Einstein, falsification and the spirit of science

There has been much written over the last few days in reaction to the news coming out of CERN that some neutrinos may have been observed breaking the “cosmic speed barrier.” I won’t go into too much detail here, as there is plenty to be found elsewhere on the web, though of varying qualities. One of the things that has bothered me is that many of the news sources refer to c as “the speed of light.” This is incorrect as the c which is used in relativistic notation is specifically “the speed of light in a vacuum.” Everyday experience tells us that the speed of light varies in different media. When you’ve seen a straw or stick in water appear to be bent, this is due to refraction. Refraction occurs because the light has a slower speed in water than it does in air.

My second slight gripe is over the fact that the result has not been confirmed. At the time of writing (Friday night/Saturday morning) the results are still subject to further scrutiny. For me, I wonder if the experiment which produced the result has been repeated. The best science must always be reproducible, given the same setup. This, of course, does assume invariance under time translation. Now *THAT* would shatter the scientific paradigm, if it were falsified.

There is also a slight laxity when discussing the idea of neutrinos breaking the speed barrier. The special theory of relativity doesn’t actually prohibit faster than light travel. If you actually work through the equations, what you end with is that you cannot accelerate a massive particle (that is, a particle that has mass, it’s nothing to do with it being exceptionally large) to c or beyond, from a speed which is less than c. The reason being that as it accelerates, it actually gains mass. The more mass it has, the harder it is to accelerate and you end up that as the speed approached c, the mass is unbounded (or in other words, it tends to infinity) and so cannot be accelerated any further. In theory, if a particle, at the point of its creation, travels faster than c, then it will remain faster, though it does throw out a whole host of other problems which I shan’t go into here.

So what if Einstein was wrong? He was still a hell of a lot smarter than I am. He wrote the paper “On the electrodynamics of moving bodies” when he was 26, younger than I am now. I still find it amazing at how much others achieve at a comparatively young age, and to be honest I find it quite depressing at how little I have achieved given that I am fast approaching 30.

If Einstein’s theory does need to be superseded, you can’t throw the baby out with the bathwater. You have to remember the historical context in which he worked. The Michelson-Morley experiment had falsified the idea of the ether, so something new was needed. Building on the work of Lorentz, Einstein’s view not only needed to be radically different from the prevailing Newtonian viewpoint that had dominated physics (or natural philosophy as it was originally known) for the previous few hundred years, but it also had to incorporate the well-tested Newtonian model in the vast majority of cases. In other words, for massive particles travelling at significantly less than c, the theoretical predictions between Newtonian and Einsteinian dynamics should differ by an unobservably small amount.

If Einstein now needs to be revised by another paradigm shift, any new model will also have to incorporate the results that have supported Einstein’s work over the last hundred years. Einstein’s remains a very accurate model of reality. Had it been a poor model, it might have been found out much sooner.

All this points me towards falsification. I think I have mentioned in another recent post that I am currently reading through Popper’s The Logic Of Scientific Discovery. Towards the start, he makes a very good demolition of positivism, and makes his proposal that scientific theories ought be falsifiable, rather than be built up via a kind of inductive method based on verification.

While this is my first time reading it, the general philosophy is very familiar, having been woven into the fabric of my scientific education.

All of science is provisional. The work of the great scientists represents our current and best understanding of the universe we live in. As Richard Feynman put it, “science is the belief in the ignorance of experts.” Nothing is to be deemed unquestionable, whether it be the work of Newton, Rutherford, Dalton, Darwin, Maxwell, Einstein, Feynman, Witten or Hawking. All are fair game.

To claim that to challenge any scientist or any theory is a kind “heresy” is a claim that could only be made by someone who has little to no understanding of the spirit of science. No theory of nature should be beyond question, even if we don’t have the answer. In fact, the nature of science is to state that there we don’t have the answer. All we can come up with are models of how the universe works that line up as closely as possible with reality. Of course, not everyone holds this view, as was demonstrated by Hawking & Mlodinow last year when they published The Grand Design in which they proposed a bizarre model of “model-dependent realism” though, thankfully, this seems not to have caught on. Yet I applaud them for at least challenging the spirit, which in itself is a spirit to challenge. A merry-go round of Russian dolls, perplexities and unknowns, and so the confidence of an earlier generation may be shown to be no more than hubris, and the quest for truth continues.

