This Sunday morning, August 17 2014, sitting in his bathtub, he hummed to himself:

“You, Vladimir Putin, President of the Russian Federation, didn’t do too badly.”

Vlad2: “But you can look at it differently too.”

Putin looked around bewilderedly.

Vlad1: “Huh ? Who is speaking to me ?”

Vlad2: “Me, Vladimir Putin, President of the Russian Federation. You know, your conscience, who started you on this path after the fall of the USSR.”

Putin relaxed. His conscience ! It was so long ago that he had this talk with himself !

Vlad1: “Hi, Vlad2 ! What a surprise ! You are trying to second-guess me again ? Please tell me what I am doing wrong. Beware, I am grateful for your advice back then, but I am not used to criticism, and if you make me angry I may send you to Siberia.”

Vlad2: “Hi, Vlad1 ! This shows again that you don’t understand what a conscience is. We never tell what a person is doing wrong. We only ask questions. Tantalising questions. Questions that cause you never to sleep again at night. Besides, we never give in to threats.”

Vlad1: “Last time I heard from you was on Chechnya and Georgia. Boy, it took me a lot of vodka and women to finally get some sleep, but I succeeded, and I got those regions fixed.”

Vlad3: “I didn’t think those women were really that swell. You had too much vodka.”

Vlad1: “I am sorry ?”

Vlad2: “Huh, who is that ?”

Vlad3: “Well, I am just Vladimir Putin, President of the Russian Federation. You suggest that there are only Vlad1 and his conscience Vlad2, but you also know that I do not follow the rules. The world is not as simple as commonly thought, and certainly not the mind of the President of Russia. And I didn’t like your women.”

Vlad4: “I fully agree to that.”

Vald0: “And I protest that Vlad3 started counting at Vald1 and not at me, Vlad0. People always forget who provided the vodka.”

Vlad1: “Okay, okay, please relax, my dear Russian Presidents. I am overjoyed that this Ukraine crisis causes me to develop such a complex personality. My next thousand years seemed lonely but now I am looking forward to your company. But just now, I want to sit in this bathtub and decide whether I will invade the Ukraine or not. Well, I shouldn’t forget that I already did, by taking back the Crimea.”

Vlad2: “Well, I started out trying to be your conscience, and I feel that I should persist, whatever those Vlad3 and Vlad (n) say. Is there any way that you are going to bring some sense into the matter ? This Ukraine issue is pestering now for more than ten years. Shouldn’t these people be allowed to get a normal life ?”

Vlad3: “You cannot hold that what I say isn’t important. My opinion is that we all should give Vlad1 an ultimatum that he should decide what to do. He has been zig-zag-ing all year, being a host to the world in Sochi and now becoming some sort of pariah. I move that we stop zig-zag-ing. Either we take our big decision now, to invade or not to invade, or we can blame Vlad1 for the next thousand years that he is another bathtub failure of which history has given us plenty already.”

The President of Russia thought at this moment of his secret admiration of the uncompromising radical Jean-Paul Marat.

http://commons.wikimedia.org/wiki/File:Jacques-Louis_David_-_Marat_assassinated_-_Google_Art_Project_2.jpg

“La mort de Marat”, by Jacques-Louis David, 1793. (Source: Wikipedia Commons)

Vladimir Putin, President of the Russian Federation relented: “Okay. So what are my options ? Currently, I have made veiled threats, put troops at the border, censored the media, sent hundred thousands of people running, shot a plane, imposed sanctions, boycotted Holland and their shiny tomato’s, sent out my 278 white trucks. I cannot back down without looking silly and weak. The Ukrainean army is on the verge of destroying the Russian patriots, and if I allow this to happen then I will also betray my promises to them and to the Russian public. I will not only look silly and weak but will actually be so. Thus, there is only one option: to invade, and block the Ukrainean army. The only question is: how far will I go ? Just to the current front line ? This is a somewhat silly objective for such an invasion. If I invade, there should be a real purpose. Thus I should go all the way to the Dnieper and divide the country. The risk is that the other half then joins NATO. Kiev will be lost for the Russian Federation. Mother Russia weaps for losing Kiev.”

Dmitry Medvedev: “There is also another option. You could call for a referendum or national elections in Russia. You against me. Ask all Russians whether they want you and war with the West or me and some form of Peace with Honour.”

