Some responses to “Gun Facts” on the UK crime

I have recently been in correspondence with Guy Smith who runs a web site call Gun Facts. I came across the site because it had some rather odd things to say about crime in the UK. From our e-mail exchange I get the impression that Guy is a very pleasant and honest person but unaware of the impression that his web site gives to a casual observer (to my amazement in one e-mail he said the site was neither pro-gun nor anti-gun).  It is a large site with thousands of “Facts” – so I am just concentrating on the “facts” he supplies about guns and crime in the UK.

Before I dive into them a preamble.

All these facts were supplied to debunk the myth:

Britain has strict gun control and thus a low crime rate

I am not aware of anyone who asserts this particular myth. We don’t have a low crime rate. However, many of the “facts” seem aimed at a different proposition:

The handgun acts of 1997 failed to reduce the availability of guns or lower homicide rates.

In fact these acts were only a reaction to Dunblane and were never expected to generally reduce homicide or gun availability (which was already very low).  As it happens the laws supplied a legal basis for some effective police action in the mid-2000s which did reduce the availability of guns and lower homicide rates. See  this brief article. It also happens that crime, including violent crime, peaked in the late 90s – possibly giving the impression that the handgun acts of 1997 caused the peak. Since then both have dropped dramatically.

And now to the “facts”:

The stuff in purple is what Guy wrote – followed by my response in normal text. It is somewhat complicated by Guy’s practice of occasionally stating a fact in the present tense without a date. I initially understood these statements to be intended to be true at the time I read them but I now think that in some cases he meant them to be true at the time of the source which he links to.

Fact: Since gun banning has escalated in the UK, the rate of crime – especially violent crime – has risen.

False – There is no source, and therefore no date, for this so I can only take it as applying to the present day. Both crime and violent crime have fallen according to both the British Crime Survey (BCS) and police reported crime. There was a short period after the handgun ban in 1997 when crime rose according to the reported crime figures (but not BCS). Since then it has dropped. See Office of National Statistics Crime report for Dec 2014..

Fact: Ironically, firearm use in crimes in the UK has doubled in the decade since handguns were banned.

Unproven – firearm use in crimes relies on the recorded crime statistics (BCS doesn’t ask the question). While these had more or less got their act together in 2007 they were a wreck in 1997 so any comparison is highly suspect (violent crime rates appeared to double in 1998/9 simply through a different method of recording). What is true that the recorded crime statistics show a dramatic decline in firearms and handgun use from 2002/3 through to 2013/14 (from 5,549 to 2,130 in the case of handguns and 24,070 to 7,709 in the case of all firearms)

Fact: Britain has the highest rate of violent crime in Europe, more so than the United States or even South Africa. They also have the second highest overall crime rate in the European Union. In 2008, Britain had a violent crime rate nearly five times higher than the United States (2034 vs. 446 per 100,000 population).

Guy’s source is a Daily Mail story written in 2009 about a European Study.

Unproven Using the Daily Mail as a source is not much better than using the National Enquirer. Unfortunately the Daily Mail doesn’t say which reports it based its story on so there is no way of checking without a lot of tedious work. It is also an old story. National comparisons of crime other than homicide – which is rather clear cut – are notoriously difficult. Different countries have different crimes and different ways of recording them and some are very much out of date. The best reference I could easily find was this – written in 2012 but using data from 2006 because some countries are that far behind. The UK certainly doesn’t come out well compared to other OECD countries – although in no case is it the worst in Europe. We do well on homicide but poorly on rape, robbery and assault. But how about compared to the USA? We do better on homicide (much), we are more or less equally bad on rape and robbery, and worse on assault. Make of that what you will.

Fact: 67% of British residents surveyed believed that “As a result of gun and knife crime [rising], the area I live in is not as safe as it was five years ago.”

Probably true – perception of crime is unfortunately frequently wrong.

Fact: U.K. street robberies soared 28% in 2001. Violent crime was up 11%, murders up 4%, and rapes were up 14%.


Fact: This trend continued in the U.K in 2004 with a 10% increase in street crime, 8% increase in muggings, and a 22% increase in robberies.

Highly deceptive. The reference is to an unnamed BBC news report so it is extremely hard to follow up. However, the figures are based on recorded crime which is discussed above.  The BCS figures which tell a different story are omitted. Moreover the figures seem to be carefully selected. E.g. Murders were up in 2002 because the Shipman enquiry concluded that year that Harold Shipman had murdered at least 215 patients between 1975 and 1998. They were all recorded against the 2002 statistics. If you remove these then murders peaked in 2001 at 854 and have declined ever since to 536 in 2013/14. I got bored looking up the other figures. They don’t change the big picture of declining crime.

