happen if we were to enter a 5th dimensional Hyper-donut, how we would persive ourselves in line w/ several other people, and when we attemted to put our hand on their shoulder, we would feel a hand on our shoulder ( in otherwords, we have reached around the donut and grabbed our own shoulder. The other people in front of us are actually us! We're seeing our backside in front of us!).

And this isn't all, thsi book is purely amazing. Everyone should read this book. As one of Professor Kaku's promises, after reading this book, "You will never look at the universe in the same way". Amazing Read.

Wow.

This book is just plain amazing. After seeing Professor Kaku on a television show call "Parallel Worlds" two years ago, I was immediately intrigued. But now that I have read Professor Kaku's book, I'm hooked!

The concepts and sheer amount of material in this book is mind boggling. But what is still so amazing to me is how Professor Kaku brings some of hte wildest ideas in Physics down to earth so a lay-person like me can understand it with no problem. Of course, it is good to have some basic knowledge about physics before you go diving into this book, but only the extremely basic stuff.

Wormholes, Time travel, Multi-dimesional spaces, it's all here, and best of all, it's all crytal clear! Professor Kaku takes the almost mind boggling idea that all matter in the universe is made from vibrating strings that are 10^-32 mm long. He also discuses the possibility of traveling through a black hole and going beack in time to "fulfill" an event (as physics shows one cannot change the events of the past, only eleborate on them). Another brilliant trait of this book is Professor Kaku's ability to make every key idea into an easily understandible anicdote. What Professor Kaku does in this book is explain the ideas first in a scientific sense, then "laymanizes" the same ideas through a story or real-world example.

Besides that this book is purely science, it is just plain facinating. Professor Kaku "shows" what it would be like to enter the 4th demension as a 3-D being. He also discusses the idea of other deminsions in our universe, and what strange happenings would occur there. One instance is what would happen if we were to enter a 5th dimensional Hyper-donut, how we would persive ourselves in line w/ several other people, and when we attemted to put our hand on their shoulder, we would feel a hand on our shoulder ( in otherwords, we have reached around the donut and grabbed our own shoulder. The other people in front of us are actually us! We're seeing our backside in front of us!).

And this isn't all, thsi book is purely amazing. Everyone should read this book. As one of Professor Kaku's promises, after reading this book, "You will never look at the universe in the same way". Amazing Read.

I'm not a science brain, just an average T.V. viewer who greatly enjoyed this book. I had no problem understanding the physics explained in this book. After seeing the television series "The Elegant Universe," I wanted to read more about it. Kaku's book "Hyperspace" explains the theories of Einstein, 10 dimentional space, superstrings, etc. I found the book very insightful and interesting. I enjoyed every page. I would rate it with more stars if I could.

I'm not a science brain, just an average T.V. viewer who greatly enjoyed this book. I had no problem understanding the physics explained in this book. After seeing the television series "The Elegant Universe," I wanted to read more about it. Kaku's book "Hyperspace" explains the theories of Einstein, 10 dimentional space, superstrings, etc. I found the book very insightful and interesting. I enjoyed every page. I would rate it with more stars if I could.

Just my humble thanks for so rewarding experience as I got from reading this book.

It is the first time I really understand the conceptual basis of Einstein's Relativity by grasping the meaning of the equality "force=geometry". This concept of force is as beatiful as profound. And it came so early as 1854 in a legendary lecture by Bernhard Riemann. In fact, the chapter on Riemann was a complete discovery to me. It was a revelation to know the place of Physics in the work of Riemann, whom I only knew from a mathematical perspective.

I never knew of the large cultural influence of the Fourth Dimension after Riemann in general in late 19th Century Society (why?). The visual metaphors of Charles Hinton to illustrate a fourth spatial dimension (Hinton's Cubes), and the science fiction tales on hypercubes are simply delicious (if you've watched the "Cube" films, you must read these pages).

Then after learning that a time-fourth dimension had already been put down by H.G. Wells in his "Time Machine" I was in full context to enter Einstein's Theory of General Relativity. The deep meaning of the equivalence principle (force=geometry) came naturally: Riemann the mathematician and Einstein the physicist coming together in a sort of inevitable, fated meeting. An ongoing fate that brought the fifth dimensional theory of Kaluza-Klein in the 20's, ending up recently in the Supergravity and Superstrings theories.

It was a revelation too to behold the place of Quantum Physics in this "hyperspace living thread". The panorama of Quantum Theory is unfolded with unsurpassed clarity and scope.

Ultimately this book was superb to me in communicating clearly and brilliantly the origins and sense of modern Physics, from where it comes and to where it might be heading.

An unvaluable source of information ... and inspiration!

Thanks!

Just my humble thanks for so rewarding experience as I got from reading this book.

