Monthly Archives: October 2013

Book Review: The Call of Cthulhu and Other Weird Stories by H.P. Lovecraft

This was my first taste of anything by H.P. Lovecraft, though I knew roughly of his work by reputation: a master of horror, a very American writer, with more than a hint of racism. Is that what I found here? Sort of.

Given the various compilations of his work that have been put together, it’s worth noting that this particular collection (published by Penguin, under their ‘modern classics’ label) contains the following stories: Dagon, The Statement of Randolph Carter, Facts Concerning the Late Arthur Jermyn and His Family, Celepaïs, Nyarlathotep, The Picture in the House, The Outsider, The Hound, The Rats in the Walls, The Festival, He, Cool Air, The Call of Cthulhu, The Colour Out of Space, The Whisperer in Darkness, The Shadow Over Innsmouth and The Haunter of the Dark.

These are roughly in chronological order, which shows. The earlier stories here are relatively short and punchy while the later ones are better developed. Indeed, the accompanying notes raise a point I noticed in that some of the later stories appear to be revisions and expansions upon the earlier ones. For example, the Call of the Cthulhu is recognisable as an alternative take on Dagon; also, Facts Concerning the Late Arthur Jermyn and His Family seems to be the seed out which grew the longest story here, The Shadow Over Innsmouth.

Before reading, having heard that it was horror, I was expecting something either like a ghost story, like a James Herbert, or more gruesome, like Stephen King. It was neither. In this respect it was a pleasant surprise. That’s not to say that there isn’t some gruesomeness here, with Cool Air possibly topping the lot in that respect. The frustrating thing early on was that Lovecraft omitted the detail almost entirely, so we get descriptions like ‘[what I witnessed was too horrible to put to paper]’. It ought to be noted that most of the stories are written in the first person, with each central character speaking with roughly the same voice, making it seem as though Lovecraft was a single character going through one disastrous lifetime to another, being reincarnated multiple times.

What did strike me, however, was how alarmingly modern his writing was. Most of the stories here were written in the early 1920s, yet there is little here to indicate them as such; had someone told me they were written in the last 10 years, I would not have instantly thought the notion absurd. Indeed, his timeline is far closer to that of Thomas Hardy than it is to my own lifetime, but one could hardly guess at this. The biggest downside to his writing that I found was his predictability; almost every story had an ending that could be guessed fairly early on. The later stories were less predictably, though I don’t think I was ever particularly surprised. They are, however, very entertaining. Not a single one was a great struggle to read, though Lovecraft does, at times, stumble over his words slightly which makes it a little clunky. But that’s a relatively small criticism.

What about the supposition of racism? Well, there are some attitudes demonstrated here which do make for uncomfortable reading, and not in the good way that a horror writer might hope for. If anything, I would say it is most prevalent in Facts Concerning the Late Arthur Jermyn and His Family, though on reading the rather extensive notes at the back of the volume, the majority of the thinking about his views on race come out in his extensive letter writing which is not included here, except for small snippets of a few letters.

By some way, The Call of Cthulhu is the best story of the bunch. The other, later stories, are also good, though the grand scale which Lovecraft manages to evoke from fairly a small-scale start is very well done. The general mythology which he develops throughout the stories, with Cthulhu being alluded to later on, along with Nyarlathotep’s appearance in more than just the story bearing his name, make for almost an alternative world. Yet Lovecraft has not delved into the fantasy realms of Tolkein or Lewis. Rather, it’s a world just slightly different from ours, shifted by a tiny amount, where the monsters which be there always may now been heard or their shadows glimpsed.

And if you read The Rats in the Walls, it’s best not to then move to a new home where you can hear the water in the pipes of a night.

Our comfort in life (A Personal Catechism #1)

Q: What is thy only comfort in life and death?

A: That I with body and soul, both in life and death, am not my own, but belong unto my faithful Saviour Jesus Christ;  who, with his precious blood, has fully satisfied for all my sins, and delivered me from all the power of the devil; and so preserves me that without the will of my heavenly Father, not a hair can fall from my head; yea that all things must be subservient to my salvation, and therefore, by his Holy Spirit, He also assures me of eternal life, and makes me sincerely willing and ready, henceforth, to live unto him.


