Monthly Archives: September 2014

I am sorry to report a breach of scientific integrity in the period 1981-2014 by Johan van Benthem, professor of logic at the universities of Groningen and Amsterdam, who is retiring these days.

The issue concerns the Liar paradox. If the professor isn’t truthful then he will assert that he is truthful. If he is truthful then his assertion that he isn’t would be true to fact. There is logical consistency when the professor is truthful and asserts this. But this hardly forms evidence. This example of the paradox can be cut short by showing that the professor committed a breach of scientific integrity anyway.

(1) Draft of A Logic of Exceptions (ALOE) in 1981

I wrote the 1981 draft of A Logic of Exceptions” (ALOE) when I was a student of econometrics in Groningen. Johan van Benthem was my professor of logic. He presented Gödel’s incompleteness theorems but did not show that these are essentially nonsense. Those derive from a form of the liar paradox. The Liar is “This sentence is false” and the Gödeliar is “This theorem is unprovable”. It merely adds a layer of complexity. The inclusion of some conditions for reasonableness – such as that what is proven is also true – causes the issue to collapse to the Liar paradox. Thus those theorems are not useful for science, but a mathematical exercise in irrelevance. Van Benthem however suggested that Gödel’s incompleteness theorems would be important for science.

Van Benthem did not react kindly to the draft of ALOE, gave up on it, but helped to find Albert Visser in Utrecht, who subsequently maltreated ALOE too. The conversation with Visser was by telephone and not an example of proper communication. In one perspective it is kind, when a professor gives up on a draft work by a student, that he helps to find a third reader. In retrospect Van Benthem should not have given up on that work but should have looked for someone to help himself e.g. on science.

When “logicians” form a sect who think that Gödel’s incompleteness theorems are more important than reasonableness, then science has a problem – and teaching of science too.

PM. In those days, Van Benthem gave priority to correcting errors for a new edition of Gödel, Escher, Bach” by Douglas Hofstadter, which will have helped his career, but which created more confusion for the general public, as if those incompleteness theorems would amount to something “deep”. Buyers of GEB should ask Hofstadter and Van Benthem their money back.

(2) First edition of A Logic of Exceptions (ALOE) in 2007

In 2007 I reread ALOE and edited and published it. I contacted Van Benthem and Visser. (The email in Dutch is here.) Van Benthem did not react. He neither reacted when I informed him about the favourable 2008 review by Richard Gill (mathematical statistics Leiden, KNAW) in “Nieuw Archief voor Wiskunde”, the journal of the Royal Dutch Society for Mathematics. Albert Visser responded in an email exchange, which appeared another exercise in non-communication.

(3) Statics vs dynamics in logic

When contacting Van Benthem and Visser in 2007, I noted that Van Benthem had got a Spinoza prize (2 or 4 million guilders in 1996) for dynamics in logic, with this Dutch book “logica in actie” with the same title. However, in 1981 I had used the distinction in economics between statics and dynamics in analysis to transfer this also to logic, calling “implication” statics and “inference” dynamics. In itself it does not change anything about implication vs inference, since that distinction was well known. But it may help to clarify the distinction to who comes to the issue afresh. This was an aspect that Van Benthem appreciated in 1981. So I wondered whether he could tell whether our conversation on it had been relevant for his apparently later research on such dynamic logic. It may be, or it may not be, as a look e.g. on wikipedia shows that there have been other writers working on dynamic and temporal logic in 1974-1977. It would be proper to give a reply to this question.

PM. ALOE 2007 contains a few pages on the paradoxes from division by zero, and proposes to solve these with the “dynamic quotient”. This was not in the 1981 draft and was new in 2007. But the notion of dynamics in ALOE fits the approach there too. See also Elegance with Substance(2009) and Conquest of the Plane(2011) and this September 2014 paper for more context and development.

(4) Making a point of it

As a student in 1981 I had mixed feelings about the situation. I graduated in econometrics in 1982 anyhow, ALOE was no priority and was shelved.

The box turned up again when I went to Curaçao in 2005-2006. After writing my book on the Caribbean economy (PENAFC 2006) I decided that I better publish ALOE since it was a good opportunity to do so and there would not be another one when I would start doing new things.

Now, looking back at the affair with my professional experience as econometrician and college teacher in mathematics, statistics, logistics and operations management, I find the reactions by the “logicians” scientifically improper.