Vlad1, Vlad3, Vlad4, Vlad (n): “What in Mother Russia’s name is Medvedev doing here ?”

Medvedev: “Wow, I thought everybody knew that I am only another figment of Putin. Well, big surprise for you then – except for Vlad2, I notice. But just to be sure: one way to get out of this mess is to call for a referendum or national elections in Russia.”

Vlad2, as always quick on the uptake in moral issues: “Let me see whether I get this correctly. We invade to the current frontline just to keep our promises to the Russian patriots. We also announce a referendum whether the Russian army should continue to the Dnieper to liberate the Eastern Ukraine from the Nazi regime in Kiev. We promise to step down as president if we lose. That wouldn’t be a loss of face with a needless massacre on the battlefield but a honorable part of democracy. You, Medvedev, will be the voice of reason, and argue for Peace with Honour. If you win the referendum, you could run for president, and continue to protect our interests. Do I understand you correctly ?”

Medvedev: “Democracy is an offer that you can’t refuse. I would insist on a free press though, to explain who shot down that plane, since I intend to win.”

Putin: “Hm, … I need to stay in this bathtub a bit longer to think this over. However, there is a knock on the door. Someone seems to want to come in with some message or so …”

On the borders of the EU the cannons are barking, and it are mostly civilians and their properties that are hit, in the Ukraine, Syria & Iraq, Israel & Gaza, and Libya.

In the Dutch Parliament, economist and Christian Democrat dr. Pieter Omtzigt calls for a recognition by the Dutch government of the genocide by the “Islam State” on the Yazidi people. The world should not allow what happened in Rwanda in 1994. He said so in a talkshow of August 11, in which he also mentioned that his priorities are Dutch pensions, persecuted Christians, and his home region Twente. The talkshow of August 11 only mentions them but the persecuted Christians get his full attention in the same talkshow of July 31.

It seems unwise to regard, define and frame the problems of the Middle East in terms of Islam, Christendom and Judaism. There are actors who have an interest in such framing. Who joins this framing supports their interests.

Obviously, it are religious fanatics who have this interest. They have little to offer except their religion, and hence they grow in importance whenever it is accepted that religion would really be the issue.

There are also other powers who refer to religion but who have a more hidden agenda. Said “Islam State” is run so well, and makes such profits, that one may wonder whether the real issue is Islam, for it may just be the robbing of the possessions of others.

Thus, I would urge Pieter Omtzigt to desist from framing his objective in terms of “persecuted Christians”. In principle it are civilians who are at issue. In principle it is freedom of religion that is at issue. That someone calls himself or herself to be a Christian is not the first point of relevance, since he or she may well be a fundamentalist on the road to a new crusade. When a Christian in the Middle East loses his or her children then this is as heartbreaking as when a Sunnite or Shiite loses his or her children. I am pretty sure that Pieter Omtzigt will agree on the latter, but he doesn’t recognize yet that he is inconsistent by putting such an emphasis on Christians. He is opening Pandora’s Box, and apparently invites Dutch Parliament to join him in doing so.

Pandora 1879

Pandora, by Dante Gabriel Rossetti, 1879 (Source: Wikimedia Commons)

Dr. Omtzigt wrote a thesis in econometrics. He is one of the few Dutch Parlementarians who has some grasp of economics and finance. He is not only on the Parliamentary Commission for Foreign Affairs but also on Commissions on Economics and Finance. For years there have been the “Economists for Peace”, now EPSEU and EPSUSA (formerly ECAAR). They study the costs of the Arms Race, or, for example, the costs of the political lies that resulted in the Iraq War. Remember that it were “re-born” Christians George W. Bush and Tony Blair who used lies to cause the Iraq War. The least that we could ask of economist Omtzigt is to look at what EPSEU has to say.

In my analysis the greatest contribution to peace will come from the solution of unemployment. Young people who have no future now and who experience the seduction of security in religion, would have better options if the economy would allow them to find a job, get economic security and the prospect to start a family. Unemployment is not a natural phenomenon, like a vulcano, that we have no control over. Unemployment is man-made, and a failure in policy. Unemployment both in the EU and the USA has been caused by neoliberal economists who adhere to dogma’s that economic science proves to be incorrect.

Pieter Omtzigt thus actually has a co-responsibility for those wars and those persecuted Christians. He should be in the seat of the accused rather than in the seat of the DA or judge.

