Book review: Love and Math

October 20, 2013

“There is a secret world out there.” This is the beginning of Edward Frenkels book about his mathematics and his story of how he fell in love with it. Popular books about mathematics are rare compared to areas of science such as particle physics, cosmology or even biology. It is hard to write a mathematics book that will appeal to the masses. You cant really play the trick of skipping all the equations or the details because these are really the essence of what makes mathematics so beautiful to those who master it.

Even rarer are such books written by the people who are at the bleeding edge of current mathematical research. There are some great maths books by Marcus de Sautoy, Ian Stewart, Simon Singh etc. , While some of these authors are maths professors their popular books cover stories of mathematical problems solved by others. I have always found that the most engaging books in popular science are the ones written by those who were closest to the discoveries themselves and this book is an excellent example.

In “Love and Math” Frenkel recounts his voyage of discovery with details of the maths and the equally fascinating story of his passage through the education system of Russia in the 1980s where he faced ridiculous obstacles placed in his way simply because his family name is Jewish. Despite glowing exam results from high school he was not permitted to attend Moscow University and has to settle for another college more geared to industrial engineering . Luckily such difficulties were compensated for by a system of informal mentoring by some of Russia’s greatest mathematicians that supported the most promising young students like Frenkel.

The tale of his progress from school to Harvard professor is interwoven with potted lessons in group theory as he had to learn it to solve the problems posed by his mentors. These are aimed at non-experts. For someone like myself who is already familiar with the standard methods but not with all the recent progress this is light and enjoyable reading right up to the final chapters where he described his work with Ed Witten on geometric Lamglands. I cant say how a complete novice would find it but young math students would surely find inspiration and useful knowledge here and others can skip the details and enjoy the human side of the story.

The book ends with a chapter about his controversial short film “Rites of Love and Math.” This is said to have made Frenkel something of a sex symbol among mathematcians, certainly a new idea. Unfortunately the film is not available through the inline rental services I use so I cant tell you any more about it. Here is the trailer from his youtube site.

Book Review: Time Reborn by Lee Smolin

April 24, 2013

Fill the blank in this sentence:-

“The best studied approach to quantum gravity is ___________________ and it appears to allow for a wide range of choices of elementary particles and forces.”

time_rebornDid you answer “String Theory”? I did, but Lee Smolin thinks the answer is his own alternative theory “Loop Quantum Gravity” (page 98) This is one of many things he says in his new book that I completely disagree with. That’s fine because while theoretical physicists agree rather well on matters of established physics such as general relativity and quantum mechanics you will be hard pushed to find two with the same philosophical ideas about how to proceed next. Comparing arguments is an important part of looking for a way forward.

Here is another non-technical point I disagree with. In the preface he says that he will “gently introduce the material the lay reader needs” (page xxii) Trust me when I say that although this book is written without equations it is not for the “lay reader” (an awkward term that originally meant non-clergyman). If you are not already familiar with the basic ideas of general relativity, quantum mechanics etc and all the jargon that goes with them, then you will probably not get far into this book. Books like this are really written for physicists who are either working on similar areas or who at least have a basic understanding of the issues involved. Of course if the book were introduced as such it would not be published by Allen Lane. Instead it would be a monograph in one of those obscure vanity series by Wiley or Springer where they run off a few hundred copies and sell them at $150/£150/€150 (same number in any other currency) OK perhaps I took too many cynicism pills this morning.

The message Smolin wants to get across in that time is “real”  and not an “illusion”. Already I am having problems with the language. When people start to talk about whether time is real I hear in my brain the echo of Samuel Johnson’s well quoted retort “I refute it thus!” OK, you can’t kick time but you can kick a clock and time is real. The real question is “Is time fundamental or emergent?” and Smolin does get round to this more appropriate terminology in the end.