Fact: In 1919, before it had any gun control, the U.K. had a homicide rate that was 8% of the U.S. rate. By 1986, and after enacting significant gun control, the rate was 9% – practically unchanged.

Irrelevant That’s nearly 100 years ago. We have a world war since then. The countries have changed vastly.

Fact: “… [There is] nothing in the statistics for England and Wales to suggest that either the stricter controls on handguns prior to 1997 or the ban imposed since have controlled access to such firearms by criminals.”

Possibly true preceding a quote by the word “fact” doesn’t make the quote true. This was presumably the opinion of Colin Greenwood in 2003. It would require some evidence to back this up. There is little doubt that things have changed significantly since 2003.

Fact: Comparing crime rates between America and Britain is fundamentally flawed. In America, a gun crime is recorded as a gun crime. In Britain, a crime is only recorded when there is a final disposition (a conviction). All unsolved gun crimes in Britain are not reported as gun crimes, grossly undercounting the amount of gun crime there. 23 To make matters worse, British law enforcement has been exposed for falsifying criminal reports to create falsely lower crime figures, in part to preserve tourism.

True. You can’t compare gun crime – nor can you compare violent crime rates.

Fact: An ongoing parliamentary inquiry in Britain into the growing number of black market weapons has concluded that there are more than three million illegally held firearms in circulation – double the number believed to have been held 10 years ago – and that criminals are more willing than ever to use them. One in three criminals under the age of 25 possesses or has access to a firearm.

Based on a source dated 2000.


Fact: Handgun homicides in England and Wales reached an all-time high in 2000, years after a virtual ban on private handgun ownership. More than 3,000 crimes involving handguns were recorded in 1999-2000, including 42 homicides, 310 cases of attempted murder, 2,561 robberies and 204 burglaries.


Fact: Handguns were used in 3,685 British offenses in 2000 compared with 2,648 in 1997, an increase of 40%. It is interesting to note:

  • Of the 20 areas with the lowest number of legal firearms, 10 had an above average level of “gun crime.”
  • Of the 20 areas with the highest levels of legal guns, only 2 had armed crime levels above the average.

Possibly true. All three of these were about handgun use in 2000. This was shortly after the handgun ban and before the police initiatives in the mid-2000s that drove down illegally held firearms. It takes time for a law to have an effect and it needs to be enforced. Police action during the mid-2000’s dramatically changed the picture.

Fact: Between 1997 and 1999, there were 429 murders in London, the highest two-year figure for more than 10 years – nearly two-thirds of those involved firearms – in a country that has virtually banned private firearm ownership.

False. Wikipedia includes a table of homicides in London from 1990 to 2014 which is based on borough level crime figures.  Guy’s statement is rather confusing. The total homicides for the three years 1997, 98 and 99 come to 495. I can’t make any two years come to 429. These were not outstandingly high compared to the previous 10 years. For example, the total for 90, 91 and 92 was 543. I have no idea about the percentage of firearms.

Fact: Over the last century, the British crime rate was largely unchanged. In the late nineteenth century, the per capita homicide rate in Britain was between 1.0 and 1.5 per 100,000. In the late twentieth century, after a near ban on gun ownership, the homicide rate is around 1.4. This implies that the homicide rate did not vary with either the level of gun control or gun availability.

Partly true. The rates are reasonable (they agree with figures in the International Handbook of Violence – the only source I could find on-line). The third sentence needs careful interpretation. If it is taken to mean that homicide rates did not correlate with gun control or gun availability – that is correct. If it is taken to mean that the figures are evidence that gun control/availability has had no effect on homicide rates then that is unreasonable. You couldn’t possibly read that into the figures without taking notice of all the other factors that affect reported homicide rates. No one who thinks about it would claim that gun control/availability is the only factor affecting homicide rates.

Fact: The U.K. has strict gun control and a rising homicide rate of 1.4 per 100,000. Switzerland has the highest per capita firearm ownership rate on the planet (all males age 20 to 42 are required to keep rifles or pistols at home) and has a homicide rate of 1.2 per 100,000. To date, there has never been a schoolyard massacre in Switzerland.

Source dated 1999.