Like the EU and the USA, Holland has a perverse system of taxation. The system in Holland is even more perverse, not only due to the larger Dutch welfare state but also because of some political pecularities. In 1997 minister of finance Gerrit Zalm (VVD) (now CEO of the ABN-AMRO bank) and secretary of finance Willem Vermeend (PvdA) lied to Dutch Parliament, when they proposed to replace tax exemption by a tax credit. Effectively they made it politically more difficult to tackle low wage unemployment. In 2013 there was a row about Bulgarian fraudsters who milked the Dutch tax credit system. The case is described in this paper: Economics as victim between lawyers and mathematics (2013).

Now, if fellow-economist Pieter Omtzigt just would take the time to study that paper, and ask questions about what would not be clear to him, then the chance for world peace could improve.

PM. Etgar Keret rightly observes that people tend to expect peace to “descend from above” while the better perspective is that you have to work hard on compromise (Los Angeles Times, July 14 2014).

Blackboards have mostly been removed from classrooms but they are still used in cafés and on terrasses.

Blackboard at The Lantern cafe

Blackboard at The Lantern cafe

Roefie Hueting (1929) is performing this Summer with also his own repertoire of jazz on the piano, on Friday evenings at The Lantern, The Hague. You can listen to “Blues for Bessie“. In the past he played with his Down Town Jazz Band in the big halls in Holland.

Hueting at the piano

Roefie Hueting at the piano in The Lantern, The Hague, July 25 2014

Hueting is also an economist, and as he has developed at least two talents, Peter van Bergeijk takes him into consideration as a “double talent”, though still has to report what he thinks about the music.

As an economist, Hueting first worked on employment and then switched to nature and the environment. At CBS Statistics Netherlands he developed the statistics on the latter. The Dutch NAMEA and UNstat SEEA are based to a large extent upon the work by Hueting, and he received the UN Global 500 Award in 1994. Hueting developed the notion of environmentally Sustainable National Income (eSNI), see his website.

In the economic theory of social welfare, it is accepted that it is rather impossible to find the (Bergson-Samuelson) Social Welfare Function (SWF) but, assuming optimality, society will choose the optimal point on the Production Possibility Curve (PPC), and the tangent of both functions at that spot will give an income measure, called “national income” (NI). A statistical observation of actual incomes and expenditures and market prices should allow, under assumption of optimality, an estimate of that tangent, and thereby provide an estimate of social welfare. Comparison over time would provide an indication of progress or regress. The relative change of real national income is generally called “economic growth”.

At least, that was the theory around 1934. Since then population growth has generated the new scarcity of the environment. While clean water was free before, it now must be produced at a cost. While CO2 was no worry before, we now have to raise the dikes and build stronger houses to withstand the storms. Curiously, all these costs are included in NI as higher income from more work, instead of being deducted as costs. For this, Hueting proposes a measure of NI exclusive of such asymmetrical bookings, NI-ex-asyms.

Subsequently, there is the notion of environmental sustainability. The present generation has the choice of consuming present resources in the manner of expletion, or, to save present resources so that future generations can also use them at a similar sustainable rate. It is the preference of the current generation that counts. The preferences of the future generations do not enter the discussion since those do not exist yet. Curiously, the preferences of our current generation cannot really be measured, because of all kinds of prisoners’ dilemma’s, lack of communication, failures in democratic processes (check voting theory for example), and so on. There are political statements about environmental sustainability, but those are seldomly implemented. But, given those pious statements and the widespread real worry about the future for our children and grandchildren, statisticians can make an assumption about a social preference for environmental sustainability. Making this assumption compares to making the assumption above on optimality. Both NI and eSNI are based upon assumptions, either on optimality w.r.t. NI or on sustainability w.r.t. eSNI. Finally, given the condition of sustainability, standards can be determined, and a model can be run on which the condition of sustainability is imposed on the current economy. The economy would adapt to a different mode, and the generated national income would be the measure of eSNI.

The relation between NI and eSNI can be clarified with a diagram and a table. Let us start with the table. One of the crucial elements in this discussion is uncertainty and how to deal with it. The current measures of NI and “economic growth” might be regarded as first approaches to measuring social welfare in 1934, but nowadays we would like to include more elements, like the disutility of unemployment, the stress of mortgages, economic inequality, and such. NI is a highly uncertain measure for economic welfare if the true preference is for sustainability. You could supplement NI with environmental indicators only, but those provide only data and no information, since you would also need sustainability standards and some form of aggregation to relate the indicators to NI itself. Overall, the publication of both NI and eSNI would be the best approach.