One might straight away ask, at the start of a confession, to ask for some definitions. Here, we have a number of words used which may be open to (mis)interpretation. These would include ‘soul’, ‘sins’, ‘devil’, ‘heavenly’, ‘salvation’ and ‘Holy Spirit’.  Yet there might be a risk of infinite regress and this whole confession might ground to a halt before it gets started. Instead, I would rather hold onto these lightly and read this as a sort of ‘executive summary’. This should be unpacked in the weeks and months to come. If they are not, then I may need to revisit this; please hold me to it.

I would use the phrase ‘body and soul’ to mean everything that I am, my whole being, my thoughts, feelings and memories. I would not dispute the idea that I am not my own, though it is an idea that prompts one to stop and think what this means. We often hear the possession is 9/10ths of the law, though since the abolition of slavery the idea of the ownership of a person has become increasingly alien to us. That should not be interpreted as a lament at abolitionism, but merely a pointing out that the analogy might be somewhat outdated.

In the modern western-world, this might be seen as more counter-cultural than ever. The ideology of ‘I’ often places the needs of individual front and foremost. When it comes round to election time, listen out for how politicians try to appeal to the desires of individuals; likewise listen to the canvassing of opinion on the streets and hear how many times people ask the question “[what will their policies do for me?]”

Yet this level of individualism is present within the Heidelberg Catechism. It is very centred on the individual beliefs and personal salvation. I am somewhat cautious about this. I would not reject it outright, by any means. Though it might have been better phrased in the corporate sense, to give the church as a body of people a greater emphasis than the person who is part of that body.

When it talks of precious blood, I must confess that I cannot help but think of the film, Dr Strangelove, and the unhinged American General’s obsession with precious bodily fluids. I don’t think this is at all what it means. Rather, it is an unambiguous reference to the implications of the crucifixion and resurrection of Jesus. In using the term ‘satisfy’, I would not read it necessarily as a pleasant thing. We might think of satisfaction in terms of being pleased, of getting what we want; yet I don’t think that’s the point that was being made. Working, as I do, in finance, I am inclined to think in terms of debt. The sacrifice that Jesus made was the payment of debt, in a sense “filling the hole” that one might think of being satisfied by a good meal. It has filled you up so that you need no more. The general idea is usually known in theological jargon as “atonement” – though this will be expanded upon later in the project.

I will not expand here on what I understand by the term ‘sin’; that will come up again soon enough. I will also make no statement here about the devil; that might be for much later. If anything, I would have been tempted to cut it out of the catechism at this stage as it might be an unnecessary distraction.

The idea of God preserving us is an odd one. I’m not sure either the composition or the translation is particularly good. The references provided are both to John’s gospel: chapter 6, verse 39 and chapter 10, verse 28. In both of these, Jesus speaks about keeping hold of what he has been given, of not losing it. It is my current understanding that these references were those used by Calvin as a basis for his idea that salvation was a once-and-for-all transaction. In other words, there could be no such thing as an ex-christian; leading to the logical conclusion that those who renounce their faith were never truly saved in the first place. I have qualms about such a view, but they may be kept for another time. I think the idea that the gospels were getting at was about the idea that no external influence could take someone away, rather than putting up a barrier against a wilful exit.

That not a hair will fall from one’s head without God’s will is an interesting one. It’s beautifully poetic, though I would caution about too literal with it. In one sense, I would say that God has laid down the foundation of the universe. That is not say I believe in ‘God the magician’ or ‘God the tinkerer’ but rather than the physical and mathematical laws which we have gotten to know, love and even understand to some extent, are ultimately authored by God. How this might be, I honestly don’t know. But the notion of how a hair falls from one’s head entails not only gravity acting between the hair and the earth, but also the complicated biology of how that hair grew and then became loose enough to fall. It is not that God goes around plucking people, but rather that God established the rules that would allow it to happen and therefore the act of falling is not a surprising act outside of nature, but just is.

I would disagree with the idea that “all things are subservient to my salvation”.  Indeed, the reference given in support of this clause is Romans 8:28 which states (NRSV), “We know that all things work together for good for those who love God, who are called according to his purpose.” I cannot see how the latter quote is equivalent to, or even, implies, the first. I might just be being a little slow on the uptake. I consider the gospel to be multi-faceted, so to emphasise one aspect over another may lead to a skewed vision. I would not rush to join the anti-evangelicals though in downplaying the message of salvation within christianity.