I might have filed an official complaint but I preferred giving ALOE a chance to be discovered and read by others without that context.

Now that Van Benthem retires in September 2014 with superlatives as if he would be such a good “logician”, I feel however that this protest must be mentioned. There is, in Dutch, (a) my letter to the board of the University of Amsterdam, (b) my letter to the ombudsman of the Volkskrant newspaper w.r.t. a biased interview with Van Benthem by journalist Maarten Keulemans.

In that interview, Van Benthem suggests that he is open to dialogue:

“Personally I have another idea about science. I find science a form of organised discussion, and the power of science lies in the quality of that discussion. The fact that we put differences of opinion up for discussion, allows us to progress.” (Volkskrant September 27 2014, Sir Edmund, p41)

This is an outright lie, given that Van Benthem did not respond to my 2007 email and completed ALOE.

Of course, journalist Maarten Keulemans has not reacted to my protest last weekend on his interview. Instead, he rather retweets the admiration of readers who he has misinformed.

Journalist Maarten Keulemans retweets admiration from readers who he has misinformed (Source: his twitter account, September 29 2014)

Journalist Maarten Keulemans retweets admiration from readers who he has misinformed (Source: his twitter account, September 28 2014)

(5) If Holland had been just a bit nicer and more competent

This issue in logic and the improper response by “logicians” has had a remarkable influence on further developments, see this earlier weblog entry or the longer paper:

After 45 years of unemployment: If Holland had been just a bit nicer and more competent, June 2014.

(6) Returning to the Liar paradox

The above is essentially a report on the breach in scientific integrity by professor Johan van Benthem. But the reader will also be interested to hear how the story continues with the Liar paradox. Well, the solution method by Kurt Gödel to use provability instead of truth thus collapses (since we want truthful models, except for mathematicians who don’t care). The other solution of Russell and Tarski is to use (meta-) levels, but this collapses because of the flexibility of language, and in particular the self-reference. This is bad news for the wonderful book Logicomix. ALOE also solves Russell’s set paradox, of the hero of Logicomix. Thus we find the third solution method, which is a three-valued logic with the notions true, false, nonsense. It appears that there is a consistent manner to deal with the versions of the Liar paradox for three-valued logic. The issue has finally been solved after bugging logic for 2300 years.

Now that Europe is threatened by Russian invasion, Chinese take-over and head-chopping terrorism, wise people make a do-list for one’s own funeral. I hope to live for another thirty weblogging years but if this hope is cut short then the survivors should know what music to play and what wine to toast with.

The wine was easy: Brunello di Montalcino. The music was difficult though, and it took a couple of bottles of BdMs to decide from Mozart’s Requiem or The Band’s The Last Waltz or Mahler’s Ninth by Bernard Haitink or perhaps something appropriate by Bob Dylan. It is amazing how tantalising it can be, this care that you want to provide your survivors with: some of who might not like classical music or some who might walk out when hearing Dylan.

My funeral choice is Spente Le Stelle (Dull are the stars), sang by Emma Shapplin and Giorgos Dalaras, see and listen to this YouTube video.

If you want to hear only enchanting Emma then see this video, which might be the original somewhat spooky clip. The latter would be your own preference though, because on my funeral I would want the duet with Giorgos. As said before, Europe must worry about the Greek economy, and this may well take those thirty years too.

Given this weblog’s vested interest in horses, I was very happy to see that Emma does riding too, see her website (more songs !).

Emma Shapplin and her horse (Source: her website)

Emma Shapplin and her horse (Source: her website)

It remains amazing what a long dress does for an apparently not too tall artist. On my funeral the ladies are thus invited to wear long dresses too, though those might be out of fashion by then, depending upon who gets Europe.

Emma Shapplin on Macadam Flower Tour (Source: her website and wikimedia commons)

Emma Shapplin on Macadam Flower Tour (Source: her website and wikimedia commons)

February 2013 already gave a weblog entry Cause and Cure of the Crisis and November 2013 a YouTube video – though with a rather slow speed of presentation.

Now in September 2014 there is a short paper (MPRA  58592) with the same title. The paper gives a review of the books DRGTPE and CSBH that are at the core of this weblog – apart for our admiration for Art Buchwald and attention to the education of mathematics.