Uncertainty in the measurement National welfare Environmental sustainability
1934 National Income (NI) acceptable as a first approach, assumes optimality -
2014 National Income (NI) unacceptable, requires amendment for unemployment and so on uncertainty so large that it fails
2014 Environmental indicators - data but no information: incomplete standards and no aggregation
2014 environmentally Sustainable National Income (eSNI) comparable to NI, subject to the condition of a societal preference for sustainability the uncertainty is described, there are more complete standards, aggregation allows comparison to NI

The diagram gives a conventional graph with convex Production Possibility Curves (PPC) and concave Social Welfare Functions (SWF). There are two sets of these, one with unsustainable reality (U) with illusionary high income (NI), and another with sustainable target (S) with realistic income (eSNI). The axes are two environmental indicators: (1) the environmental function that allows the use of CO2, (2) the environmental function that allows the use of fresh water. Note that the axes thus must be read somewhat inversely. The production of more fresh water causes an increase in the output of CO2 and thus reduces the function value for its availability.

Comparison of NI (high) and eSNI (low)

Comparison of NI (high) and eSNI (low). The axes give availability of environmental functions. Red arrows: sustainable standards. Black arrows: current unsustainable use.

The diagram comes with these observations: (a) SWF-S is the social welfare function under the condition of a social preference for environmental sustainability. Hence the PPC is selected that satisfies the standards of sustainability (the red arrows). The tangent provides the eSNI measure. (b) SWF-? indicates some kind of implied SWF when we consider only the observed uses of the functions (the black arrows). If the indicators are given only by themselves then they provide relatively little information, but in this present setup we assume that they are aggregated into the NI measure. Still, it is not clear what this SWF-? and its NI mean. The assumption of optimality is only an assumption, and quite unrealistic. But given its conventional use, it seems best to have both NI and eSNI available. Of course, eSNI is work in progress. Here is a discussion of what can be done for new research. But if we want to deal with the uncertainties then we need more and not less research.

Calculating eSNI would cost only 1/4 % of the budget of CBS Statistics Netherlands (see here). The reason is that the ground material already is available so that only a model must be run. This is cheap for an important figure that could dramatically affect economic policy.

CBS Statistics Netherlands has a leading world position in the statistics on economics and the environment. They got that position because of the work by Hueting. In the past, Hueting had full support from Nobel Prize winner Jan Tinbergen (1903-1994). The last 20 years have shown a gradual reduction of attention so that it is close to zero now. See Hueting’s website and my paper The Old Man and the SNI. For further readeing, see my (draft) book on economics and ecological survival.

National accounting was started by economists and supported by the government because it was applied economics, embedded in theory. In the past national accounting was guided by economic theorists like Keynes, Hicks, Frisch, Tinbergen, Meade, Stone, Kuznets, Samuelson. Obviously, Hueting belongs in that list of distinguished authors. But CBS apparently doesn’t know what it is doing anymore. It has turned the project into accounting without theory. It is no longer applied economics but accounting for multiple purposes such as legal reasons and tax collection. CBS Statistics Netherlands prefers to publish only NI and various environmental indicators. The table and diagram above show that this produces data and not information, while the 1934 idea of NI is increasingly disinformative for our current policy objectives and possibilities. Sic transit gloria.

NB. Frits Bos (formerly CBS and now CPB) wrote a thesis and an ongoing series of articles on national accounting, calling for a greater awareness on theory, but his exception rather proves the rule, while he apparently still doesn’t delve into Hueting’s seminal contribution.) Importantly, Henk van Tuinen (vice-director at CBS till 2003) has this important article in the open access Journal of Official Statistics (JOS), Vol.25, No.4, 2009. pp. 431–465, in which he agrees with the reduced relevance of NI, and in which he explicitly mentions eSNI as a scope for the future, see sections 3.5, 6.3 and 7.2. The key stumbling block for Van Tuinen is the uncertainty in the assumptions attached to it (page 451). This essentially reduces to the question whether eSNI is a proper “statistical measure” or not. My suggestion is that statistics also deals with uncertainty, and that eSNI clarifies the uncertainty that remains a mystery in the other measures.

But Hueting can be happy that he still has one other talent, and a good one too: music.

