Book Review: The Limits of Science by Peter Medawar

I can’t remember where it was that I first saw this referenced. It took a little bit of finding, as I could not find it print in any major bookstore either on the high street or online. Eventually, I managed to get my hands on a second hand book. The cover is a bit, well, utilitarian. I’ll include a photo, so you make of it what you will:

As soon as you see it, you’ll realise it’s a tiny book. The book is comprised of 3 essays and in totality it is less than 100 pages. The first is entitled “An essay on scians” where the author has used an alternative, archaic spelling of ‘science’ to make his point. It is a very general essay on the nature of science. There is some detail in there but it is only there to make a point rather than educate the reader in any particular point. It is greatly enjoyable; I would describe its style as an Englishman attempting to write like Richard Feynman. After all, where else would you find a subsection entitled ‘Science and cricket’? In a short essay he manages to cover issues of sociology, politics, history and the public perception of science.

I would recommend this to anyone considering taking an undergraduate degree in any science. It is a real gem; concise, clear, passionate and well thought-through.

The second essay has as its title a very straightforward question: “Can scientific discovery be premeditated?” This is an even shorter essay, at just 8 pages. Medawar uses 3 examples to demonstrate his argument that the answer to the question is “no.” His main target seems to be the industrialisation of science in modern academia where research is often only funded if an application of the science is foreseen. This goes very much against the spirit of science that prevailed in the 18th and 19th centuries.

His final essay is the culmination of these, where the main question posed is that of whether or not there are questions that science cannot answer. Specifically he has in mind “childlike elementary questions having to do with first and last things – questions such as “How did everything begin?” “What are we here for?” “What is the point of living?””

It would be very easy to heap praise on Medawar because his views line up roughly with my own. That is to say, he thinks there are questions that cannot be answered by scientific means though he rejects the school of positivism as put forth by AJ Ayer and the Vienna Circle, by accepting that such questions do make sense.

Probably the most interesting part of the essay which I had not previously considered was his consideration of ‘The Law of Conservation of Information’ which is stated thus:

“No process of logical reasoning – no mere act of mind or computer-programmable operation – can enlarge the information content of the axioms and premises or observation statements from which it proceeds.”

He finishes the essay with a consideration of ‘The Question of the Existence of God’ – a subject that tends to divide opinions like few others. I shan’t tell you what his conclusion is on this. I would heartily recommend that you read it for yourself. You can get a second-hand copy from Amazon (as I did) for a couple of quid, as it seems to be out of print now. But it is well worth it; eloquently written, sharp, witty and not overflowing with superfluous words.

Book Review: God's Philosopher's by James Hannam

When I first saw this book (I forget where) it seemed just about as ‘up my street’ as a book could me. My main two passions are christianity and science. So books that cover the two (without being needlessly antagonistic towards each other) tend to end up on my reading list.

In his introduction Hannam sets out his aim which can be summarised as “myth-busting.” Some may regard it as revisionist, though I think that would be a little harsh. The central myth is that the latter middle ages did not contribute much to scientific thought, and that the Enlightenment emerged out of a medieval intellectual vacuum of The Dark Ages; the latter two terms Hannam regards as prejudicial and which are then subsequently rarely, if ever, used again.

Hannam also goes so far as to cite the particular examples which he considers have given rise to popular misconceptions, with John William Draper’s History of the Conflict between Religion and Science being probably the most famous example.

The structure of the book is one of multiple mini biographies. These are given in pretty much chronological order. The timeline covered is roughly A.D. 999, when Gerbert of Aurillac became pope, through to 1642 which saw the death of Galileo. Given this time period and the number of figures involved, it can be hard to keep track of who is who, though the appendix does contain a very helpful timeline as well as a list of characters with a 2-4 line summary of why they are important.