This may be occasion to pay a small tribute to John Maynard Keynes (1883-1946) and Jan Tinbergen (1903-1994). The analysis on the cause and cure of the crisis is based upon their work, and thus the world can only cure the crisis by properly reading up on Keynes and Tinbergen as well. It requires an understanding not only on economic theory but also econometric methods, with a role for mathematics.

There is another storyline that links up to mathematics education.

Tinbergen studied physics and wrote his thesis with Paul Ehrenfest (1880–1933). As a student he walked in Leiden, saw the poverty, decided to study economics, and doing so he created econometrics.

Ehrenfest’s wife Tatyana Afanasyeva (Kiev, 1876 – Leiden, 1964) wrote on math education too. Her work was hotly debated in small circles. One of the discussants was Hans Freudenthal (1905-1990), another German immigrant to Holland. Freudenthal became the promotor of Pierre van Hiele (1909-2010), which makes the circle round, see this entry on this weblog.

Paul Ehrenfest’s students, Leiden 1924. Left to right: Gerhard Heinrich Dieke, Samuel Abraham Goudsmit, Jan Tinbergen, Paul Ehrenfest, Ralph Kronig, and Enrico Fermi. (Source: Wikimedia commons)

Both President Obama of the USA and President Putin of the Russian Federation have somewhat illogical positions. Obama repeats the ritual article 5 “An attack on one is an attack on all” but the Ukraine is not a fraction of NATO. So what is the USA going to do about the Ukraine ? Putin holds that Russia defends all Russians everywhere but claims that Russia is not involved with the combatants in the Ukraine. His proposed 7 point plan contains a buffer zone so that he creates fractions in a country on the other side of the border. Overall, we see the fractional division of the Ukraine starting, as already predicted in an earlier entry in this weblog.

What is it with fractions, that Presidents find so hard, and what they apparently didn’t master in elementary school, like so many other pupils ? There are two positions on this. The first position is that mathematics teachers are right and that kids must learn fractions, with candy or torture, whatever works best. The second position is that kids are right and that fractions may as well be abolished as both useless and an infringement of the Universal Declaration of Human Rights (article 1). Let us see who is right.

An abolition of fractions

Could we get rid of fractions ? We can replace 1 / a or one-per-a by using the exponent of -1, giving a‾¹ that can be pronounced as per-a.  In the earlier weblog entry on subtraction we found the Harremoës operator H = -1. The clearest notation is aH = 1 / a. Before we introduce the negative numbers we might consider to introduce the new notation for fractions. The trick is that we do not say that. We just introduce kids to the operator with the following algebraic properties:

0H =  undefined

a aH =  aH a =  1

( aH ) H = a

Getting rid of fractions in this manner is not my idea, but it was considered by Pierre van Hiele (1909-2010), a teacher of mathematics and a great analyst on didactics, in his book Begrip en Inzicht (1973:196-204), thus more than 40 years ago. His discussion may perhaps also be found in English in Structure and Insight (1986). Note that aH = 1 / a already had been considered before certainly in axiomatics, but the Van Hiele step was to consider it for didactics at elementary school.

From the above we can deduce some other properties.

Theorem 1:

(a b) H = aH bH

Proof. Take x = a b. From xH x =  1 we get  (a b)H (a b) =  1. Multiply both sides with aH bH, giving (a b)H (a b) aH bHaH bH, giving the desired. Q.E.D.

Theorem 2:

HH = H

Proof: From addition and subtraction we already know that H H = 1. Take a a H = 1, substitute a = H, get H HH = 1, multiply both sides with H, get H H HH = H, and thus HH = H. Q.E.D.

It remains to be tested empirically whether kids can follow such proofs. But they ought to be able to do the following.


The expression 10 * 5H or ten per five can be simplified into 10 * 5H = 2 * 5 * 5H  = 2 or two each.

Equivalent fractions

Observing that 6 / 12 is actually 1 / 2 becomes 6 * 12H = 6 * (2 * 6)H = 6 * 2H * 6H = 2H. Alternatively all integers are factorised into the primes first. Note that equivalent fractions are part of the methods of simplification.


a bH * c d H  = (a c) (b d ) H

Comparing fractions

Determining whether a bH  > c dH or conversely: this reduces by multiplication by b d, giving the equivalent question whether a d > c b or conversely.