In the preface he tells us what he means when he says that time is real. This includes “The past was real but is no longer real” “The future does not yet exist and is therefore open” (page xiv) In other words he is taking our common language based intuitive notions of how we understand time and saying that this is fundamentally correct. The problem with this is that when Einstein invented relativity he taught me that my intuitive notions of time are just feature of my wetware program that evolved to help me get around at a few miles per hour, remembering things from the past so that I could learn to anticipate the future etc. It would be foolish to expect these things to be fundamental in realms where we move close to the speed of light, let alone at the centre of a black-hole where density and temperature reach unimaginable extremes. Of course Smolin is not denying the validity of relative time, but he wants me to accept that common notions of the continuous flow of time and causality are fundamental, even though the distinction between past and future is an emergent feature of thermodynamics that is purely statistical and already absent from known fundamental laws.

His case is even harder to buy given that he does accept the popular idea that space is emergent. Smolin has always billed himself as the relativitist (unlike those string theorists) who understands that the principles of general relativity must be applied to quantum gravity  How then can he say that space and time need to be treated so differently?

This seems to be an idea that came to him in the last few years. There is no hint of it in a technical article he wrote in 2005 where he makes the case for background independence and argues that both space and time should be equally emergent. This new point of view seems to be a genuine change of mind and I bought the book because I was curious to know how this came about. The preface might have been a good place for him to tell me when and how he changed his mind but there is nothing about it (in fact the preface and introduction are similar and could have been stuck together into one section without any sign of discontinuity between them)

Smolin does however explain why he thinks time is not fundamental. The main argument is that he believes the laws of physics have evolved to become fine-tuned with changes accumulating each time a baby universe is born. This is his old idea that he wrote about at length in another book “Life of the Cosmos” If this theory is to be true he now thinks that time must be fundamentally similar to our intuitive notions of continuously flowing time. I would tend to argue the converse, that time is emergent so we should not take the cosmological evolution theory too seriously.

I don’t think many physicists follow his evolution theory but the alternatives such as eternal inflation and anthropic landscapes are equally contentious and involve piling about twenty layers of speculation on top of each other without much to support them.  I think this is a great exercise to indulge in but we should not seriously think we have much idea of what can be concluded from it just yet.

Smolin does have some other technical arguments to support his view of time, basically along the lines that the theories that work best so far for quantum gravity use continuous time even when they demonstrate emergent space. I don’t buy this argument either. We still have not solved quantum gravity after all. He also cites lots of long gone philosophers especially Leibniz.

Apart from our views on string theory, time and who such books are aimed at I want to mention one other issue where I disagree with Smolin. He says that all symmetries and conservation laws are approximate (e.g. Pages 117-118). Here he seems to agree with Sean Carrol and even Motl (!) (but see comments). I have explained many times why energy, momentum and other gauge charges are conserved in general relativity in a non-trivial and experimentally confirmed way. Smolin says that “we see from the example of string theory that the more symmetry a theory has, the less its explanatory power” (page 280). He even discusses the preferred reference frame given by the cosmic background radiation and suggests that this is fundamental (page 167). I disagree and in fact I take the opposite (old fashioned) view that all the symmetries we have seen are part of a unified universal symmetry that is huge but hidden and that it is fundamental, exact, non-trivial and really important. Here I seem to be swimming against the direction the tide is now flowing but I will keep on going.

Ok so I disagree with Smolin but I have never met him and there is nothing personal about it. If he ever deigned to talk to an outsider like me I am sure we could have a lively and interesting discussion about it. The book itself covers many points and will be of interest to anyone working on quantum gravity who should be aware of all the different points of view and why people hold them, so I recommend to them, but probably not to the average lay person living next door.

see also Not Even Wrong for another review, and The Reference Frame for yet another. There is also a review with a long interview in The Independent.

The Particle at the End of the Universe: Review

December 3, 2012

Somebody kindly offered me a review copy of Sean’s book in the comments so to encourage others to do likewise I shall offer my opinion of “The Particle at the End of the Universe: The Hunt for the  Higgs and the Discovery of a New World” by Sean Carroll.

The book I got was actually a virtual one which has the advantage of being searchable so the first thing I did was check to see if I got a mention. Apparently this blog (or rather its comments) turns out to be the place where the 125 GeV rumour first arrived on the internet. It is not what I would have chosen to be mentioned for but it’s better than nothing I suppose.