At the start of the book, one could be forgiven for questioning whether or not it’s a science book, as much of the discussion is theological in nature, and could be considered a summary of medieval church history, particularly given the inclusion of several popes into the discussion as well as Thomas Aquinas, famous for his Summa Theologica. But that’s kind of the point. As the book progresses, we get more and more towards what our modern 21st century sensibilities recognise as science, but it is a gradual process with no sudden great leaps.

I know from having read some other reviews of Hannam’s book that his viewpoint is not universally accepted. I myself am no expert in this period of history so cannot really comment on its validity. The strength of the book is its meticulous cross-referencing, where original sources are preferred over secondary and an extensive bibliography is also included. So any time a claim is made that may go against one’s preconceived notions, the author gives the reader all the help they need to check the relevant facts. But this is not merely a scholarly book; it’s written with evident enthusiasm for the subject being discussed, like a highly energetic tour guide taking you round an exhibit for which they have a passion. It’s this exuberance that comes off the page which makes it pleasure to read, as well being highly informative.

Book Review: The Logic of Scientific Discovery by Karl Popper

I bought this book back in the spring, but had hesitated to read it. The reason for that is I found it quite intimidating, given the thickness of the spine. I will admit that the philosophy of science is something I have dabbled in only as an interested amateur though, of course, years of scientific training and discussions as a student have enabled me to reach (if you will allow me a moment of immodesty) a reasonably sophisticated understanding of my own view of science. Now, though, it seemed appropriate that I ought to look at what others have said.

Before reading this, I was aware that Popper’s views are not universally accepted and that he shared something of a professional rivalry with Bertrand Russell. Also, as a Christian, I find it interesting that I have seen Popper referenced far more by Christian scientists, whereas Russell tends to be more favoured by atheistic scientists. Of course, this is only a trend and there are exceptions. While Russell was a well-known opponent of Christianity, I was keen to learn more about what it is in their competing philosophies that has appealed to the different sets of scientists. So, of course, I will be following this up with some reading from Russell at some point, though if you have any good suggestions as to where to begin, I would be very grateful.

The book begins in a surprisingly accessible manner. I was expected some very high level philosophy that would be difficult to understand, but the translation is very easy to follow. Where he gets a little more obscure, he brings it back down-to-earth with examples that help to put his argument in context. I would describe the argument that Popper creates as being cumulative; that is, there are lots of references to earlier sections and, in particular, definitions. So you have to concentrate or else you can find yourself reading about “singular statements” and not know what he’s talking about if you haven’t followed it earlier.

For this reason, I would not recommend reading this book over a long period of time. I think it demands to be read quite intensively in as short a time as possible in order to ensure that one may follow it all.

The main thrust of Popper’s argument is to say that theories are never verified, they can only be falsified. He dismantles the positivist point of view which led to empiricism and shows that empiricism reduces to mere psychologism. From here, he then needs to discuss the degree of falsifiability. He considers a theory to be less likely the more ways it can possibly falsified. From here, what I think he should have done would then be to talk about corroboration and how a theory stands up to attempts to falsify it. Unfortunately, he leaves this to the end and instead goes off on a rather long and tortuous tangent talking about probability.

This quite long section was the downside for me, as his discussion (and in particular, notation) was quite obscurantist, making it difficult to follow and quite oblique. From here, he moves on to talk about quantum mechanics and in particular the Heisenberg Uncertainty Principle. It has to be noted that this was written during the years that quantum theory was still being formed and, having a background in quantum mechanics myself, I found many of his ideas to be simply wrong. They are a noble attempt at getting to grips with quantum mechanics but ultimately, they have not stood up to subsequent theory and experiments. So in a weird twist, you could say that his argument in this aspect has been falsified.

This brings me to my last point. If his theory is to be thought of as a scientific theory at all, then it must play by its own rules. That is to say, there must be a set of singular statements from this theory that can, in principle at least, be subject to testing to see if they can be falsified. Such a set of statements is not presented to the reader, so I could only conclude that while Popper’s contribution is to be valued and considered, it doesn’t constitute a scientific theory. It remains an application of metaphysics.