It is the first time I really understand the conceptual basis of Einstein's Relativity by grasping the meaning of the equality "force=geometry". This concept of force is as beatiful as profound. And it came so early as 1854 in a legendary lecture by Bernhard Riemann. In fact, the chapter on Riemann was a complete discovery to me. It was a revelation to know the place of Physics in the work of Riemann, whom I only knew from a mathematical perspective.

I never knew of the large cultural influence of the Fourth Dimension after Riemann in general in late 19th Century Society (why?). The visual metaphors of Charles Hinton to illustrate a fourth spatial dimension (Hinton's Cubes), and the science fiction tales on hypercubes are simply delicious (if you've watched the "Cube" films, you must read these pages).

Then after learning that a time-fourth dimension had already been put down by H.G. Wells in his "Time Machine" I was in full context to enter Einstein's Theory of General Relativity. The deep meaning of the equivalence principle (force=geometry) came naturally: Riemann the mathematician and Einstein the physicist coming together in a sort of inevitable, fated meeting. An ongoing fate that brought the fifth dimensional theory of Kaluza-Klein in the 20's, ending up recently in the Supergravity and Superstrings theories.

It was a revelation too to behold the place of Quantum Physics in this "hyperspace living thread". The panorama of Quantum Theory is unfolded with unsurpassed clarity and scope.

Ultimately this book was superb to me in communicating clearly and brilliantly the origins and sense of modern Physics, from where it comes and to where it might be heading.

An unvaluable source of information ... and inspiration!

Thanks!

Kaku's "Hyperspace" is a book on theoretical physics with all the "boring and unimportant" bits removed. Stripped down to the essentials for easy understanding, the book gives the lay reader a decent overview of theoretical physics, the main figures and the historical struggles that have presented themselves to physicists over the years.

The book follows the line that the laws of nature simplify in higher dimensional thought, and most of it is aimed at this theme of a unified theory. For the most part, the book is very easily understood, with some very helpful diagrams to aid you along the way. Particularly helpful are Kaku's analogies with everyday objects, such as beach balls. These really bring the ideas to life in a form that is accessible and visualisable.

One point that I found personally daunting is the idea of metric tensors, which I still really struggle with. I honestly don't understand them, despite Kaku's explanations and further use of them.

As far as introductions go, "Hyperspace" ranks as one of the easiest to start with, having only a very minimal amount of mathematics for you to wade through. Even when it is there, the mathematics is fairly easily grasped and requires little to no mental effort.

Will you be able to calculate the quanta of a neutrino impacting with an electron after this book? Simple answer: no. The book will give enough detail to interest you, and give you enough to decide if you want to read more and in more detail. If you have ever been curious about theoretical physics, but frightened of it at the same time, (like me), then "Hyperspace" may be just the book you are looking for. I really enjoyed it and learned heaps.

Kaku's "Hyperspace" is a book on theoretical physics with all the "boring and unimportant" bits removed. Stripped down to the essentials for easy understanding, the book gives the lay reader a decent overview of theoretical physics, the main figures and the historical struggles that have presented themselves to physicists over the years.

The book follows the line that the laws of nature simplify in higher dimensional thought, and most of it is aimed at this theme of a unified theory. For the most part, the book is very easily understood, with some very helpful diagrams to aid you along the way. Particularly helpful are Kaku's analogies with everyday objects, such as beach balls. These really bring the ideas to life in a form that is accessible and visualisable.

One point that I found personally daunting is the idea of metric tensors, which I still really struggle with. I honestly don't understand them, despite Kaku's explanations and further use of them.

As far as introductions go, "Hyperspace" ranks as one of the easiest to start with, having only a very minimal amount of mathematics for you to wade through. Even when it is there, the mathematics is fairly easily grasped and requires little to no mental effort.

Will you be able to calculate the quanta of a neutrino impacting with an electron after this book? Simple answer: no. The book will give enough detail to interest you, and give you enough to decide if you want to read more and in more detail. If you have ever been curious about theoretical physics, but frightened of it at the same time, (like me), then "Hyperspace" may be just the book you are looking for. I really enjoyed it and learned heaps.