After a year of Higgs madness that swamped the media there will be plenty of people wanting to read more about it, so Sean has done well to get this book out in time for Xmas with the full story (so far). There is an obvious list of questions about the boson that people would like to ask and Sean conveniently answers them all chapter by chapter. Sean has been answering these kinds of questions on blogs and usenet before blogs for a long time, so he is pretty good at it, but explaining what the Higgs boson is and does in general terms is notoriously difficult. Sean does his best with a mixture of analogies and more direct explanations. Whether he succeeds would have to be judged by someone who does not already know the answers but I think it would be hard to do much better than this book.

There were two chapters that I found especially interesting. The first was about the thorny question of the Nobel prize for the Higgs. I compiled a list of contributions to the Higgs prediction a while back, but Sean goes one better by fleshing it out with the full story. It is very balanced and will be essential reading for the Nobel committee next year, but they will have to find their own solution to who gets the prize.

There is another side to the story of the Higgs discovery that sets it apart from previous discoveries in physics. It happened in the age of the blogs and social media. Sean is well placed to talk about the impact this had and his chapter about nit is the second one I liked a lot.

So overall it is a very good book. Enjoy.

Physics on the Fringe: Book Review

May 9, 2012

I dream of a new age of curiosity.We have the technical means for it; the desire is there; the things to be known are infinite; the people who can employ themselves at this task exist. Why do we suffer? From too little, from channels that are too narrow, skimpy, quasi-monopolistic, insufficient. There is no point in adopting a protectionist attitude, to prevent “bad” information from invading and suffocating the “good.” Rather, we must multiply the paths and the possibility of comings and goings.

Those are not my words. They were written but 20th century philosopher Michel Foucault, but if I had the same gift for words I would like to say things like that. This was quoted at the front of “Physics on the Fringe”, a book by Margaret Werthem that I read last month while I was on holiday. The book is about “outsider” physicists who work on their own theories outside of the physics mainstream. This is a subject of special interest to me as founder of viXra where many independent physicists (and other scientists and mathematicians) can publish their research, so I was keen to see what kind of picture the author painted. ViXra is not mentioned in the book. Instead there is a chapter about the Natural Philosophy Alliance, another web-based initiative for fringe physicists which has been around much longer.

You can read the manifesto of the NPA on their home page which has statements like “Reigning paradigms in physics and cosmology have for many decades been protected from open challenge by extreme intolerance, excluding debate about the most crucial problems from major journals and meetings.” Let me first make my own position clear. I have written articles on this blog about how some new ideas in the history of science have been attacked as “crackpot” only to be found right. In some cases you could say that the reigning paradigms were protected in that way, so this statement is not completely out-of-order. However, they are talking here about quantum mechanics, general relativity, the big bang theory and the standard model of particle physics. These things have extensive support from experiments performed over a wide range of scales. We know that they are not the final word because there are untested scales where they become inconsistent. They must ultimately be replaced by some new ideas that are likely to look very different from the existing theories. This is what professional physicists work on so presumably the NPA is referring to something more radical. Everyone is entitled to their own view and viXra is open to anything, but personally I don’t think that standard physics is that radically wrong.

“Physics on the Fringe” is all about people who are looking for alternative ways of doing physics that does not use the mathematics of quantum mechanics and general relativity. The impression it gives is that all “outsider” physicists are doing research of this sort. This is not the case. If you look through the physics categories of viXra you may find that about 50% of the papers make it clear that the author does not accept the standard models of physics and is trying to find an alternative. That is a lot but it leaves another 50% who at least believe they are working within the accepted paradigm. Many of these also have what professional physicists would consider to be obvious errors but there remains a smaller percentage where the ideas may still be radical and highly speculative, but they are mathematically sophisticated and apply to the physical regimes where experiment has not yet reached. Personally I think there is value to be found in the full spectrum of research from the craziest ideas to the most sublime, some are more like creative works of art with very little real science, but they may still inspire interesting ideas. Others may contain obvious errors but could still have a gem of knowledge buried within that someone might find. Perhaps a few are genuine new theories that could turn out to be right. This is why I believe that everything should be allowed to be published in non-peer-reviewed archives such as viXra. This does not mean that I do not value peer-review, but peer-review takes many forms. I don’t like peer-review as a closed process that is hidden and determines whether someones work is fit to be seen. I would like to see criticism that is public and where the author can respond. Perhaps now that the closed journal system is being taken apart we will see some new better ways to do peer-review.

