An open society is no maze

The Dutch government wants to determine the national research agenda to 2025. Not only the minister of education and science but also the minister of economic affairs expressed an interest in this. These ministers set up a “knowledge coalition” consisting of some research institutes and users of science like an organisation of employers. This “coalition” formed a “steering group”, under the joint chair of Alexander Rinnooy Kan (ARK) (1949) and Beatrice de Graaf (BdG) (1976).

ARK & BdG thought it a good idea to allow all Dutch people to send in their research questions. This caused 11700 questions. Also using text recognition software by Piek Vossen of Vrije Universiteit (VU), these were reduced to 252 umbrella questions, except for some 2000 that were not reduced. It is not guaranteed that this “wisdom of the crowd” will generate anything useful. Hence there is a “phase of dialogue” till the end of October, in which the mandarins of the “knowledge coalition” discuss what they really want to do. Perhaps the 11700 questions make for interesting wallpaper but it is not unlikely that the final report will give some evaluation of the entire exercise.

My own 14  questions are here, and I am wondering whether I am in an open society or in a maze.

My first contribution to the dialogue was a debunking of some questions on religion studies, see this PDF in Dutch, or see below. My second contribution to the dialogue are the following comments.

Linking up and down

A compliment for the people at the research agenda project is that they have linked the umbrella questions to the underlying separate questions, and vice versa. This is handy.

It increases the feeling that you are in a maze but it at least you can see where you are in there. Now we don’t need to discuss a question but only whether it has been allocated to the right umbrella.

This linking might actually also be done with internet pages of individual scientists. They normally state their research interests, and these might be processed in similar manner. The advantage of this particular ARK & BdG project is the common format: title, 200 words, keywords, use of Dutch. There is a “complaint” that some scientists have been “abusing” the “crowd sourcing” to advocate their own research, but I would rather have that input.

One modest question arises too: I am wondering what would happen when my 14 questions were taken as umbrella questions: would the total increase to 252 + 14 or would it reduce to say 250, with less than 2000 left-overs ? These would be marginal changes in terms of software results, but the advantage would be that the discussion could also focus on those 14 questions, instead of hiding and dispersing them all-over. Perhaps other people feel the same about their submissions. Results of course depend upon the software rules.

K.P. Hart on mathematics

Klaas Pieter Hart of TU Delft apparently was struck by the occurrence of lay questions on mathematics, and started a weblog on “math questions that have been answered already”. He frequently refers to wikipedia pages, and one indeed wonders why the questioners did not look there first. My impression is that Hart makes too much of the matter. We can also regard it as very kind of him to take more time to explain that such questions have already been answered.

A less kind interpretation is that mathematical arrogance is at play again. Hart’s weblog has the attitude that lay people do not understand mathematics, and that more explanation should close the gap. This is a strange attitude. People have been getting education in mathematics for ages 6-18. This would not be enough to settle the basic questions that Hart discusses ? This education is not enough to clarify to people that they should first study the question e.g. on wikipedia before submitting it to the national research agenda ? My diagnosis is that something is wrong with math education. It is strange that Hart doesn’t arrive at the same diagnosis. He puts the error with people, I put the error with him and his fellow mathematicians.

There is more to it. Let us look at some issues.

(1) There is my question on the training of teachers of mathematics. Hart hasn’t written on this yet. Perhaps it is safe to conclude that this is not “answered already”. But we must wait till Hart stops his weblog to be sure. This makes for a difficult dialogue. It would be more efficient if he could state ahead what he will be writing about.

My question has also been moved under the umbrella question on future education, with a total of 10 sub-questions. I wonder whether that is a useful allocation. Mathematics education is such a core issue that I feel that it deserves umbrella status by itself. For the diagnosis of the other 252 umbrella questions it is important to grow aware that many (social) problems are being caused by bad education in mathematics.

(2) On Pi, Hart misses the opportunity to point to Archi = 2 Pi (check the short movie).

Imagine shoe shops selling only single shoes instead of pairs of shoes. Or builders selling only half houses instead of whole houses. Mathematicians however don’t mind making life difficult for you. It is your problem that you don’t get it, and they will be kind enough to explain it again. Well, perhaps it isn’t kindness: what’s in it for them is that they can feel superior in understanding. This psychological reward system works against the student.

(3) On the sine function, Hart writes that sine and cosine might also be identified by the co-ordinates of the endpoint of the arc on the unit circle. [Dutch: “Eigenlijk hadden we ook kunnen zeggen: cos(t) en sin(t) zijn respectievelijk de x- en y-coördinaat van het eindpunt van het boogje.”]

