Memphis Shake

Posted in Jazz with tags , on November 7, 2009 by telescoper

Today has been a very busy day, so I haven’t had time to put finger to keyboard at all. I always feel I’m letting the side down if I don’t post every day, but I’ve only got a few minutes before going for dinner. Fortunately I’ve got a list of little fillers for such occasions so I thought I’d try this one on you. Experience suggests you will either love it or hate it!

I’ve blogged before about the pioneering clarinettist Johnny Dodds, who appeared on an astonishingly high fraction of the greatest recordings of the era of classic jazz. But although he was a jazz age superstar he remained until his death in 1940 a modest and self-effacing man who never tried to hog the limelight.

One day in December 1926, Johnny Dodds happened to be in the Chicago studios of the Victor record company. The band that happened to be recording at that time was an obscure folk group from Louisville (Kentucky)with the unpromising sounding name of The Dixieland Jug Blowers. After some discussion, Johnny Dodds agreed to sit in with them while they recorded a tune called Memphis Shake. They weren’t really a jazz band and didn’t use the usual jazz instruments. There is what sounds like an alto sax on this record, but there is also a fiddle, banjo and, of course, the “jug”  (an earthenware whisky jar or some such item, played  by blowing across the top to produce a whimsical kind of bass). The idea of a jugband probably sound very hokey now, but were in fact extremely popular in the pre-jazz era and well into the 1920s. Other than the fact that they were led by a chap called Earl Macdonald and the fiddle is played by Clifford Hayes, I really don’t know anything else about the personnel.

As you’ll hear, Johnny Dodds takes quite a back seat, but his presence on this record turned it into a little  piece of jazz history and original 78s of this are much sought after among collectors. It is a bit of an oddity. It’s not really jazz and it’s not really folk, but what it is is one of the most joyously carefree pieces of music you will ever hear in your life. Even if it’s not your cup of tea, I hope it at least brings a smile to your face as it does to mine whenever I hear it.

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Valley Comprehensive

Posted in Poetry with tags , , on November 6, 2009 by telescoper

The other day I wandered into a bookshop in Cardiff and happened upon a collection of poems by Patrick Jones called darkness is where the stars are (published by the wonderful Cinnamon Press). In case you weren’t aware, Patrick Jones a Welsh poet who is the brother of Nicky Wire, the bass player of the Manic Street Preachers and he has collaborated with the band extensively over the years.  You can find his official website here.

This particular collection of poems was at the centre of a controversy around this time last year because a campaigning group called Christian Voice decided it was blasphemous and protested in large numbers outside Waterstone’s Bookshop where the book was to be launched at an event at which poet was planning to read some of his work. The launch was cancelled at  the advice of the local Police, for  “safety reasons”. Jones later read some of his poems at the Welsh Assembly.

Whatever its motivations this protest clearly backfired because the book gained  more publicity than a publisher of modern poetry could ever dream of. It certainly made me curious about it last year, although I soon forget about it. However, seeing it again more recently, I finally decided to buy it.

As an atheist, I’m not competent to pronounce on whether or not it is blasphemous, although some of the poems do deal uncompromisingly with themes about which many are extremely sensitive, especially religion and sexuality.

I thought I’d put one of the poems on here by way of an advertisement for the collection as a whole which Peter Tatchell describes on the cover as “thoughtful, provocative and challenging”.  I picked a poem called Valley Comprehensive. Although written from the point of view of an English teacher bemoaning the regimentation of modern school education, it struck a chord with me in the light of yesterday’s post. Science education nowadays also has too much of an emphasis on the memorising of facts and too little on the drawing about the creative abilities of the human brain. I always thought the main problem is that the word “learn” can be taken to mean “memorise” as well as “discover”. Too much education concentrates on the former rather than the latter.

