Anatomy of Holland

The Dutch research subsidy allocator NWO had its annual Spinoza Prize event, in which science meets journalism. About this annual event I reported critically in 2012.

The event this year carried the theme of “The scientist as activist”. NWO had invited Alice Dreger as keynote speaker to explain about the advantages and pitfalls of mixing research in the morning with social activism in the afternoon.

Thus, all of a sudden we have sex change on the table. Also, when there is controversy, then one is obliged to look into details. Thus I spent Friday morning listening to Dreger and the discussion, and was forced on Saturday “the morning after” to fact-check it all.

NWO Bessensap in Amsterdam

The invitation at the NWO website was:

“On Friday 10 June 2016 the Netherlands Organisation for Scientific Research (NWO) will organise the sixteenth edition of Bessensap together with the Dutch Association of Science Journalists (VWN). The event will take place at the Rode Hoed in Amsterdam. Bessensap has been revamped this year to be even more in keeping with current developments, both in science and scientific communication.

The goal of Bessensap is and remains to encourage interaction between researchers, science and mainstream journalists, and other communication professionals. The former title ‘science meets the press’ is being replaced by an annual current theme, however. This year it is ‘the scientist as activist’: professors protesting against cut-price meat and climate scientists warning of the present and future disastrous effects of climate change. What role should scientists play in the public debate? And how should science journalism approach activist researchers?

Keynote speaker this year is the American activist researcher Alice Dreger []. As a historian, she studies the history of science and medicine. At Bessensap, Dreger will discuss what happens when science (the search for truth) and activism (the search for justice) collide. After her keynote address, Dreger will continue her discussion with visitors during a debate on this theme.” (NWO website)

Dreger informed us about her personal experience. She had participated in a social controversy, defending a fellow scientist J. Michael Bailey against harrassment, and had become a target of harrassment herself too. Her own university also hit her work with censorship, after which she eventually resigned as professor of Clinical Medical Humanities and Bioethics at Northwestern. She relates her experiences in the bookGalileo’s Middle Finger: Heretics, Activists, and the Search for Justice in Science“.

Dutch journalist Asha ten Broeke was in the audience and praised Dreger’s book, as a thriller that should become a movie. Google shows a twitter exchange between Ten Broeke and Dreger, and an earlier report in a newspaper, Volkskrant June 4, that opens with the issue of prenatal dexamethasone.

Alice Dreger, 2016-06-10, NWO, "The scientist as an activist"

Alice Dreger about “The scientist as activist”

Developing a hypothesis on the controversy

I only want to develop a hypothesis about what is happening. I have spent a major part of the mornings of Friday and Saturday on this issue, with the only objective to have a fair grasp of the situation. It will not be possible to look into all details, which would require e.g. buying and reading Dreger’s book and all commentary. Dreger observes that books are often not read and still rejected, but I don’t intend to read a full book nor to reject or accept it. Once I have my hypothesis, then it is a later option to test it, but I doubt whether I will ever have time to do so.

The situation is complicated by that Dreger may be right on many aspects, like on the matter of prenatal dexamethasone. Dreger seems also to be right in the protest against censorship at Northwestern, but one can doubt whether resignation was the proper response.

Eliminating noise, it appears that the core issue is relatively simple. This is whether Michael Bailey has a sound scientific approach or only a journalistic report on the “Clarke Institute theory of gender crossing”.

Let me invite you to read these two texts, and for readers of Dutch also a third:

Bailey apparently states that there are only two types of crossing and when McCloskey states that her personal experience doesn’t fit those two categories, then Bailey must either call her a liar or revise his theory. Why not respect personal testimony ? There is no need to concentrate on McCloskey, for there are more people for empirical testing. Thus there is no need for controversy but need for more research, and the research question is already clear too.

We find light in the tunnel by the following approach: (1) Common sense. (2) McCloskey is a brilliant economist, and I am an economist who appreciates her work very much. Her statement is to the point. For example, McCloskey is a world authority on ethical theory, and when she observes that Dreger is shallow on ethics, while Dreger’s chair is on bioethics, then this is very relevant observation. McCloskey agrees with Dreger that Andrea James is an activist and no scientist, and this is actually easy to check.

The Huffington Post article has a curious treatment of McCloskey’s position. Using your thumb to invent that two critics of Dreger “talked many times” and still disagree, and implying that both then are wrong, is bad logic.

“Well, which is it? “Proven wrong” by “almost everyone” (McCloskey) or “unfalsifiable” and without “predictive capabilities” and “untestable” (Conway)? McCloskey and Conway must have talked many times. This discrepancy in how they attacked Blanchard’s theory shows how little they cared about its truth — or that they knew it was true.” (Seth Robert)

Robert also argues: “Deidre McCloskey and Lynn Conway are both powerful persons.” This is a misrepresentation. McCloskey has no power and can only use words. People who read her work tend not to take things for granted. I have no information about Conway.

As a scientist, McCloskey is Dreger’s best ally, and it is curious when these two minds don’t meet. When McCloskey invited Dreger to send a draft text so that she could comment to prevent later confusion, then this was proper science.

A background check on potential sources of bias

Bailey’s website informs us that he originally had a BA in mathematics, and after teaching secondary school for a couple of years went to graduate school in clinical psychology. Mathematicians are trained for abstraction, and it is not impossible that Bailey’s attitude still is rather abstract and theoretical rather than focused on empirical observation, even though he has been an intern in psychiatry. An empirical scientist would be much interested in the evidence that causes a rejection of a theory.

Dreger earned her PhD in History and Philosophy of Science. The topic of the PhD study apparently was on the history of “Hermaphrodites and the Medical Invention of Sex“. This background suggests that she has read about methods of science, but has no training by actually doing so. Dreger’s historical research apparently has alerted her to misconceptions by so-called scientists in the past, but dealing with current science today is a different issue. My impression is that Dreger has misread McCloskey’s accurate criticism of Bailey’s approach, and did not properly distinguish this criticism from social activists.

