Making errors is so common in mathematics that there is not too much embarrassment about it. For example, both Cauchy (1789-1857) and Kummer (1810-1893) made a very serious error in attempting to prove the Fermat conjecture, which was finally proved by Andrew Wiles at the end of the previous century, using tools Cauchy and Kummer could not have dreamed of. Cauchy (a really very famous mathematician, whose name pervades mathematics in all kinds of results) had to withdraw a paper he had submitted to the French Academy of Sciences which claimed to prove Fermat’s conjecture. Kummer made a similar error, but after the mistake was pointed out to him by the mathematician (and successor of Gauss in Göttingen) Dirichlet, he set out on a completely new track. E.T. Bell (see p. 522 of: “Men of Mathematics, volume 2″, Pelican Books) says about this event: “*This failure of Kummer’s was one of the most fortunate things that ever happened in mathematics*. Like Abel’s initial mistake in the matter of the general quintic, Kummer’s turned him into the right track, and he invented his “ideal numbers””. Abel (1802-1829), another outstanding mathematician…

The book by Ton Derksen, “Lucia de B. Reconstruction of a Miscarriage of Justice” (in Dutch), discussed the errors made by the prosecutors, judges and consulted experts in the case of Lucia de Berk. Like the mistakes of Cauchy, Kummer and Abel, admitting these mistakes might conceivably set the people in the Dutch legal system who are involved in this case onto the right track. It did not happen… Instead, there seems to be a culture of denial of mistakes made. Outside the rather closed group of Dutch lawyers consisting of prosecutors, judges, etc. (including the Supreme Court), scientists and other non-lawyers fear that because of all recent cases of judicial errors in the Netherlands (the most conspicuous one is the so-called “Schiedam Park murder”, see Miscarriage of justice, where the judicial errors came to the surface just because someone other than the convicted person confessed having committed the crime, and not because of efforts of persons inside the Dutch system of law; the Court in the Hague still claims not to have committed any errors!), the people involved in the Dutch legal system will refuse to reopen cases where there is a serious suspicion of miscarriages of justice. Just for fear of more embarrassment and for getting publicly a bad (or worse) name.

As I mentioned in my blog Lucia de Berk and the amateur statisticians, the cheapest “argument”, which has been used to fight people who have an opinion on the Lucia de Berk case which runs against the Court decisions, is to say that they have no understanding of how the Dutch law system works. And, since I stated that the “statisticians” consulted by the court were amateurs or acting as such, the corresponding cheap reply of persons defending this Court verdict is to say that I am an amateur lawyer and should therefore keep my mouth shut about law cases. And the same reproach has been addressed to Richard Gill who spends a large part of his time nowadays in fighting for justice in a number of cases where he (and also I) suspect that serious miscarriages of justice in the Netherlands have happened.

But there is an essential difference between my reproach of the amateur statisticians not doing a proper job and the “counter reproach” that I am an amateur lawyer and should therefore keep my mouth shut. The amateur statisticians come forward with statistical statements. These statements should be evaluated by statisticians. Richard Gill and I do not comment on law or make statements of a judicial nature. Our observations are external to the legal system itself, in that they do not concern the system but rather the way this appears to be (mis)used or (mis)applied. Any person in society, not just lawyers, can and may make such statements. The same cannot be said of doing statistical computations, though.

Of course everyone can try to do amateur statistical computations, like Mr. Smits, general director of the Juliana children’s hospital and the Red Cross hospital in the Hague, the law psychologist prof. Elffers, or Prof. Mr. de Mulder in his role of explaining to the Court the computations of his colleague prof. Elffers, but these calculations are open to criticism from statisticians. And this is indeed what happened: the flaws in these calculations have been exposed in, for example, Elffers corrected. People in the Netherlands have been using the Dutch expression “Tailor stick to your trade!” in saying that Richard Gill should not have pointed out the implications of these errors for the Lucia de Berk Court case. What kind of repressive mentality is this? In fact, Richard Gill was sticking to his trade by correcting the calculation! The next step was to point out the implications of this for the Court case. Is this next step not allowed? Should he just have let it pass, waiting for the people involved in the Dutch legal system to do something with this information? I personally think that he would have waited forever.

The the Hague Court verdict in the Lucia de Berk case (after appeal) is publicly available. I have made the print version of this verdict available in: the Hague Court verdict (in Dutch). On page 1 of the print version we read the statement (I translate literally): “Statistical evidence in the form of probability calculations has not been used”. What is the meaning of this statement? *Amateur statistics have played a role in every phase of the Court case*, as I will now explain more fully.