I don’t think it really matters so much whether you use words or equations to express ideas. Poets and physicists are not as different as you might think, except writing poetry is harder.

when questions become answers
when stars are merely facts
as the white board becomes all knowing lord
and red pens stamp our destiny on our stooping backs

the beauty of learning dies
when minds cannot search and find
just swallow factations whole
when exam results and league tables
fire the engines of education
it’s the premiership in the classroom
no room for the least able
the noose tightens on free thought
as sets slyly amputate aspiration

only those who will pass the tests
will be allowed to take the tests

as
the unchosen
stammer in silence
tread water in clock watched anticipation
until their failure is legitimised
and school becomes brain asphyxiation

no wonder in the universe
no questions for their gods
i’d rather a tree taught me how to grow
than
tell a class how not to write

only those who will pass the tests
will be allowed to take the tests

shouldn’t education be
about teaching children

how,

not

what

to think?

(reproduced with the kind permission of Cinnamon Press).

9 Comments »

Godless Uncertainty

Posted in Bad Statistics with tags , , , , , , on November 5, 2009 by telescoper

As usual I’m a bit slow to comment on something that’s been the topic of much twittering and blogging over the past few days. This one is the terrible article by A.N. Wilson in, inevitably, the Daily Mail. I’ve already fumed once at the Mail and didn’t really want to go off the deep end again so soon after that. But here goes anyway. The piece by Wilson is a half-baked pile of shit not worth wasting energy investigating too deeply, but there are a few points I think it might be worth making even if I am a bit late with my rant.

The article is a response to the (justifiable) outcry after the government sacked Professor David Nutt, an independent scientific adviser, for having the temerity to give independent scientific advice. His position was Chair of the Advisory Council on the Misuse of Drugs, and his sin was to have pointed out the ludicrous inconsistency of government policies on drug abuse compared to other harmful activities such as smoking and drinking. The issues have been aired, protests lodged and other members of the Advisory Council have resigned in protest. Except to say I think the government’s position is indefensible I can’t add much here that hasn’t been said.

This is the background to Wilson’s article which is basically a backlash against the backlash. The (verbose) headline states

Yes, scientists do much good. But a country run by these arrogant gods of certainty would truly be hell on earth.

Obviously he’s not afraid of generalisation. All scientists are arrogant; everyone knows it because it says so in the Daily Mail. There’s another irony too. Nutt’s argument was all about the proper way to assess risk arising from drug use, and was appropriately phrased  in language not of certainty but of probability. But the Mail never lets truth get in the way of a good story.

He goes on

The trouble with a ‘scientific’ argument, of course, is that it is not made in the real world, but in a laboratory by an unimaginative academic relying solely on empirical facts.

It’s desperately sad that there are people – even moderately intelligent ones like Wilson – who think that’s what science is like. Unimaginative? Nothing could be further from the truth. It takes a great deal of imagination (and hard work) to come up with a theory. Few scientists have the imagination of an Einstein or a Feynman, but at least most of us recognize the importance of creativity in advancing knowledge.  But even imagination is not enough for a scientist. Once we have a beautiful hypothesis we must then try to subject it to rigorous quantitative testing. Even if we have spent years nurturing it, we have to let it die if it doesn’t fit the data. That takes courage and integrity too.

Imagination. Courage. Integrity. Not qualities ever likely be associated with someone who writes for the Daily Mail.

That’s not to say that scientists are all perfect. We are human. Sometimes the process doesn’t work at all well. Mistakes are made. There is occasional misconduct. Researchers get too wedded to their pet theories. There can be measurement glitches. But the scientific method at least requires its practitioners to approach the subject rationally and objectively, taking into account all relevant factors and eschewing arguments based on sheer prejudice. You can see why Daily Mail writers don’t like scientists. Facts make them uncomfortable.

Wilson goes on to blame science for some of the atrocities perpetrated by Hitler:

Going back in time, some people think that Hitler invented the revolting experiments performed by Dr Mengele on human beings and animals.

But the Nazis did not invent these things. The only difference between Hitler and previous governments was that he believed, with babyish credulity, in science as the only truth. He allowed scientists freedoms which a civilised government would have checked.

Garbage. Hitler knew nothing about science. Had he done so he wouldn’t have driven out a huge proportion of the talented scientists in Germany’s universities and stuffed their departments full of ghoulish dolts who supported his prejudices.

It was only after reading the article that it was pointed out to be that this particularly offensive passage invoked Godwin’s Law: anyone who brings Hitler into an argument has already lost the debate.