That (a / b = c)  ⇔  (a / c = b) may be shown in this manner:

a bH  = c

a bH  (b cH) = c  (b cH)

a cH  = b  


Van Hiele’s main worry was that we can calculate 2 / 7 + 3 / 5 = 31 / 35 but without much clarity what we have achieved. Okay, the sum remains smaller than 1, but what else ? Translating to percentages 2 / 7 ≈ 28.5714% and 3 / 5 = 60%, so the sum ≈ 88.5714%, is more informative, certainly for pupils at elementary school. This however requires a new convention that says that 0.6 is an exact number and not an approximate decimal, see Conquest of the Plane (2011). The argument would be that first calculating 31 / 35 and then transferring to decimals would give greater accuracy for the end result. On the other hand it is also informative to see the decimal constituants, e.g. observe where the greatest contribution comes from.

Another argument is that 2 / 7 + 3 / 5 = 31 / 35 would provide practice for algebra. But why practice a particular format if it is unhandy ? The weighted sum can also be written in terms of multiplication. Compare these formats, and check what is less cluttered:

a / b + c / d = (a / b + c / d) (b d) / (b d) = (a d + c b) / (b d)

a bH + c d H  = (a bH + c d H) (b d) (b d) H = (a d + c b) (b d) H


In this case kids would have to see that H can occur at two levels, like any other symbol.

a bH + H c d H  = (a bH + H c d H) (b d) (b d) H = (a d + H c b) (b d) H

Mixed numbers

A number like two-and-a-half should not be written as two-times-a-half or 2 1/2. Elegance with Substance (2009) already considers to leave it at 2 + 1/2. Now we get 2 + 2H .


Part of division we already saw in simplification. The major stumbling block is division by another fraction. Compare:

a / b / {c / d} = (a / b)(d / c) / { (c / d) (d / c) } = (a / b)(d / c)  / { 1 } = (a d) / (b c)

a bH * (c d H)H =   = a bH  * c H d = (a d) (b c ) H

Supposedly, kids get to understand this by e.g. dividing 1/2 by 1/10 so that they can observe that there are 5 pieces of 10H = 1/10 that go into 2H = 1/2. Once the inversion has been established as a rule, it becomes a mere algorithm that can also be applied to arbitrary numbers like 34H (127H)H = 1/34 / (1/127). The statement “divide per-two by per-10” becomes more general: divide by per-a is multiply by a.

Dynamic division

A crucial contribution of Elegance with Substance (2009:27) and Conquest of the Plane (2011:57) is the notion of dynamic division, that allows an algebraic redefinition of calculus.

With y xH = y / x as normal static division then dynamic division y xD = y // x becomes::

y xD ≡ { y xH, unless x is a variable and then: assume x ≠ 0, simplify the expression y xH, declare the result valid also for the domain extension x = 0 }.

A trick might be to redefine y / x as dynamic division. It would be somewhat inconsistent however to train on xH and then switch back to the y / x format that has not been trained upon. On the other hand, some training on the division slash and bar is useful since it are formats that occur.

Van Hiele 1973

Van Hiele in 1973 includes a discussion of an axiomatic development of addition and subtraction and an axiomatic development of multiplication and division. This means that kids would be introduced to group theory. This axiomatic development for arithmetic is much easier to do than for geometry. Since mathematics is targeted at “definition, theorem, proof” it makes sense to have kids grow aware of the logical structure. He suggested this for junior highschool rather than elementary school, however. It is indeed likely that many kids at that age are already open to such an insight in the structure of arithmetic. This does not mean a training in axiomatics but merely a discussion to kindle the awareness, which would already be a great step forwards.

His 1973 conclusions are:

  1. In the abolition of fractions 1/a a part of mathematics is abolished that contains a technique that stands on its own.
  2. One will express theorems more often in the form of multiplication rather than in the form of division, which will increase exactness. (See the problem of division by zero.)
  3. Group theory becomes a more central notion.
  4. In determining derivatives and integrals, it no longer becomes necessary to transform fractions by means of powers with negative exponents. (They are already there.)
  1. Teachers will have to break with a tradition.
  2. It will take a while before people in practice write 3 4H instead of 3 / 4.
  3. Proponents will have to face up to people who don’t like change.
  4. We haven’t studied yet the consequences for the whole of mathematics (education).

His closing statement: “We do not need to adopt the new notation overnight. It seems to me very useful however to consider the abolition of the algorithms involving fractions.”