Book Review: You Are Here by Christopher Potter

I was first made aware of this book some time ago by an article in the Guardian which interviewed him. I cannot find the link for the particular article in question, nor can I recall the details of it. What I do recall, however, is that it piqued my interest and sounded like the kind of casual science reading that is right up my street. So I bought it, and then it sat on my shelf for a couple of months, unread, while I got on with other reading (just hit the tag “book reviews” to see all the others I have done lately).

The opening chapter was a bit mixed, where he talks a little bit about his own history, plus a fairly random smattering of other things, with no real structure to it. It turns out that Potter had a very similar background to me, being as he did his undergraduate studies in maths, before going on to pursue other things for a career, while maintaining an interest in science. There did seem to be a metaphysic which he laid on top of what he regarded science to be which I have only ever come across in those who are entirely untrained in science and yet talk it about confidently as the answer to everything. However, the rest of the book showed that if were ignorant about science, that that was entirely hidden.

He does a whistle-stop tour of the major philosophical developments of science over the last 2,500 years or so, along with a brave and noble attempt to summarise quantum mechanics and general relativity for the lay reader; a task which he does with some aplomb and not a little dexterity.

From here, there was a slightly peculiar list of seemingly random things which were listed in order of size. Potter’s aim was to look at bigger and bigger scales, effectively zooming out from our world to look at the wider universe. From here, Potter takes on a parallel journey, though instead of going from the smallest size to the largest size, he wants to take us from the earliest time right through to the present day, taking in an overview of the developments in cosmology and high energy physics.

Overall, the book is very much at the lightweight end of science writing, but nonetheless thoroughly enjoyable. It is spoilt a little by technical errors, though these are relatively minor (for example, he states that “Humans are often carnivorous” when he should have said omnivorous). The other drawback that is has, which is specific for his advocacy of the scientific method, is that he does not include references. All we have is a bibliography of further reading, where there is no linking between the books referenced and the relevant passages. The reader is left to work this out by the titles, I think. However, that would not stop me from recommending as a great book, especially a “starter” for someone not overly familiar with ‘pop science.’

Did you know that there was an 19-digit number that has never been spoken by any human ever?

Well, it’s true. I want to show you why it is true. Before I do that though, I have to explain why I am writing this. During my time studying maths at university, I was never particularly impressed by most “existence theorems.” On the whole, I don’t find it particularly exciting or helpful to set about proving the existence of something without any prospect of actually calculating it (Examples of these include the Ham Sandwich Theorem and the Hairy Ball Theorem). The exception to this is the pigeonhole principle, which I first came across on an open day at Leicester University. The day sticks in my mind because it was pouring down with rain and one of the first guys we spoke to said that he didn’t expect many of the applicants present to go on there, on the basis of the poor weather. His idea was the first impressions were lasting and that bad weather left an overall bad impression, in spite of whatever efforts made by the university staff on the day, the applications would likely think of Leicester as a rainy place, compared to another university they may have visited on a sunny day.

I did not end up going to Leicester University.

But in their open day they did introduce me to the pigeonhole principle, by which one may prove all sorts of odd things. One of these, for example, is that there are at least two people in Newcastle with the exact same number of hairs on their head.

You can look up more details of the pigeonhole principle here, as I would rather assume it is known and then use it rather than recapitulate the whole thing.

A while ago I came across a number called Graham’s number, which was a peculiar for the fact that it was immensely large, no one has calculated it, but we do not that it ends in a 7 (when written in base 10, at least), which is the kind of quirky thing that really piques my interest. [I ought here to note that the episode of QI on which I first saw this was repeated on Monday night, after I wrote most of this, but before I put it online]

So I got thinking what is the potentially the smallest number that no person has ever written down, spoken aloud or actually even thought about. I wanted to ensure that I would be right so where I have had to make estimations, I have erred on the side of caution, leading me to suspect that though I am convinced I am right, I have over-shot the mark in at least one respect.

The first trouble was to estimate how many people have ever lived. Here, we are instantly presented with a problem of trying to define the demarcation of the first homo sapiens as opposed to an earlier ancestor and to then consider at what point in human evolution numeracy developed. As I had no idea I resorted to Wikipedia, who gave a statistic cited from an American study that estimated there had been between 100,000,000,000 and 115,000,000,000 people who have ever lived. So naturally, I added on a bit (just to be on the safe side) and assumed for the purpose of my calculation 120,000,000,000.