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.

Testimony & Epistemology

After recently reading Jesus and the Eyewitnesses by Richard Bauckham, some thoughts crystallised in my mind that had been floating around for a bit. This post is my attempt to articulate those thoughts.

Epistemology is a subject in which I have a steadily growing interest. I have just started reading Karl Popper’s The Logic of Scientific Discovery, though it’s a bit of a beast of a book, so don’t expect to see the review much before October. I may come back and revise this post after I have finished that.

As alluded to in my review of Bauckham’s book, the willingness to accept eyewitness testimony (hereafter, to be simply referred to as testimony) does not immediately imply a hermeneutic of credulity. There is a word for those who would accept without critique what they are told as testimony: gullible. Now, in spite of how often I have heard that accusation levelled at all Christians, it simply doesn’t stand up to scrutiny; if it were true then everyone who has ever professed faith must be intellectually retarded, but a brief look around the world today, and in history reveals this to be untrue. Of course, that is not to say that every Christian has reached their faith by careful reasoning and the examination of the available evidence; indeed I have met many who prefer to not think about the challenges posed to the claims of Christianity, but these are the minority. There is also then the adage that if you have met a Christian who doesn’t seem to have any doubts, then you just don’t know them well enough.

When I read or talk to critics of the bible, there is a phrase I often hear is “there’s no evidence for….” At which point a look of puzzlement usually smothers my face. The reason for this is that the person I am speaking to has completely disregarded the fact that we have the collection of books known as the bible, which is evidence. I think a far more honest term would be “there’s no corroborative evidence for…” which is a very different statement.

I have heard it said that Christianity is the religion of the historian. I am increasingly coming round to this point of view as most of the strongest arguments come from history, rather than science, philosophy or sociology. That is not to say that these don’t have important things to say about Christianity (and vice versa), rather I just don’t find them as convincing as I do for the historical basis for the person, death and resurrection of Jesus. Where certain ideas taken as cherished by Christians have had to be thrown out of the window because of subsequent research, there do not appear to be any scholars who have credibly formed and tested hypotheses for the origins of Christianity on an historical basis; there may be plenty of supposition, but very little evidence to support this. If anyone knows of a suitable riposte, please let me know as I would love to read it/them.

As I have said before, my worldview is that the set of things for which there is evidence is smaller than the set of things which are true. That is to say, there may be many truths for which there is no evidence. Of course, this then raises the question, “How do we know it’s true?” which is perfectly valid and deserves serious consideration. I still don’t have a definitive answer for that.

One of the key differences between history and science is the ability to generate evidence. Science can devise experiments in order to gather new evidence from well-designed experiments in order to confirm or deny an hypothesis. History, on the other hand, has to build the most reasonable explanation, based on the evidence available. Of course, you can always do archaeological excavations, or search through ancient libraries, but you can’t always find what you want. To go back to Bauckham, much of his book was based on the testimony of Papias, but we have no surviving manuscripts of his; only some quotes from Eusebius a couple of centuries afterwards.

To give a somewhat trivial example, I could tell you what I had for dinner last night. It happened to be a chicken curry. I can testify that that is true, and I know it to be so. However, I ate alone, with the blinds shut, so there are no other eyewitnesses, as far as I know. So how might one determine whether or not my testimony is true? Well, one could go through my bins and examine the contents thereof to find evidence of the ingredients of a chicken curry. This would certainly not constitute proof as there would be no way to pin the ingredients down to a specific date (it could have been the night before) or to ascertain that the ingredients were used together, as opposed to being used in the cooking of two separate meals.

An alternative approach may be to pump my stomach and examine the contents. Now this is a pretty extreme measure, but if you really wanted to find out, then this may be an option; albeit one that I would resist with what little physical strength I have! Also, this method would only work for the last couple of meals. If my question had been posed about what I ate on the 10th of February this year (or last year) then the answer would be quite unknowable; although in this case, I couldn’t testify myself, as I don’t have that good a memory.