At this juncture, the Holy Spirit seems somewhat bootstrapped on, though this is not wholly a bad thing. If one regards this as an executive summary then it is good that it contains some evidence of Trinitarian thinking. The phrase “eternal life” may be problematic for some, not least because of over-simplifications and consequent misunderstandings, not least about “where” that life will take place. The more modern trend is to use the phrase “life in the age to come” which, though more clunky, maybe conveys the message better.

The final clause “makes me sincerely willing and ready, henceforth, to live unto him” is a good touch to end on, as it brings us back to the present life, reminding of us of our obligations here. I have heard some preachers take reformed theology too far, in my view, encouraging people to have their eyes fixed on eternal life, that it may be easy to take our eyes off the world around us. At this stage, the instruction is fairly vague, but that might be left as it is for now, I think.

So having said all that, how might I respond to the question with my own personal catechism?

Alternative Answer

I cannot say that have an ‘only comfort’. Rather, I might respond with what my ‘greatest assurance’ instead. That greatest assurance, then, is that with everything I am and have, I must recognise that I am not king of my own world; I am a part of someone else’s world, along with billions of others. I regard myself as a sinner; though I am not a sinner because I sin; I sin because I am a sinner. But ‘sinner’ should not be seen as a pejorative term. It could just as well be a synonym for human. Yet there is one exception. The one human, Jesus, to whom the royal title of Christ is conferred, was crucified and later resurrected, to pay the debt created by the sin of all humankind. Though we constantly strive to understand how the cosmos works and how it arose, I believe that it is because of the work of the one who created it – or rather, who created the means by which it was created. This was done wilfully and with a plan, so that acts of nature accord with that plan. It is this God, who is one and the same as the man, Jesus, whose Holy Spirit gives us assurance that we are to take part in the resurrection, where Jesus led the way, in new and incorruptible bodies.  Until then, though, we are to live for God – and all that entails.

Book Review: History of the Peloponnesian War by Thucydides

In my ongoing fight against ignorance, I once again return to ancient history. Having battled my way through Herodotus’ Histories last year, Thucydides seemed like the natural follow-on as the period he writes about takes place shortly after the period at which Herodotus stops. There is a distinct change in tone however, between the two, with Thucydides being far more focused on his task in hand, whereas Herodotus wrote about pretty much anything that took his fancy. The translation I read was that of Rex Warner. As far as making the ancient Greek intelligible in modern English, he did a splendid job. Whether it is the most faithful translation, I cannot tell. This was the one and only translation I picked up.

One cannot begin a review without commenting on its sheer length. It took me several months to work through the 8 books. It would have taken even longer had it not been for a very accessible translation and the help of the introduction. The title of the book really gives it away. It’s a detailed account of a war that took place some 4 centuries before the birth of Jesus, predominantly between the forces of Athens and those of the Peloponnese, though the war also brought in warring parties from other parts of the Mediterranean.

I could not hope to give a synopsis of this 600+ page tome, except to say that it’s pretty much wall-to-wall war. Thucydides gives detailed accounts of the military movements of each side as well as the discussions that took place between the various warring faction when negotiating terms and treaties.  In these discussions, there is an important point to be made regarding the accuracy of what was recorded. I wrote about this when I started the books, some time ago. So while there may be some lingering questions over the precision of some of the details, the fact remains that Thucydides is the most reliable witness and author about the events described whose work survives today.

In trying to remain as factual as possible, Thucydides doesn’t give his reader any great sense of scale. One must discern for oneself what was important and what was recorded merely for the purposes of record-keeping. Indeed, Thucydides is poignantly silent on the matter of why he wrote the history. There is no grand narrative, no lessons to be had. Or rather, Thucydides doesn’t give them to us. There is very little by way of analysis, which is in stark contrast to more modern exponents of history and even current affairs.

This is not a book to be picked up lightly and it will draw you in. There are times when it gets quite turgid, you must be warned. But if you liked Herodotus (particularly the second half) then this should appeal to you. It won’t be for everyone; indeed, talking to some people who had attempted to read it, about half gave up and the other half thought I was mad.

A book more to be admired than enjoyed, I think.