Next, I had to estimate how long they live for. Again, without any detailed research to hand, I made a guess by using the current average age of around 80 years. I suspect that over the course of human history, it has not been less than this, so my estimate is suitably conservative (if that phrase is not an oxymoron).

Of this, there are likely to be times (such as childhood and old age) when the ability to count to large numbers will not be present. So I took off 10 years, which I think is not unreasonable.

Next, how much of that time is spent asleep. I have heard that people spend a third of their lives asleep, and that the average person gets 8 hours sleep a night. Personally, I don’t know where these people get the time from. I get 6 hours a night, so I estimated that each person was only awake for 52.5 years.

Of course, most people do not spend every waking moment thinking about numbers. As a mathematician by training and an accountant by profession, I probably do it more than most, although even then I would estimate that I don’t spend more than 5% of my waking time thinking about numbers. There are far more everyday concerns that take up much of my thinking time. Again, erring on the side of caution, I plumped for 10%.

This means that on my grossly optimistic assumptions, the average human can spend 165,672,864 seconds in their lifetime thinking about numbers. Given our earlier estimate of the number of people, this gives the total thinking time to date as somewhere in the region of 19,880,743,680,000,000,000 seconds.

Now, even though it can be very quick to count to 10, the numbers we are interested are not likely to be small. So how long does it take to say them? Of course, this will depend on language, so I admit my figure is a plucked out of thin air. I would opt for 2 seconds. I think when you get the scale of the hundreds of thousands, that’s not unreasonable. Order of magnitude higher than that will probably take considerably longer, so 2 is a fair estimate to use for a conservative guess.

So what’s the answer then? I believe that there is a number which is less than 9,940,371,840,000,000,000 which no person in human history has ever spoken, written or thought about.

I am sure that this is far too high an estimate, as we have considered numbers like a googol and googolplex which are many orders of magnitude larger and I haven’t taken into account repetition. Goodness knows how many times the number 100 has been considered by humans over the years!

I know for certain that the number in question cannot be 4,724,557,109,087,242 because I just thought about it. In fact, any number I think about is, by definition, the wrong answer, because as soon as I think of it, it can no longer remain “un-thought-of.” I’d love to think that I “discovered” a number by being the first one to think about it. Of course, by continuity, we know that it must have existed, but I have no way of verifying if I was the first one to think of it.

It strikes me a little bit of quantum mechanics where a system will collapse into its eigenstates as soon as it is observed. Truly fascinating and enjoyable.

That’s why I love science!

On creationism/ID

I would like to thank Lewis S for his well-considered post in reply to an earlier post I made. Lewis had clearly thought through the issues discussed and the challenges he raises deserve an equally considered response, I feel. They also touch on a number of subjects which I think concern a lot of Christians and critics of Christianity. Having started to write a reply, it quickly began to get lengthy, in spite on what I considered to be little more than a surface-level review of the topics at hand. So I have decided to split my response across several posts, in which I admit here that I am likely to stray off topic. I do not pretend that these replies will answer every query satisfactorily for all, though my hope is that is conveys a reasonable portrayal of my views on the matters concerned.

After the initial response (which was the quickest to write), I will look to cover:

The Bible as a tool of social control
The genocial god
Biblical accuracy

While Lewis indicated that the last point was the key one, I have left this ‘til last as it is taking the longest to write and reference. So then, on with the first response:

Creationism/ID

For the record, I do not subscribe to young earth creationism or to the Intelligent Design (ID) hypothesis. I think there is a quite profound difference between the belief that God created the world and the belief in a particular method of how He/It did it. As you will be able to read elsewhere, I recently read through Darwin’s The Origin of Species, and found that apart from the introduction which was not written by Darwin, there is nothing overtly atheistic about it. It seems to me that the idea of “special creation” has been bound up in many people’s minds with the core of the Abrahamic religions, and that by undermining the former, that the latter is then consequently undermined too. I do not agree with this view, as I consider it to demonstrate a poor grasp of theology (which I think is true in a lot, though not necessarily all, creationists) and a stretching of the good science into conclusions where the evidence does not reach.

I have no issue with creationists or ID proponents believing what they do, and am perfectly happy to worship in church alongside them. While I believe them to be mistaken, it is no reason to break up personal relationships or to adopt any kind of haughty attitude. To me, the core of Christianity is the person, death and resurrection of Jesus of Nazareth, along with the subsequent soteriology that that entails. Anything else is a distraction and I would not want anything petty to break apart such relationships.