Of course, we could try to falsify the proposition, yet what are the falsification criteria? Perhaps I was seen elsewhere, eating something different; but in the absence of other eyewitnesses, this cannot be a possibility. It is not clear to me that there are, given what the circumstances outlined above, any criteria upon which can be based any level of falsifiability. To draw the analogy to a close, before it gets over-strained, the fact that I ate a chicken curry is, for all practical purposes, unfalsifiable. However, this does not impact on the truth of the assertion. So it is with testimony. There may be many potential ways in which a testimony may be falsified (e.g. by direct contradiction with another testimony – although we need to be careful about the possibility of two different views of the same thing appearing radically different, or contradiction with other corroborative evidence, etc.). However, as noted above, the historian cannot generate additional evidence. He or she may search for it, but it may simply be the case that what they are searching for has been lost.

So then, if testimony is all we have, what can we say about it? Bauckham’s approach was to give them the benefit of the doubt. In this, I would somewhat agree with him, but with a word of warning. If a witness is shown to be untrustworthy in related key areas, then extra doubt may of course be cast on their testimony. I would think it unwise to reject them outright because of this.

There has been a recent example, when such a rejection has taken place. That is, in the case of Dominique Strauss-Kahn (DSK). The case was dependent on an eyewitness, but the case was ultimately thrown out because of a lack of corroborative evidence and aspersions made against the eyewitness. For my part, I do not hold an opinion as to the guilt or innocence of DSK. I merely include this paragraph to get you thinking at how relevant, and thorny, the issue still is today. It is not a problem restricted to historical theology, and one which I think we will continue to wrestle with for many years to come.

Round-up of interesting stuff.

It’s been a while since I did a roundup of interesting stuff to look at, so here are a few snippets that have caught my eye:

The Guardian’s religion correspondent, Riazat Butt is currently writing a series from Afghanistan entitled “Religion on the frontline” where she is spending time with troops in the desert.

Have recently come across Rogue Stardust, who has an excellent quality of writing. Here’s a particularly good post on depression.

The New York Times has a fund little feature on “name that scientist” – I scored a paltry 5/10 (and a couple of those were guesses)

Phil’s Treehouse ponders the question, who actually saw England become the world no. 1 in Test Cricket?

Meanwhile, something caught my eye, but not the reasons you might expect. The web’s friendliest atheist, Gurdur (who is also the wearer of the most awesome hat – seriously, have a look), has had a disagreement with someone on twitter. It just so happens that it was a bloke I went to school with some 20 years ago! And considering it was a small, private Christian school that has since shut down, having only turned out a few hundred students in its ~20 year history, I marvel at how small a world it can be sometimes!

The Independent has a roundup of the best acts from the Edinburgh Festival, in which WitTank get a favourable mention, although the paper have sadly overlooked the excellent Gentlemen of Leisure.

And to finish, something utterly silly which I hope will delight: an orang-utan on a bicycle! However, note how the article and the picture don’t quite line up with another in terms of the safety message.

On procrastination

I sometimes wonder what it is that makes us procrastinate. I am terrible at this. I often find myself completing 80-90% of whatever I’m doing, when I suddenly “remember” that there’s something else I need to do that I haven’t started yet. So it often ends up that I have a lot of things mostly done but nothing complete. I’m not very good at sticking at one thing.

The same is true of blog posts. I have about half a dozen that I have been writing for some time, taking a look at, putting away again and not feeling ready to put them online because I’m not happy about them for one reason or another.