So the book is limited in scope and ignores the more interesting work, but what does it have to say?  Chapter 3 tells an interesting story about 19th century mathematician Augustus de Morgan who wrote a book “A budget of Paradoxes” about his collection of theories by outsiders. It may be surprising to learn that the phenomena of amatures with crazy ideas goes back well before the existence of the internet. De Morgan was himself an almost outsider who had rejected a position at Oxford (or was it Cambridge?) because he objected to signing their theological test. Instead he worked at the newly founded University College London. His work on logic may seem ordinary to us now but at the time it was radical. Mathematics was going through a transition from a subject which studied quantity and form to more general ideas founded on pure logic and abstraction and de Morgan was at the forefront of the revolution. The obstacles to acceptance he faced may have given him some affinity with the “paradoxians” who touted their mad ideas at his door. It makes for interesting reading.

The central section of the book covers the work of Jim Carter and his theory of circlons. This is an example of work at the extreme end of fringe physics. Jim Carter did a degree in engineering and made money from his invention of a divers lifting bag. He had a good intuition for physics but his mathematical ability did not match. Like so many people of this ilk he formed his own alternative ideas that tried to explain the world in more mechanical and less mathematical terms. He used experiments where smoke rings are formed and allowed to interact to demonstrate his ideas. Wertheim has spent much time with Carter at his country adobe and has a sympathetic attitude towards his work, but she quite rightly regards it as more like a creative work of art than a valid scientific theory. Experiments with smoke rings are well-known to people who work on fluid dynamics and are great fun, but can they tell us anything about fundamental physics? If you study the mathematics of the soliton like vortexes that maintain surprising stability you will indeed find ideas that are used in quantum field theory, but of course this is not what Carter is doing. Valuable new ideas can indeed be formed in this way but mathematical ability is required. That is the way nature works.

So could the writings of someone like Carter inspire original ideas in others at least? Let me give another example of his ideas. Carter believes that the force of gravity does not really exist. Instead, he says, everything is expanding at an exponential rate and it is the ground accelerating up that appears to make us cling to Earth. This he thinks is a much better idea than general relativity which is all wrong. Physicists would laugh but there is a deep irony underneath. The theory that the Earth expands in this way is actually highly unoriginal and has been proposed many times. It is possible that such a crazy idea was known to Einstein. Perhaps when he discussed physics and philosophy with his friends at their “Olympia Academy” one of them may have proposed something similar as a topic for discussion. Einstein with his better analytic mind would have seen immediately that such an idea can only explain terrestrial gravity. In space everything would just fall towards the centre of the expansion. planetary orbits would require a different theory but that would be a step back to pre-Newtonian physics that undid the highly successful unification of gravity. However, Einstein was at that time an outsider himself unable to get a professional position as a physicist so he had more sympathy for crazy ideas. He might have seen that there was still some part of the theory that was right. Gravity really is like the pseudo forces caused by acceleration as experienced when in a moving lift. In time this would lead to the equivalence principle and the realisation that the idea would work if the explanation was that spacetime is bending instead of objects expanding. This was the birth of general relativity. In “Physics on the Fringe” Wertheim does not seem to appreciate this aspect of such ideas.

It the turn of the twentieth century Carter’s ideas could have been inspirational, but 100 years later I doubt that they have much value beyond the esthetic. Other more advances ideas at the other end of the fringe physics spectrum however, can be more useful. A good example is the work of Ed Fredkin who has published in viXra. He is well-known for his ideas about cellular automata as an underlying theory of physics (similar to Wolfram but predating) . Fredkin was an IT pioneer who invented some of the concepts used in modern operating systems and he was a professor at MIT, but his greater interest is in physics. Because of his position and his warm personality he has been able to discuss his ideas at length with Feynman and ‘t Hooft amongst others. His explanations of computing to Feynman led to the foundation of quantum computing and it is probably no coincidence that ‘t Hooft’s first paper on the holographic principal uses a cellular automata as a model. So Fredkin has been influential with his theories but of course he is not satisfied if they don’t accept his underlying idea. The problem is that a cellular automata is at odds with the principles of both relativity and quantum mechanics. Fredkin is not dissuaded by arguments that something is impossible. He was told the same thing about reversible computing and found a way to do it. He also likes to point out that cellular automata have the power of universal computation so there is no limit to what they can do. Sometimes the most interesting thoughts lie behind the craziest ideas.