The other day, sometime late after dinner, I was drawn into a little conversation regarding party politics. Somebody mentioned that Ed Miliband was more comfortable at attacking the Daily Mail than he was in putting forward his policies.

In response, I made a quip to the effect that it was surprising that Ed Miliband had policies (as in plural). After all, the mainstream coverage around the Labour party conference was split between his one policy of freezing energy prices and the coverage of Damian McBride’s new book, along with his publisher attacking an old man on Brighton seafront.

For pointing out that it’s a mystery as to what Labour’s current policies are, I received some criticism. Some of this was from party members.

I would add, at this point, that I am not and have never been a member of any political party. If anyone would like me to elaborate why, that would be a separate blog post!

The episode brought to my mind the idea that we all live in our own little bubbles. I look on the political bubbles with some interest, but I am not within any of them. I have my views and I will, from time to time express them (for example here, here or here), but I am certainly not part of the ‘Westminster village’. As such, I am reliant on the unreliable media that we have in the UK as my source of information. I don’t read party manifestos from cover to cover, but I will give each a fair hearing, even if I am inclined against them.

In the example above, I am sure there was much more discussed at the Labour party conference than the proposed freezing of energy prices (a proposal condemned by the bosses of the energy companies, who then started offering their customers price freezes themselves – though not after hiking their prices up at a rate far in excess of inflation) yet this one idea and the ensuing debate dominated the coverage.

Time is short in this life, and there is much to care about. Some may choose to be political aficionados. I am comfortable to know my own mind and will express this to my elected representatives from time to time. When it comes to vote, I am resigned to the fact that we live in a part political system. Much as I would like to vote for those who are most closely aligned to my view, the first past the post voting system is rigged against those like me. So instead, I usually vote tactically between the 2 main parties in my constituency, voting for the least immoral of the two.

IT Problems

I’ve run into a bit of a snag on the blogging front. The computer I use to write my posts is having some severe issues. After a key got stuck down, I had to give it a thump to unstick the key. It seems that in doing this, the hard disc may have been damaged.

This is the first time it’s crashed in the 3 or 4 years I’ve had it, but it’s giving me a bit of trouble. It will take about 5 minutes to boot into safe mode and if I eventually get into normal mode, nothing works. The only way to close it is a forced shut down. I did try the normal shut down method from the start menu but after waiting for an hour, still nothing had happened.

So I’ll try posting what blog entries I had completed and was able to save. But after this, there may be an interruption to normal service.  Not sure if the computer’s salvageable or if it’s time to get a new one. I really only use it for word processing and spreadsheets, so I would opt for a cheap netbook, but I’ve never seen one with a usb port, which is an essential. 

Oh well.

Book Review: Mathematics: A Very Short Introduction by Timothy Gowers

Carrying on a look at some of the books in the Very Short Introduction (VSI) series, I wanted to revisit some of the joy of university life by returning to mathematics, the subject in which I obtained a first class Masters degree. With the title as it is, one might wonder what sort of level as it’s pitched at. Here, one could be lulled into a false sense of security by mistaking it for “Arithmetic: A Very Short Introduction”. Do not expect this to be “a very simple introduction”. To anyone who has studied maths at university, this will be a very simple book. To anyone studying maths at A-level, they should find it a little challenging in places, but it should provide good food for thought, building on some familiar principles. The author says that it should be OK for anyone with a good GCSE grade, though I would express a little scepticism at that sentiment.

That said, I do think it’s a marvellous little book. One of the first things that Gowers discusses is the cumulative nature of maths. i.e. some things can be very simply stated, but only in terms of other things which need to be well-defined and understood. The danger then is how far back do you regress to be able to find ground which is widely understood?

Gowers deals with this brilliantly by having his opening chapter on mathematical modelling. In so doing, he grounds mathematics in the real, the physical, the tangible, instead of diving off into the realms of pure mathematics straight away. Though I must admit, the appeal to me comes about primarily because he enunciates the way I have thought of maths for most of the last 3 decades.

From here, he starts to ask some more fundamental questions about the nature of numbers, including complex numbers (but not quaternions) and some “proper” algebra though he cunningly avoids the use of terms such group, ring or field whilst ensuring the reader is familiar with their rules by means of definitions followed-up with examples. He also touches on some rules regarding logarithms which perplex some people, but are dealt with very well.