I have also been lacking time lately, as I’ve been busy with work, often only getting half an hour or so spare in the evenings, as well as the fact that I was away for the entire weekend. Although that was quite nice. I was trying to teach my 7 year old niece about the idea of a “characteristic” by describing something that:

• Has four legs
• Has fur
• Has a tail
• Has teeth & claws
• Says “meow”

It was only at this last clue that a broad grin slipped across her face. I then asked her what characteristics uncles have (as well as me, she has quite a few other uncles). Here response was that they:

• Are grown-up
• Are male
• Have a special talent.

Naturally, at this point, I asked her what special talents I had. “You’re good at maths and tickles,” she said. That made me smile.

I have a relatively free weekend coming up, so I hope to be able to finish some of these half-creations. There has been much to think about recently, probably a lot of which I shan’t put online. I was sorry to hear of the departure of the departure of John Stott. Though I have not read any of books for many years, I always found them honest, heartfelt and challenging. I did not agree with 100% of what he taught, though I have a great respect for him. There have, however, been losses of those much closer to me and much younger, that it would be inappropriate for me to comment on further in public. I have also been trying to find the time to do some thorough reading on the potential discovery of the Higgs boson both at CERN and Fermilab, though I have not had the chance to read more than the first paragraph of any article, nor have I surveyed what evidence has been published so far. I am also trying to find time to read Steve Jones’ report on science reporting in the BBC. Again, I have only read a brief summary of his findings.

I will share one thought I had recently. I’ve been going through the gospels of Matthew and Mark lately, and noted that both of them contain mention of Jesus talking about “taking up a cross.” (Matt 16:21-28, Mark 8:31-38) Most Christians, I think, read this in the context of a complete picture of the gospels, post-crucifixion. I think there are some redaction critics who suppose this was added by the gospel writers at a later date, knowing the method of Jesus’ execution. Now, while I’m no expert at anything much, and especially redaction criticism, I’m not sure what the evidence is to suppose this was a later insertion. So, assuming it was a truthful testimony, was Jesus making some kind of prediction as to his own method of execution? Was it a common phrase in use in Roman-occupied Judea/Israel/Palestine at the time? What would those around him have thought he meant by it? What, crucially, did Jesus himself think he meant by it?

I’ve heard some very platitudinous answers to this, though I am not convinced by them. I shall continue to search and to think.

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.

Reader's digest

Hello again

Busy week, this week, so I don’t have much time to write my own material. So please find below a selection of recommended reading that I have come across. Some of it is new, some old, but all of which I find interesting. I hope you do too.

A new, private university is to be set up in London, charging fees of £18,000 per year. While this has been reported in a few media circles along similar lines (outrage at the privatisation of education and the exorbitant fees) I think The Church Mouse has hit the nail on the head with the real agenda. The only surprise in the coverage is that I’ve yet to come across anyone who thinks the idea has been nicked from Jamie’s Dream School.

Sometimes I wonder if these are made up, but apparently a formula for making a home-made bomb was replaced by a cake recipe. What I really want to know is how good were the cakes?

In the world of science, news reached me about anti-matter. I’ve been interested in anti-matter since I was a teenager and have spent many hours pondering its existence and properties. Unfortunately, I lack the necessary equipment to be able to conduct meaningful experiments with it. Fortunately, the folks at the Large Hadron Collider don’t have so many limitations as I. They have been able to contain some anti-matter for 1,000 seconds. For the laymen’s article on this, visit the BBC, but for the hardcore among you, the paper is freely available on arXiv (though it is large and takes a while to download on a broadband connection)

Not a new article to read by any long stretch of the imagination, but worthwhile nonetheless. This is something I’ve had renewed interest in of late. I’m still working my way through NT Wright’s Christian Origins and the Question of God series (albeit that I cheated by starting at volume 3. I’m currently about a third of the way The New Testament and the People of God, and the follow-up, Jesus and the Victory of God is sitting on my bookshelf, looking very inviting. This, combined with the reaction I got from some quarters to my review of Thomas O’Loughlin’s book about the Didache, has prompted me once more to look at the Jesus Seminar and its critics, amongst whom Wright is almost unquestionably the most prominent.