Wilson’s piece seems to be a modern-day manifestation of old problem, famously expounded by C.P. Snow in his lecture on Two Cultures. The issue is that the overwhelming majority of people in positions of power and influence, including the media, are entirely illiterate from a scientific point of view. Science is viewed by most people with either incomprehension or suspicion (and sometimes both).

As society becomes more reliant on science and technology, the fewer people there are that seem to understand what science is or how it works. Moronic articles like Wilson’s indicate the depth of the problem.
Who needs scientific literacy when you can get paid a large amount of money for writing sheer drivel?

I’m sure a great many scientists would agree with most of what I’ve said but I’d like to end with a comment that might be a bit more controversial. I do agree to some extent with Wilson, in that I think some scientists insist on claiming things are facts when they don’t have that status at all. I remember being on a TV programme in which a prominent cosmologist said that he thought the Big Bang was as real to him as the fact that the Sun is shining. I think it’s quite irrational to be that certain. Time and time again scientists present their work to the public in a language that suggests unshakeable self-belief. Sometimes they are badgered into doing that by journalists who want to simplify everything to a level they (and the public) can understand. But some don’t need any encouragement. Too many scientists are too comfortable presenting their profession as some sort of priesthood even if they do stop short of playing God.

2006-11-09-1525-20The critical importance of dealing rationally with uncertainty in science, both within itself and in its relationship to society at large, was the principal issue I addressed in From Cosmos to Chaos, a paperback edition of which is about to be published by Oxford University Press..

From the jacket blurb:

Why do so many people think that science is about absolute certainty when, at its core, it is actually dominated by uncertainty?

I’ve blogged before about why I think scientists need to pay much more attention to the role of statistics and probability when they explain what they do to the wider world.

And to anyone who accuses me of using the occasion presented by Wilson’s article to engage in gratuitous marketing, I have only one answer:

BUY MY BOOK!

22 Comments »

I want it painted … beige?

Posted in The Universe and Stuff with tags , , , , , on November 4, 2009 by telescoper

I was quite pleased when I saw that Pass Notes No 2,677 in Today’s Guardian was about “the universe”. Like the other pieces in this series, it looks at the subject matter from a deliberately bizarre angle, focussing on the fact that it appears to be coloured beige, or at least if you blend the light from all the stars we can see in the right proportions, that’s the colour you would get.

Actually the work discussed in this item was done quite along time ago; it was featured in a New Scientist article in 2002. One of the authors, Karl Glazebrook had previously claimed that the colour produced by all the stars in all the galaxies that could be seen was in fact something like turquoise. For some reason, this trivial bit of science fluff captured the (obviously limited) imagination of journalists around the world. However it turned out to be have been wrong and a grave announcement was made pointing out that the Universe was actually more like beige. This story gave a few people their 15 minutes of fame, but I think the episode made cosmologists as a whole look very silly.

I had hoped this would be forgotten but, the Guardian decided to revive memories of the affair today, with obviously humorous intent. They also called Glazebrook an “astrologist”, although that appears to have been a mistake rather than a joke as it has now been changed to “astrophysicist”.

Anyway, this important observation requires a theoretical explanation and I now want to step into the limelight beigelight to offer a radical insight into the vexed issue of cosmological chromaticity.
My hypothesis has its inspiration in TV shows like House Doctor in which homeowners wishing to impress prospective purchasers are always advised to paint everything beige or magnolia. Since the Divine Creator appears to have decorated the Universe according to the same prescription, the obvious inference is that the cosmos is about to be put on the market. He might have had the courtesy to tell the sitting tenants.

Come to think of it, Glazebrook missed a trick here. We astrophysicists are always being castigated for not doing anything that leads to wealth creation. What he should have done was to produce a paint with the same colour as the Universe. Glazebrook Beige has a nice ring to it.

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Highlights

Posted in Biographical, The Universe and Stuff with tags , , on November 2, 2009 by telescoper

Despite popular demand, here is more of the Unravelling the Universe show I posted a little bit from a few days ago. My total screen time on this programme only amounted to a couple of minutes, so I asked if it was possible to do an appropriate edit of the hour-long footage. Unfortunately, Ed got the wrong idea, so removed most of the highlights and left practically only the few minutes with me in them. You just can’t get the help these days.