Peter Harremoës wondered whether zero is a natural number, arXiv:1102.0418v1 [math.HO]. He starts out by admitting that it is a matter of definition, but then proceeds with the issue of ordinal and cardinal numbers, so perhaps I should rephrase his true question as I did now in my own title above or to the left. A google on “Is zero a natural number ?” and “Is 0 a natural number ?” generates some 15,000 hits. A bit to my amazement there are more people pondering the question (though close to 0.0% of mankind in statistical approximation (in writing and not reading)).

While Harremoës approaches the issue from a set-theoretic point of view, though visits Kindergarten with some nice observations, let me start from a didactic point of view from Kindergarten.

Kids learn the sequence S = {1, 2, 3, … }, and tally off their fingers. When they count the elements of a set A (apples), they bring the elements in A in a one-to-one relation with the elements in S, and also in that order {1, 2, 3, … }. The last element counted gives the total number of elements in A.

For terminology, an ordered sequence gives an ordinal measure and the total gives the cardinal measure for the number of elements in a set.

The kids learn also the sequence O = {1st, 2nd, 3rd, ….}. Now this is interesting ! It is rather this list O that gives the ordinals ! Rather than saying “This is apple one, this is apple two, this is ….” they learn to say “This is the first apple, this is the second apple, this is …”.

When counting elements in a set A then it does not matter in which order the elements are put – and the cardinal number has the property that it has the same value in whatever order its elements are put. But, for O, the order must follow the order of the elements of the set A that is being considered.

Thus, kids first learn ordinals and cardinals in a mixed manner with S. Then the ordinals are created separately in O. Then S becomes important for the cardinals. The introduction of O requires a bit of unlearning alongside learning.

Set A is counted using ordered {1, 2, 3, …} Order in A is not relevant Order in A is relevant
Counting (process) (“Order some or all.”) {1, 2, 3, ….} for first training {1st, 2nd, 3rd …}
Cardinal (result) (“How many elements are there ?) {1, 2, 3, ….} {1, 2, 3, ….}

With this established, I think that I must object to the use of the idea that “ordinal numbers” and “cardinal numbers” would be separate sorts of numbers. We only have the numbers S. The “cardinal number of a set A” is just idiom to identify the number of elements, but this does not suggest that “cardinal number” is a specific kind of number (like rational number or complex  number).  It is less common to speak about the “ordinal number of an element”. While “What number are you in line ?” indicates such ordering, still you are not a number, and “ordinal number” is not a special number but merely S applied to ordering.

Thus “Is zero an ordinal or cardinal number ?” is a nonsensical question. Zero can be the value of the cardinal number of a set. Whether you start counting with 0 is an issue of convenience, and probably not practical in Kindergarten (but this needs testing). The true issue at hand is not quite arithmetic but actually part of the theory of measurement, with nominal, ordinal, interval and ratio scales.

Note that Dutch has different words for number (“getal”, as in the list of natural numbers, or the pure decimal system, old-English “tale”) and cardinal number (“aantal”, the number of elements, English “tally”). Teaching in Dutch is a bit easier than in English. See Google Translate on this. In etymology we can find these origins: “Origin of tale: (Webster) Middle English ; from Old English talu, speech, number, akin to German zahl, number, Dutch taal, speech ; from Indo-European base an unverified form del-, to aim, reckon, trick from source Classical Greek dolos, Classical Latin dolus, guile, artifice”.

Let us consider kids in Syria, Israel, Gaza or Ukraine who have N[10] = {0, 1, 2, 3, …, 10} fingers left. Since the places of these fingers on their hands or the way how these fingers are ordered doesn’t matter, the natural point of view is that the numbers are cardinal values (“how many left ?”). There also arises a natural order that one set is larger than another, and with thus cardinal values 0 < 1 < 2 < 3 … < 10.

The Egyptians already had a symbol for “none”. They didn’t regard it as a number though. However once you set up a system of arithmetic then it becomes convenient to regard 0 as a number, so that 1 – 1 = 0. Slowly language adapts to that use. Given the naturalness of the question for kids to ask “How many fingers do I have left ?”, thus with the focus on cardinality, and given that the answer may also be “zero”, it is more reasonable to include 0 in the list of numbers that are regarded as natural, giving = {0, 1, 2, … }.