He then goes on to probably the most important idea in maths: proof. Though touching on a little philosophy, he tries to skirt around it and give a robust exposition of what a mathematician means when (s)he talks about proof and how it differs from the more lackadaisical use of the word in everyday (and even some other areas of scientific) usage.

Though any book on serious mathematics probably ought to contain a good amount on calculus, Gowers avoids this quite ostentatiously. Rather, he lays the groundwork for an understanding of it with a chapter on limits and infinity. In so doing, one might think he’s dodged a potential bullet of losing the interest of readers, though I think that anyone who hasn’t done calculus but who has understood this chapter will be well-placed to start studying calculus.

Moving on, we start to get a bit more geometrical. The first of these two chapters looks solely at the idea of dimensionality. One might instinctively have an idea of what a dimension is or how to count them. However, maths is rather more refined than such instinctive generalities and Gowers gives us some examples that any student would find in a 1st year linear algebra course. If anything, this is the acid test for those considering doing maths at university; if this is incomprehensible to you, then it’s best to turn away. But if, on the other hand, you can see there’s something there that can be grasped, if you don’t quite get it exactly at this stage, then you’re standing in good stead. The second of the geometrical chapters looks at much more fundamental geometry, looking at the classic issue of Euclid’s 5th postulate and the consequences of abandoning it.

The last main chapter is on one of my least favourite topics: estimates and approximations. This was a topic I did to death in my 2nd year at uni, not getting on with the lecturer (an angry Scot called Alan) and having a nightmare on the exam, barely scraping a 2:1 in it. Gowers doesn’t hide from the fact that this is not neat maths, as most of the rest of the book is, though he spares the reader from an insight into the gory detail of numerical analysis (or num anal, as we disparagingly called it). If there’s any downside to this wonderful introduction, it is this chapter. Not because it is badly written or poorly explained, it isn’t. But merely because it lacks the sexy panache that the rest of the topics have.

This is redeemed somewhat at the very end when he puts in some frequently asked questions, along with his answers. If anything, these give a far better insight into the working life of the mathematician than anything found in the rest of the book. He addresses some myths and common (mis)conceptions, giving an honest assessment on some issues where he needn’t have done so.

Overall, it’s a great book. If you hated maths at school, then this isn’t the book to get you back into it and loving it. But for anyone with a keen interest in science and how it’s done, then this is a gem. If you know any A-level students considering doing maths at uni, give them this book. Hey, they are students, so £8 for a little book is a lot of money. Go on!

A personal catechism

Those of you who know me well or who otherwise read this blog regularly will probably be aware that I am advocate of each person questioning their beliefs and having regular re-evaluations of where they stand on various issues. I do this myself so frequently that I have started to wonder if I have ever actually finished any piece of thinking. In other words, I start down one route but before I reach the end of it, I turn around and go back to the start.

Because of this, I aim to undertake a fairly large task. Using one of the earliest reformed statements of faith as my template, I plan to lay out a statement of my beliefs. The document I shall use will be the Heidelberg Catechism, which I understand dates back to 1563. There were others I could have chosen, such as the Belgic Confession or the Westminster Catechism, but I opted for Heidelberg for a few reasons. Firstly, I think the questions that are asked are more amenable to a series of blog posts. Some will be rather long, possibly broken into several parts, though others will be rather short.

My intention is to ask the question as originally asked (in the English translation) and the answer from the Catechism, followed by own response. Each response will be in two parts. Firstly, I shall aim to critique the answer given by the catechism; secondly, by providing my own answer. By forcing myself to answer someone else’s set of questions, I hope to be forced to think. This may result in me changing my ideas on some matters, or at least clarification of things which I don’t think about too much. So this is as much an exploration as an exposition.

So what’s in it for you? Well, I hope, as ever, to prompt you into thinking. You are, of course, free to disagree and state why in the comments. You may even be prompted to undertake your own version, possibly using a different reformed confession as your basis. I strongly doubt that any one person will agree with my on all points, though I would hope to find solidarity with many christians, whether liberal, conservative, baptist, anglican, methodist, etc.

Though I often describe myself as non-denominational, there are some ideas or traditions which I adhere to more closely than others, some which I outright reject. When asked to sum up my denomination by someone recently, I described myself as ‘a liberal, reformed, pentecostal baptist’. Aspects of each of these will come out, but to help you understand where I come from I’ll briefly expand each term.