1. Henk Elffers convinced the police that “so many incidents could not be a coincidence”.

2. He secondly convinced the (two) Courts (second one after appeal) that “so many incidents could not be a coincidence”. As possible alternative explanations (besides murder) for “so many coincidences” he offered 5 explanations on page 7 of his first NSCR report (in Dutch), by way of example (Henk Elffers has to be praised for making this publicly avalaible). He also stated that an explanation should be given for “so many coincidences”.

3. Prof. Mr. de Mulder in his role of “expert in statistics” has stated that “Yes, Elffers’ computation is correct, and yes, an explanation for the coincidences has to be found”. The Court has interpreted this as: our suspect Lucia de Berk should provide the explanation.

The Court has presented Lucia de Berk with 3 of the 5 alternative explanations of the “coincidences” on page 7 of first NSCR report Elffers. The following two other explanations were not applicable or not applied:

a) Lucia de Berk preferred to work with another nurse who caused the incidents.

b) Someone tried to “frame” Lucia de Berk.

Explanation a) was not applicable and explanation b) was not applied, and, in any case, Lucia de Berk was not in a position to comment on the truth or falseness of this explanation.

The three other explanations on p. 7 of Elffers’ report were:

c) Lucia de Berk (denoted by “V” in Elffers’ report) often did night shifts and there is a higher chance during the night that a life-threatening situation is not discovered in time.

d) Lucia de Berk is a bad nurse and does not spot dangerous situations in time.

e) Lucia de Berk always takes the most difficult cases.

One can read the use of this in the the Hague Court verdict, (see p. 77 and pages thereafter, if one can read Dutch). As an example, p. 79 of the verdict says:

“One cannot consider as a plausible explanation that the suspect is not a good nurse, where one’s attention should in particular be on her functioning in the Juliana Children’s hospital. Suspect has declared in the Court session, March 22, 2004: “I think that I have been a good nurse. I cannot think of anything which I often did wrong or should have done differently and where there is a causal connection between one or more incidents. It is correct that I have declared in an earlier Court session that I consider myself to be a good nurse.””

This does away with explanation d). And explanations c) and e) are discarded by the Court in a similar way. This leads the Court to say, see 11.13, p. 78: “No plausible explanation has been found for the fact that suspect was present with so many deaths and life-threatening incidents in such a short period”.

Well, the Court now argues (somewhat implicitly perhaps): “The five alternative explanations in Elffers’ report do not apply. Then only one possibility remains for the coincidences: Lucia de Berk must be a murderer”. In the pages preceding p. 77 it is argued that there were two cases where there was “hard evidence” (for example, digoxin intoxication). This “hard evidence” has dissolved into thin air, as discussed in my blog Lucia de Berk and the amateur statisticians and further detailed in the book by Ton Derksen, see also Lucia de Berk.

So it is clear to everyone who takes the trouble of reading the 90 pages of the the Hague Court verdict that, *quite contrary to what the opening remark “Statistical evidence in the form of probability calculations has not been used” (also issued to the Dutch newspapers) suggests, (bad use of) statistics is everywhere in the verdict*.

There is still something else. Everybody is free to make a statement about a mathematical problem. Mathematicians will never say: you should keep your mouth shut because you cannot show that you have a certificate showing that you finished a study in mathematics. My distinction between “amateurs” and “non-amateurs” cuts across the distinction between people having a diploma or not having a diploma. Ramanujan is famous for his results in number theory, but did not have any formal training in mathematics. To make a living, he worked as a clerk in the accountant general’s office at the Madras Port Trust Office, see the Wikipedia on Ramanujan. It shows the open-mindedness of the community of mathematicians that Hardy invited him to come to Cambridge and discuss mathematical problems with him. None of the reluctance of Dutch lawyers to listen to Dutch statisticians.

If the the Hague Court or the committee Grimbergen now would come with: “Smits, Elffers and de Mulder are our Ramanujans of mathematical statistics!” (although, formally, in their point of view, they might find that they have no obligation to do this for the law psychologist Elffers, since he received a diploma in mathematics 30+ years ago), then we really have reached the end of the tunnel and can say: “Pardon me, papers of Ramanujan and Hardy have appeared in mathematical journals. Our profession of statistics has international journals like the Annals of Statistics, with refereed papers. Persons publishing in journals of this type, for example Richard Gill and Piet Groeneboom, to name just two, have looked at the work of your three Ramanujans and concluded that it is humbug. You should at least pay some attention to that!”.

The petition for reopening the Lucia de Berk can still be signed, see: Petition for reopening the Lucia de Berk case.