Adding to confusion and reducing it again

You should read the two or three texts above but let me mention that there are more sources, that contribute to information overload. For example there is Julia Serano, who has this criticism. Or there are withdrawn nominations for lammies. Etcetera, etcetera.

The bottom line is: it would be up to professor Bailey to answer to his critics.

It has been kind of Dreger to want to protect a fellow scientist from abuse by social activists. It is better to avoid the risk of becoming the next target. Best is to provide for a climate in the scientific world itself, so that Bailey indeed provides such answers. For example, Dreger might have translated McCloskey’s criticism into words such that Bailey would have understood better that this is criticism that needs a reply. One should not think that management of controversy is simple.

Insert of Tuesday June 14 2016

Though I really didn’t want to spend more time on this, I now located Dreger’s article at PubMed 2008, in which she clarifies that Bailey’s book, published at a scientific publisher, was not purely science but also intended to express personal opinions and speculations.

“From the start, Bailey intended this book to be very different from anything he had published before. Whereas most of his previous work consisted of peer-reviewed articles for scientific journals, this book would be a popularization—based on certain sexological findings of his lab and others, but replete with vivid stories of people the author had met, stories provided to put a human face on those findings. Along with accessible, abbreviated accounts of key scientific studies, the book would also feature the author’s hunches, speculations, and personal opinions. It would include suggestions for further reading, but no other documentation (Bailey, 2006b). Thus, TMWWBQ was never envisioned as a work of science in any traditional sense; instead, Bailey viewed the book as his chance to expose to the masses what he saw as the often politically incorrect truth about “feminine males”: boys diagnosable with “gender identity disorder” (GID); surgically feminized, genetic male children; male homosexuals; drag queens; heterosexual male crossdressers; and MTF transsexuals. Bailey also saw the book as an opportunity to make some money; when he was ready to sell the book, he engaged an agent, Skip Barker, who negotiated in November 2000 a contract and an advance from Joseph Henry Press (p.e.c., Bailey to Dreger, October 2, 2006). Joseph Henry Press is “an imprint of the National Academies Press […] created with the goal of making books on science, technology, and health more widely available to professionals and the public” (Bailey, 2003, copyright page).” (Dreger’s article at PubMed 2008)

Thus, Bailey was an activist himself, and it looks like Dreger may have defended not a fellow scientist but an activist.

Obviously, there is no objection to personal opinions and speculations, and these actually are an important source of information, as these for example might guide future research. However, the issue is to clearly distinguish those from corroborated findings. For example, I use a science name Colignatus. Apparently Bailey nor Dreger nor the editors of the Joseph Henry Press nor the editors of the journal that published Dreger’s article have been careful enough. Both Bailey’s book and Dreger’s article better be retracted. The abstract of Dreger’s article states:

“Dissatisfied with the option of merely criticizing the book, a small number of transwomen (particularly Lynn Conway, Andrea James, and Deirdre McCloskey) worked to try to ruin Bailey.” (In the abstract of Dreger’s article at PubMed 2008)

This fails as a description of what actually happened. Reading McCloskey’s statement on Dreger, referred to above, shows her position on content. This shouldn’t be misrepresented as being targeted deliberately at ruin. Perhaps others have stated such explicitly but McCloskey (p7-8) even explicitly denies this. Thus retract.

Dreger is right that the case causes some questions. When Bailey’s book is published at a science publisher, then McCloskey is right that research may be needed to have been submitted to the Institutional Review Board (IRB). If the book is “science journalism”, then this IRB is not needed, but then it shouldn’t be at that publisher. One cannot use one argument for the other issue. Dreger may also be right that “oral history” is excluded from IRB rules, but if Bailey uses such reports to put a face on statistical results, then he himself creates a mix that still falls under IRB (because one aspect is). Again you cannot use one argument for the other issue. Also Dreger should ask Bailey to retract and restate his views in a manner that avoids confusion.


Given this hypothesis, some tentative conclusions are:

  • The organisers at NWO should have had the same problem as I had, in needing to understand the situation. They should have been able to reason as above. They didn’t do so. They gave Dreger the floor, as if there all of this was entirely new and nobody had time to look into this. This is misleading to the audience, and generates a wider circle of confusion. It is costly to the audience, like I lost time in recovering what they should have done. The better alternative would have been to present the hypothesis as above, and allow both Dreger and others to comment, so that there would have been an informed discussion, leading to more information and reduced confusion.
  • The organisers at NWO left it there, and after Dreger had reported on the censorship, there was no statement by the board of NWO that they were appalled, and would investigate and potentially write a letter of protest to Northwestern. NWO has a department of science communication and they found it useful to give Dreger the floor for their own reasons of selling NWO, but, apparently, there was no commitment to really defend science against censorship.
  • This framing doesn’t help Dreger much. The newsmedia reported on the Spinoza Prize winners but not on the censorship of science at Northwestern.
  • Journalist Asha ten Broeke already reported on Dreger but should look into above hypothesis, in order to prevent misleading people.

After this discussion on controversy and censorship in the NWO lecture hall, various people in the audience went out onto the street, not to protest with banners, but to enjoy the good weather and the view of Amsterdam’s canals. Dutch people aren’t easily shocked about censorship of science.


It is awkward to state the obvious, but let me do it anyway.