The film  was shot in a studio in Greenford and I had to hang around there a long time before they even started shooting. I think that was because of the lights. I need a special form of  illumination if I am to present the illusion of having three dimensions. The director had insisted I wear my leather jacket for the sequence and under the very powerful lights I was sweating so much I had to wear make-up to stop me shining.

They reckon that there is a ratio of about 100:1 of film shot to film broadcast on programmes like this, and this is probably even higher when the subject is as inarticulate as me. In my memory it certainly took several hours just for my little bits.

If nothing else this tape gives you the chance to see Rocky Kolb in a splendid jumper that puts that of the new Lucasian professor well and truly in the shade. What was that about chromodynamics?

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Brake Points

Posted in Uncategorized with tags , , on November 1, 2009 by telescoper

I thought it would be worth giving a short update on the Mark Brake affair I posted about a couple of weeks ago. If you don’t want to go back to the original post let me just say that Mark Brake is  Professor of Science Communication at the University of Glamorgan and it recently emerged that in 2006 he falsely claimed to have a PhD when applying for a research grant.

The biggest development since then is that the Times Higher – a magazine for professionals working in Higher Education – has now picked up the story and ran an article in last week’s issue. That piece also refers to the sacking of an (unnamed) employee who blew the whistle on Brake’s conduct and also to the circumstances surrounding the resignation of Dr Paul Roche from the University of Glamorgan in 2003. I don’t know the full story behind these wider allegations so won’t comment on them here, except to say that I hope that they will be investigated more thoroughly so that the true facts can emerge about what is clearly a very murky affair.

However, these wider issues do not alter the fact that Mark Brake misrepresented his qualifications. There is documentary proof that he did so, and the University of Glamorgan doesn’t deny it either. The UoG is keeping very quiet over the press coverage, simply repeating that it had investigated the matter and let Brake off because it was an “isolated incident”. Presumably this means that it is acceptable to misrepresent your qualifications as long as you only pretend to have one doctorate you haven’t got.

I’m staggered that Brake wasn’t immediately dismissed for this offence, which seems to me to amount to gross misconduct. Most of the people commenting on the news item in the Times Higher seem to agree with me on this, although there is one individual called “Skeptic” who appears determined to defend Brake with whatever  argument he/she could muster no matter how specious. The identity and motivation of this individual remain unclear.

Another commenter, however, raised a very interesting point. Here is Section 2 of  the 2006 Fraud Act:

2 Fraud by false representation

(1) A person is in breach of this section if he—

(a) dishonestly makes a false representation, and

(b) intends, by making the representation—

(i) to make a gain for himself or another, or

(ii) to cause loss to another or to expose another to a risk of loss.

(2) A representation is false if—

(a) it is untrue or misleading, and

(b) the person making it knows that it is, or might be, untrue or misleading.

(3) “Representation” means any representation as to fact or law, including a representation as to the state of mind of—

(a) the person making the representation, or

(b) any other person.

(4) A representation may be express or implied.

(5) For the purposes of this section a representation may be regarded as made if it (or anything implying it) is submitted in any form to any system or device designed to receive, convey or respond to communications (with or without human intervention).

I’m no kind of legal expert, but it certainly looks to me that this might apply in this case. The grant application wasn’t in fact successful, but the offence of fraud as defined by this act simply requires intent. The amount of the application was around £285,000, a sizeable sum by any standards. Maybe the Police should look into it.

If Brake didn’t think it would improve the chances of the application being successful, why did he put false information on it? Are we expected to believe that it was an oversight? That he somehow forgot he didn’t have a PhD? I simply can’t believe that to be the case. It is true that many of us are forced to do rapid cut-and-paste jobs when applying for grants and we can make errors that way. However, that would imply that there is a document somewhere from which the cut-and-paste was made that lists a non-existent PhD alongside a genuine MSc. Who would maintain such a document and why?

Even if this were an “isolated incident” it does seem to me to be an extremely serious case of misconduct. However, I note also that numerous references to “Dr” Mark Brake can be found on the internet, including the BBC website. Isn’t it a bit strange how so many people can have formed the opinion that Mr Mark Brake had a PhD?