Given the widespread use of 1 / a, we cannot avoid explaining that aH = 1 / a. The fraction bar is obviously a good tool for simplication too, check 6 * (2 * 6)H .

Similarly, issues of continuity and limits x →1 for expressions like (1 – )  (1 + x) H would benefit from a bar format too. This would also hold alternatively for (1 – ) (1 + x) D.

But, awareness of this, and the ability to transform, is something else than training in the same format. If training is done in algorithms in terms of aH then this becomes the engine, and the fraction slash and bar merely become input and output formats that are of no significance for the actual algebraic competence.

Hence it indeed seems that fractions as we know them can be abolished without the loss of mathematical insight and competence.

Europe tends to be divided between North and South by Rhine, Alps and Danube. There is also the cultural divide between East and West by the historical split of the Roman Empire. Northern Europe tends to be Protestant, Southern Europe Roman-Catholic and in the East we see the Orthodox Church of Constantinople.

The Dutch minister of Foreign Affairs and now candidate EU Commissioner Frans Timmermans (1961) speaks about troubles in the Ukraine at the “European border“, but he means the EU border, since the continent of Europe extends beyond Moscow. There is a price when one doesn’t study some history.

My warning alert on Frans Timmermans consists of the following points.

EU federalist

He is a EU federalist. Given the differences in Europe it is rather silly to be such a federalist, see this mind map for a better perspective. But Timmermans was member of the 2003 EU Convention to create a EU Constitution, wanting to abolish the sovereignty of the Member States. In the Dutch referendum he lobbied for Yes but fortunately the majority said No. He has been uttering words of understanding afterwards but we better be cautious given his background as a diplomat.

Blind to Russian revanchism

He did not warn us for the last 23 years about Russian revanchism. See my text on the Repeat of Versailles. Timmermans had an early training on Russia and in Russian. When in the army in 1986 Timmermans was trained to interrogate simulated Russian captives, and later worked at the Embassy in Moscow in 1990-1993. His command in Russian was remarkably useful in last year’s diplomacy. But why not warn us over the last 23 years ? In a speech in 2008, Timmermans said about Putin:

“For all his faults, he has brought the necessary stability that will allow Russia to develop into a democracy based on giving people the chance to work for their own prosperity.”

Playing with dynamite on Maidan Square

He was at Maidan Square increasing that revanchism. In this Dutch TV broadcast of December 2013 he visited the Maidan Square opposition to Janukovich, claiming that he was impartial, but the reporter indicates that his visit of course was interpreted as a sign of support. In his September 2014 lecture he is aware of the threat: “The fear of Putin is not that protesters wave blue flags with yellow stars on Maidan Square, the fear of Putin is that they wave those blue flags with yellow stars on the Kremlin Red Square.” So explain: why provoke revanchism ?

Double standards on MH17

His MH17 diplomatic success should not distract us. Timmermans’s major diplomatic success is his performance in the EU in July and in the UN on the 2014 MH17 disaster, in which he succeeded in getting the world to stop and consider the loss of 298 lives. He must be complimented for this, and for his soothing role in Dutch society. This success as a diplomat should not be confused with competence as a policy maker.

But, he does not take responsibility. There are also the 2593 local civilian deaths due to the conflict, see the UN estimate for April to August. Timmermans might have explained that almost 2900 deaths were partly his own responsibility for not warning about Russian revanchism since 1991 and stimulating it in 2013 on Maidan.

Civilian deaths in the Ukraine, the conflict vs MH17

Civilian deaths in the Ukraine, the conflict vs MH17

Blind to the energy trap, blind on sanctions

In that 2008 speech, on energy:

“Another widespread belief, which I disagree with, is the notion that since Russia is a provider of energy and we are its customers, dependency only goes one way. We depend on their energy, and therefore they call the shots. This is simply untrue. Look at the facts. Yes, it is true that they provide the energy; yes, it is true that we are the customers. Yet given the nature of their energy sector and the nature of the energy they provide, customers like the European Union can dictate a lot of the behaviour of the supplier country.”

Now in his September 2 2014 lecture (in Dutch) he simply states that the EU has become too dependent upon Russian energy. Instead of acknowledging that this has been also his own responsibility, for having been so dumb and not seeing the problem of revanchism and dependence.