Liberal. This is the most easily misunderstood when it comes to theology. This more describes my outlook on socio-economic matters as well as my view of church. I would affirm an ‘orthodox’ view of the bible, rather than “liberal” in the sense of playing fast and loose with theology. This is in opposition to conservative views (small ‘c’) which are more .

Reformed. Though I would not wholly accept the teachings of Luther, Calvin, Zwingli, Knox and their ilk, I do think that the reformation was the most important theological movement since the 1st century. This entails the rejection of Catholicism, which is best regarded as an heretical offshoot from christianity in the same vein as Mormonism or Unitarianism. I know this is a minority opinion and is deeply unpopular with some. Though there may be great similarities between Catholicism and christianity, as there between chimpanzees and humans, similarly due to having common ancestors, it is incorrect to mistake one for the other or to conflate the two.

Pentecostal. In my various travels across churches, I have noticed that very few seems to get a balance when it comes in Trinitarian thinking and practice. Where I perceive the lack of balance to be most prevalent is in the treatment of the Holy Spirit. Though cessationists are rare, the Holy Spirit is often given little more than lip service, with the praxis of the more traditionalist churches seeming to ignore the actions of this person of the Trinity. This does not mean that I embrace all the excesses that have sometimes stemmed from the charismatic churches.

Baptist. I believe that as christians we are supposed to be baptised. This is not something that should be done by anyone who does not profess a faith, but is an act of obedience. Therefore, churches which advocate and practice infant ‘baptism’ are, I believe, in error. This will be expanded more in questions 69-74.

So that’s the plan. I can’t promise that I’ll be able to stick to it, but I hope you’ll join me in my progress. Any prodding and poking that you can provide to get me through it will be much appreciated.

Book Review: A Broad Place by Jurgen Moltmann

Quite some time ago, I bought this at a bargain price from an SCM Press sale. Having read The Crucified God a couple of years ago and with Theology of Hope still on my reading list, I had gotten to know a little about Moltmann through hearing and reading little snippets. Although I also read some negative reviews of this, his autobiography, I nonetheless purchased it, along with another theological autobiography, Stanley Haeurwas’ Hannah’s Child which I read a few months ago.

He works pretty much chronologically, starting with a cursory glance of his childhood, but he quickly moves on to his life as a young adult, where he served in the German army during the second world war. Here, he was witness to the firebombing of Hamburg and experienced survivor’s guilt after he lived, while a friend who was standing next to him was killed. At the end of the book, he states that almost his entire career was an attempt to answer the question, “Why me and not him?”

He gives a vivid account of his eventual capture and his time spent as a prisoner of war, which extended until long after VE day. From here, he takes us on a tour of his theologically formative years, first as a student and then as a young pastor. In this, though, we get a hint of why the book got some negative reviews. Moltmann clearly must have kept some kind of detailed diary, from which much of the book is derived. The level of detail there is unnecessary for most purposes. So we get a list of names of people he met, places he went to and even what meals he had at what restaurants. At these junctures, you get the idea that Moltmann was very much writing for himself rather than for others.

There are passages like this which run through the book and which make it longer than it ought to have been. However, if one is willing to forgive Moltmann for these more tedious passages, there is much reward to be had elsewhere. For example, though I have not yet read Theology of Hope, it was fascinating to read how he wrote it and in particular how he reacted to the responses that it got. Later on, he does something similar for The Crucified God.

Possibly the most interesting section is that between the two alluded to immediately above, that of his political theology. I confess that I am not overly knowledgeable about liberation theology, but it was (is?) a passion of Moltmann’s. One of the striking things about it, though, was that while it was embraced in South America and, given its temporal proximity to the civil rights movement, it was embraced by the disempowered and downtrodden, yet the most prominent theologians in the movement were white Europeans. Does this in any devalue or invalidate their work? I would argue not and Moltmann does the same. His pursuit of it is derived primarily from an understanding of the gospel which burgeoned his love of humanity. Though he doesn’t describe himself as much, he comes across as a true humanist, in the proper, classical sense of the word. Having his wife as a feminist theologian also made for an interesting working relationship.