Debatable. Although the source was dated 1999 I think the argument holds today (the UK and Swiss murder rates have both  dropped). Switzerland very likely has the highest proportion of households owning a gun as this is required by law. However, it is far from having the most guns per capita. According to the 2007 small arms survey the Swiss have about 45.7 guns per 100 people. The US has 88.8 guns per 100 people. Nevertheless it is true that gun ownership in Switzerland is much higher than in the UK (6.2 per 100 people). However, this is a misleading. Switzerland has high gun ownership but pretty strict gun control. For example, it is illegal to carry a loaded firearm in public without special permission and there are rules on carrying any firearm loaded or not.

Fact: “… the scale of gun crime in the capital [London] has forced senior officers to set up a specialist unit to deal with … shootings.”

Source dated: 2001 

True.  England has a low tolerance of gun crime. The unit was effective, reducing gun homicide, homicide and gun availability in the capital. Gun control is not just laws.

Some Gun Control Maths

(updated with another example 4/10/15)

For some reason I am fascinated by the debate over US gun control.  I have the good fortune to live in a country where it isn’t an issue but it I still find myself reading about it extensively. I think it is partly the role that statistics plays in the argument. I really liked this article in Slate which pointed out how the statistics are used to bolster existing positions and not to settle things. Also the way the issue acts as a touchstone of the division between red and blue USA.  

Nevertheless that are a few bits of basic maths that occurred to me recently that do seem relevant (even if they bolster my prejudices).

Do Large US Cities Account for the US High Homicide Rate?

There is myth going around that if you take out the homicides from a few (usually four) large cities that

(a ) are liberal controlled

(b ) have relatively strong gun laws

then the rate for the rest of the USA is not much different than most Western European countries. This is clearly wrong. The named cities vary, but if you take the four largest: New York, Los Angeles, Chicago and Houston then the total population is about 17 million and there were a total of 1233 homicides in those 4 cities in 2014. The population of the USA is 320 million and there were about 14,000 murders in 2014. So the rate including the largest cities is: 14,000/320,000,000 = 4.4 per 100,000. The rate excluding the largest cities is 4.2 per 100,000. It really doesn’t matter which four cities you choose, or if you choose 5 or 6, the numbers aren’t nearly big enough to have a noticeable effect on the national rate.


Mental Health

Those who argue against gun control often argue that the way to tackle gun violence is through a better mental health strategy.  They point to the significant proportion of mass killers who have some kind of mental health issue. These are of course a small proportion of all homicides (and there is no evidence that killers in general are more likely to be mentally ill than average) but it is still really important to try and prevent them.  This study suggests about a quarter of mass murderers have some kind of psychiatric history – a much larger proportion are unusual in being a bit of a loner or similar but have no diagnosed mental illness. I am not clear what kind of mental health strategy is being proposed (politicians tend to stick on phrases like “we need to look at mental health”) but presumably it involves identifying those who have mental health issues, giving some kind of treatment, and (as mental health treatment is lengthy and unreliable) limiting them in some way – at a minimum limiting their access to guns or more drastically their freedom in general. Now here’s the rub – over 43 million US adults suffer from some kind of mental illness (this does not include substance abuse such as drugs and alcohol) and 10 million of those suffer from serious mental illness. Furthermore it is extremely hard to tell which of those 10-40 million might be violent (even though very few of them will be). So what is the strategy?   Prevent between 10-40 million people having access to guns most of whom will never do anything violent – even though this would still let about 75% of mass murders get access? How could this be done without introducing some kind of gun control?  I am all for better treatment for the mentally ill – but don’t be fooled into thinking this is going to do anything to reduce homicides unless you introduce gun control for everyone.

Yes every child should have the opportunity to learn a musical instrument–but how, where and when?

The concert pianist James Rhodes is conducting a campaign to get the UK government to give every child the opportunity to learn a musical instrument. He is presenting a series of programmes on C4 where he starts a school orchestra in primary school which is on special needs (i.e. doing really badly). He has started an on-line petition. And I have no doubt there is/will be a lot of activity as well. The result is a sort of combination of Jamie Oliver on school dinners and Gareth Malone on school choirs. (The C4 series is made by Jamie Oliver’s production company).

I really, really like the idea and have signed the petition but am also quite concerned it may all back fire. Rhodes is quite candid that all he is doing is demanding the government provide the opportunity. The details of how to do it are “for the policymakers”.


This is a complex problem and experts agree it’s about more than just money. We need action: whether it’s providing teachers with proper music training or asking Ofsted to pay specific attention to music in their inspections or even a guarantee of funding until the end of the National Plan. But the details of how to achieve it are for the policymakers. What I’m asking for is something simple

Nevertheless a lot of energy and enthusiasm without thinking about the implementation could backfire, kill this campaign and endanger similar campaigns for reforms in education. If it ends up with mouldering heaps of unused instruments cluttering up schools and headteachers being harassed to do the impossible, then it will be a backward step not a forward one.