3D graphics and animation is impressive, creative....high art at its finest. But above 3D there is 4D (although isn't time more of a control on 3D shape and behavior) and astoundingly still higher dimensions of invisible, vibrating string-like matter/quantum fluctuations/whatever-the-heck-this-stuff-is. Michio Kaku, in my estimation the finest intellect gracing planet Earth, unfolds page-by-page a deeper, more abstract, altogether more comely universe. A universe that wants to make sense out of itself, but seems to take a liking to infinite possibility, random chance; not to mention utterly wild and counterintuitive physical phenomena.
Kaku, who in this tome on free thought (odds are he's nearly right on, if not the first to crack some higher orchestrated code well past opinion) paves grudgingly complex, unexpectedly connected paths through the realms of what makes the ultimate realm, the known universe - and he takes it to the beyond - tick and tock.
In the cruel world of a child growing up, a shallow place of misguided human emotion and greed and desirous mistake, the drastically strange and different world painted by Kaku has a resoundingly nastalgic, nearly tragic, edifice propping it up. As I've read others state: Why can't science be taught this way in primary school? Kaku should serve as the integral player to anyone whom rethinks their existence, whom asks what it is that trully matters most, and whom finally reaches that crisis in conscience of simply not accepting everything and anything thrown at them, the lessons and beliefs which have hereby proved themselves false. While I myself am semi-crazed with the dynamics, precision, and seemily impossible complexity surrounding three dimensional forms, those newly discovered/invented geometrical objects - and I'm not avidly sticking to the elementary models (spheres, pyramids, cylinders) which when combined or extended can in themselves produce a stunning array of 3D realization - which determine our world's touch and feel.
As Newton contemplated the aprochryphal concept of a strictly mechanical universe, so does Kaku firmly investigate and eventually reject the classical, the primarily calculus-based, vision of reality so starkly upheld and trusted (I still love the vastness and truth in calculus based fields). Kaku shatters misconceptions, maybe upsetting some who've devoted an entire lifetime to related pursuits. Meanwhile, it is a safe bet to assume even these folks are fascinated by what Kaku has to tell. While there is not solid or evidenciary grounding in much of what is laid bare, there is plenty of analogy and thought-experiments to make one want to cling to what Kaku teaches. If Michio Kaku is wrong, then the universe is indeed a sorry place, for without the more reasonable, yet somehow more exciting viewpoints which he shares based on computational evidence (suppose he does have scientific support) pointing towards a universe of amazing construct, well, then we are left primitive, competitive, and spiteful to the bitter end.
In a "Big Thinkers" episode made for Michio Kaku to elaborate all about his ideas, theories, and often times objections to the set-in-stone so-called necessary norms, he puts forth a performance unmatched by not only any scientist I've seen, but also any other person on camera. Kaku, for the first time in my life, spelled out a physical realtiy which I've suspected in some ways. Kaku discussed how the "right hand and the left hand" - representative of the theory of the very big (relativity) and the very small (quantum mechanics) "don't go together." But not getting ahead of himself, he portrays vividly several commonplace scenarios: ducktaping a plattypuss and some other life form together and calling it natures finest creation; how a monkey cannot carry out mathematical analysis due to genetic incapability or an unevolved brain; how the topsy turvy world of city streets and the stressful souls trapped therein even contains some degree of inherent beauty or at least explainability....all the while Kaku inches near clueing you to his finer interpretation of life. However, he reaches into dark corners (perhaps there being no divine being or supreme mind behind the curtain afterall, the repressive lives of the lowly fish stuck in their peripheral 2D ponds, etc.), leaving one with their remaining emotional imbalances....enough to make you that much more convinced of his credibilty and genuine genius.
If there are but two choices of whose computer game, with its own separate rules, to enter (meaning that increasingly becoming commercialzed media mess of a maze called The American Experience), one being the game crafted by the self-righteous bussiness guru or self-delusional conspiracy nut, the other being the carefully plotted fairly structured resultant manifestation of the mind of a peaceful visionary, I'll pick the latter on every single occasion with vigor.
If anything, Michio Kaku is refreshing, deserving of respect in addition to adulation, and an imperative physicist for the age we're in. Michio Kaku: The only scientist whose words will haunt your dreams.

