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Hidden In Plain Sight 6: Why Three Dimensions?
Why are there three dimensions of space? It is surprising that science does not know the answer, though there have been some inventive and controversial ideas. This book considers many of those ideas and presents a new solution why three is the magic number.
170 pages, Paperback
Published July 12, 2016
182 people are currently reading
122 people want to read
About the author
Andrew H. Thomas
14 books11 followersDr. Andrew H. Thomas studied physics in the James Clerk Maxwell Building in Edinburgh University, and received his doctorate from Swansea University in 1992.
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Displaying 1 - 13 of 13 reviews
March 10, 2020
Dr Andrew H Thomas has written 11 books in the Hidden in Plain Sight Series. I decided to start with the one in the middle, Why Three Dimensions, because of its mathematics implications. I DO love reading books about math.
The chapters!!
Chapter 1 The Magic Number where he discusses the prime number, the number of significant magnitude, Occam's Razor and the natural numbers.
Chapter 2 Dimensions: the definition of a dimension and the concept of spacetime (the fourth dimension)
Chapter 3 The Geometry of Three Dimensions: the Platonic solids, the stability of orbits and anthropic (!) theories
Chapter 4 General Relativity: the curvature of space, tensors and tidal waves
Chapter 5 Into the Fifth Dimension: potential, the circular dimension and microscopic dimensions
Chapter 6 String Theory: the music of strings, the best kept secret in mathematics (its still a secret to me!!) and the hidden dimensions of string theory
Chapter 7 Why Three Dimensions: the good doctor puts it all together and introduces us to his own original ideas as well
Review
OK, I did not understand it all, but I am pleased to say that I can at least recognize some new terms and concepts. Thomas has an engaging way of writing. Sometimes he lapses into conversation mode as if he talking to his reader and knows (s)he is out there. At least one of the concepts was not explained very well (that best kept secret thingy) so I subtracted a star for that.
All of Thomas's Hidden in Sight books are available on Kindle Unlimited. At least three more interest me: Hidden In Plain Sight 9: The Physics Of Consciousness, Hidden In Plain Sight 8: How To Make An Atomic Bomb and Hidden In Plain Sight 3: The secret of time.
4 stars
The chapters!!
Chapter 1 The Magic Number where he discusses the prime number, the number of significant magnitude, Occam's Razor and the natural numbers.
Chapter 2 Dimensions: the definition of a dimension and the concept of spacetime (the fourth dimension)
Chapter 3 The Geometry of Three Dimensions: the Platonic solids, the stability of orbits and anthropic (!) theories
Chapter 4 General Relativity: the curvature of space, tensors and tidal waves
Chapter 5 Into the Fifth Dimension: potential, the circular dimension and microscopic dimensions
Chapter 6 String Theory: the music of strings, the best kept secret in mathematics (its still a secret to me!!) and the hidden dimensions of string theory
Chapter 7 Why Three Dimensions: the good doctor puts it all together and introduces us to his own original ideas as well
Review
OK, I did not understand it all, but I am pleased to say that I can at least recognize some new terms and concepts. Thomas has an engaging way of writing. Sometimes he lapses into conversation mode as if he talking to his reader and knows (s)he is out there. At least one of the concepts was not explained very well (that best kept secret thingy) so I subtracted a star for that.
All of Thomas's Hidden in Sight books are available on Kindle Unlimited. At least three more interest me: Hidden In Plain Sight 9: The Physics Of Consciousness, Hidden In Plain Sight 8: How To Make An Atomic Bomb and Hidden In Plain Sight 3: The secret of time.
4 stars
September 25, 2016
Three is the special number...
And three stars are what this book gets - not entirely convincing that the many worlds interpretation can be ruled out or that higher numbers of spatial dimensions are possible, particularly in light of the 1/2n(n-1) equation for rotational degrees of freedom: in 5-space, there are two independent spin directions for each of the linear spatial dimensions, and similarly for progressively larger, odd numbered dimensions (e.g., 3 for 7-space).