Giving every child the opportunity to learn an instrument would be something unprecedented in UK education. It may that there is even less emphasis on music education now than in recent years – but it has never been the case that the majority of  schools offered a serious opportunity to all children.  In most schools music education has always been of secondary status to mainline subjects such as maths, science, English, history and languages. I went to seven primary schools (my father was in the air force and we travelled a great deal) and an academically excellent grammar school during the 50s and 60s. I was never even shown a musical instrument. My children fared little better when they went to reputable state schools in middle class Hampshire in the 90s. So this is a new venture and we don’t know how to do it.

Some things to bear in mind.

Music is not alone in its case for more attention/funding in schools. Sports, drama, cooking, citizenship, home economics – the list of topics that the education system is asked to support is seemingly endless. Yes music brings immense benefits to those that learn it. So do many of these others.

The methods used by Rhodes in the C4 programme were not scalable to schools as a whole or sustainable over an extended time. They were great for getting attention and rather moving – but required his  time, energy, and very rare skills; many volunteers with a musical background; and a one-off campaign to obtain gifts of instruments. It also appeared to disrupt the rest of the school quite extensively -  we heard that other teachers lessons were badly affected during music lessons because of the noise but never heard how this was resolved.

Offering children the opportunity to learn an instrument is a lot harder than offering them decent school dinners. It needs a great deal of the time and commitment from the child and teacher. It needs suitable space and equipment. Ideally is needs opportunities to perform to an audience. There is no reason why changing school dinners should disrupt the rest of the school’s activities in  significant way. There is good reason to think that the opportunity to learn an instrument will effect every other aspect of the school.

But I think the thing that concerns me most is that the campaign positions this as a problem to be solved by schools.  It doesn’t matter what goes on in schools if the child is not practicing at home. On the other hand if the parents are supportive and the child is practicing at home then it probably doesn’t require much of the schools. In the first programme Rhodes goes to visit the family of a child who is apparently not practising. It turns out most of her time is consumed by gadgets – i-phone, tablets and playstation. He successfully persuades her parents to encourage her to spend less time on gadgets and more on practice. But this is not going to happen for every family in the land. We have to look beyond the formal education system if this is to work.


“I really seriously do not understand how anyone can believe materialism.”

Barry Arrington has a post on UD If My Eyes Are a Window, Is There Anyone Looking Out? which contains some fairly standard arguments for dualism.  What caught my eye was the comments. Here is a sample:

How do you argue against someone who does not see the obvious self-contradiction in the statements –

“I choose to believe in materialism”. “I choose not to believe in free will.”

To believe these statements takes denial of basic logic.

I think some people just like to believe and say counterintuitive things because they think it sets them apart from the average Joe. Believing that I am just a machine has got to be the MOST counterintuitive thing I could possibly believe. It’s possible that you are just a machine, I can’t be sure about that, but I’m sure I’m not and, and as you say, any theory that provides the wrong answer to this question will not get serious consideration from my (average) mind.

This subject goes to the heart of the questions I’ve been puzzling on recently and has resulted in the few comments I’ve made here at UD.
It starts with the question, “Why don’t people accept sound arguments?”
The answer appears to be that their worldview will not allow it.

It is an ironical that comments like this appear just when Denyse is making post after post about how evolutionists/materialists/the liberal elite are suppressing intellectual freedom.  This group that cannot understand the materialist case so they dismiss materialists as at best deluding themselves and possibly being deliberately deceptive because they want to show off. It amounts to “they are obviously wrong so the only interesting question is why do they say these things”. This is not a good basis for debate. In Barry’s case this has extended to banning arguments he believes to be “obviously” wrong from his debates (there are some UD regulars who do respect opposing views – most notably vj torley). What I cannot work out is how to engage with this mind set or if there is any point in trying to.

There are of course many responses to all the points that Barry makes. They have been covered many times both in the blogosphere and serious writing and there seems little point in repeating them here. Interestingly in one comment Billmaz raises some of these objections. He/she appears to be an IDist acting as Devil’s Advocate and shows a real intellectual interest in seeing both points of view so can hardly be dismissed as deluding him/herself.  This will presumably lower the emotional baggage that gets in the way of any serious debate. It will be interesting to see to what extent Barry and the commenters engage with what Billmaz writes – after all as far as they are concerned he/she is obviously wrong.