3D graphics and animation is impressive, creative....high art at its finest. But above 3D there is 4D (although isn't time more of a control on 3D shape and behavior) and astoundingly still higher dimensions of invisible, vibrating string-like matter/quantum fluctuations/whatever-the-heck-this-stuff-is. Michio Kaku, in my estimation the finest intellect gracing planet Earth, unfolds page-by-page a deeper, more abstract, altogether more comely universe. A universe that wants to make sense out of itself, but seems to take a liking to infinite possibility, random chance; not to mention utterly wild and counterintuitive physical phenomena.
Kaku, who in this tome on free thought (odds are he's nearly right on, if not the first to crack some higher orchestrated code well past opinion) paves grudgingly complex, unexpectedly connected paths through the realms of what makes the ultimate realm, the known universe - and he takes it to the beyond - tick and tock.
In the cruel world of a child growing up, a shallow place of misguided human emotion and greed and desirous mistake, the drastically strange and different world painted by Kaku has a resoundingly nastalgic, nearly tragic, edifice propping it up. As I've read others state: Why can't science be taught this way in primary school? Kaku should serve as the integral player to anyone whom rethinks their existence, whom asks what it is that trully matters most, and whom finally reaches that crisis in conscience of simply not accepting everything and anything thrown at them, the lessons and beliefs which have hereby proved themselves false. While I myself am semi-crazed with the dynamics, precision, and seemily impossible complexity surrounding three dimensional forms, those newly discovered/invented geometrical objects - and I'm not avidly sticking to the elementary models (spheres, pyramids, cylinders) which when combined or extended can in themselves produce a stunning array of 3D realization - which determine our world's touch and feel.
As Newton contemplated the aprochryphal concept of a strictly mechanical universe, so does Kaku firmly investigate and eventually reject the classical, the primarily calculus-based, vision of reality so starkly upheld and trusted (I still love the vastness and truth in calculus based fields). Kaku shatters misconceptions, maybe upsetting some who've devoted an entire lifetime to related pursuits. Meanwhile, it is a safe bet to assume even these folks are fascinated by what Kaku has to tell. While there is not solid or evidenciary grounding in much of what is laid bare, there is plenty of analogy and thought-experiments to make one want to cling to what Kaku teaches. If Michio Kaku is wrong, then the universe is indeed a sorry place, for without the more reasonable, yet somehow more exciting viewpoints which he shares based on computational evidence (suppose he does have scientific support) pointing towards a universe of amazing construct, well, then we are left primitive, competitive, and spiteful to the bitter end.
In a "Big Thinkers" episode made for Michio Kaku to elaborate all about his ideas, theories, and often times objections to the set-in-stone so-called necessary norms, he puts forth a performance unmatched by not only any scientist I've seen, but also any other person on camera. Kaku, for the first time in my life, spelled out a physical realtiy which I've suspected in some ways. Kaku discussed how the "right hand and the left hand" - representative of the theory of the very big (relativity) and the very small (quantum mechanics) "don't go together." But not getting ahead of himself, he portrays vividly several commonplace scenarios: ducktaping a plattypuss and some other life form together and calling it natures finest creation; how a monkey cannot carry out mathematical analysis due to genetic incapability or an unevolved brain; how the topsy turvy world of city streets and the stressful souls trapped therein even contains some degree of inherent beauty or at least explainability....all the while Kaku inches near clueing you to his finer interpretation of life. However, he reaches into dark corners (perhaps there being no divine being or supreme mind behind the curtain afterall, the repressive lives of the lowly fish stuck in their peripheral 2D ponds, etc.), leaving one with their remaining emotional imbalances....enough to make you that much more convinced of his credibilty and genuine genius.
If there are but two choices of whose computer game, with its own separate rules, to enter (meaning that increasingly becoming commercialzed media mess of a maze called The American Experience), one being the game crafted by the self-righteous bussiness guru or self-delusional conspiracy nut, the other being the carefully plotted fairly structured resultant manifestation of the mind of a peaceful visionary, I'll pick the latter on every single occasion with vigor.
If anything, Michio Kaku is refreshing, deserving of respect in addition to adulation, and an imperative physicist for the age we're in. Michio Kaku: The only scientist whose words will haunt your dreams.

This is a pretty good book, don't get me wrong, but I'd really hoped to get 'lay person' explanations for some of the esoteric aspects of string theory. What I found were paragraphs making analogies between wood and seeing things as made of particles and marble and seeing things as made of geometry. He then proceeds to say wood or marble, assuming that the lay person will "get it" better than saying "seeing things as made of particles" or "seeing things as made of geometry" without ever really attempting to explore the implications of each, in plain English or incomprehensible English. You'd think a mathematician would realize that a mere substitution of one term for a series of terms doesn't explain things better.

Now, I did get a few mild ah-ha's out of this book, but nothing like I got, as a teen, from George Gamow's great book "1,2,3 Infinity", which went to much greater lengths to try to actually EXPLAIN things. There are a few points at which he does help illuminate something, but not mostly, in my opinion. He mentions things and the people who came up with them. Mentions the conflicting opinions and those who have them. He does not, however, spend significant time trying to make analogies that help non-mathematicians "get it".

After purchasing this book and "Visions", I was left with a desire to sell both books (I never *sell* books) and a need to look further to get the explanations I continue to hope for.

Very interesting book for those who seek to learn more about "trancedental physics". You don't need to be graduated in physics to understand its contents because the book is written for lay readers on the subject. Hyperspace describe the ultimate world of physics, a highly advanced subject that we commonly see only in science fiction movies such as Star Wars and Star Trek. Indees, most of the technology that is about to exist or to be invented, depends on advances in this field of physics such as interstellar travel, mastering and manipulation of the gravitational force, etc. In my opnion this is one of the best book about the great theory of unification for lay readers.

This is a pretty good book, don't get me wrong, but I'd really hoped to get 'lay person' explanations for some of the esoteric aspects of string theory. What I found were paragraphs making analogies between wood and seeing things as made of particles and marble and seeing things as made of geometry. He then proceeds to say wood or marble, assuming that the lay person will "get it" better than saying "seeing things as made of particles" or "seeing things as made of geometry" without ever really attempting to explore the implications of each, in plain English or incomprehensible English. You'd think a mathematician would realize that a mere substitution of one term for a series of terms doesn't explain things better.