This is precisely my suggestion: to use functions xur and yur, see my paper Trig rerigged (2008), seven years ago, and books Elegance with Substance (2009, 2015) and Conquest of the Plane (2011). (Best link to the 2nd edition EWS 2015.) Thus, there exists a didactically much better presentation for sine and cosine than mathematicians have been forcing down the throats of students for ages. Hart mentions it in passing, but it is a core issue, and an important piece of evidence for my question on the training of math teachers.

Note also that wikipedia today still has no article on xur and yur. Neither on my proposal to take the plane itself as the unit of account for angles, even though Hart refers to that wikipedia page in his text on “90 graden“. The mathematics pages on wikipedia tend to be run by students from MIT who tend to copy what is in their textbooks, and who lack training on keeping an open mind. See here how wikipedia has been disinforming the world for some years now.

In that weblog article Hart confirms that sine and cosine can be defined by some criteria on the derivatives. This is the approach followed by Conquest of the Plane (2011). It is nice to see agreement that this is the elegant approach indeed. I think that it is advisable that Hart reads COTP and writes a report on it, so that he can also check that the slanderous “review” by his TU Delft colleague Jeroen Spandaw is slanderous indeed – see here.

(4) On numerical succession – a.k.a. mathematical induction but see my discussionHart holds that this does not exist for the real numbers. This is essentially the question whether there is a bijection between the natural numbers N and the real numbers R. Please observe:

  • Since 2011-2012 I present the notion that there is a “bijection by abstraction” between N and R. See my book FMNAI (2015).
  • In his research, Hart has a vested interest in that there is no such bijection.
  • Hart has been partly neglecting the new alternative argument, partly sabotaging its dissemination, partly disinforming his readership about the existence of this new approach. This is a breach in scientific integrity. See my documentation of Hart’s malpractice.
  • It is okay when Hart wants to say that this issue has been “answered already” in his view, e.g. by traditional mathematics. There is freedom of expression. However, as a scientist, he is under the obligation to give all relevant information. This he doesn’t do.

Overall: Hart’s weblog is biased and unscientific.

Religion studies

One of my questions for the research agenda is how to arrive at a deconstruction of Christianity. I also observed that the Dutch national research school on religion studies and theology NOSTER had submitted four questions. I looked at those questions and their 200 word summaries, and found them scientifically inadequate. See my discussion of this (in Dutch). I informed the research agenda secretariat of my finding, in an email of June 10. To my surprise, one of these inadequate questions from NOSTER has been selected as an umbrella question S14, and my own question that debunks it has become a sub-question for it !

The software for doing this has been developed at originally religious Vrije Universiteit (VU), but I presume that this heritage has nothing to do with this.

Censorship at CPB

My question on the censorship of economic science since 1990 by the directorate of the Dutch Central Planning Bureau (CPB) has not been allocated to an umbrella question yet. I suppose that this doesn’t disqualify the question.

Economic Supreme Court

My question on the Economic Supreme Court (ESC) has been allocated to umbrella question S06, that looks at maximizing national sovereignty in an international legal order. Beware though, since the phrasing of S06 might also be read as a ploy by international lawyers to get more attention for international law. The umbrella contains 29 sub-questions, many of which indeed deal with globalisation.

Admittedly, when each nation has its own ESC then international co-operation will be enhanced, since the ESCs will exchange information in scientific manner. This is part of my analysis e.g. on money.

However, the ESC is also very relevant for national issues, e.g. in umbrella question G7 on social-economic institutions. Such institutions could differ with or without an ESC. Findings from this realm would provide evidence in support of an ESC, and thus be relevant for parliament that must decide on amending the constitution to create an ESC.

These matters of CPB and ESC affect one’s view on the social order. This would warrant umbrella status for them.

Democracy and voting theory

I would hold that it is important to have a clear view on democracy and voting theory. My question for the research agenda on this was how one could convince the editors of that their website contains a misleading article. I have been trying for years to get this corrected but they will simply refuse to look into this. This question has been moved to umbrella S31 on issues of privacy and database monopolies. I don’t think that it belongs there. Indoctrinating school students with mathematically proven false information is not the same as privacy and database monopolies. This doesn’t mean that the question should be removed to the 2000 unassigned ones, and further forgotten because there are too many of those.

Other questions

I have some comments on the other questions but a weblog should not be too long.

Conclusion: An appeal to ARK and BdG

Rinnooy Kan has a background in mathematics and De Graaf was in the news with her personal background in Christianity.  Jointly they would be able to recognise the points raised here. My appeal to them is to take my 14 questions as umbrella issues, and work from there.

The breach of scientific integrity by K.P. Hart and his misleading weblog must be dealt with separately.


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