His answer to the Ukrainean conflict is sanctions for Russia, without explaining that this runs the risk of stimulating revanchism. He now hopes to get natural gas from Iran, when the sanctions there are lifted, but does not mention that Russia would be needed to solve the problems in Iran.

Under the lure of heroism and fighting

His closing statement on September 2 that the borders of Europe are there ‘where there is fighting about them’, sounds like the frustrated child that starts thrashing about.

Deaf to criticism

He apparently neglects crucial criticism. Karel van Wolferen, renowned for his analysis on Japan, wrote on August 15 a remarkable criticism of the US neo-conservatives who meddle with world peace: The Ukraine, Corrupted Journalism, and the Atlanticist Faith (Dutch text here). It is difficult to judge on various points but one would assume that the Dutch minister of Foreign Affairs would have had such sources before and would have a clear reply by now: but we find none of this. Instead, Timmermans September 2 lecture claims that the extension of NATO to the East brings stability, instead of showing some understanding that it increases Russian revanchism. Timmermans also presents the George W. Bush and Tony Blair lies, on WMD as the excuse for the invasion of Iraq, as mere incidents. It is actually a quite confused lecture, also with a ritual calling for “realism” but then criticizing Russia for supporting Assad.

Little understanding of economics and its importance

He has little understanding of economics. Timmermans studied languages and EU law and mostly worked in diplomacy. Apparently he has not extended his studies on the key issues that have to do with economics (in a setting of history, culture, world politics). Beware of politicians who think that they do not need to study economics. Yes, he says that much in diplomacy is guided by economics, but that does not mean that he draws the conclusion that he must study it. It only means that he continues doing the same as before but now calls it economics.

He takes a position that Holland originally preferred for Jeroen Dijsselbloem. This is my weakest objection. I just mention it for completeness. The selection of Timmermans might be presented as a success for Holland and the EU, certainly by himself, but it actually means a defeat. There has been some discussion about Dijsselbloem’s remark on Juncker’s drinking. This strange discussion raises eyebrows. The best way for Juncker to show the contrary is to agree to stop drinking when in office and accept Dijsselbloem rather than Timmermans. NB. As economists argue for a bit less austerity in the present economic stagnation, this better be argued by Dijsselbloem rather than Juncker  & Timmermans.

A minister in an undemocratic coalition government

He is a member of an undemocratic coalition government. In the 2012 elections, the free market conservative party VVD and social democratic party PvdA strongly opposed each other. This attracted voters who wished to prevent that the other party would be strong enough to form a government. VVD and PvdA managed to jointly collect more than 50% of the seats, and actually formed a joint coalition government, in betrayal of the earlier claims of ‘vote for us so that those others will be blocked’ (no actual quote). It is still somewhat a minority government since they lack seats in the Senate. The betrayal and the political mess make the present Dutch government quite unpopular. The VVD-PvdA coalition now has 45 seats in a Parliament of 150 seats (recent poll). Timmermans joined in that voter betrayal, though he now gained much popularity because of his performance on MH17.


FransTimmermans (source: EU put into public domain)

PM. Potentially a victim of revanchism himself

The text above puts much emphasis on Russian revanchism. There is also a source of revanchism in Dutch politics. This weblog reported on the cultural divisions in Holland before, and indicated the inferiority complex and revanchism from the Southern Catholic provinces Brabant and Limburg that had been under Northern Protestant rule. See the entry on the Dutch Taliban, and Geert Wilders from Limburg.

Frans Timmermans comes from a Northern country but is actually from the province of Limburg from below the Rhine too. In an interview, Timmermans says “to miss Wilders as a buddy” (VN December 27 2013), meaning that he disagrees with him politically e.g. on Islamistic Terrorism or the Polish Hotline, but can appreciate him “personally as a very nice guy”.

The latter doesn’t mean that Timmermans himself suffers from an inferiority complex and revanchism or would be at risk of becoming a Dutch Taliban too. There is no need to delve into these deeper psychological questions since the arguments above on his general failure as a policy maker are sufficient to advise to block his appointment as a EU commissioner.

Jeroen Dijsselbloem (1966) isn’t perfect either, of course, see here. He also partook in that voter betrayal, and comes from the other Southern Catholic province of Brabant. His only advantage is having little responsibility w.r.t. policy w.r.t. Russia.