There is one other chapter in the book that is worth commenting on. Wertheim describes her experience of attending a conference about quantum cosmology with its talk of multiverses, eternal inflation and the like. She compares this with the crazy ideas she had seen at an NPA conference, leaving the impression that the only real difference is that one set of crazy ideas is produced by outsiders and the other by insiders.  Here’s my opinion for what it is worth. I think string theory will turn out to be important in physics and will be the answer to unifying quantum gravity once we can work out the maths that underly it although for now we can only speculate about how that will work out. The multiverse landscape is another layer of speculation on top that I like philosophically but speculation on top of speculation has to be seen for what it is. Eternal inflation is yet another layer of speculation on top of that and I think the base of temporal causality and fluctuation from nothing are just bad philosophy so I just don’t believe it. I still think that it is right to explore that kind of theory but it should be shown for what it is, i.e. it is speculation upon speculation upon speculation. As Werthhiem recognises, this physics is popular because it sounds great on science documentaries and is promoted by a culture of superstar physicists (she mentions. Personally I am more excited by the work of someone like Nima Arkani-Hamed on non-locality and emergent spacetime that comes from Super Yang-Mills scattering amplitudes, but this kind of thing is harder to present on prime-time TV. Just my opinion, you are entitled to differ.

Nevertheless, there is a qualitative difference between such work on quantum cosmology and the theories presented by the NPA. The former assumes that quantum mechanics, general relativity and the big bang theory are correct up to the points where they are untested and theory suggests they will break down. Mathematics is used along side speculative ideas to try to understand what is possible within the constraints of logical consistency and confirmed observation. The physicists of the NPA throw all that away (OK to be fair that is too much of a generalisation to cover the wide range of ideas they present but that is how it is presented.) This means that it is more likely to lead to important new ideas that tell us something real about the world we live in.

Looking back at what I have written I see that I have been quite critical of the book, but on the whole it is full of interesting facts and presents a thought-provoking point of view. I think that anyone involved in fringe physics would enjoy the read.

BBC: Faster Than the Speed of Light?

October 20, 2011

Yesterday evening the BBC ran a documentary about the OPERA neutrino results. If you are in the UK and missed it you can watch repeats over the next few days or view it online here. Probably it will be available in other countries in some form soon.

The program was presented by mathematician and author Marcus du Sautoy who has become a familiar science host on the BBC in recent years. The tone of the show was skeptical but open-minded and I think this reflects the range of views that scientists have on the subject. Marcus described the results and surrounding debate as “a great example of science in action”. The show must have been put together very quickly but it follows clear logical steps and includes most of the relevant points that should be discussed at a popular programme level. I think they did a great job of bringing in the more exciting possibilities without hype. Here are a few highlight quotes from the guest scientists.

Marcus du Sautoy: “You can almost feel the shudder that passes through the entire scientific community when a result as strange as this comes out. Everybody’s talking about it. Is this the moment for a grand new theory to emerge that makes sense of all the mysteries that still pervade physics, or has there just been a mistake in the measurement?”

Marcus du Sautoy

Chiara Sirignano (OPERA): “On top of us we have 1400m of rock, the top of Grand Sasso mountain. Here the cosmic rays are very few because outside they are 200 per square meter per second and here it is just 1 per square meter per hour. This is a very huge shielding”

Chiara Sirignano

John Ellis: “If the speed of light turned out not to be absolute, we would just have to tear up all the textbooks and start all over again. On the other hand it would be nice if it were true.”

John Ellis

Fay Dowker: “For me it would mean that the direction of my own research was wrong, so it would be a revolution but to me it would also mean that nature is just playing tricks with us”

Fay Dowker

Jon Butterworth: I actually heard about this result in the coffee bar at CERN about two weeks before it came out, and I laughed. I have to say that was my thought, they have got something wrong haven’t they?