One of the labels that is often applied to YEC/ID proponents is “anti-science” which I personally think is a bit harsh, particularly on the ID supporters. To quote Richard Feynman,

“Science is the belief in the ignorance of experts.”

Those who dissent from scientific consensus tend to fall into one of two categories: genius or crackpot. It is by questioning what we commonly accept that a lot of progress may be made. But there may also be a lot of wayward pot-shots that happen along the way. In my experience, there are often a few gems hidden within the criticisms of YEC/IDers that deserve serious consideration, but given how far their main hypothesis lies from mainstream science, they are disregarded wholesale.

Where I see the failings of YECers is that while they may well accept scientific methodologies, their conclusions are biased, based on a pre-existing paradigm. IDers are merely pursuing a route of falsification which Darwin mentions several times in Origin. So the fact that they keep coming up with possible examples of potentially irreducibly complex structures which do turn out to be explainable by means of natural selection, I think, adds to the body of evidence supporting Darwin. All too often in debates around creationism and evolution, I think those on the side of evolution don’t put up the best possible argument but instead refer to rhetoric and name-calling, unwilling to engage with those who disagree with them. At times, it seems as though it is a default position to adopt simply because of their distaste with any possible alternatives. To me, scientific integrity means it should be questioned and challenged; if it can be falsified, then it is important that serious attempts should be made to pursue such lines of enquiry.

I find it interesting to compare the approaches taken by creationists such as Ken Ham to that of Fred Hoyle’s view of the Big Bang theory. Ham objects to evolution, not because of any particular flaws in the theory but because he disagrees with a particular conclusion that may be reached from it; namely the undermining of his worldview of the creator god. Hoyle objected to Big Bang theory because he felt it accorded too well with the Judaeo-Christian view of the world having a beginning, which may then imply a creator (c.f. Thomas Aquinas and the “first-mover” idea). Both of these men start out by objecting to a possible corollary and then went in search of the evidence to undermine the theory. As far as I know, Hoyle never adopted the big bang model of the origin of the universe, in spite of its near universal acceptance in modern science (an interesting recent exception being the severe modification proposed by Roger Penrose’s conformal cyclic cosmology hypothesis). While I do not agree with Ken Ham, I think he sometimes given a rougher time than he deserves, as some of his critiques are not without basis.

To my view, the problem with Christians who reject evolution is shared with some atheists who reject Christianity. It is the problem of throwing the baby out with the bathwater. I fully acknowledge there are problems with Christianity, and I will touch on one or two of these later on. At the same time I acknowledge that there are problems with evolution. If there weren’t, there would be no need for research; we would know everything. But the fact that both have their difficulties does not mean that I will reject them outright. Indeed, I am happy to embrace both as working hypotheses.

To return to what I think Lewis S was getting at, even though he didn’t phrase it quite as such is this: how do I reconcile the creation account in Genesis with evolution? To me, the key is about trying to understand Genesis in the context in which it was written and what would have been observed by the writer(s) and readers. Without an extensive knowledge and study of biology, as Darwin, Russell and their contemporaries had, it would be highly surprising indeed if the author(s) of Genesis would have come up with a description that mirrored our current understanding of the development of life. They were merely expressing themselves in the best way they possibly could. There is some indication, though I would not like to stress the point too much, that the civilisation which produced the book of Genesis had a grasp of what structures in nature were more complicated. This is given by the “order of creation” in the genesis account which, with a few exceptions, broadly mirrors the current scientific consensus. Andrew Parker has recently written a book entitled The Genesis Enigma which goes a lot further than I would consider reasonable along this route, though I shall say no more about it here.

It was also long before Darwin that Christian scholars and apologists warned against taking the start of Genesis in what we would not call a literalist manner. Augustine of Hippo wrote a piece called De Genesi ad litteram in which he advocated such a view. And this was written in the late 3rd/early 4th century!