However, when you know that a set is non-empty, then you can use N+ = S for the positive integers. Hopefully the little ones still have a thumb to suck on, to fall asleep, and be ready for another day of counting.

I received a sobering email today about the UK “supposed serial killer nurse” Ben Geen, of which a description is given in this weblog page.  Naturally, I don’t know whether Ben Geen is innocent or not, I just was informed about that weblink, and pass it on.

The good news though is that Holland succeeded in getting a release and acquittal for Lucia de Berk. She had also been accused of being a serial killing nurse, and somewhat close to being a witch with her Tarot card reading. Key roles for her eventual release were for Metta de Noo – Derksen MD for analysing the medical data, her brother Ton Derksen, professor of methodology of science, who wrote the eye-opening book on the case, and professors of econometrics Aart de Vos and, crucially, mathematical statistics Richard Gill who broke the statistics of the case and who showed that the courts had been misinformed by their “statistical experts” (who still haven’t offered apologies). In this case I joined in the statistical effort to clarify the issue, see here at arXiv. Whatever the statistics, it are the medical data that are crucial here, since it is the expertise of MDs to decide about issues of life or death. Thus, the greatest heroin in this issue remains Metta de Noo MD. People in the sector should be aware of the legal settings though, see for the USA e.g. the LNC Educational Center with another heroin, Donna Rooney.

Thus, while I overall advise the world to boycott Holland, just now: Three cheers for Holland !

Overall, I hope you agree that it is better to aspire for improvement of the country that you boycott, to ever greater perfection. It is no use to boycott a country that is rather worthless to boycott anyhow. It isn’t quite clear what the EU intends to achieve by boycotting Russia over the Ukraine for example. If the goal is to insult people and a nation, yes, go ahead, and boycott all shops and nations of the world, and be happy with all the insult and misunderstanding that you spread around. But if your objective is some noble goal, like the freedom of economic science, then you should focus on Holland, notwithstanding that wonderful great result with respect to Lucia, that hopefully inspires confused residents in the UK.

PM. A point remains that while Lucia now is free and acquitted, none of the originally responsible MDs, directors, lawyers, experts and judges have apologized or met with some disciplinary measure. If I am correctly informed some continue to believe that Lucia was guilty or at least that they themselves didn’t make any error. See this tv broadcast how director Paul Smits argues that he would do the same: when such suspicion arises, call the police. His defence is that it is bizarre that other agencies simply adopt that suspicion instead of looking into it critically. The critique however is that he didn’t treat Lucia in the manner of “innocent until proven guilty” but rather conversely, while it is difficult for the police to be critical about “medical evidence” (that isn’t really such). Smits later moved on to become director of Maasstad Ziekenhuis, where he mismanaged a klebsiella infection that caused the death of some patients. After that he was given a “second chance” (in which Lucia was forgotten, well, she was acquitted) for the Medical Center Leeuwarden. At least we can say that as science progresses and society becomes increasingly complex, there are ever more ways to make statistical errors of type I and type II.

In Medical Schools, doctors are trained while doing both research and treating patients. Theory and practice go hand in hand. We should have the same for education. Teachers should get their training while doing theory and learning to teach, without having to leave the building. When graduated, teachers might teach at plain schools, but keep in contact with their alma mater, and return on occasion for refresher updates.

Some speak about a new education crisis in the USA. The above seems the best solution approach. It is also a model to reach all existing teachers who need retraining. Let us now look at the example of mathematics education.

Professor Hung-Hsi Wu of UC at Berkeley is involved in improving K12 math education since the early 1990’s. He explains how hard this is, see two enlightening short articles, one in the AMS Notices 2011 and one interview in the Mathematical Medley 2012. These articles are in fact remarkably short for what he has to tell. Wu started out rather naively, he confesses, but his education on education makes for a good read. It is amazing that one can be so busy for 30 years with so little success while around you Apple and Google develop into multi-billion dollar companies.

Always follow the money, in math education too. A key lesson is that much is determined by textbook publishers. Math teachers are held on a leash by the answers books that the publishers provide, as an episode of The Simpsons shows when Bart hijacks his teacher’s answers book. As a math teacher myself I tend to team up with my colleagues since some questions are such that you need the answers book to fathom what the question actually might be (and then rephrase it properly).