It’s probably also worth drawing your attention to Mark Brake’s wikipedia page. If you have a quick look at the discussion page of this item you will that an individual by the name of “Rosit” made repeated attempts to block the insertion of a statement of the fact that  Brake had falsely claimed a PhD, arguing that this was libellous. Of course it isn’t. It’s true. Fortunately, the Wikipedia page  is now factual, at least in this specific respect. Most of the rest of it was written by Rosit also and the accuracy and impartiality of the  content is heavily disputed.

You might ask who is this “Rosit” who seems to be so anxious to prevent the truth coming out? Well, Mark Brake’s partner is called Rosi Thornton. Coincidence?

Just in case anyone accuses me of some sort of vendetta, let me make it clear that I have never met Mark Brake and didn’t know anything at all about the false PhD claim until I read it in the local newspaper. I only moved to Cardiff in 2007, after this affair took place. Apart from my incredulity at their behaviour over this matter, I have no axe to grind with the University of Glamorgan either. My persistence in this stems from concern that what appears to be grave  misconduct has gone unpunished. We academics are in the public eye and are at least partly funded by the taxpayer. We and our employers  have to set an appropriate standard. Without that our standing will continue to be eroded.

As I said, the University of Glamorgan appears to be keeping the lid on a matter they appear to have tried to bury once already. I think they would  be much better off getting it all out in the open. If they don’t people might form the opinion that Universities are willing to turn a blind eye to clear examples of gross misconduct when the individuals involved are good at bringing money in.

And I’m sure that never happens….

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The Monster Mash

Posted in Biographical, Music with tags , on October 31, 2009 by telescoper

I explained this time last year how I’m not really a big fan of Halloween and don’t tend to celebrate it. However, I decided to make an exception this year and post the following little video which seems to be appropriate for the occasion. It’s made of bits of old horror B-movies but the music – by Bobby “Boris” Pickett and the Crypt-kickers is actually the second single I ever bought, way back in 1973. I wonder if you can guess what the first one was?

5 Comments »

The Michael Green Experience

Posted in Biographical, The Universe and Stuff with tags , , , on October 30, 2009 by telescoper

It’s been a couple of weeks since the University of Cambridge announced that the successor to Stephen Hawking as Lucasian Professor  of Mathematics would be Michael Green, who is best known for his work on string theory. Heartiest congratulations to him for reaching a position of such eminence.

I was trying to think of a suitable way of marking the occasion of his election to this prestigious post when I suddenly remembered that we were actually on a TV programme together years ago. The show in question was called Unravelling the Universe and was first broadcast in December 1991 as part of a science documentary series called Equinox.

I eventually found my ancient VHS copy of the broadcast master tape of this show and persuaded Ed and Stephen, two of the excellent elves that work in the School of Physics & Astronomy here at Cardiff University, to transfer it to a digital format and put a bit on Youtube for all to see. Many thanks to them for their help.

Other people involved in the programme included Rocky Kolb, Chris Isham and Paul Davies but the short (2-and-a-half minute) clip below features just Michael Green (who basically put the show together) and myself (who was just there to make up the numbers), plus wonderful narration by the late great Peter Jones.

Michael Green hasn’t changed a bit in 18 years. In fact, I saw him last year and am sure he was even wearing the same sweater.

I, on the other hand….Oh dear.

8 Comments »

The Edge of Darkness

Posted in The Universe and Stuff with tags , , , on October 29, 2009 by telescoper

I just picked up an item from the BBC Website that refers to news announced in this week’s edition of Nature of the discovery of a gamma-ray burst detected by NASA’s Swift satellite.  The burst itself was detected in April this year and I had a sneak preview that something exciting was going to be announced earlier this month at the Royal Astronomical Society meeting on October 9th. However, today’s press releases still managed to catch me on the hop owing to the fact that a rather different story had distracted my attention…

In fact, detections of gamma-ray bursts are not all that rare. Swift observes one every few days on average. Once such a source is found through its gamma-ray emission, a signal is sent to astronomers around the world who then work like crazy to detect an optical counterpart. If and when they find one, they try to measure the spectrum of light emitted in order to determine the source’s redshift. This is very difficult for the distant ones, and is not  always successful.