And three stars are what this book gets - not entirely convincing that the many worlds interpretation can be ruled out or that higher numbers of spatial dimensions are possible, particularly in light of the 1/2n(n-1) equation for rotational degrees of freedom: in 5-space, there are two independent spin directions for each of the linear spatial dimensions, and similarly for progressively larger, odd numbered dimensions (e.g., 3 for 7-space).
September 22, 2016
Waiting for 7
Dr. Andrew Thomas has the rare ability to present complex information in an enjoyable and readable format! Can't wait for the next one.
Dr. Andrew Thomas has the rare ability to present complex information in an enjoyable and readable format! Can't wait for the next one.
January 24, 2021
I enjoyed this book, it was good to read the history of how people have tried to prove there are more than 3 dimensions. Andrew Thomas also does a very good job is explaining why polygons are what they are and how they are structured. I would even go as far as saying that his theory at the end about particle spin and why it can only happen in 3 dimensions makes a lot of sense! However, I'm sure there is still a lot of work required to go into it.
However.. like many people in these reviews, I didn't like the -1/12 formula. It seemed far too loose and didn't make sense. If you have two patterns and you're adding them together why must you shift the lower one to the right one place? I've never heard of doing this in maths so it might be some advanced level process I've not seen but it just seems like it's manipulating to fit the answer. Also, if you have two formulas where the answer is either 0 or 1 then you can't take an average because there can't be one. It's binary! These two points put me off that altogether, then string theory.... it just seems like it's now at a point where it's going to be extremely difficult to prove it's true but the people that have overrated so much time into it can't let go! From a layman's perspective, string theory is a very weak argument for the unifying theory of everything.
I can't mark Andrew down for these two points because he hasn't made them up, they are just unfortunately something that he's decided to put in his book!
Still recommended, and I'm still going to finish the series!
However.. like many people in these reviews, I didn't like the -1/12 formula. It seemed far too loose and didn't make sense. If you have two patterns and you're adding them together why must you shift the lower one to the right one place? I've never heard of doing this in maths so it might be some advanced level process I've not seen but it just seems like it's manipulating to fit the answer. Also, if you have two formulas where the answer is either 0 or 1 then you can't take an average because there can't be one. It's binary! These two points put me off that altogether, then string theory.... it just seems like it's now at a point where it's going to be extremely difficult to prove it's true but the people that have overrated so much time into it can't let go! From a layman's perspective, string theory is a very weak argument for the unifying theory of everything.
I can't mark Andrew down for these two points because he hasn't made them up, they are just unfortunately something that he's decided to put in his book!
Still recommended, and I'm still going to finish the series!
February 27, 2018
As good as the others in the series
Excellent approach to the problem of exploring why we have three spatial dimensions instead of one or any other number. My only caveat has to do with the demonstration in chapter six of the result in summing up the whole series of natural numbers (1 + 2 + 3 + ...), with the result being -1/12. Andrew Thomas, the author, suggest to watch a You Tube video that gives you the demonstration but also, in the same screen, you can check for a more serious approaching to the topic that belies, in fact, this counterintuitive result. Nevertheless, it doesn't affect the core idea of the book that, as all the previous ones, has so much to offer in terms of information and highly valuable insights.
Excellent approach to the problem of exploring why we have three spatial dimensions instead of one or any other number. My only caveat has to do with the demonstration in chapter six of the result in summing up the whole series of natural numbers (1 + 2 + 3 + ...), with the result being -1/12. Andrew Thomas, the author, suggest to watch a You Tube video that gives you the demonstration but also, in the same screen, you can check for a more serious approaching to the topic that belies, in fact, this counterintuitive result. Nevertheless, it doesn't affect the core idea of the book that, as all the previous ones, has so much to offer in terms of information and highly valuable insights.
July 21, 2017
I like the answer
The book started a bit booting but then turned to be very interesting. The last chapter is the best. The biggest discovery for me after reading this book I a new perspective on the famous E=mc2 - the combined relative speed of every object in the universe is equal to the speed of lite. Thus, the explanation of why the treveller clock is ticking slower becomes simpler, because the bigger part of the energy is spent on the motion through the space the less is left for the motion through the time. I.e. he higher the speed of the object relatively to another object the slower it's clock.