See here, for his comeback on the methodology of the Jesus Seminar and a collection of their writings. To be honest, I don’t know how seriously these guys are taken these days, as it has been over a decade since the publication of JVG and the linked article. I don’t hear much about them in the mainstream press and if they are evident on the blogosphere, it must be in a different sector to the one I peruse.

Sticking on the theme of NT Wright, I stumbled across this the other day. It is a curious blog which denounces Wright as a “wolf” and on the surface appears very conservative and fundamentalist (in the modern sense of the term) . Yet, unusually, it doesn’t seem quite as bleating as some other “false teacher” sites I have come across. Wright himself is quoted quite a lot, though I myself have not yet had sufficient time to read the full catalogue of all his writings, so cannot tell if he is being quoted out of context.

The blog makes quite a lot of reference to New Perspectives on Paul, an idea which I have heard of though know precious little about. I am well aware that Wright has written a few books on Paul in the build up to volume 4 in his Christian Origins series, Paul and the Faithfulness of God, currently due for publication in 2012. From what I can gather, this is to be the magnum opus in the New Perspectives movement, though at the moment I choose to concentrate my own theological focus on Christology, rather than Pauline soteriology.

Finally, to end on a lighter note (possibly), what is the best way to reduce the emission of methane in the atmosphere? Well, according to one Australian gentleman, you need to get in either a jeep or a helicopter and shoot camels!

Book Review: The Meaning of It All by Richard Feynman

This is a very short book from Feynman (~120 pages of actual text) and comprises of the transcripts of 3 lectures he gave in April 1963. They are as far removed from his technical lectures as can be imagined, so are easily accessible to the lay reader. The impression I got was that these lectures are Feynman trying to find his own mind, by talking out loud and seeing where the train of thought goes. In fact he admits that he covers all the key ground he wants to in the first two lectures, and these are noticeably more coherent than the last one, which takes up nearly half the book.

He covers various topics, though the key themes are uncertainty and the limits of science. He does touch on some potentially incendiary ground such as religion and politics, though he always measured and reasonable, never resorting to polemicism or off-handed dismissal. There is some evidence of the threat presented by the Cold War in the lectures.

Feynman's virtue as a scientist is present throughout, as he is quick to put down the “argument from authority” though he doesn't quite name it as such. Probably of most interest to the modern reader is the interaction between science and religion. Here, Feynman takes a very reasonable and fair-minded approach, more akin to Stephen Jay Gould than the ranting polemic of Richard Dawkins. He is also quite firm in the belief that scientific methodology cannot rule on morality; that is, there are subjective things in this world that are beyond the reach of science.

At times, he does get close to waffling a little bit, and the fact the book is taken verbatim from his lectures means that he interrupts himself on more than a few occasions. The book certainly provides food for thought, and I would recommend it to anyone interested in the place of science in society. It is probably not the best introduction to Feynman and his work (for that, I would recommend Surely You're Joking, Mr Feynman) though for those familiar with this other work, this will be a valued addition to your RPF library.

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)!!!

Proof of why a transposition error is always divisible by 9

Here's a little proof I knocked up over the weekend. Sorry it's in a picture format, the platform on which this blog is based can't deal with simple mathematical symbols, so I had to convert a document into a couple of pictures. If you click on the pictures, you should be able to see a larger version of each of the two pages of the proof.

Book Review: The Origin of Species by Charles Darwin

I have a particular bug-bear with isms and ists. These are often named after people with the ism or the ist being added on to the end to indicate a particular worldview represented by that individual. But how often do they bear relation to the work of the person themselves? In the past, I have sought to battle my own ignorance by reading Plato when I was sick of hearing about Platonism or of something being Platonic. I have also done similar with Euclid and Newton. So here we come to Darwin, the giant of biology and perhaps the father of Darwinism; or perhaps not.