However, what happened in this case – called GRB 090423 – was that a spectrum was that not one but two independent teams obtained optical spectra of the  object in which the gamma-ray burst must have happened. What each time found was that their spectrum showed a sharp cut-off at wavelengths shorter than a given limiting value.

Hydrogen is very effective at absorbing radiation with wavelengths shorter than 91.2 nm (the so-called Lyman limit, which is in the ultraviolet part of the spectrum), and all galaxies contain large amounts of hydrogen; hence galaxies are virtually dark at wavelengths shorter than 91.2 nm in their rest-frame. The position of the break in an observed frame will be at a different wavelength owing to the effect of the cosmological redshift.

The Lyman break for the host of  GRB 090423 appears not in the ultraviolet but in the infrared, indicating a very large redshift. In fact, it’s a truly spectacular  8.2.

Together with the direct observations of galaxies at high redshifts I blogged about a month or so ago, this discovery helps push back the frontiers of our knowledge of the Universe not just in space but also in time. A quick calculation reveals that in the standard cosmological model, light from a source at redshift 8.2 has taken about 13.1 billion light years to reach us. The gamma-ray burst therefore exploded about 600 million years after the Big Bang.

Another interesting thing about this source is its duration. The optical afterglow of a gamma-ray burst  decays with time. Gamma-ray bursts are usually classified as either short or long, depending on the decay time with the dividing line between the two classes being around 2 seconds. The optical afterglow of GRB 090423 lasted about ten seconds. But that doesn’t make it a long burst. We actually see the afterglow stretched out in time by the same redshift factor as an individual photon’s wavelength. So in the rest frame of the source the optical glow was only a bit over a second in duration, i.e. it was a short burst.

Long gamma-ray bursts are thought to be associated with core-collapse supernovae which arise from the self-destruction of very massive stars with very short lifetimes. The fact that such things die young means that they are only found where star formation has happened very recently. One might expect the earliest gamma-ray bursts to therefore be of this type.

I don’t think anyone is really sure what the shorter ones really are, but they  seem to happen in regions without active star formation in which the stellar populations are quite old, such as in elliptical galaxies. The fact that the most distant GRB yet discovered happens to be a short burst is very interesting. How can there be an old stellar population at a time when the  Universe itself was so young?

If the Big Bang theory is correct, astronomers  should eventually be able to reach back so far in time that the Universe was so young that no stars had had time to form. There would be no sources of light to detect so we would have reached the edge of darkness. We’re not there yet, but we’re getting closer.

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A Dutch Book

Posted in Bad Statistics with tags , , , on October 28, 2009 by telescoper

When I was a research student at Sussex University I lived for a time in Hove, close to the local Greyhound track. I soon discovered that going to the dogs could be both enjoyable and instructive. The card for an evening would usually consist of ten races, each involving six dogs. It didn’t take long for me to realise that it was quite boring to watch the greyhounds unless you had a bet, so I got into the habit of making small investments on each race. In fact, my usual bet would involve trying to predict both first and second place, the kind of combination bet which has longer odds and therefore generally has a better return if you happen to get it right.

imageresizer

The simplest way to bet is through a totalising pool system (called “The Tote”) in which the return on a successful bet  is determined by how much money has been placed on that particular outcome; the higher the amount staked, the lower the return for an individual winner. The Tote accepts very small bets, which suited me because I was an impoverished student in those days. The odds at any particular time are shown on the giant Tote Board you can see in the picture above.

However, every now and again I would place bets with one of the independent trackside bookies who set their own odds. Here the usual bet is for one particular dog to win, rather than on 1st/2nd place combinations. Sometimes these odds were much more generous than those that were showing on the Tote Board so I gave them a go. When bookies offer long odds, however, it’s probably because they know something the punters don’t and I didn’t win very often.

I often watched the bookmakers in action, chalking the odds up, sometimes lengthening them to draw in new bets or sometimes shortening them to discourage bets if they feared heavy losses. It struck me that they have to be very sharp when they change odds in this way because it’s quite easy to make a mistake that might result in a combination bet guaranteeing a win for a customer.