The book started a bit booting but then turned to be very interesting. The last chapter is the best. The biggest discovery for me after reading this book I a new perspective on the famous E=mc2 - the combined relative speed of every object in the universe is equal to the speed of lite. Thus, the explanation of why the treveller clock is ticking slower becomes simpler, because the bigger part of the energy is spent on the motion through the space the less is left for the motion through the time. I.e. he higher the speed of the object relatively to another object the slower it's clock.
November 29, 2022
Short answer to the journey: “we define our space in terms of fermions, which are the matter particles such as electrons. A fermion has to comply with the rules of special relativity (is said to be Lorentz invariant) and hence requires a plane of rotation in order to spin. But only in three-dimensional space is a single plane of rotation uniquely specified which is perpendicular to the particle's direction of motion.”
This entire review has been hidden because of spoilers.
February 25, 2018
Another step in understanding physics.
This volume talked about a lot of things that I have never pondered. The author, as always did a great job explaining things and, as always, the last chapter was strange. Still fun. On to volume 7
This volume talked about a lot of things that I have never pondered. The author, as always did a great job explaining things and, as always, the last chapter was strange. Still fun. On to volume 7
January 11, 2019
Reads very well and I appreciated the part on string theory .
There are, however some statements that I did not agree with ( I am a lecturer in physics ).
Overall, entertaining.
There are, however some statements that I did not agree with ( I am a lecturer in physics ).
Overall, entertaining.
August 21, 2016
Good overview of SR and GR
Andrew Thomas presents an excellent overview of special and general relativity by covering the fundamentals of tensor algebra and explaining Einstein's thought process. The question of why there are three dimensions is postponed until the final chapter.
Chapter 6 makes a strange digression into string theory. In that chapter, Dr. Thomas "proves" the infinite sum of natural numbers is equal to minus one twelfth, somehow causing the existence of 25 dimensions, which string theory then whittles down to 10 (or maybe 11). I think all this proves is just how silly string theory is. The proof concerning the infinite sum relies on a sleight of hand that appears in step 2, namely the assertion that 1-1+1-1+... = 0.5 which is false. If that assertion were true, then 0.5 = 1 which is obviously false. I don't know why Dr. Thomas took this strange detour -- this adds nothing and it only detracts from an otherwise sound presentation.
The final chapter sets out to prove why there are three dimensions instead of two or four. To Dr. Thomas' credit, he does not invoke what I feared would be the anthropic principle. I agree with both Thomas and Lee Smolin that anthropic arguments can be used to prove virtually anything, and they should never be used in science. Instead, Dr. Thomas argues that space-time emerges from the properties of matter, although this argument seems circular. The argument is that fermions are required to spin in order to move through space-time at light speed, as all non-zero masses are required to do per SR; however, SR itself is predicated on the existence of space-time. Putting that apparent circularity aside for the time being, the number 3 satisfies the condition that the number of translational degrees of freedom equals the number of rotational degrees of freedom, which also happens to equal the number of dimensions itself. It isn't exactly clear WHY that condition needs to be satisfied, however. Is it required due to some underlying symmetry in nature? Dr. Thomas needs to expand on that, although he definitely seems to be on the right track.
There are a couple of minor corrections that should be made in the final chapter. Dr. Thomas states that photons do not experience time, which is quite true. But photons also do not experience space, because space collapses around a body that is approaching light speed due to relativistic aberration and Lorentz length contraction. Thus, a photon is literally everywhere in the universe in its own reference frame, although it appears to be in specific locations in our reference frame. Finally, there is the misconception that elementary particles "age" and then decay. Particle decay is "uncaused" and has nothing to do with the "age" of the particle. Half life is a statistical effect that WE observe through the decay of many particles. Quantum mechanics is quite clear that there are no invisible timers ticking away inside those particles, because these would amount to local hidden variables. Violations of Bell's inequality, as verified in numerous experiments, prove beyond the shadow of doubt that local hidden variables do not exist in quantum mechanics. It seems as if high relative particle speeds produce local "time dilation" that delays particle decay, but it is actually wrong to infer that. Dr. Thomas' original statement was correct: without entropy, there is no arrow of time.