  • This weblog advises to boycott Holland till the censorship of science since 1990 by the directorate of the Dutch Central Planning Bureau (CPB) has been lifted (see the About page)
  • the censored analysis concerns unemployment and poverty
  • resolution of unemployment and poverty is crucial for resolution of world hunger (unless you want to distribute food for free, which isn’t likely to happen)
  • when I was a highschool student in 1972 and wanted to resolve world hunger, I decided that I better study econometrics rather than archeology
  • when I studied econometrics I decided that unemployment was the key topic, since this affects the basic needs. At that time I also wrote an article (in Dutch) that the New International Economic Order (NIEO) was no basic needs programme. Jan Tinbergen read the article and responded on the phone that I very likely was right on this. There is some rumour in Holland that Tinbergen was an impractical dreamer who tragically pursued unattainables, but see my In Memoriam (in Dutch) for praise of his wisdom and common sense.

Jan_Tinbergen_1982-smallThus this weblog is of key importance for world hunger too. It is almost impossible to make a dent into world hunger when you don’t get the economies up and running, with systems of social welfare that are supportive of full employment.

Jean Ziegler has called attention to the issue in clear words, though he lacks the economic theory that has been hit by censorship by the Dutch CPB directorate. See this article “We let them starve” in The Guardian. I haven’t read his 2013 book but I am convinced that it is depressing reading, especially when you know that the solution is at hand, and blocked by censorship. It is depressing too, to read this report on Ziegler’s flirt with Gadaffi (and then check out the pictures of Gadaffi’s visit to Paris and president Sarkozy in 2007).

zieglerMartin Caparros also takes issue at world hunger. See this article in the New York Times. See this interview at the University of Barcelona. Remarkably, there appears to be no English edition of his book yet, and the German edition of his book costs close to $100. Readers of German may also check out this article in Die Zeit.


There are various organisations worldwide that try to deal with world hunger. However, their approach is bottom up in the Third World, and not targetted at protecting science in the Western World and debunking fallacies by Western governments. They are fighting symptoms and not tackling the causes. Admittedly, someone who is hungry is helped immediately with food, and thus it is difficult to be critical of micro management. However, the leaderships of such organisations should be aware where the real solution would come from.

It is the same in Holland. The Dutch chapter of The Hunger Project interviewed Martin Caparros (in English). Let me quote two questions and answers:

You argue that hunger is the consequence of a system. Capitalism is the culprit. At the same time you say that of all the major problems, hunger is easily fixed. It seems too simplistic: changing the system is not simple, is it?
“That’s a problem. Because what would it mean to solve hunger? Make sure people take in more calories each day? That is easily done. It requires some technical changes, but you can realize those if you invest enough money on for instance roads or agricultural innovations. But the point I am making is that hunger is a metaphor for poverty. You cannot solve hunger if you do not first solve the problem of poverty. And that requires an overhaul of our system.”

How do we do that?
“Well, who knows? Until the 80s and 90s people thought equal welfare and justice could be reached with socialism or communism. By now we know better. I think politics should help us change to a moral economy.”

(Quoted from an interview of Martin Caparros by Leontine Aarnoudse, OneWorld, 2016-02-19)

Morality would help but, but the track record of morality shows its limits. People will be willing to help out, but the economic process must support this. Thus, there is my economic analysis, that however has been censored since 1990 by the directorate of the Dutch CPB.

Obviously, when these Dutch organisations like The Hunger Project do not question the censorship of science by the directorate of the Dutch CPB, then they convey an image as if there would be freedom of thought in Holland, and that the problem indeed cannot be solved except by micro management and global morality. What can one do, to make these blind and deaf Dutch people grow aware of their blindness and deafness ?

I collaborated on a book in Dutch that discussed unemployment and poverty. When Holland has such difficulty to manage its own unemployment and poverty (with its level of education and technology and natural gas resources) then one should be modest about claims for the Third World, unless more can be said along the lines of this censored economic analysis. Not all is in this booklet yet, since there is this censorship. Economic scientists should look at DRGTPE. I did not yet collaborate on a book on world hunger. Is that the reason why the coin does not drop ?



The Hunger Project Nederland apparently was founded in 1980, and they “celebrated” the 35th anniversary in 2015. I find this difficult to square, for how can you celebrate continuation of something that should have ended in 1981 ? The official text reads that they celebrate the progress towards elimination of world hunger, with a new target for “in the next generation”, but this reads as an official excuse. The subject is a minefield, with this “celebration”, Ziegler & Gadaffi, and other such issues. I suppose that it is quite acceptable to have parties, for man is not only an animal but also a party animal, but please avoid the cognitive dissonance created here.



  • In October 2014 I explained that Edward Frenkel abused “love” with his book “Math & Love“. As a mathematician he has no training in the empirical science of mathematics education, and what he states about mathematics education is often delusional. The situation is rather typical of the arrogance that is so common among mathematicians. The attitude is “the best way to teach and learn mathematics is to do mathematics”, but this confuses the context of mathematics research with the context of education. See here for a recent comment on the USA Common Core for mathematics.
  • In November 2015, Dutch NRC Handelsblad science journalist Margriet van der Heijden discussed the book, labeled him a “glamour-nerd” and expressed doubts about his book as a “cocktail of superficial superlatives, incomprehensible math and touching memories of his youth”. Unfortunately, Van der Heijden did not explicitly mention the gap between mathematics research and education in mathematics.
  • In April 2016, Dutch NRC Handelsblad USA correspondent Diederik van Hoogstraten recycled the story, flew from Los Angeles to San Francisco and drank wine with Frenkel, resulting in this interview. The catchy title of the interview is “Math anxiety ? Don’t be afraid anymore !Apparently professor Frenkel has found the medicine that we have all been waiting for. The label “rockstar-mathematician” is used (in quotes), and while there is proper reference to the criticism by Margriet van der Heijden, Frenkel gets the last word to state the good intentions of his book.