I have to say that I am not a biologist, so can boast no evolutionary training beyond the average. Instead, my master’s degree was in mathematics, with a very heavy dose of physics (in the last couple of years, subjects covered included quantum mechanics, general relativity, twistor theory, string theory, fluid dynamics and electrodynamics). For that reason, the particular areas of creationism that I felt most able to look at were their physics explanation for a young earth. The two dominant ideas here were the slowing down of the speed of light (which, if true, could help explain the red-shifting of galaxies and get past the rather awkward fact of any object being more than 10,000 light years away) and the decreasing strength of the earth’s magnetic field (where an extrapolation is taken and an argument is made than with a much stronger magnetic field, life could not exist on earth). The former argument was dependent on a single paper that has since been debunked, as the author cherry-picked his data and made an arbitrary cut-off date at which light stopped slowing down. This happened to coincide with the most accurate measurements of the speed of light. The author also supposed that all measurements (including those where the only available light was a candle!) were entirely accurate. The latter theory may have seemed more promising, were it not for the mathematical uncertainties that creep in when using any form of extrapolation model. Here, I think of the GCSE experiment in Hooke’s law using a spring where the students discover that you can’t extrapolate your results, as it misses a change in the molecular structure that changes the deformation from elastic to plastic. Also, the discovery of geomagnetic reversal was the final nail in that particular coffin.

This was roughly the route by which I largely came to reject creationism. One line I have heard a few times from creationists who cannot fathom that someone can both be a Christian AND be persuaded by the evidence for evolution is “well, if you don’t believe the first chapters of the Bible, how can you say you believe it?” I consider this argument to be both fatuous and vacuous. It fails to recognise the Bible as a compendium of books, not a single book by a single author. It also draws on some strange form of logic whereby rejection or acceptance of one part (in a literalist manner) compels you to reject or accept the whole. It is rather like saying you disagree with an editorial piece in a newspaper, and thereby being forced to reject the entire contents of the said paper.

So what shall I say in conclusion, then? The fact that I am persuaded by the evidence for evolution in no way diminishes my Christian faith. It would be truly astonishing if the authors of the book of Genesis had given an account that was technically accurate, as it would have required a breadth of study and technology that was far beyond what was available at the time.

Reader's Digest

Welcome to another of my readers’ digests.

This has been under composition for a little while, so I apologise if some of the stories linked to seem a little out of date. This one is quite short and sweet.

I am always fascinated by how the mind works, and this story from the Independent shows what can happen when things go wrong. I can barely imagine what it would be like to wake up one day and suddenly find I had aged nearly 20 years. It certainly made me have a quiet think about what I’d like to do with my life.

In the world of particle physics, some scientists in Japan have claimed that neutrinos may vary from one form to another. The full paper is here. I remember when I went to the cinema to be subjected to the awfulness that was 2012, that I nearly fell off my seat laughing at the prospect of neutrinos “mutating” to heat the earth. While that still seems far more in the realm of fantasy, this research, if true, may go 0.1% of the way towards seeing that as a possibility.

There’s an interesting piece in the New York Times about a new book by someone called Simon Baron-Cohen (I wonder if he’s related to Sacha) on the science of evil. It looks like it could be a thought-provoking read, though it won’t be jumping to the top of my reading list. The NY Times article also has a link to an extract from the book, if you’re interested.

More science, here. This time a black hole may have been observed destroying a nearby star. The paper can be found here

Has a new particle been detected? Can’t find the paper reference for this one. If anyone has it, let me know and I’ll add the link.

Finally, there’s a lovely article here in the Indy about books, which you may have worked out are of particular interest to me.

Another Reader's Digest

This week, we’re sticking mostly the BBC for the most interesting stories.

First up, there is a terrible story of my own alma mater accepting money from British American Tobacco to fund scholarships.

On a brighter note, the university did regain its place in the top 10 universities on the Guardian’s rankings, though they have insisted on going with status over substance, by looking at the top few.

Surely, the headline says it all: Exploding watermelons!

A fascinating look at corporate branding. It should tie in well with my forthcoming reading, as I’ve got Naomi Klein’s No Logo near the top of my reading list at the moment.

Here’s one for all you science geeks: planets orbiting backwards! As Nature doesn’t believe in the open democratisation of science, you can’t view the article in the magazine without paying through the nose. However, the paper in question was issued as a pre-print last year on arXiv and can be downloaded at no extra cost here.

Back to the Beeb for this one: coffee reduces risk of cancer in men! Of course, any such story needs to handled with the scepticism due to any such sensationalist article. I certainly won’t be increasing my coffee dosage in light of this.

Finally, another science article. This time on one of my all time favourite subjects: Non-Euclidean Geometry (in Amazonian tribes)!!!