Now, I did get a few mild ah-ha's out of this book, but nothing like I got, as a teen, from George Gamow's great book "1,2,3 Infinity", which went to much greater lengths to try to actually EXPLAIN things. There are a few points at which he does help illuminate something, but not mostly, in my opinion. He mentions things and the people who came up with them. Mentions the conflicting opinions and those who have them. He does not, however, spend significant time trying to make analogies that help non-mathematicians "get it".

After purchasing this book and "Visions", I was left with a desire to sell both books (I never *sell* books) and a need to look further to get the explanations I continue to hope for.

Very interesting book for those who seek to learn more about "trancedental physics". You don't need to be graduated in physics to understand its contents because the book is written for lay readers on the subject. Hyperspace describe the ultimate world of physics, a highly advanced subject that we commonly see only in science fiction movies such as Star Wars and Star Trek. Indees, most of the technology that is about to exist or to be invented, depends on advances in this field of physics such as interstellar travel, mastering and manipulation of the gravitational force, etc. In my opnion this is one of the best book about the great theory of unification for lay readers.

ýThere is something fascinating about science. One gets such wholesale returns of conjecture out of such a trifling investment of fact. Mark Twainý--Life on the Mississippiý

This is a lovely book full ofý fascinatingýý info on theý evolution ofý physicsý and cosmology.ý Its mainý themeý is how the idea ofý higherý dimensionalý geometryý createdý by Riemann,ý recently extended to 24 dimensionsý byý stringý theory,ý has revolutionizedý ourý understanding of theý universe.
ý
Everyoneýý knows that Riemann createdýý multidimensional geometry iný 1854 butýý it is amazing to learný that he also was aý physicist who believed' that it heldýý the key to explaining the fundamental lawsý of physics.ýý Maxwell'sý equationsý did not exist then and Riemann'sý untimelyýý deathý at ageý 39ý prevented his pursuit ofý these ideas. Both heýýand hisý Britishý translatorý Clifford believed that magneticý andýý electric fields resulted fromý theý bending of space in the 4thý dimension--moreý than 50 years beforeýEinstein!ýý The fourthýý dimension became aý standardý subject in the popular mediaý forýý theý next 50 years with severalý storiesý by HG Wells using itýý and even Leniný wroteý about it.ýý The American mathematician' Hinton had widely publicized hisý ideaýý that light is a vibrationýý in the 4thý spatial dimension.

ýAmazingly,ýý physicistsýý and most mathematicians forgot about it and whenýý Einsteinýý wasý looking for the math needed to encompass general relativity' 60ýý years later, heý had never heard of Riemannian geometry.' Heý spent 3 yearsý tryingý to find theý equations for general relativity andý onlyý afterý a math friend told himý about Riemanný was heýý able toý complete hisý work.ýý Riemann's equations withý fourý dimensionalýý metricý tensorsý describing every point in spaceý wereý incorporatedý almostý unchangedýý into relativity.ý

String theory caný be said to dateý from 1919ý when aný obscureý mathematicianý namedý Kaluza added theý tený components of Einstein`sýý gravitationalý field with theý 4ý componentsý of Maxwell's electromagneticý fieldsý and time toý get the 15ý componentsý of a 5 dimensional field.ýý He evený producedý the idea that the 5thý spatial dimension isý a sphereý smaller than aný atom (ie, too small to beý measured)--whichýý remains a fundamental idea in stringý theory'sý 10ý dimensions.

ýIný 1936 the mathematician Oscar Klein postulatedýý that the 5thý dimensioný has theý Planck length(10 to minus 33cm)ýý which isý indeed far tooý small toý measure by anyý forseeableý means(itýý requires an accelerator of 10 toý 19thý BEV) andý this, withý theýý arrival in 1925 of quantum theory and theýý uncertainty principleýý pushed theý geometry based Kaluza-Kleiný and, to someýý extent,ý evený relativity theory into theý backgroundý for nearly 60 years.

Inýý quantum theory, the differentý forces are created by the exchangeýý ofýý differentý quantaý and no geometry is used.ý This led to theýý Yang-Mills field,ýý QED, QCDý and the Standard Model of particleýý physics whichý is: all matter isýý quarks andý leptons which interactýý byý the exchange of different types ofý quantaý asý described byýý theý Maxwell and Yang-Mills equations.