At one point, the publishers apparently even ask Wu whether he has an example textbook that they might use as a reference or standard that he wants to support. The situation in US math education appears to have become so bad that Wu discovers that he cannot point to any such book. Apparently he doesn’t think about looking for a UK book or translating some from Germany or France or even Holland or Russia. In the interview, Wu explains that he only writes a teacher’s education book now, and leaves it to the publishers to develop the derived books for students, with the different grade levels, teacher guides and answers books. One can imagine that this is a wise choice for what a single person can manage. It doesn’t look like an encouraging situation for a nation of 317 million people. One can only hope that the publishers would indeed use quality judgement and would not be tempted to dumb things down to become acceptable to both teachers and students. In a world of free competition perhaps an English publisher would be willing to replace “rigour” by “rigor” and impose the A-levels also in the US of A.

In my book Elegance with Substance (2009) I advise the parliaments of democratic nations to investigate their national systems of education in mathematics. Reading the experience by Wu suggests that this still is a good advice, certainly for the US.

About the subject of logic, professor Wu in the interview p14 suggests that training math teachers in mathematical logic would not be so useful. He thinks that they better experience logic in a hands-on manner, doing actual proofs. I disagree. My book A Logic of Exceptions (1981, 2007) would be quite accessible for math teachers, shows how important a grasp of formal logic is, and supports the teaching of math in fundamental manner. The distinction between necessary and sufficient conditions, for example, can be understood from doing proofs in geometry or algebra, but is grasped even better when the formal reasons for that distinction are seen. I can imagine that you want to skip some parts of ALOE but it depends upon the reader what parts those are. Some might be less interested in history and philosophy and others might be less interested in proof theory. Overall I feel that I can defend ALOE as a good composition, with some new critical results too.

Thus, apart from what parliaments do, I move that the world can use more logic, even in elementary school.

I am sorry to report that Holland also fails on the integrity of science in the research on the didactics & education of mathematics. This is my letter (in Dutch) to the Scientific Integrity body LOWI of the Dutch Royal Academy of Sciences KNAW.

Earlier, in my book Elegance with Substance (2009), I made the empirical observation that mathematicians are trained for abstraction while education is an empirical issue. The training of mathematicians to become teachers of mathematics apparently can often not undo what has been trained for before. This basically means that many have lost the ability to observe. Math teachers tend to solve their cognitive dissonance by adhering to “mathematical tradition” that however is not very didactic, and that in fact collects the didactic debris of past centuries.

A key example here in Holland is the difference between Hans Freudenthal as the abstract topologist and Pierre van Hiele who as a mathematician and actual teacher however kept his ability to observe. We need only look at the debris in math textbooks to observe that the majority of math teachers aren’t like Van Hiele. See Elegance with Substance if you cannot identify the debris yourself.

An international example on statistics is the difference between Fisher and Gosset on “statistical significance”. Mathematicians tend to consider mathematical statistics only, and are little aware of empirical significance. Math educators who nowadays use statistics might fall victim to ‘garbage in, garbage out’ but nevertheless be praised as ‘empirical’.

Now in 2014 that empirical observation comes with a sting. When abstract thinking mathematicians make statements about the empirical reality of didactics & education, they actually make statements out of their province, about something they haven’t studied: which is a breach of research integrity. This especially holds when they have been warned for this, say by my 2009 book (listed in the AMS Book List, Notices Vol 58, No 11, p1474), or perhaps even directly by me.

In Holland there now is the case of internationally known Jan Karel Lenstra, who did work in operations research, (linear) programming, scheduling and the traveling sales person, who was selected in 2009-2010 by theoretical physicist and KNAW President Robbert Dijkgraaf to chair a KNAW “Committee on Mathematics in Primary Education”. The Dutch complaint is that children don’t learn arithmetic so well anymore, e.g. aren’t trained on long division as a sure method. It often happens that a committee is chaired by a person who doesn’t know much about the subject beforehand, but then that person tends to be aware of this, and is willing to learn. In the case of Lenstra, he apparently thought that he knew enough about “Mathematics in Primary Education” so that he also understood the didactics & education itself.