A Response to Larry Correia on Gun Control

Amongst the furious debates on gun control in the USA following the Newtown massacre there is one blog post by the novelist Larry Correia that is particularly popular with those who oppose gun control. At the time of writing it has had 1700 responses- many of them links from other blogs. What I can’t find in all those responses (although it may be there) is a systematic critique of what he has written. Which is a pity, because, while I learned a lot, and even sympathised with some of what he had to say, it is full of logical and factual errors.

The heart of the problem is that  Correia sees the world as a fight between the good guys and the bad guys.  As he explains, his career has been in guns, law enforcement, self-defence training and eventually writing adventure novels (I haven’t read them but the covers and titles suggest strongly that they are full of good guys killing bad guys). In his world we (the good guys) are under threat from bad guys with weapons and the way to deal with this is for  the good guys kill the bad guys before they do too much harm. So for him the solution to Newtown is to arm teachers; gun free zones are invitations to bad guys to attack defenceless victims; limitations on magazine size make it harder for the good guys to kill the bad guys and so on.

He appears to be unable to conceive of an alternative, but they do exist. Indeed most affluent democracies are that alternative. It is the United States that is the outlier having by some distance the highest rate of gun ownership in the world and a homicide rate that is four to five times that of comparable countries. The difference is even greater for “rampage” murders such as Newtown.  For example, there has been one such event in the UK since 2000.  There have been four events that clearly count as rampage murders in the USA in the last two years alone (Newtown, Aurora, Tucson and Oak Creek) and several others that might count.  He wants to arm teachers. Wouldn’t it be better if it was not necessary to arm teachers because the chances of a mad gun man attacking a school are so small they can be ignored? Guess what – for most comparable countries that is the case.

Correia does write about other countries but this section of his post is the most erroneous and misleading. For example, he writes of Australia:

Australia had a mass shooting and instituted a massive gun ban and confiscation …. As was pointed out to me on Facebook, they haven’t had any mass shootings since. However, they fail to realize that they didn’t really have any mass shootings before either.

Australia had many mass shootings in the 18 years prior to the gun ban (estimates vary from 13 to 16 depending on definitions) and just one possible event since (the event at Monash University where two students were killed).

Like many pro-gun US writers he seizes on the fact that both Australia and England introduced very stringent gun control legislation in the late 1990s following massacres and since then violent crime has risen in both countries. But this is reading far too much into that specific legislation and those statistics.  In both countries there was extensive gun control for decades before the 1990s. In England  virtually no civilians have carried guns for self-defence since the war, and no sane criminal would have been concerned about the possibility their victim was armed. Yes violent crime increased in both countries in the late 90s early 2000s, but this was part of a worldwide trend that had already started and has reversed in the latter part of the 2000s. This violent crime did not extend to homicide which remained low – far, far lower than the USA (In England the big increase was in assault –  a very broad category which covers everything from a minor scuffle in a bar to a major mugging). The explanation of this pattern is debateable and complicated – but one thing it certainly was not caused by was criminals suddenly finding their victims could not defend themselves.  The 1990s legislation was  a reaction to specific rampage murders – important and horrific but responsible for a negligible proportion of homicides. In the case of Australia it appears to have succeeded dramatically. In the case of the UK it is hard to tell because such incidents were so rare in the first place.

What Correia appears not to understand is that the USA has a unique gun culture. By a gun culture I mean more than lax gun control laws or even the high availability of guns. I mean that the use of guns as defensive weapons is accepted and actively promoted. Other countries do not have advertising campaigns suggesting you need a gun to defend yourself. In England  most people would be shocked if a friend declared they had a gun for self-defence even if that gun were legal. Outside the USA people do own guns (even in England!) but they are for professional or sporting reasons. I believe this cultural difference is far more important than the difficulty of obtaining a gun legally.  Even in England it is not that difficult to own a gun. The one rampage killing in England since the late 1990s legislation was done using legally obtained guns. Likewise, Norway’s only rampage murder – the horrific Breivik massacre – was committed using legally obtained weapons (he even got formal training – much as Correia would like teachers to get). The reason there are far less rampage murders in England is because such murders are extremely hard to do without guns and people in England just don’t think about guns as a realistic option for killing fellow citizens.  Even in countries such as Switzerland, where famously guns ownership is high, guns are treated as instruments of sport not as weapons. Although gun ownership is  required for men of military age there are strong restrictions on carrying guns. To quote a website that advises foreigners on living in Switzerland:

Strict legislation in Switzerland has made it extremely difficult to obtain a license to bear arms, and the trend is moving towards even stricter laws. For information purposes only, 400 people had a license to bear arms in the canton of Geneva in 1998. Only eight "survivors" still have authorization today. Understandable when you realize how little violent crime there is in Switzerland.