The introduction of the book states that is important to distinguish the work of the man from the philosophical interpretations that have followed from it. Unfortunately, the rest of the introduction by Jeff Wallace (no relation to Alfred Wallace, as far as I know) shows that he has fallen prey to the mistake that he warns about himself in that he makes various claims about evolution which go beyond the biological evidence available.

So, moving onto the main text: Darwin begins with the mundane, to say the least. The subject of his opening chapter is pigeons, which he talks about at some length and which, to be honest, is pretty uninteresting to those of us who are not pigeon-fanciers. From here, where he looks at variation under domestication, he goes on to look at variation in the wider world, where man’s influence is not felt quite so directly.

Throughout the book, Darwin stresses the difficulty in trying to classify whether two animals (or plants) are variations within the same species or are different species altogether. His point, really, is that there is no sharp definition. Though it is clear that a horse is not of the same species as a mouse, there are grey areas elsewhere in the natural world; and examples of these are given as evidence to back up the point.

Having started with this preamble, Darwin moves onto the heart of the book, which is his theory of natural selection (note, the word ‘evolution’ is never used and the word ‘evolved’ is only the last word in the concluding chapter). It seems hard to come to this afresh, with it being such a well-known phenomenon that has been built upon over the years; so to put yourself in the shoes (glasses?) of the first readers for whom this was a new concept is a challenge for the modern-day reader.

From here, Darwin then spends the rest of the book looking at potential problems with his theory as well as outlining the evidence in favour of it. It was his honest approach at pointing out his own weaknesses that has garnered him so much high esteem in the scientific world, possibly more so than for the theory of natural selection itself. This, of course, was a two-edged sword, as it has provided ammunition for creationists and adherents of the intelligent design movement. The self-effacing lacunas in his theory take the form of falsification; in other words, Darwin is saying that if just one of many pillars on which his theory is founded would be proved false, then his whole theory would collapse. This book is completely lacking in the intolerant rhetoric and hysterical bleating found in the writings of so many of Darwin’s later adherents, which is why I was pleased to have read that Darwin himself was clearly not the model upon which the likes of Dawkins has based himself.

Darwin gives his reasoning for why he thinks these potential problems are not as great as they might seem at first and why natural selection is true. This latter part is done with several references to the notion of special creation as there are certain instances and observations which are well-explained by Darwin’s theory but which are unexplained (at least without some twisted explanation only concocted with hindsight) by the alternative.

The book is not without its flaws, however. On the one hand, Darwin is attempting to form, and give evidence for, a new scientific framework of understanding. At the same time, though, he is attempting to reach as wide an audience as possible. What this leaves us with is a mixture, where some parts of the book go into too much detail for the ordinary reader, making it turgid and really quite boring, while at other times skimming over detail and leaving the narrative sounding very much like an ancestor of Kipling’s Just-So stories.

This is somewhat remedied by the final chapter, where Darwin does finally break free from the constraints of evidence and reason, allowing himself a few flourishes of rhetoric, where he acknowledges that his book is only an introduction and that much more work is needed on tracing the family trees of species and tracing back to an original progenitor.

There are two elephants in the room with regards to the book. One is the origin of humans. The only time this is mentioned is right at the end of the book as an avenue for future research, though the topic is not broached in the main body of the text. The other is the absence of genetics. The book was written before genetics really became a major part of mainstream biology, and so numerous references are made to how unknown are the methods of transmission of characteristics and variations.

It can hardly be doubted how important this book is to biologists, though it is not a comprehensive review of the field. For that reason, I would not class it in the same category of “great” books such as Euclid’s Elements or Newton’s Principia. As far as understanding the history of the development of biology in the modern era, this is an essential book to read, and important for anyone wanting to sift the wheat from the chaff in terms of what Darwinism truly means.