Veneziano andý Suzukiýý discovered the basis for string theory in 1968 whenýý they usedýý Euler's betaý functions to describe the strongý interactions of' subatomicý particles. In 1970ý two Japaneseý scientists used theý idea ofý vibratingý strings to exapand oný it. Itý is now halfwayý through the book andýKaku describesý how he invented the firstý field theory of strings.ýý Then itý wasý shown thatý string theoryý is selfý consistent only inýý 10 and 26 dimensions andý researchýý nearly stopped for 10ýý years.
Then in 1984 Green and Schwarzýý showed that superý stringý theory wasý the onlyý self consistentý theory ofý quantumý gravity.ý Edward Wittený becameýý interested iný the higherý dimensioný geometric equations in physicsý iný 1982ý whený he realized thatý gravityý was impossible in quantumýý field theory butý inevitableý in the 5thýý dimension. In 1985ýý he used the highly advanced math ofý cohomologyý theory toý deriveýý a field theory of strings. This led eventuallyý toý theý useýý ofý someý of the most advanced(and previously unrelated)ý fieldsýý of mathý known toýý describeý the 26 dimensional space ofýý counterclockwiseý vibrations ofýý heteroticý string theory andý iný some sense, theý explanation of everything.'

Then thingsýý stalledý again becauseý millions of potential solutions to theýý equations areý known,ý but which one describes only our universe;ý ie, whichý oneýý givesý theý correct field theory of strings(FTS)ý defined in our 4ý dimensions?' Nobodyý knows howý to solveý the equation using nonperturbativeýý methodsý and it is oftenýý stated thatý we need more advancedý math, ie, mathýý that doesý not yet exist.ý Almost everythingýý known in particle physicsýý hasý used perturbative methods.

Oneý of the majorý problemsý is that nobody knows why string theoryý works--ie, whatý is theýý underlying geometricý or physical principle that makesý it relevant and allows allý of physics to be incorporatedý intoý theý 10(when condensed)ý dimensionsý of string theory?ýý It isý the only quantumý theory that requiresý aý fixed numberý ofý dimensions.ýý Another bizarre resultý is thatý it has toý use theý modular functionsýý invented some 60 years beforeýý by the self taught Indian mathý prodigyý Ramanujan,ý who asý a teenagerýý reinvented much of modern mathý in hisý head.ýý One of hisý bizarreý modularý functions containsý a term raisedý to the 24thý power and thisý isý exactly theý numberý of vibrationalý modes needed(24 plus 2ý forý spacetime orý generalizedýý iný the FTS it's 8 plus 2 or 10).ý Theýý symmetries of theýý subatomicý realm(ie, particles) become the resultý ofý theýý curlingý up of the higherý dimensional spaces.

Meanwhile, the standard model of physics was evolving but it hasý evený more arbitraryý assumptions than the inflationary theory of the big bang(Kaku says little about inflation but see my review of Guth's book The Inflationary Universe).ýý Soý GUTs(Grandý Unified Theories)ý appeared andý faded to beý supplantedý byý supersymmetry(basedý on bizarreý supernumbers)ý whichý integratedý fermions andý bosonsý with their spins.ýý Thisý led(1976) to theýý lovely gauge theoryý ofý supergravityý in which all particlesý haveýý superpartners(sparticles).ý

Usingýý an 11 dimensional versioný of theý Klein-Kaluzaý theory to describeýý the 11 dimensionalý supergravityý field allows theýý incorporationýý of matter(ie, quarks and leptons).ýý But sparticles were neverýý found and supergravity turned out toý beý nonrenormalizable(ie,ýý it led toýý infinities) so SG died.

ýThený cameý hypersurfacesý described by complexý numbers, on which theý waveýý functions ofý the particles vibrate, thus acquiringý the symmetriesýý ofý theýý hyperspheres.ý So if you then apply the Kaluza-Kleinýý theoryýý for 4 plusý Ný dimensions and split up its metric tensorý you getýý everything--the Einsteinýý equations for gravity,ý the Yang-Millsýý equations forý strong and weak forces,ý andýý the Maxwell equationsýý for the electromagneticý fields.
Amazingly,ý it turnsý outý that not only had Klein described theýý Yang-Millsýý field inýý 1938(25 years before Yang and Mills--and they got the Nobel Prizeýý for it!)ýý butý Y-M is now based on quantum theory which hadý killed interestý inýKaluza-Klein forý almost 60 years!!!

Thisý bringsýý us back to Edwardý Witten(whom some regard as the successorý toýý Einstein)ýý and superstringý theory, in which matter isý now the harmony ofýý extremelyý small vibratingý strings whichý can fuse and break up.ýý It accountsýý forýalmost everything andý is theý first quantum theoryý of gravity withý finite quantumýýcorrections.ý In spiteý ofý its highly abstractý nature, lacký of anyý experimentallyý verifiableýý predictions, lacký ofý a unique solution for ourý universe-it hasýý millions ofý solutions(orbifolds),ýý many(all?) of which couldý haveý properties thatý mightý makeý ourý universe impossible- and anyý rationalý explanation forý why itýý works(ieý no conceptual frameworký uniting gravityý andý quantum theory), itý hasý aý compelling,ý almost religiousý appeal for manyý physicistsý because, startingýý onlyý fromý geometry and the condition thatý stringsý move selfý consistentlyý iný spacetimeý we get magnetism, electricity,ýý spacetime,ýý general relativity,ý Klein-Kaluza,ý supergravity, theý standardýý modelý and the Grand Unifiedý Theory--it binds matter,ý energy' and spacetime. Stringý theory does not however, predict or explain theý properties of particles nor the paradoxesý of quantum mechanics, uncertainty andý entanglement(Bell's theorem).ý