To: Professor I. Daubechies
From: Thomas Cool / Thomas Colignatus
Subject: For IMU / ICMI: Integrity of science in Dutch research in didactics of mathematics
Cc: secretary of the IMU, president of KWG, professor Andre Ran

To the president of the International Mathematical Union (IMU),
that has the International Commission on Mathematical Instruction (ICMI)

Dear professor Daubechies,

My email of July 16 can be updated integrally as follows, and I will put this present email on my weblog.

Let me invite you to read these two weblinks:

Let me invite you to also read this paper: “Pierre van Hiele and David Tall: Getting the facts right” (version 2, 2014-08-30) at

Let me invite you to keep the matter on your desk with priority, involve others in IMU / ICMI who could advise you on this, and aim at board decisions that result into proper resolution.

Since this email concerns research in didactics, your tendency would be to forward it to ICMI. My suggestion is not to give them total freedom but set up an overall IMU committee to monitor the process within ICMI on this. In itself it might be proper to hand the issue to ICMI, since when they succeed in resolving the issue, then it would meet with greater acceptance in their own circles. On the other hand, there will be a tendency to reject criticism. Hence my suggestion to keep the issue on your desk as well.

One of the problems is that ICMI has a “Hans Freudenthal Award / Medal“, which indicates that ICMI has not been able to detect the fraudulent nature of Freudenthal’s “research” and appropriation of ideas of Pierre and Dieke van Hiele. A related problem is that the Dutch representative to ICMI might not have transferred my earlier message on didactics in general.

Since your background is Belgian, I presume some knowledge of Dutch, and then let me also directly include the link to my letter to KNAW-LOWI, which is the Integrity of Research department of the Dutch Royal Academy of Sciences:

I imagine that IMU might not have the resources available at KNAW-LOWI. My suggestion is that IMU supports my suggestion to KNAW-LOWI to look into this, even though they have already declined my original suggestion. In that case I would hope that there is international monitoring of the investigation at LOWI too, since they might be less critical on what went wrong in Holland. There are some issues here, some of which seem quite local but that still would greatly benefit from international monitoring: (1) the habit of abstract thinking mathematicians and such teachers to forget about the real world and empirical methods, (2) Hans Freudenthal and his “work” (much in Dutch), (3) the renaming of the ICMI Award, say to a “Piaget & Van Hieles Award / Medal”, (4) the abolition of the Dutch “Freudenthal Head in the Clouds Realistic Mathematics Institute” (FI = FHCRMI) here in Holland. It would seem that the last would not be in the ballpark of IMU but it is important to be aware that the institutional drive of that institute is to defend Freudenthal’s “legacy”, and thus to oppose criticism on the other points too, at the detriment of IMU / ICMI. It is better to be straightforward on the logic from the outset, and have international monitoring.

I alerted the Presidents of MAA (Bob Devaney) and AMS (David Vogan) and the director of the US Institute of Education Sciences (IES, John Easton) on the two weblog links, but not on my recent paper on Van Hiele and Tall (yet). After putting this letter on my weblog, I will alert the board of NCTM (Diane Briars) to this. I now copy to the IMU secretary and the chair of the Dutch KWG, now professor Geurt Jongbloed but formerly Andre Ran. In my perception KWG has been seriously failing on this issue but if IMU would indicate that there is an issue indeed then they might perhaps be willing to help out, with some international monitoring.

My position in all of this is quite limited, and mainly described in my books “Elegance with Substance” (2009) and “Conquest of the Plane” (2011) and the Dutch “Een kind wil aardige en geen gemene getallen” (2012), see my website, where the PDFs of the first two can be found. I do not claim particular expertise on Freudenthal’s “work” but what I have read didn’t appear so practical, except for what he took from Pierre van Hiele. I am amazed both by RME’s adoption for education and the lack of interest to repeal it now that everyone can see that it doesn’t really give results, except for the part taken from Van Hiele. My main point is no 1 above: the habit of abstract thinking mathematicians and such teachers to forget about the real world and empirical methods. My suggestion is that we need “engineers in education” rather than such mathematicians, and that education requires the “medical school” model in which education and its research are attuned, see this other link:

Sincerely yours,

Thomas Cool / Thomas Colignatus
Econometrician (Groningen 1982) and teacher of mathematics (Leiden 2008)
Scheveningen, Holland


PM. Readers of this email may also be interested in: Elizabeth Green: Why Do Americans Stink at Math?, NY Times July 23 2014