Towards the end, he states his desire to finish some strands of thinking and others that he will leave for others. What made this a delight was that one of the things he expressed a desire to do he later did. While was scanning some his works I noticed a recent release in the spring of this year which bore the title of a topic he wanted to explore.

The book will not be for everyone. I would hope that someone considering it will have read at least one of his other books or at least looked into his thinking. The details are extraneous and even the most keen reader will find themselves glossing over at times. But there is an underlying richness here that will be of value to many.

Book Review: Around the Moon by Jules Verne

Having finished From the Earth to the Moon without enjoying it as much as I had hoped I nonetheless carried on with the sequel, perhaps in the hope that it would be an improvement on the original.

The book opens with a brief recapitulation of the first book which might have saved me the effort of having to go through it. Though given the simplistic writing style, it was not much of a chore. Neither, it must be said, was the sequel. Our cast is now reduced to just 3, President Barbicane being  one (president of the gun club, not of any nation state) and two others who were so unmemorable that a mere week after finishing it, I had forgotten. I could look it up, but it would be more effort than it is worth.

Our insipid explorers conjecture about the nature of space and, in particular, what the moon is like. They have taken dogs and chickens with them on the flight, though there is a noticeable absence of disruption, given the enclosed space they are in. One aspect that this reader noticed was also conspicuous by its absence was any mention of sanitation. Though Verne may have thought this somewhat vulgar or base, it is nonetheless a vital aspect to consider which is woefully overlooked.

The mistake that Verne focuses on though, is one of speed. As they slowed on their exit as they were shot out of the enormous cannon, they have not attained sufficient velocity to reach the moon. Instead, they just miss the target and are pulled into orbit around it, from where they make various observations and further conjecturing. I wish I could say more, but that pretty much encapsulates the whole book. Much of it is wildly incorrect and is neither enlightening nor entertaining.

To cap it all off, the book ends with a deus ex machina whereby rockets are suddenly said to be attached to the craft, having not been mentioned before in either volume. Yet these rockets are suddenly employed and allow the 3 men to return to earth to recount their tales, rather than stay stuck in orbit and eventually die of dehydration, starvation or, more likely, asphyxiation.

I had been hoping this would be a gentle and entertaining read, though I have to report it failed to live up to expectations. Though it is easy to read, I cannot think of anyone to whom I would be likely to say, “You must read this.”

Friday fun: Am I any good at playing Hearts?

As it’s Friday, I decided to take a bit of a break from the relatively serious blog posts I’ve been turning out of late and take a light look at probability and games. Games, after all, are a great arena for testing out ideas in combinatorics and statistics.

The question posed might seem to be an obvious ‘yes’ but just because something might seem obvious doesn’t always mean it’s true. I’ve had my current laptop now for a little over two years. In that time, I’ve played 345 games of Hearts on that computer. I will assume most of you have either played it, or at least know how to play. If not, here’s a quick guide.

Given that there are 4 players, if the game were entirely random, one would expect, over time, to win roughly a quarter of the games played. If your win percentage was higher, you might be justified in thinking that you’re better than the computer. If your win percentage was lower, you might think you were worse, though most people would quickly move on from that thought to trying to find an excuse.

So, how many games do you think I’ve won? Is it not 345/4 = 86.25? Obviously not, because I can only have won a discrete number. So should my expected number of wins be 86 or 87? Obvious rounding would say 86. Though since 87 is so close, that would also seem a reasonable number to have won. What about 90, though? That still seems to be within the realms of possibility. 100, perhaps? How about 120? That might seem less likely, as that would mean I’ve won over a third of the games, yet I only expect to win a quarter.

The answer is in fact 188, giving me a win percentage of just over 54%. Does that really prove that I’m good at Hearts? To try to give it some meaning, I’d like to know what the probability is of winning 188 games out 345 and compare this to the odds of winning 86 time out of 345. But there might be a snag. We would expect that the odds of winning 86 times would be the highest, but there are 345 different possible outcomes. So is one really much more likely to win 86 times than 87? Instinctively, it seems not, but we need to quantify to this to make much sense of this, and confirm or deny what “feels” right.

How do we work out the probability?

I’ll start off with a simple case, where we have only played 2 games. If it were random, we would expect to win 25% of the games. i.e. the probability of winning any given game is 0.25. Similarly, we would expect to lose 75% of the games i.e. a probability of 0.75.