Though Iý don't think Kakuý says this anywhere,'ý it is soý general and so powerful thatý one gets theý feelingý thatýý it could explain anythingý in any possible universeýý and iný thatýý case it does not really explain anything atýý all--it becomes the' mathematical equivalent of `God made itý that way`.ýý So, itýý mayý eventuallyýý begin to lose itsý appeal as a final explanation(as it has for many physicists).ý
So,ýý we still caný ask theý same question as Kaluza in 1919--where isý theýý 5thýý dimension?--and still pursueý the same answer givený by Kleinýý in 1926.ý

Quantum theory and quantumý tunnelingý explainýý the apparent violation ofý theý conservation of energyý shownýý byý radioactive decay.ý It might explain theý suddenýý appearanceý ofý a 4 and a 6ý D universe from a 10D one.ý Becauseý theý falseý vacuumý of a 10D universe wasý unstable we assume, but cannotý prove, thatý it quantum tunneledý to aý lowerý energy state,ýý breaking symmetry andýý creatingý a true vacuum iný 4D space.ý But if it is not theý true vacuumý thený oneý day a smallýý bubble may appear and enlarge at the speedý ofý light untilý itýý destroysý our universe.ý Our 4D universeý can curl up in 4 waysý butý a 10Dýý oneý can curl up in millionsý of ways.ý So, toý find the right one,ý we needý toý solveý theý field theoryý of strings using the theoryý of phaseý transitions--theýý mostýý difficult problem in quantum theory.ý

In 1994ý the heteroticý string theory ofý David Gross(oneý of the fourýý Princeton physicistsý known as the Princetoný stringý quartet)showedý that theýý quantumý unit of gravity emerges as theýý smallestý vibration of a closedýý string.
Sinceý the laws ofý physics break downý at the veryý small distances andýý largeýý energies of the big bang, we needý aý string theory with 10 dimensionsýý thatý breaks into 6 plusý 4 to create twiný universes of whichý theý 6 is aný orbifold tooýý small to observe.ý Kaku says thatýý only 10Dý superstring theoryýý can explain whatý happens beforeý the big bangý butý of courseý Valenkin andý Hawking and othersý haveý alternatives. (see my review of Guth).

Evený in the string theory of the bigý bang,ý a small piece of the universeý must inflate by a factor of 10 toý the 50th,ý so apparently allý of inflation isý included.ý Itý has been frequently theorizedý thatý black holes may be tunnelsý iný spacetime to other universes.ýý But itý appears we don'tý know if black holesý really pinch off hyperspheresý ofý spacetimeý in which light is trapped.ý

Along with its untestability andý lacký of any conceptual foundation, a further problem is that theý math is so generalýthat it has millions of solutions(orbifolds) which include all ofý physics(General relativity, Grand Unifiedý Theories etc) and there is no way to decide which one of themý describes our universe.ý Some(or all?) of the solutionsý haveý properties that might make life, or even our universe, impossible.ýOneý cannot simply put a computer to work to decide whichý solution is right for ourý universe for the sameý reasons one cannot solve quantum tunneling etc.--infiniteý time is required.ý

ý Thoughý neither Kaku nor anyone else I have read has said so, itý seems that the math ofý 26 D geometry is so powerful that it couldý describe any possible universe.ý Iný this case it is understandableý why it lacks a conceptual foundation as it has noý special relationý to our universe.ý Anything expressible as an algorithm or number can be derived from anything else by writing the appropriate algorithm or codec, so the rules of chess, Avogadro's number, the dimensions ofý the great pyramid and the dynamics of ant colonies are deriveableý too.ý

One of theý thingsý that makes many think math is outý thereý in the universeý rather than in here in our minds.ý Naively, one could say that the structure ofý the universeý makesý our mind so is it aý surprise that our thoughts(eg,ý mathematics)ý mirror theý universe?ý The debate continues today.

The compelling way in which pure math yields physical results is illustrated by theý discovery of a mathematician who wasý just looking forý anotherý solution to theý equations ofý generalý relativity.ýý By assumingý aý black hole rotates, Roy Kernýý in 1963 found a solutioný andý thus an exactý representationý of black holes. Theyý will collapseý into a ring so that objectsý approaching from the top or bottomý willý experience a finiteý curvature(gravity)ý so it might be able to getý to theý mirrorý universe which exists on the ýtherý side`of spacetime.ý But,ý at thisý density of mass-energy, general relativityý breaksýý down and quantum effectsý probably dominate so maybe we can findýý aný answer with string theory.ý Likewiseý with time travel.