“It has to go wrong only once. You must solve a problem in arithmetic in front of the class. You can’t do it. You are scolded, because we are focused on the result and the result was wrong. You feel dumb. A nightmare. (…) Then you are afraid for the rest of your life. Afraid to make an error and be “dumb”. This is a shame, for it is a wonderful subject. In this way we deny millions of people this knowledge, wisdom and beauty. (…) I want to find a way to the heart of all those people with youth trauma’s. It is okay, I say, you don’t have to be afraid.” (Edward Frenkel, NRC 2016-04-23, my translation)

It may well be that there are still many math teachers who abuse their students, but we must wonder whether Frenkel bases his view upon statistics or folklore. Normal teachers tend to ask up front only those students who are likely to get the result (e.g. have shown this already on paper). The normal discussion is on method and not merely on result. Thus Frenkel’s view on “math anxiety” is rather folklore than a result of research in current mathematics education. Subsequently, people with math anxiety will not read and be cured by a book that has so much mathematics, however much “love” you will put in the title. Both diagnosis and treatment are delusional.

Dutch is a language sink. Why was it considered useful to translate this delusional book from English into Dutch ? Would there really be readers who would grasp Frenkel’s math but not be able to read English ? Translators from English into Dutch have an easy job, and publishers can piggy-back upon international bestsellers. It is more difficult to translate from Dutch into English, and market this in the English reading world, but it would be more relevant to open up Holland to the world. Why did Van Hoogstraten want to interview Frenkel ? Perhaps the Dutch publisher of the Dutch translation sent him a copy of the book with Frenkel’s telephone number ? Alongside money laundering there is also delusional book laundering (that sells for cash too).

This is not without cost.

  • NRC Handelsblad has misinformed its readership twice now. Readers who have the idea that mathematics is inaccessible actually have seen this idea confirmed.
  • There is nothing in their reports on Frenkel that explicitly shows that mathematics is accessible to more people than commonly thought, albeit that this can be found elsewhere and not with Frenkel.
  • NRC Handelsblad has never reported on my books since 2009 on mathematics education. The newspaper likely finds mathematics sexy and mathematics education both boring and no science.

Holland is not an open minded country. Holland is a country where books are sold that have been translated into Dutch.

Edward Frenkel in 2010 (Source: wikimedia commons)

Edward Frenkel in 2010 (wikimedia commons)

My book Elegance with Substance (EWS) (2009, 2015) (pdf online) has the theme that mathematics education requires fundamental re-engineering. Mathematicians are trained to think abstractly and are not trained for the empirical science of didactics. When they meet real life students in class, mathematicians suffer from cognitive dissonance, and resolve this by sticking to traditional ways of teaching, which tradition has not been designed for optimal didactics. In this manner, mathematics education is in shambles for some 5000 years.

EWS documented this with a long list of examples and hence I should not be surprised anymore to find another example. However, I was very surprised to discover the following for the quadratic function. This function is so familiar for at least some 3000 years, and you would expect that mathematicians had optimized its teaching. However, be amazed as well.

A starting point for all approaches

The quadratic function is introduced in all cases by presenting the square of x. The formula is supported by text (explaining what the function does), table (first row for effect y, second row for cause x, namely allow for Δy / Δx), and graph. Write functions with square brackets.

f[x] = x2

Properties are:

  • The vertex or turning point can be found at the origin {0, 0}.
  • There is symmetry for left and right along the line x = 0 because f[x] = f[-x].
  • There are no outcomes f[x] < 0, unless by use of the complex plane with = i2 = -1.
  • Also f[x] and –f[x] mirror, but one would say that this requires a coefficient a = -1.
Continue re-engineered: a focus on understanding

Changing and moving (transforming and translating) the function gives the basic form.

f[x] = a (x h)2 + v

  • The vertex or turning point can be found at {h, v}.
  • Coefficient a stretches or squeezes, while a negative value flips or mirrors upside down. Making coefficient a negative turns a convex form into a concave form. (Seen from the origin, concave is hollow or h-shaped, and convex is bulging or b-shaped.)
  • The value h shifts the parabola horizontally. For example, x must have a higher value if some positive h is subtracted from it. If h is negative, then the graph moves leftwards.
  • The line x = h is also the mirror-axis for left and right.
  • The value v shifts the parabola vertically. If v is negative, then it shifts downwards.

A key question for a parabola is where it intersects with the horizontal axis. Even when we want to find the points of intersection with a line y = d, then this only means an adjustment to v’ = v d. Finding the solution to this quadratic equation is straightforward.

f[x] = a (x h)2 + v = 0

(x h)2 = – v / a

x1,2 = h ± √(- v / a)

It is easy to check that all solutions must have this symmetric form, since substitution back first eliminates h and then squares the remainder, and reduces to zero. This solution thus also gives the rule:

  • When v = 0 then there is a single solution, or it is touching the horizontal axis.
  • When – v / a > 0 then there are two solutions.
  • When – v / a < 0 then there is no intersection with the horizontal axis. A solution can be found in the complex plane however. There is no need to be squirmish about complex numbers because these would have been discussed before, when discussing the system of co-ordinates (see here).

These graphs show the solutions for f[x] = 1 (x – 0)2 + v, for values v = -2, 0, 2. The relevant intersection value is √2 ≈ 1.414…. The complex solution can be found by flipping the function, giving g[x] = -1 (x – 0)2 + 2, solve for the intersections, and circle these a quarter turn. Here x1,2 = ± i √2.


Given the (two) solution(s) x1,2 = h ± √(- v / a), let us write for ease or w, and observe that the function can be written in the factored form: f[x] = a (x – u)(x – w). The vertex or turning point lies in the middle, so that = (u + w) / 2. Substitution of x = h gives v =  – a (u – w)2 / 4.