Crime is very, very low in Switzerland – but it is not because criminals are frightened of their victims defending themselves with a gun.  Switzerland has extensive gun control – it is just that it applies to bearing arms not owning them.

So, the USA is stuck in a unique culture where guns are closely linked to violence and self-defence. Other countries have far lower homicide rates and far lower rates of rampage killings (and very little debate about the need for gun control).  But does that mean increased gun control would change that culture in the USA? Given the vast number of guns already in circulation, the almost religious belief in the second amendment, and the deep political divide it represents – maybe the best way forward is to accept that the culture cannot change and concentrate on making sure the good guys have the weapons they need?

The problem with this argument is that it turns crime prevention into an arms race. If the teachers/guards are armed then maybe they will kill the bad guys first, but the bad guys are the ones who take the initiative and can research their their targets. What is to say he (it is almost always a male) will not simply increase his body armour and weapons to whatever level is necessary (remember the extensive kit used by the Aurora killer) and make sure he kills the armed guard/teacher first? In an arms race the side that is waiting for the possibility of attack on one or two out of thousands of possible targets is always going lose  out to the side that can choose and survey its target and pick its time and weapons.

Laws are both the result of culture change but also contribute to it. They not only prevent people doing what society considers to be wrong. They also help to define what is wrong. Speed limits define what is an acceptable speed even on roads where there is no possibility of being caught. People report income for taxation purposes even though there is no way they will be found out. Drink driving and smoking legislation have changed our ideas about what is acceptable behaviour. Gun control laws can do something similar for guns. They can contribute to breaking that cultural link between guns and violence. If selling certain types of weapon is illegal then they will not be advertised and they will not be seen in gun shops. If carrying them is illegal then they will not be shown off at gun shows or other occasions. If someone has doubts about owning a powerful gun but feels peer pressure to have one – the law gives them a great excuse for not having one. Of course, laws by themselves are not sufficient, if they are not promoted and at least to some extent enforced, they will be meaningless.  But if the USA really wants do something about its high homicide rate and particularly its rampage murders then surely this has to be worth a try.

Continuation of discussion of Gpuccio’s challenge from TSZ

This post is a continuation of a debate that has been going on for some time on TSZ – moved here because TSZ is having technical problems.

These are my most recent comments repeated.


More to the point – I think I have another example which would give you reason to refine your dFSCI process if you want to preserve 100% specificity. Before I do the work let me check the function is acceptable:

“The string identifies for each month over a period of 120 months whether the London monthly mean high temperature is above or below long-term average.”  

As I have given you the function before working out the string you can see that I am prespecifying it!


With the other two functions, instead, relying only on an explicit, non contingent property, the computation of dFSI would not change in the prespecified or postspecified case. The target space and the search space remain the same in both cases.

That’s false. For the other two examples if they were post-specified this would be something like taking the string, studying the papers it points to, and seeing what you can find that they had in common. As all papers have something in common (even if it is just a distinctive phrase somewhere in the text) then the probability of success is 100%. That’s why I suggest you simply amend the process to say no post-specified functions. Any function could potentially be post-specified.

But, to be complete, I would obviously ask what the period is (and in particular, if it is a future period or a past period whose values are already known), and what the long term average reference is.

I was thinking of the last 10 years – 2002 to 2012 – I could do a longer period but it would be tedious. I was going to use for the averages. Although the values for 2002 to 2012 are known I was not going to use them to generate the string. That’s why I said “identify” rather than “predict”. I will not even look at the actual temperatures until after I have generated the string – although I won’t be able to resist checking it has worked when I have finished. The string will simply be a string of 120 bits with 1 for above average and 0 for below average. I realise you want 500 bits but that would be really tedious to look up all the data, so I hope 120 will be sufficient to prove the case.

The Law of the Conversation of Information and Bernoulli’s Principle of Insufficient Reason

I have just been rereading Bernoulli’s Principle of Insufficient Reason and Conservation of Information in Computer Search by William Dembski and Robert Marks. It is an important paper for the Intelligent Design movement as Dembski and Marks make liberal use of Bernouilli’s Principle of Insufficient Reason (BPoIR) in their papers on the Law of Conservation of Information (LCI) and many ID friendly authors, including Dembski, use it extensively elsewhere. Without BPoIR many of the arguments presented for Intelligent Design would collapse. The point of Dembski and Marks paper is to address some fundamental criticisms of BPoIR. I hope to show that they fail to do this.