With six possible winners it takes a while to work out if there is such a strategy but to explain what I mean consider  a  race with three competitors. The bookie assigns odds as follows : (1) even money; (2) 3/1 against; and (3)  4/1 against. The quoted odds imply probabilities to win of 50% (1 in 2), 25% (1 in 4) and 20% (1 in 5) respectively.

Now suppose you  place in three different bets:  £100 on (1) to win, £50 on (2) and £40 on (3).  Your total stake is then £190. If (1) succeeds you win £100 and also get your stake back; you lose the other stakes, but you have turned £190 into £200 so are up £10  overall. If (2) wins you also come out with £200: your £50 stake plus £150 for the bet. Likewise if (3) wins. You win whatever the outcome of the race. It’s not a question of being lucky, just that the odds have been designed inconsistently.

I stress that I never saw a bookie actually do this. If one did, he’d soon go out of business. An inconsistent set of odds like this is called a Dutch Book, and a bet which guarantees the better a positive return is often called a lock. It’s the also the principle behind many share-trading schemes based on the idea of arbitrage.

It was only much  later I realised that there is a nice way of turning the Dutch Book argument around to derive the laws of probability from the principle that the odds be consistent, i.e. so that they do not lead to situations where a Dutch Book arises.

To see this, I’ll just generalise the above discussion a bit. Imagine you are a gambler interested in betting on the outcome of some event. If the game is fair, you would have expect to pay a stake px to win an amount x if the probability of the winning outcome is p.

Now  imagine that there are several possible outcomes, each with different probabilities, and you are allowed to bet a different amount on each of them. Clearly, the bookmaker has to be careful that there is no combination of bets that guarantees that you (the punter) will win.

Now consider a specific example. Suppose there are three possible outcomes; call them A, B, and C. Your bookie will accept the following bets: a bet on A with a payoff xA, for which the stake is pAxA; a bet on B for which the return  is xB and the stake  pBxB; and a bet on C with stake  pCxC and payoff xC.

Think about what happens in the special case where the events A and B are mutually exclusive (which just means that they can’t both happen) and C is just given by  A “OR” B, i.e. the event that either A or B happens. There are then three possible outcomes.

First, if A happens but B does not happen the net return to the gambler is

R=x_A(1-P_A)-x_BP_B+x_c(1-P_C).

The first term represents the difference between the stake and the return for the successful bet on A, the second is the lost stake corresponding to the failed bet on the event B, and the third term arises from the successful bet on C. The bet on C succeeds because if A happens then A”OR”B must happen too.

Alternatively, if B happens but A does not happen, the net return is

R=-x_A P_A -x_B(1-P_B)+x_c(1-P_C),

in a similar way to the previous result except that the bet on A loses, while those on B and C succeed.

Finally there is the possibility that neither A nor B succeeds: in this case the gambler does not win at all, and the return (which is bound to be negative) is

R=-x_AP_A-x_BP_B -x_C P_C.

Notice that A and B can’t both happen because I have assumed that they are mutually exclusive. For the game to be consistent (in the sense I’ve discussed above) we need to have

\textrm{det} \left( \begin{array}{ccc} 1- P_A & -P_B & 1-P_C \\ -P_A & 1-P_B & 1-P_C\\ -P_A & -P_B & -P_C \end{array} \right)=P_A+P_B-P_C=0.

This means that

P_C=P_A+P_B

so, since C is the event A “OR” B, this means that the probabilityof two mutually exclusive events A and B is the sum of the separate probabilities of A and B. This is usually taught as one of the axioms from which the calculus of probabilities is derived, but what this discussion shows is that it can itself be derived in this way from the principle of consistency. It is the only way to combine probabilities  that is consistent from the point of view of betting behaviour. Similar logic leads to the other rules of probability, including those for events which are not mutually exclusive.

Notice that this kind of consistency has nothing to do with averages over a long series of repeated bets: if the rules are violated then the game itself is rigged.

A much more elegant and complete derivation of the laws of probability has been set out by Cox, but I find the Dutch Book argument a  nice practical way to illustrate the important difference between being unlucky and being irrational.

P.S. For legal reasons I should point out that, although I was a research student at the University of Sussex, I do not have a PhD. My doctorate is a DPhil.

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