The basic form can be expanded into the standard (polynomial) form.

f[x] = a (x h)2 + v

= a (x2 – 2 h x + h2) + v

= a x2 – 2 a h x + a h2 + v

f[x] = a x2 + b x + c in which b = – 2 a h and c = a h2 + v

Thus, conversely, whenever one meets the form f[x] = a x2 + b x + c then h and v can be solved as:

h = – b / (2 a)

v = c – a h2 = – (b2 – 4 a c) / (4 a)


  • After re-engineering the above, I knew what to look for, and found this video by MIT graduate Nancy (mathbff) who calls the basic form the “vertex form” but who still has it in 2nd place instead of 1st place. There is also this lesson plan at MARS that mentions the three forms, but their order is standard, factored, basic, and the latter is called “completed square form”. I would rather put basic first and express this in its name. The lesson is what you can directly recognise in each form, which is a fair question, but not the most relevant first question on the graph of the quadratic function.
  • The complex graph comes from Norton & Lotto 1984, reproduced by Francis Su et al. here. Su et al. don’t use the basic form whence it is difficult to see how to flip the function and why complex solutions have the real part h and the imaginary part √(- v / a). The complex solution is also mentioned by wikipedia here, but this doesn’t flip the graph and doesn’t explicitly make the quarter turn, so the solution remains mysterious.
The shamble tradition: starting from theory

Mathematicians have developed a theory of polynomials. The traditional approach in teaching the quadratic function is to treat it as a special case of such polynomials.

Thus students are presented with the polynomial format, called the standard form.

f[x] = a x2 + b x + c

The standard form is intransparant. Teaching thus proceeds by presenting tricks, only to recover what is already obvious for the basic form.

(1) Students are presented with the quadratic formula and must learn it by heart. This is the fail-safe approach for students without much interest in or understanding of mathematics.

x1,2 = (-b ± √D) / (2 a) with discriminant D = b2 – 4 a c.

The possible solutions are cataloged with D < 0, D = 0 and D > 0.

  • It is not clear where D comes from and what it means. (It is only a freak result of the polynomial form.)
  • The traditional approach takes so much time in general that there often hasn’t been time to explain about the complex plane, and thus it is often said that D < 0 has no solution rather than that it has a complex solution.

(2) More interested or advanced students can be shown where the quadratic formula comes from. This generates the ritual called derivation of the quadratic formula. There are a number of approaches (wikipedia), but, “surprisingly” the following approach may not be mentioned (not in wikipedia today), and the reason must be that the tradition has lost track of the basic form.

a x2 + b x + c = a (x h)2 + v

For x = 0: c = a h2 + v hence v = c – a h2

For x ≠ 0: a x2 + b x + c = a x2 – 2 a h x + a h2 + v

b x = – 2 a h x and hence h = – b / (2 a) and substitute this in v again

Subsequently resort to above disucssion, and find x1,2 = h ± √(- v / a)

Didactic conclusions

Didactic conclusions are:

  • The basic form is transparant, provides a clear path to the standard (polynomial) form, and also provides clarity for the return path from the standard form back to the basic form.
  • Starting with the standard form is convoluted. It starts from some distant theory about polynomials in general and creates clutter and mystery about solutions. This tradition has lost track of the basic form and thus also requires more intricate solution methods or reliance on memory for the “quadratic formula”.
  • Making math opaque for such simple issues puts a heavy burden on more intricate issues.
  • Making math opaque for such simple issues also causes a flight into alternative approaches, such as reliance on applications (“realistic mathematics education” (RME)). Interesting applications are here, but my impression is that students will study those applications with more interest once they have mastered the basic form first. The general format for teaching is: (a) psychologically prime notions with a basic example (here the square of x), (b) develop the theory, (c) apply the theory.

PM. Wikipedia is not a didactic environment but a portal. When you want to know what the “quadratic formula” is, then wikipedia presents it, and wikipedia doesn’t give a didactic presentation of the underlying issue. Wikipedia has other entries like on the quadratic equation, but following these links doesn’t generate a didactic exposition. Thus beware: mathematics in wikipedia is created by math students who copy their textbooks.

Examples: two English websites and a Dutch textbook for grade 9 (age 14-15)

A traditional presentation of the quadratic function that “completes the square” without giving the general form is here. Another website is here, and it gives the basic (“vertex”) form somewhere at the end.

A Dutch textbook for grade 9 at subtop-level (“Moderne wiskunde”, HAVO 3ab, together 400 pages, edition 8, 2005) includes the following approach to the quadratic function.

  • Ch 3 (some 25 pages): Transformation and translation of functions (linear, quadratic, hyperbolic, powers and roots). It makes sense to review the different functions. However, for the quadratic function only a and c are manipulated. Given above discussion, it would make more sense to discuss each function separately with its transformations and translations.
  • Ch 5 (some 25 pages): Factoring polynomials. This is a basic algebraic skill. It is enlightened in the textbook with graphs of rectangles and indeed a parabola. When the treatment of the parabola is as convoluted as it is now, then this order can be understood, for the solution of a quadratic equation can be found by factoring. A more didactic approach however would be to (a) discuss factors using rectangles, (b) discuss the parabola in the re-engineered fashion, and (c) only later practice also on the skill of factoring. The advantage of the re-engineered approach is that we can have text, formula, table and graph in a single review at a much earlier stage, which enhances understanding.
  • Ch 8 (some 30 pages): Quadratic formulas. The traditional f[x] = a x2 + b x + c with vertex and symmetry, quadratic formula, the use of D, graphical form, and solution of quadratic equations. In the re-engineered approach, this would be integrated in the earlier chapters 3 and 5.
  • Ch 9 (some 25 pages): Manipulating more functions: Addition and multiplication of graphs. Periodic formulas. This deepens earlier notions and provides more practice. This might be less needed in the re-engineered approach when issues are transparant.
  • Ch 11ab (some 50 pages): Graphs and equations. Intersection of graphs and finding solutions. However, finding the intersection of parabola a x2 + b x + c and line b’ x + c’ reduces to a x2 + b x + c = b’ x + c’ or solving a x2 + (b – b’) x + (c – c’) = 0, which is just solving for another parabola, which has already been discussed. This split chapter only practices earlier notions, which might be less needed when the presentation was transparent enough.