For Dembski and Marks BPoIR provides a way of determining the probability of an outcome given no prior knowledge. This is vital to the case for the LCI. The idea of the LCI is that outcomes such as genes or proteins can be seen as successful searches for limited targets in a large search space. The improbability of hitting that target without any prior information (determined using BPoIR) is the total amount of information in that outcome. They then go on to argue that the chances of finding any strategy for increasing the probability of hitting the target (i.e. reducing the information) are always so low that it is not possible to increase the overall probability of hitting the target. The more the strategy increases the probability of success, the lower the probability of finding the strategy. Or as they put it – the information lost through introducing the strategy is always made up for by the information gained in finding the strategy – so that information is conserved – and overall the information based on using BPoIR without prior knowledge is preserved. Their proof of this also relies on BPoIR. So the LCI is deeply dependent on BPoIR.

Dembski and Marks are well aware that BPoIR has been severely criticised by philosophers and statisticians as eminent as J M Keynes. In particular Keynes pointed out that the BPoIR does not give a unique result. A well-known example is applying BPoIR to the specific volume of a given substance. If we know nothing about the specific volume then someone could argue using BPoIR that all specific volumes are equally likely. But equally someone could argue using BPoIR all specific densities are equally likely. However, as one is the reciprocal of the other, these two assumptions are incompatible. This is an example based on continuous measurements and Dembski and Marks refer to it in the paper. However, having referred to it, they do not address it. Instead they concentrate on the examples of discrete measurements where they offer a sort of response to Keynes’ objections. What they attempt to prove is rather limited point about discrete cases such as a pack of cards or protein of a given length. It is hard to write their claim concisely – but I will give it a try.

Imagine you have a search space such as a normal pack of cards and a target such as finding a card which is a spade. Then it is possible to argue by BpoIR that, because all cards are equal, the probability of finding the target with one draw is 0.25. Dembski and Marks attempt to prove that in cases like this that if you decide to do a “some to many” mapping for this search space into another space then you have only a 50% chance of creating a new search space where BPoIR gives a higher probability of finding a spade. A “some to many” mapping means some different way of viewing the pack of cards so that it is not necessary that all of them are considered and some of them may be considered more often than others. For example, you might take a handful out of the pack at random and then duplicate some of that handful a few times – and then select from what you have created.

What is the significance of this? It is not totally clear. I think their point is that a “some to many mapping” is equivalent to changing the probability of the individual items in the search space from the BPoIR assumption of every outcome being equal, to any other distribution of probabilities e.g. making one amino acid more probable than another when building a protein. So they have attempted to prove that if instead of assuming all amino acids are equal you take another probability distribution at random, you have a 50% or less chance of happening on a probability distribution which will improve your chance of meeting the target.

There are two problems with this.

1) It does not address Keynes’ objection to BPoIR

2) The proof itself depends on an unjustified use of BPoIR.

But before that it is worth commenting on the concept of no prior knowledge.

The Concept of No Prior Knowledge

Dembski and Marks’ case is that BPoIR gives the probability of an outcome when we have no prior knowledge. They stress that this means no prior knowledge of any kind and that it is “easy to take for granted things we have no right to take for granted” (They compare it to the physics concept of nothing that preceded the big bang). However, there are deep problems associated with this concept. The act of defining a search space and a target implies prior knowledge. Consider finding a spade in pack of cards. To apply BPoIR at minimum you need to know that a card can be one of four suits, that 25% of the cards have a suit of spades, and that the suit does not affect the chances of that card being selected. The last point is particularly relevant. BPoIR justifies us in claiming that the probability of two or more events are the same. But the events must differ in some respects (even if it is only a difference in when or where they happen) or they would be the same event. To apply BPoIR we have to know (or assume) that these differences are not relevant to the probability of the events happening. We must somehow judge that the suit of the card, the head or tails symbols on the coin, or the choice of DNA base pair is irrelevant to that the chances of that card, coin toss or base pair being selected. This is prior knowledge.