Hans Freudenthal had a huge impact on arithmetic in Dutch primary education. Lenstra observes about the Freudenthal madness:

“The core is that we must get more evidence-based research [education ?]. The ‘realistic arithmetic’ has been adopted without the empirical evidence to make it obvious. And also the PABO [training of elementary school teachers] has been constituted on the base of beliefs instead of scientific research.” (my translation, comments in brackets)(Akademie Nieuws July 2011 p5) 

But Freudenthal and his followers did claim that ‘realistic mathematics’ was scientifically warranted and based upon evidence. Thus professor in mathematics Lenstra observes a fraud with respect to empirical research, but doesn’t do anything about it. He doesn’t call for a repeal and annulment of earlier “research” that claimed empirical relevance but without such base. He is quite happy that his fellow abstract thinking mathematician Freudenthal invented a theory and let others suffer the consequences. Lenstra is another abstract thinking mathematician who now thinks that he has solved a problem and then lets others suffer the consequence – like the international community that still considers Freudenthal’s work “research”.

Lenstra’s solution to the arithmetic problem in Dutch primary education is not to retrain the 150,000 elementary school teachers, but shift the problem to the 4,000 math teachers in secondary education. The formula is that “arithmetic skills must be maintained” in the highschool curriculum. Lenstra suggests that it must be tested, but doesn’t quite specify how. The Dutch state secretary on education, Sander Dekker, wants mandatory arithmetic tests for highschool graduation. If you cannot calculate with pen and paper then you can’t get your highschool diploma. Lenstra thinks that this is too strict (see here) but doesn’t provide a practical alternative how to test whether arithmetic skills have been “maintained”. The state secretary apparently is quite happy that he doesn’t have to retrain the 150,000 elementary school teachers, many of whom are likely to fail too, and that it suffices to increase the burden for the 4,000 secondary school teachers, and of course the burden for the kids who turn 16 or 18 and discover that the educational system has given them a raw deal. (It is a bit too easy to blame them that they should have worked harder.)

One might say that Lenstra’s 2009 KNAW Report and recent June 30 2014 KNAW conference presentation (my report in Dutch) aren’t quite research themselves but rather evaluations on educational policy. It may well be that Lenstra’s texts here don’t register under scientific integrity in a strict legal sense, even though Parliament regards it as scientifically warranted. In another respect, Lenstra’s case is just an example, and it is a collective problem that abstract thinking mathematicians expound about empirical issues that they haven’t studied. Hence, my letter to KNAW-LOWI suggests a general exploration into the issue, so that the scientific community grows aware of the issue. Hopefully the specific issues on Freudenthal and his Institute are taken along, as explained here.

PM 1.

Above mentioning of Abstraction vs Empirics might cause the idea that those would be opposite, but these are rather separate axes. We might score the different professional groups on the study hours in each category, with mean and dispersion. I mention two example individuals for lack of an accepted term like “empirical mathematical statistics”. Since teachers teach they aren’t in research like other professions.

Abstraction vs Empirics

Example scores in the Abstraction vs Empirics space (might be tested)

PM 2.

This weblog concentrates on failure on integrity within Dutch economic science, with the case at the Dutch Central Planning Bureau (CPB) concerning economic co-ordination and the example of unemployment. That censored analysis is relevant for the current crisis in the European Union, and for economic recovery in the United States, and for economic policy in the “emerging markets” too. My advice is to boycott Holland till the censorship of economic science here is resolved. KNAW-LOWI cannot officially tackle the case since its mandate concerns universities while the CPB falls directly under the national government.

But now there is a breach in integrity in research in math education as well. I have two academic degrees, one in econometrics and one in teaching mathematics, and it is disappointing to observe that my degrees open up to vista’s of non-integrity. It might soon become a personal thing. But, as Art Buchwald would advise us: while there is a whole country to blame we might as well take a look at the facts. And boycott that country till they get their act together.

The world chooses to use English rather than Dutch or Latin, and hence we fall in the Dutch language sink again. As my letter is in Dutch, we might need to look to whom in Belgium, South Africa or Suriname still understands the gibberish. I presume that the people in New York (“New Amsterdam”, if they only knew) would need a certified translator. There might be some expats living in Holland who have learned some Dutch but I am afraid that some issues are getting complex, and then even many Dutch people would not be able to follow things. Foreigners would have even more difficulty in understanding local conditions. Hence I am quite hesitant to translate that letter.

For comparison on KNAW-LOWI, we may look at the US bureau for research in education, IES, and the office of research integrity ORI of public health, and then also the ethical codes of AMS and MAA.  There are a lot of ethics to look into.

But let us not forget about education itself, and thus let me also alert you to this issue of CF with Forty Years of Radical Constructivism in Educational Research and hope that they put students before method.

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