My own conclusion from reading it is that Darwin would be aghast at the arrogance adopted by his successors in the advocacy of his theory, and the extent to which notions which he originated within the bounds of observable evidence have been stretched beyond their limit. I am thinking, here, particularly of Nietzsche’s idea of the superman and how that led to Aryanism and the Holocaust. While these ideas may have been seeded in Darwin’s work, I don’t doubt that Darwin himself would have regarded them as aberrant forms.

Book Review: Gaia by James Lovelock

It has to be noted, first of all that this book is now 30 years old. Much has changed since it was written and to that end the author has included a new preface which acknowledges this. He also acknowledges that there are some factual errors within the book but that he would rather the original text be preserved as it was originally written, rather than constantly be revised.

The starting question is this: how could we identify if there is life on another planet? In other words, what are the signatures that distinguish life from non-life? The answer is not that straightforward, though Lovelock, with some acknowledgement given to some other scientists, comes up with a working definition for what characterises that which is living. But what Lovelock then does is to apply these criteria to the whole of planet earth and comes to the startling conclusion that the earth (or at least the biosphere) is a living thing; not just that it contains living things, but rather that it is itself a living entity, which has then been dubbed Gaia, after the greek goddess of the earth.

From here, Lovelock then looks at various aspects of biology and chemistry on earth and seeks evidence for this claim. His central argument is that of homeostasis: that the earth is self-regulating in order to maintain the conditions needed for life.

The book is characterised by two different personalities, so to speak. On the one hand, there is a quite reasonable scientific discourse (mostly focused on chemistry) about the make up and balances within the atmosphere and oceans, while on the other hand there is an impassioned environmental polemic on what mankind has done to harm the planet. While I do disagree, per se, with having these two styles married together, the way it is done seems to take the edge off the level of scientific credulity that Lovelock might have otherwise been afforded. My impression of it was that the scientific overview of feedback systems was immensely interesting, but the overarching Gaia hypothesis was itself unnecessary. Though this book has been hugely influential, particularly within the environmental lobby (rightly, I believe) the weight of scientific evidence for the master narrative is small and yet to be convincing.

Book Review: A Place For Truth ed. by Dallas Willard

This is a fascinating, thought-provoking and highly enlightening collection from some highly notable thinkers and authors. I won't go through all 15 chapters, but will highlight a few. These are all taken from lectures and discussions which have been presented at the Veritas Forums over the course of several years. They do seem to have been copied verbatim, which does mean that some slips of the tongue or mishearings have crept into the text, though this is a minor point that could be addressed by a second issue.

The start of the book is saturated with the idea of truth. In fact the word itself is used so many times, the reader can start to feel as though they are beaten over the head with it. However, the discussions do widen out and cover various topics such as, inter alia, science, morality, theodicy, ontology and philosophy.

The reason I chose this book was because of a few particular names that jumped out at me; my having been impressed by other works of theirs which I have read: Francis Collins, Alister McGrath and N.T. Wright. Now the contributions by these particular individuals is pretty much taken from their other works which I have already read. So for example, if you have read Francis Collins' The Language of God, then his chapter will contain little that is new to you. So the most novel chapters were those from whom I had not come across before.

There is a distinct Christian bias to the book, though there are some discussions which put across alternative views which help to add some amount of balance to the proceedings.

As with the nature of any composite work such as this, the contributions do vary in quality and style. There will be some that you agree with and some that you disagree with. The one disappointment I had was with the chapter by Hugh Ross, whose arguments appeared very weak and insubstantial, particularly given the high quality of thinking and delivery that was evident elsewhere. On a few occasions, there was also a bit of a bias towards the american education system, which distances a few of the speakers from the non-american audience.

This is very much a book of the current time with the issues being discussed and the other recent writings referred to being very much focused on issues that have come to the fore in only the last decade or so. So as a comment on the status of truth and various related issues, this is a very good guide on the modern thought, though I suspect that it will not have a shelf life of more than 10 years, as by then discussions will have moved on and some of the contributions may appear outdated.

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.