In addition, as Keynes pointed out, the more we try to dispense with assumptions and knowledge about an event then the more difficult it becomes to decide how to apply BPoIR. Another of Keynes examples is a bag of 100 black and white balls in an unknown ratio of black to white. Do we assume that all ratios of black to white are equally likely or do we assume that each individual ball is equally likely to be black or white? Either assumption is equally justified by BPoIR but they are incompatible. One results in a uniform probability distribution for the number of white balls from zero to 100; the other results in a binomial distribution which greatly favours roughly equal numbers of black and while balls. To choose the correct assumptions we would have to know more, for example the process by which the bag was filled.

Now I will turn to the problems with the proof in Dembski and Marks’ paper.

The Proof does not Address Keynes’ objection to BPoIR

Even if the proof were valid (I believe I show below that it is not) then it does nothing to show that the assumption of BPoIR is correct. All it shows is that if you make an assumption other than what Dembski and Marks believe follows from BPoIR then you have 50% or less chance of improving your chances of finding target. The fact remains that there are many other assumptions you could make and some of them greatly increase your chances of finding the target. There is nothing in the proof that in anyway justifies assuming BPoIR or giving it any kind of privileged position.

But the problem is even deeper. Keynes’ point was not that there are alternatives to using BPoIR – that’s obvious. His point was that there are different incompatible ways of applying BPoIR. For example, just as with the example of black and white balls above, we might use BPoIR to deduce that all ratios of base pairs in a string of DNA are equally likely. Dembski and Marks do not address this at all. They point out the trap of taking things for granted but fall foul of it themselves.

The Proof Relies on an Unjustified Use of BPoIR

The proof is found in appendix A of the paper and this is the vital line:


This is the probability that a new search space created from an old one will include k members which were part of the target in the original search space. The equation holds true if the new search space is created by selecting elements from old search space at random; for example, by picking a random number of cards at random from a pack. It uses BPoIR to justify the assumption that each unique way of picking cards is equally likely. This can be made clearer with an example.

Suppose the original search space comprises just the four DNA bases, one of which is the target. Call them x, y, z and t. Using BPoIR, Dembski and Marks would argue that all of them are equally likely and therefore the probability of finding t with a single search is 0.25. They then consider all the possible ways you might take a subset of that search space. This comprises:

Subsets with

no items

just one item: x,y,z and t

with two items: xy, xz, yz, tx, ty, tz

with three items: xyz, xyt, xzt, yzt

with four items: xyzt

A total of 16 subsets.

Their point is that if you assume each of these subsets if equally likely (so the probability of one of them being selected is 1/16) then 50% of them have a probability of finding t which is greater than or equal to probability in the original search space (i.e. 0.25). To be specific new search spaces where probability of finding t is greater than 0.25 are t, tx, ty, tz, xyt, xzt, yzt and xyzt. That is 8 out of 16 which is 50%.

But what is the justification for assuming each of these subsets are equally likely? Well it requires using BPoIR which the proof is meant to defend. And even if you grant the use of BPoIR Keynes’ concerns apply. There is more than one way to apply BPoIR and not all of them support Dembski and Marks’ proof. Suppose for example the subset was created by the following procedure:

· Start with one member selected at random as the subset

· Toss a dice,

o If it is two or less then stop and use current set as subset

o If it is a higher than two then add another member selected at random to the subset

· Continue tossing until dice throw is two or less or all four members in are in subset

This gives a completely different probability distribution.

The probability of:

single item subset (x,y,z, or t) = 0.33/4 = 0.083

double item subset (xy, xz, yz, tx, ty, or tz) = 0.66*0.33/6 = 0.037

triple item subset (xyz, xyt, xzt, or yzt) = 0.66*0.33*0.33/4 = 0.037

four item subset (xyzt) = 0.296

So the combined probability of the subsets where probability of selecting t is ≥ 0.25 (t, tx, ty, tz, xyt, xzt, yzt, xyzt) = 0.083+3*(0.037)+3*(0.037)+0.296 = 0.60 (to 2 dec places) which is bigger than 0.5 as calculated using Dembski and Marks assumptions. In fact using this method, the probability of getting a subset where the probability of selecting t ≥ 0.25 can be made as close to 1 as desired by increasing the probability of adding a member. All of these methods treat all four members of the set equally and are equally justified under BpoIR as Dembski and Marks assumption.


Dembski and Marks paper places great stress on BPoIR being the way to calculate probabilities when there is no prior knowledge. But their proof itself includes prior knowledge. It is doubtful whether it makes sense to eliminate all prior knowledge, but if you attempt to eliminate as much prior knowledge as possible, as Keynes does, then BPoIR proves to be an illusion. It does not give a unique result and some of the results are incompatible with their proof.


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