Book Review: Cycles of Time by Roger Penrose

This is a very interesting read on Penrose's new hypothesis: conformal cyclic cosmology. Before he gets to this in the third part of the book, he first needs to give the reader the background to his thinking. To that end, the first part of the book looks at the Second Law of Thermodymanics, which plays a pivotal role in this work. So if you don't yet have any idea what this is, I would recommend a little preliminary reading before tackling Cycles of Time.

If you are not familiar with Penrose's writings, then this perhaps is not the best starting point. He jumps straight into the Second Law and doesn't shy away from the necessary maths. For a science graduate, this is relatively easy reading, though those without a formal background in maths or physics may struggle, although Penrose's styles of diagrams are immensely helpful. One thing that is helpful is that even if you haven't grasped all the detail in a given section (and I certainly didn't) then that doesn't mean you cannot grasp any of the later concepts.

No one could ever accuse Penrose of patronising his audience, and though many topics will be familiar to scientists, Penrose's particular style always stretches you and makes you think in a slightly different way; so that which you thought you knew quite well suddenly has a few extra question marks posed against it. One thing that is very praiseworthy in this book is Penrose's modesty and his clearly laying out of what is well evidenced scientific consensus and what is his own minority view, as well as pointing out the drawbacks in his own theory. This style contrasts greatly with the brash optimism that Hawking & Mlodinow put forward in their book, The Grand Design, published within a few weeks of Cycles of Time. The fact that Penrose does this raises some interesting questions. For example, he does state that in order for his hypothesis to be correct, we would have abandon many well-established theories, such as the invariability of rest-masses of fundamental particles.

I could not claim to have fully understand all the nuances and detail of this book at the first, but that does not diminish my enjoyment of it or my ability to get the overall gist of it. I will be re-reading this book, going over each line in more detail in order to get the complete picture.

Book Review: The Three Roads to Quantum Gravity by Lee Smolin

First off, I need to explain why I wanted to read this book. I thought the 3 roads of the title would be string theory, loop quantum gravity (LQG) and twistor theory. I have studied both string theory and twistor quite extensively, so was looking forward to a recap of those two with a nice easy introduction into LQG. This is not the case though. The book begins by trying to take the issue of quantum gravity in as broad a scope as possible, before looking at LQG and string theory. After reading it, I was still none the wiser as to what he thought the third road was.

I have to say I was quite disappointed with the start of this book. In chapter 3, Smolin makes the very correct observation that “If one is not careful, [the superposition principle] can lead to a kind of mysticism in which its meaning is over-interpreted far past what the evidence calls for.” However, he fails to take note the irony that the first two chapters contain conclusions which over-step the boundary set by evidence, and so the foundation of the book is based on some unjustifiable assumptions. Along with that, on page 22, there is possibly one of the least helpful diagrams I have ever seen in any scientific literature. Though he acknowledges that he is not the most eloquent of writers, he unfortunately seems to want to emphasise this point with some very hand-wavey descriptions of general relativity (GR). If you have not studied GR at university or even read other popular science literature on the subject, then the introduction will likely leave you completely baffled and clueless. If that sounds like you, I'd recommend going for A Brief History of Time first to get a clearer picture of GR.

From here, Smolin goes on to talk about quantum cosmology and the restrictions it can impose on our worldview. This was quite interesting to read, though probably not for the reasons intended. The book is (at the time of writing this review) 10 years old and it is quite fascinating to see how scientific opinion has shifted in even this short space of time. Smolin dismisses the many-worlds hypothesis as an interpretation of quantum mechanics (QM) though he doesn't really explain QM particularly well. What we are left with is a chapter that tries very hard to explain things in a lively, straightforward way, but which fails in that aim and is quite garbled and confusing, which is a terrible shame.

However, it's not all doom and gloom. The book picks up significantly in terms of quality and clarity when Smolin goes on to give the background to his own speciality: loop quantum gravity. He makes a good case for pinning it to sound and well evidenced basis, even if no direct evidence has yet been found to confirm it. He is also keen to stress that LQG is not necessarily a candidate for a theory of everything, and treats his own subject with a level of humility and healthy scepticism that is very welcome in a science text. There is also a hint at the end of the book of the introduction to his later book, The Trouble With Physics, which details certain sociological problems that surround and inhibit some aspects of research into quantum gravity.

There is a helpful critique of string theory given, though possibly not enough time is spent explaining it properly, and readers interested in that could do a lot worse that Brian Greene's The Elegant Universe.

Overall, it is worth reading but prepared to quite frustrated, particularly early on.