The conclusion is that this textbook provides key ingredients, but in less didactic format and order, such that the textbook resorts to a lot of practice to allow students to replace insight by routine. (Routine should not be called skill when insight is lacking.)


There is scope for re-engineering the didactics of quadratic functions into a much more transparant manner. The focus must be on what is essential to understand (at this level) and on starting from some abstract general theory (relevant for understanding issues at another level).

This re-engineered approach can likely already be used in elementary school. See the other book A child wants nice and no mean numbers (CWNN) (2015) (pdf online).

It remains to be tested whether the re-engineered approach indeed is as transparant as suggested here, and whether pupils would have a fast road to insight and skill and improved attitude. It always are the students themselves who show what works for them.

I am no expert on terrorism and wonder whether the supposed experts aren’t either.

Dutch historian and “expert on terrorism” Beatrice de Graaf gave a lecture on Dutch TV on March 11 (or see Utrecht University) about David Rapoport‘s four waves of terrorism (his original article).

Her main message was that people might find some comfort in the idea that waves die out. March 22 saw the bombs in Brussels.

This theory of four waves of terrorism appears to be rather silly. Below gives my common sense rejection.

De Graaf is not the only academic who regards the theory of the four waves as serious. The West is vulnerable to terrorism when its “experts on terrorism” are academics lost in theory. It is okay to sooth people not to worry too much, but intellectuals should present effective approaches rather than fairy tales.

The so-called “four waves”

Jeffrey Kaplan summarizes (and then proceeds in adding his own fifth wave) (while Dutch readers can check Edwin Ruis’s review of March 13):

“Rapoport’s theory, first published on the web before finally finding a home in a printed anthology, posited four distinct waves of modern terrorism (anarchist, nationalist, 1960s leftist, and the current religious wave). Each wave had a precipitating event, lasted about 40 years before receding, and, with some overlap, faded as another wave rose to take center stage. Most terrorist groups would gradually disappear, a few (the Irish Republican Army for example) proved more durable. Rapoport’s theory was elegant, simple, inclusive, and had a high degree of explanatory power. In short, it provides a good academic model.” (Kaplan 2008).

Jeffrey D. Simon holds (and wonders about a fifth wave too):

“David Rapoport’s “The Four Waves of Modern Terrorism” is one of the most important pieces ever written in the vast literature on terrorism (Rapoport 2004).  What Rapoport did in his classic study was take the complex phenomenon of terrorism and put it in a historical context that not only explained different periods of international terrorism, but also set forth theories and concepts that can be used to attempt to anticipate the future of terrorism.  That is no easy task.  There haven’t been many assessments and articles written about Rapoprt’s “Four Waves” theory, although this volume of papers initiates a discourse about his important thesis (See Thompson and Rasler, this volume).  Despite the numbers of scholars, policymakers, and others who have joined the field of terrorism studies after the 9/11 attacks, there does not appear to be a great deal of interest in the history of terrorism.  In today’s instant access and information-overload society, we are inundated with analyses of current affairs but pay scant attention to what we may learn from what has transpired in the past.” (J.D. Simon on the Lone Wolf, likely 2010)

I googled to find some criticism, but didn’t see much, though perhaps I didn’t google well. I noticed a critical text by Ericka Durgahee. I didn’t have time to look into this, and the following are my own common sense short remarks.

The anarchists 1880-1920

The dynasties of Hohenzollern, Romanov and Habsburg collapsed. Perhaps the anarchists didn’t really win because we don’t have anarchy now, but those anarchists were replaced by communists and fascists, and we ended up with two world wars, which isn’t quite “die out”.

Anti-colonialism 1920-1960

The anti-colonialists won. Winning isn’t quite “die out”.

Leftists 1960-1989

Leftism became impopular because of the Great Stagflation (unfavourable unemployment and inflation) and the collapse of the Berlin Wall. Young radicals were more motivated by Ronald Reagan and Margaret Thatcher.

In Germany, the police managed to isolate the Rote Armee Fraktion (RAF). In another article, Beatrice de Graaf explains how the Dutch radicals (Rode Jeugd, Krakersbeweging) lost their motivation by incompetence of the Dutch police. The Dutch police intended to adopt the tough German approach, but mismanaged this, and both radicals and the general population got the impression of an atmosphere of tolerance and dialogue. In that atmosphere, potential supporters saw no need for radicalisation, and radicals had the example of the dead-end street in Germany.

These events rather concern the transformation of European society after World War 2. There are pockets of terrorism, but there doesn’t seem much difference between RAF and other groups like IRA and ETA: except that each group requires specific attention for its idiosyncracies.

Religious terrorism 1979-now

Religious violence is of all times. There is no reason to predict that it will pass. This is no wave.

Alternative approach

Terrorists tend to be higher educated who are frustrated w.r.t. opportunities in society. They may feel sympathy with the unprivileged. They may adopt any ideology to recruit others in the resistance against the establishment. To counter this, one must look at society as a whole, create fair opportunity, and encourage people to participate. My own work contains aspects that are key to reduce terrorism.

  • Create a social welfare state that works. See DRGTPE.
  • Make democracy work. See VTFD.
  • Provide for good education, e.g. re-engineer mathematics. See EWS.
  • Let people learn how to deal with the human capacity for abstraction. See SMOJ.
Beatrice de Graaf, soothing Dutch viewers that a wave dies out

Beatrice de Graaf, soothing Dutch viewers that a wave of terrorism dies out


On the filos-nl server last January, F.A. Muller invited: “Everyone is welcome.” (Translation from: “Iedereen is welkom.”) This concerned a colloquium on February 19 2016 for the NWO-project “From criticism to methodology”.