Byý making variousý assumptionsý about the universe one can come up with manyýý differentý solutionsý to relativity.ý In 1949 Godel(he of Incompleteness Theorem fame) showed that if one assumesý theý universeý rotates, time can bend in a circle or CTC(Closedý Timelikeý Circle).ýý Itý turns out that van Stockum had derivedý aý CTC solution iný 1936(pointed out by cosmologist Frank Tipler who recently became infamous for his book proving the existence of God from physics) and manyý have done so sinceý Godel, usually using blacký holes or aný expanding universe.' It is now realized that thereý are an infinite number ofý suchý `pathological`ý solutions to theý equations of general relativity.ý Itý appears that all CTC willý violateý causality.ý

As oneý of the principalý founders of quantumý cosmology, Hawking proposedýý that wormholes could be usedý to enterý other universes.ý Everý daring, he usedý quantum theory to treatý theý entire universeý as a quantum particle represented byý a waveý function whichý willý be large for our universe but small for others.ý

Assuming they are connected by wormholes,ýý Sidney Coleman summed the contributions of an infiniteý series of universes, to show that if theý cosmological constant(CC) is zero then the wave functionýis large(ie, highý probability).ý Ifý the CC is not zero, then that universe has zeroýý probability(ie,ýthe effect of an infinite number of parallel universes is toýkeepý CC zero in ours), which means the CC cancels to one part in 10 toýtheý100th!

Acting on a request from Carl Sagan, Thorneý et al(1985) discovered `transversible wormholes` --the first ones thatýwere actually feasible in the sense that a human might actuallyýsurvive using them.ýIt seemsý theoreticallyý possible to createý one using the negativeý energy(ie, less thaný in a vacuum) ofýý the Casimir effect(a quantumýeffect thought to occur everywhere allý the time) in whichý particle-antiparticleý pairs appear and selfý annihilate atý very high rates.ý

Godel showed that math is incomplete and physicists have shown that quantum theory is also incomplete(eg, Schrodinger'sýcat is dead and alive at the same time,) but theý stringý theory of quantum gravity has an equation(waveýfunction)for the entire universe and there is no longerý aný observer and an observed because itý is a 10ý dimensionalý theoryý and so renormalizable.ý

However the cosmicýwave function isý a composite of all possible universes so indeterminacyýý remains.ý The smallestý quantum unit is the space of all possibleýuniverses, inýsome of which the catý is dead and some alive. Quantum theory and stringý theory seem very reductionistic but one equationýfor the universe seems as holistic as it's possible to get!ý

Superstringý theory(SST) has stretched math to its limitsý and needs more advancedý math to evolve.ý Physics needsý the self consistentý structures of math so it combines topology and theý Reimannian geometry of generalýrelativity (ie, groups of quantum fieldý theories)ý toýeliminate the infinitiesý (ie, renormalize) of the quantumý theoryý of gravity.ýý

It seems to me that the most complexý products of theý brain-SST andý topology, are recursive to quantum field theoryý and the behaviorý of particlesý and the entire universe. thoughý Kaku does notý discuss incompleteness, we know that math isýý proven(Godel, Chaitin, etc.)ý to be foreverý necessarily incompleteý --ie, infinitely manyý well formedý theorems in anyý mathematicalý system can never be provený to be true or false.ýý Then, sinceý mathý and physics are now fusedýat the highest level(Superstring theory), one wondersý if there is aý nontrivial senseý in which physics and the wholeý universe and theý mind areý incompleteý as well.ýWhat is the significance ifý many laws of physics in someýpossible universes(or ours) and/or many thoughts in our brain are never to be consistent with or derivable from the others?
Stringý theory unites physics with many of the most advanced andý formerly separate areas of math--SuperLie and Kac-Moody algebras,ý modularý functions, finite groups, algebraic topology, Riemannianý geometry and cohomologyý theory.ý It remains without a conceptualý basis so we are left to wonder if there is anything other than powerfulý math that unites quantum theory and gravitation.ý

Kaku does not dwell on the problem of emergence, but physical scientists can rarelyý resist reductionism.ý However, the quantum field equations areý so difficult that they cannot be solved forý one atom and not evený for a vacuum.ýThey require an infinite time to compute. One only finds out the emergentý propertiesý of things that result from combining smaller things by seeing whatý they are like after the fact-whether they are quarks making aý proton, molecules making cells, or stars making a universe.ý One also has uncertainty andý chaos.ý We have no way to determine in what way and when a pile of sandý will collapse.ý Physics has to wait forý the results at the micro(subatomic particles) and macro(cosmologicalý observations) scalesý before advancing and it is full of uncertainty and bizarre phenomena.ý Also, there seems to be no way we can ever test SST(the theoriesý change constantly but the bottom line is that we will never be able to do experiments at