I gave this book an overall rating of 4 stars. It is interesting and easy to read, and offers a very simple explanation of a difficult topic of special and general relativity. I think Chapter 6, dealing with string theory, should be changed or omitted entirely. If it weren't for Chapter 6, I'd have given this book 5 stars.
sites.google.com/site/amateurscientis...
Andrew Thomas presents an excellent overview of special and general relativity by covering the fundamentals of tensor algebra and explaining Einstein's thought process. The question of why there are three dimensions is postponed until the final chapter.
Chapter 6 makes a strange digression into string theory. In that chapter, Dr. Thomas "proves" the infinite sum of natural numbers is equal to minus one twelfth, somehow causing the existence of 25 dimensions, which string theory then whittles down to 10 (or maybe 11). I think all this proves is just how silly string theory is. The proof concerning the infinite sum relies on a sleight of hand that appears in step 2, namely the assertion that 1-1+1-1+... = 0.5 which is false. If that assertion were true, then 0.5 = 1 which is obviously false. I don't know why Dr. Thomas took this strange detour -- this adds nothing and it only detracts from an otherwise sound presentation.
The final chapter sets out to prove why there are three dimensions instead of two or four. To Dr. Thomas' credit, he does not invoke what I feared would be the anthropic principle. I agree with both Thomas and Lee Smolin that anthropic arguments can be used to prove virtually anything, and they should never be used in science. Instead, Dr. Thomas argues that space-time emerges from the properties of matter, although this argument seems circular. The argument is that fermions are required to spin in order to move through space-time at light speed, as all non-zero masses are required to do per SR; however, SR itself is predicated on the existence of space-time. Putting that apparent circularity aside for the time being, the number 3 satisfies the condition that the number of translational degrees of freedom equals the number of rotational degrees of freedom, which also happens to equal the number of dimensions itself. It isn't exactly clear WHY that condition needs to be satisfied, however. Is it required due to some underlying symmetry in nature? Dr. Thomas needs to expand on that, although he definitely seems to be on the right track.
There are a couple of minor corrections that should be made in the final chapter. Dr. Thomas states that photons do not experience time, which is quite true. But photons also do not experience space, because space collapses around a body that is approaching light speed due to relativistic aberration and Lorentz length contraction. Thus, a photon is literally everywhere in the universe in its own reference frame, although it appears to be in specific locations in our reference frame. Finally, there is the misconception that elementary particles "age" and then decay. Particle decay is "uncaused" and has nothing to do with the "age" of the particle. Half life is a statistical effect that WE observe through the decay of many particles. Quantum mechanics is quite clear that there are no invisible timers ticking away inside those particles, because these would amount to local hidden variables. Violations of Bell's inequality, as verified in numerous experiments, prove beyond the shadow of doubt that local hidden variables do not exist in quantum mechanics. It seems as if high relative particle speeds produce local "time dilation" that delays particle decay, but it is actually wrong to infer that. Dr. Thomas' original statement was correct: without entropy, there is no arrow of time.
I gave this book an overall rating of 4 stars. It is interesting and easy to read, and offers a very simple explanation of a difficult topic of special and general relativity. I think Chapter 6, dealing with string theory, should be changed or omitted entirely. If it weren't for Chapter 6, I'd have given this book 5 stars.
sites.google.com/site/amateurscientis...
December 5, 2016
All the interesting information that was taught on the previous books, mainly the first ones, is not present in this book. It talks too much about the reason and explanation why there are only three dimensions and not more or less. It is too philosophical, and unfortunately not so practical. I could not take much good information out of this book as I did on the previous ones, and started to get a little bored by the repetition of the same subject over the book.
October 29, 2016
Another good one
Awoke at two AM to realize the value of -1/12 (you'll see). Great short read for us interested in physics. One wouldn't have to have read the other five in the series but any one of them will pique interest in the others
Awoke at two AM to realize the value of -1/12 (you'll see). Great short read for us interested in physics. One wouldn't have to have read the other five in the series but any one of them will pique interest in the others
September 27, 2016
Wonderfully explained. Loved it!
Displaying 1 - 13 of 13 reviews