As each game is independent, we need to multiply the probabilities together. So the odds of winning:

  • 0 games out of 2 would be 0.75*0.75 = 0.5625
  • 1 game out of 2 would be 0.25*0.75 = 0.1875
  • 2 games out of 2 would be 0.25*0.75 = 0.0625

But there’s a problem. Add them all up and you should achieve certainty, a probability of 1. But instead, our total is 0.8125. It falls short of 1 by 0.1875. It’s no coincidence that that matches the probability of winning 1 game out of 2. That’s because there are 2 ways we would that single game: we could win the first and lose the second, or lose the second and win the first. So we have to multiply that by the number of ways you can choose 1 ‘slot’ given 2 ‘slots’ to choose from.

How about we try it with 5 games now (to 4 decimal places):

  • 0 games out 5 would be (0.25^0)*(0.75^5) = 0.2373
  • 1 game out 5 would be (0.25^1)*(0.75^4) = 0.0791
  • 2 games out 5 would be (0.25^2)*(0.75^3) = 0.0264
  • 3 games out 5 would be (0.25^3)*(0.75^2) = 0.0088
  • 4 games out 5 would be (0.25^4)*(0.75^1) = 0.0029
  • 5 games out 5 would be (0.25^5)*(0.75^0) = 0.0010

Again, we have undercounted. With the 0 and 5 cases, there is only one arrangement each by which you can win or lose all 5 games. But to win 1 game (or to lose 1 game) there are 5 ways to do this. So we need to multiply the 1 & 4 cases by 5.

But what about 2? How many ways are there to choose 2 games to win (or to lose) from 5 opportunities? Without going into all the detail it is 5!/((5-2)!)*2!) = 120/(2*6) = 10

So to take into account the multipliers, we get the probabilities:

  • 0 out of 5 = 1*0.2373 = 0.2373
  • 1 out of 5 = 5*0.0791 = 0.3955
  • 2 out of 5 = 10*0.0264 = 0.2637
  • 3 out of 5 = 10*0.0088 = 0.0879
  • 4 out of 5 = 10*0.0029 = 0.0146
  • 5 out of 5 = 1*0.0010 = 0.0010

Adding up, we get back to our reassurance that the sum of all probabilities is 1.

What about 345 games then? Well, we just extend the pattern. The odds of winning 188 games are:

(345!/((188!)*((345-188)!)))*(0.25^188)*(0.75^(345-188)) = well, something very small indeed.

A standard calculator won’t be able to do the calculation, but with a little help from a more powerful computer (aka Excel on my laptop), the answer is roughly 0.00000000000000000000000000000012063

That seems pretty darn small. But there are a lot of options (345 to be precise) and most look pretty small. What about our expected figure of 86?

The odds for that (which I leave to you check) are 0.049574108. It is the highest probability for any number of wins, but it may surprise some that the odds of getting 25% of the wins given the odds of winning are 25% are in fact slightly worse than 1 in 20, or 19/1 against. Suddenly, the idea of a direct comparison doesn’t seem so sensible anymore.

Though our odds of winning 86 games are about 410,937,214,868,030,000,000,000,000,000 greater than winning 188 games, I’m still sceptical. What we need to do is look at some kind of spread around our two values of 86 and 188.

Let’s look at each plus or minus 20 (arbitrarily chosen, I admit, please feel free to suggest or try alternatives). So what are the odds of winning between 66 and 106 games? And what are the odds of winning between 168 and 208 games?

For that, I refer back to the working spreadsheet (which I can send you if you don’t believe me and can’t figure out how to design it yourself) and we get the former to be a quite reasonable 0.992543. In other words, if there was no skill in Hearts than you would have more than a 99% probability of winning between 66 and 108 games out of 345.

The latter turns out to be 0.00000000000000000000230188 or 1 in 434,427,345,316,048,000,000.

It is not impossible that my winning so many games is a fluke of the probabilities and that I have hit upon a streak that no one else in the history of the universe will have ever likely encountered before. It just seems very very very very very unlikely.

Maybe, then, it’s not just luck. Maybe I am more skilled at playing the game than the computer is. I’d certainly like to think so, though ‘liking to think so’ can be the downfall of anyone look at statistics…