  • On February 23 2016, Muller confirms this open access, and only advises me not to waste my time on this because I am no historian.
  • On March 17 2016, cc others, Muller writes me: “The gatherings (…) are a closed shop (…).” (Translated from Dutch.) This misrepresents and is a deliberate lie.

The events are documented here:  The earlier case w.r.t. H.C.M. de Swart was reported about in the earlier weblog entry, and (A) file with emails, and (B) its sequel. Now there is (C) this document, that contains the listserver message and the selected emails by De Swart and Muller.

On the sequence of events:

  • In the letter of February 23, the advice and referral to my background of not being a historian is uncalled for. It misrepresents my historical interest and the relevance of history for my research on Mannoury, see here and here. Such a suggestion might create a bias amongst others, and prime a reflex. Perhaps I have a question at one point, and someone might react: “What are you saying and doing here ? You are not a historian.” (no quote). Muller doesn’t cc his email to others, but De Swart’s behaviour must be explained, and apparently Muller regards this as an issue.
  • In the letter of February 23, Muller does not fully correct the breach by H.C.M. de Swart, and he actually provides a form of excuse for De Swart that he might also have thought about my not-being-a-historian. The latter is only a suggestion and Muller doesn’t clarify whether he has tried to discover the true reasoning behind the breach by De Swart.
  • Whence I have submitted Muller’s response of February 23 to the integrity officer of Erasmus University, Patrick Groenen, as well. Apparently the email of March 17 is a result of subsequent talks.
  • In my opinion Groenen has handled the case badly. He should have first discussed the results of the talks with me, before allowing for next steps. Groenen concentrated on the fast conclusion “mediation is not possible” and forgot about the breach of integrity. Groenen apparently didn’t see that the switch from February 23 to March 17 is a deliberate lie.

Thus, from the frying pan into the fire:

  • Muller breaches integrity of science too.
  • Muller implicates project team researchers dr Gerard Alberts (UvA), dr Paul van Ulsen (UvA) and PhD-student Mireille Kirkels (EUR) too.
  • Muller implicates guest Henk Visser too (co-author with De Groot on Forum Theory – and presently it is at issue who belongs to the forum on Mannoury).
  • Muller suggests that I have been “impolite”, without stating what specifically, and gives that as an argument for not inviting me to the closed shop gathering. He is accuser, judge and executioner, without being specific and presenting evidence.
  • The integrity officer and/or secretary have handled this disastrously.


The colloquia are open for everyone Lie: “a closed shop” Ad hominem
Twice in 2015 on the listserver
2016-01 listserver about 2016-02-19
Two emails: Van Ulsen and Kirkels, see (A)
H.C.M. de Swart, 2016-02-18 first email (A)
De Swart, 2016-02-18 second email (A)
F.A. Muller, 2016-02-23, see (B) Cover-up of what De Swart is doing Advice against attendance (B)
Muller, 2016-03-17 You are not invited because of “shown rudeness just now”

Given President’s Obama’s visit to Cuba today, it is quite fitting that wikipedia illustrates the saying in the following manner.

Wikipedia illustration for "Out of the frying pan into the fire"

Wikipedia illustration for “Out of the frying pan into the fire”

Historians of science study the genesis and development of ideas, e.g. the interaction between scientists via the letters between authors. Van Ulsen (2001:1) reports:

“Beth operated at the difficult boundary of disciplines. Philosophers denounced him as mathematician and logician, while the mathematicians and logicians regarded him, neither in a positive sense, as a philosopher.”

My documentation w.r.t. my own results serves this purpose as well. When I protest against maltreatment of my work then this does not imply that I lack good judgement or would be impolite.

On February 18 & 19 prof. dr. H.C.M. (Harrie) de Swart (EUR) (wiki) (born 1944, age 71) blocked my attendance at some colloquia on the history of science, first with the argument that these would be a “closed shop”, subsequently, when this was shown to be untrue, with refusing to give any kind of argument. This amounts to a breach of the integrity of science. The following is a summary of the case. The email exchanges with a discussion in English are here: part 1 with De Swart and part 2 with prof. dr. F.A. (Fred) Muller, the project manager.

NWO projects 2012-2017 on Mannoury, Beth, Heyting and Van Dantzig

There are (1) a NWO-project 360-20-301 running in 2012-2016 on Mannoury and philosophy of language and (2) a NWO-project 360-20-300 running in 2012-2017 on Mannoury, Beth, Heyting and Van Dantzig, with a budget of 617,000 euros.

I have an interest in these authors since my student days around 1977. I referred to Heyting in my book “A logic of exceptions” (1981 unpublished, 2007, 2011), Mannoury & Van Dantzig in 2012 (referring to a study by Gerard Alberts), and referred to Mannoury and his students Van Hiele and De Groot on my weblog in 2015. This is a draft paper of February 18 2016 on Mannoury & Van Hiele concerning the overlap of ideas that can be found in their work. (Historians would have to check whether Mannoury and Van Hiele stayed in touch after university.)

I discovered the NWO-projects around New Year 2016. The projects mention manager prof.dr. F.A. Muller and researchers PhD-student Mireille Kirkels (Mannoury), dr. Paul van Ulsen (Beth & Heyting) and dr. Gerard Alberts (Van Dantzig). For my current focus Kirkels and Van Ulsen are the relevant contact persons. They wrote that I was welcome to attend (Kirkels January 11 and Van Ulsen January 13 2016).

I do not know what the official position of De Swart is with respect this NWO-project, other than that he apparently manages an email list for the colloquia. I actually was a bit surprised to see his involvement since the project summary did not mention him.

The breach by De Swart on February 18 & 19 2016

On February 19 2016 there was a colloquium for this project. On Februari 18 2016, perhaps not coincidentally just the day before, De Swart blocked my attendance for all of these colloquia.