Jon Butterworth

Stefan Söldner-Rembold: “MINOS and T2K will both work very hard to get a similar measurement with a similar precision in the next few years, but it will take a few years I think”

Stefan Soldner-Rembold

Joao Magueijo: “Obviously this result contradicts what you find in textbooks, but if you are actually working in the frontier of physics, if you are really trying to find new theories this is not as tragic as you might think. It is a crisis, but we need a crisis because there are a lot of things in physics in those textbooks which don’t really make any sense.”

Joao Magueijo

Mike Duff: “Well, I have been working on the idea of extra dimensions for over 30 years so no one would be happier than I if the experimentalists were to find evidence for them. However, To be frank, although I like the idea of extra dimensions, this is not the way they are going to show up in my opinion. So I am not offering extra dimensions as an explanation for the phenomenon that the Italian physicists are reporting.”

Mike Duff

Tara Shears: “This could be one of those moments that turns our understanding on its head yet again, let’s us see further into the universe, let’s us understand more about how it ticks, how it sticks together, how things are related inside. If it does that, if we understand more, then it’s one of those magical moments that you get in the history of physics that just twists your understanding and brings the universe into focus, and if we are seeing the start of that now, and we are documenting it, then we are really, really, really privileged to be doing so.”

Tara Shears

BBC Horizon: What is Reality? (and will the holometer see it?)

January 21, 2011

Last time I commented on a BBC Horizon program it was quite popular so perhaps people will be interested in the latest one entitled “What is Reality?” which aired in the UK this week.

I thought the title did not sound promising but it turned out to be a whistle stop tour through a number of interesting current ideas in theoretical and experimental physics. It started with Jacobo Konisberg talking about the discovery of the Top quark at Fermilab. Frank Wilceck then featured to explain some particle physics theory at his country shack using bits of fruit. Anton Zeilinger showed us the double slit experiment and then Seth Lloyd showed us the worlds most powerful quantum computer, which is not very powerful. Lloyd has some interesting ideas about the universe being like a quantum computer which I encorporated into my FQXi essay, but somehow I dosed off at that point in the program so I will need to watch it again 🙂

Lenny Susskind then made an appearance to tell us about how he had discovered the holographic principle after passing an interesting hologram in the corridor. The holgraphic principle was illustated by projecting an image of Lenny onto himself. Max Tegmark then drew some of his favourite equations onto a window and told us that reality is maths before he himself dissolved into equations.

The most interesting part of the program was a feature about an experiment to construct a holometer at Fermilab described by one of the project leaders Craig Hogan. The holometer is a laser inteferometer inspired by the noise produced at the gravitational wave detectors such as LIGO. It is hoped that if the holographic principle is correct this experiment will detect its effects. Some sceptisicm might be fair dues, but it has to be worth trying. There is info about the holometer here.

I can find the program on Youtube but I wont link because I don’t know if it is an official version that will stay, or whether it is available everywhere or just limited to the UK.

A Christmas Puzzle

December 26, 2010

I was given “The Big Book of Brain Games” by Ivan Moscovich for Xmas. Most are too easy but here is a nice one (number 331):

Construct a square from four identical linkages hinged at the corners. Such a figure is capable of moving on its hinges to become a rhombus. How many linkages of the same length must be added to make the square rigid? The linkages must be in the same plane as the square and each one can be connected only at the hinges.

My best solution so far has 43 extra linkages which must be far too many.

Update 28-Dec-2010: Lubos has given a nice solution with no overlapping links which requires only 31 extra edges or 29 if you allow the links to cross. However I have found out that this is still not the best solution for the case where overlaps are allowed! so keep trying.

Final Update: Since posting this puzzle I have learnt that a version of it was posed in Martin Gardner’s SciAm column in 1963. His version required that the bracing links do not overlap. Seven readers sent in the solution with 23 added links shown below.

Erich Friedman considered the case where links can cross in 2000 and posted results on his Math Magic website. His best solution had 17 extra links. However, someone later informed him that Andrei Khodulyov had found a solution some time ago with just 15 extra links.

Well done to all those who posted solutions here and over at The Reference Frame.