  • His first motivation was that the colloquia were a “closed shop”.
  • When I showed De Swart the email by Van Ulsen (preferring the accomplished PhD above the PhD-student) and stated the inference that there is no “closed shop”, whence his statement was untrue, De Swart replied that I was not welcome, refusing to give me a motivation.

This is a breach of scientific integrity. It blocks the flow of information. A colloquium is not organised for nought. De Swart implicitly slanders to others as if there would be cause to block my attendance. There is a legal distinction between “not welcome” and “forbidden”, but this does not apply here scientifically given De Swart’s original reference to “closed shop”.

I informed De Swart of these implications, but he did not remit. I decided not to attend, if only to protect myself from further abuse. Perhaps De Swart has given a motivation to others (but not to me). If participants have information on this, it should be forwarded to me since it concerns my position.

An educated guess what might have motivated De Swart to breach science

Given the lack of stated motivation, one can only guess about it. The event however must be explained to others.

It is likely relevant to mention an earlier case when De Swart maltreated my work, namely in 2001 on the subject of social welfare and voting theory. I protest against this maltreatment in 2001, see the documentation on my website. This issue is not resolved yet.

  • I do not know of a public statement by De Swart that replies to my protest.
  • I do not know about a public statement on content by De Swart concerning my book “Voting Theory for Democracy” (VTFD) (2001, 2004, 2011, 2014) (stable text, different versions of Mathematica). I would applaud it when he would finally find time to study VTFD, and state explicitly whether or not he sees some of his misconceptions on social welfare and voting theory corrected.
  • My criticism doesn’t only apply to De Swart but also to the Dutch community of researchers on social welfare and voting theory, i.e. that they allow De Swart’s malconduct and do not protect me against it. They apparently also neglect VTFD and related work.
  • Dutch readers can benefit from my webpage that warns about mathematics about social choice and voting theory.
  • Dutch readers can also benefit from De Swart’s valedictorian speech for his departure from Tilburg in 2010: speech, Volkskrant may 19, Volkskrant June 5. De Swart sins against science on (at least) two points.

(1) He gives a wrong summary of Arrow’s Theorem, suggesting that there would be proof that no voting scheme is ideal. VTFD explains that Arrow cannot tell us what is ideal, and that his words on rationality, consumer sovereignty and moral necessity do not fit his mathematics. De Swart’s scientifically proven false statement in Dutch is on page 10:

“Nu zijn er vele andere kiesmechanismen, maar geen van hen blijkt ideaal.”

(2) De Swart proposes that the electorate does much more work in the ballot box, e.g. by giving report card numbers (10 to 0) or scores (A to F) to parties, or by ranking political parties by order of preference. Perhaps the effort can be reduced by simply sorting physical logo’s of the parties, but still it is a significant job, given the empirical numbers of parties. De Swart refers to Balinski and Laraki, 2007, in which 2000 voters scored 12 presidential candidates with apparently relative ease. I have my doubts on this. De Swart may have his personal opinion, but it is not scientific to neglect another proposal that may be even better. De Swart obstructs current discussion about electoral reform by advocating impractical ways and closing his eyes for a practical approach towards improvement. Again he appears to be an abstract thinking mathematician without proper attention for empirical matters. My suggestion is that it not only suffices but may even be optimal when people have only one vote. The relevant point is that the professionals in Parliament use the more complex mechanisms. Thus voters form the weight that is attached to the party of their choice. The power of voters can be enhanced by having annual elections. Populism can be checked by having an Economic Supreme Court. Let Parliament investigate these options, so that politicians know what these options actually are. See the Dutch booklet “De Ontketende Kiezer“.

Harrie de Swart, valedictorian speech 2010 on voting

Harrie de Swart, valedictorian speech 2010 on voting

Political economy and social dynamics of having a grudge

It would not be rational when De Swart links this issue on voting since 2001 to my attendance at these colloquia for this NWO-project. However, he may not like that I protest.

My website documents what happens with my findings. This documentation cannot be construed as a grudge on my part (i.e. an emotion that interferes with good judgement). I politely greet De Swart and hope that he finds his way towards science. It would be slander w.r.t. me to suggest that I would confuse the topic of the NWO-project in 2016 with the issue on voting since 2001, and that I would not be able to respond in scientific and civilised manner when my work and person are abused.This present text is another example of a scientific and civilised response to abuse.

When De Swart does not provide decent motivation, breaches the integrity of science and implicitly slanders w.r.t. my person, then there arises an asymmetry. It would be slander to suggest that I would have a grudge against De Swart, yet it is not slander but an unavoidable hypothesis to explain events by that he might have a grudge w.r.t. this issue of voting since 2001.

Three strikes and you are out (wiki)

It would not be the first time that De Swart breaches rules of science.

  1. Thus on voting 2001, above.
  2. De Swart also is in error in 2008 advising the EU to use square root (Penrose) weights in voting, with neglect of the refutation by Andrew Gelman in 2007.
  3. De Swart is also in error in his management (not necessarily the content) in 2007-2008 of the thesis by M. Cabbolet. De Swart tried again in Eindhoven without telling that it had been rejected in Tilburg, only to be found out later on, see Fiers 2008 and Gerard ‘t Hooft 2014.
  4. Thus on colloquia on Mannoury in 2016, above.

The blockage of my attendance of these colloquia should be lifted. Independently, the breach by De Swart w.r.t. this attendance must be looked into. Resolution of the issue since 2001 w.r.t. voting is required as well. These issues should not be confused. However, De Swart’s breach in 2016 may help readers to grow aware that I had reason to protest in 2001 indeed, and to grow dismayed that the Dutch researchers on social welfare and voting did not resolve this over 15 years, and neither the censorship of science since 1990 for at least 25 years by the directorate of the Dutch Central Planning Bureau (CPB) (see the About page).