A disciplinary board for mathematicians

You can read this best while listening to the beautiful Eleftheria Arvanitaki and her rousing Metrisa on YouTube. I don’t know what she actually sings about, and I don’t want to know, but you can sense the thunder clouds forming on the horizon, with already some flashes of lightning.

The Italian election result feels like that too. A deadlock, commentators say. Europe is in crisis again, they hold. Perhaps it is a blessing in disguise. Belgium needed 18 months to create the Elio di Rupo government, and many thought that the country actually did well and got a much needed period of rest.

There is discussion about a grand coalition of leftist Bersani and rightist Berlusconi, or perhaps a minority government but supported by Grillo. Grillo wants to judge proposals on their merits separately and refuses to bargain about a full programme. In these political analyses the habit of thinking in majority governments wreaks havoc again. According to this view you team up to kick out a minority. Why would it not be possible to have an inclusive government, in which (most of) all parties partake ? It is a good idea indeed to judge proposals on their merits, to keep out pork barrel, but still with the intention that all have to live in the same country.

We see an example in this duet with Arvanitaki. The somewhat aged beauty who sings Na Na and who keeps breaking her earthenware bells is Haris Alexiou, who has produced wonderful albums and who performed in great concerts. Listen to her stately singing, the vivacious apopse with images from her younger years, and the touching oles, a classic. Or Ximeroni ! (Unfortunately with bad sound quality.)

I admit, illustrating Italian election results by Greek singers may come across as farfetched, but the association actually is rather sound, because co-operation is also a form of art. Many people regard democracy and elections as sport, and they only notice the winner. In reality, those winners and their supporters may be the barbarians, lost to culture and civilisation.

Some suggest to break the deadlock in Italy with new elections. In that case we might see what I have been advising for some years now: (1) governments that mirror parliament, (2) annual elections. This gives voters more power and still forces politicians to co-operate. Two other crucial advices: (3) select the prime minister with a Borda Fixed Point method, so that he or she has broad support and still can function in impartial manner above the parties (see this application to Holland), (4) create an Economic Supreme Court that watches over the quality of information. These four elements improve the responsiveness to popular sentiment without turning into populism, and they increase the quality without turning into technocracy.

Notice that there is a fundamental problem here. Election methods normally are a disaster. In the US election between Bush, Gore and Nader the winner was Bush while Gore would have beaten each of the others in pairwise comparisons. In the French election between Chirac, Jospin and LePen the winner was Chirac, while Jospin would have beaten each of the others in pairwise comparisons. Lawyers who write electoral laws tend not to understand much of mathematics, and then ask advice from mathematicians, who however create math from thin air and apply it to reality without understanding reality. Democracy disappears in the ravine between alpha’s and beta’s, the Two Cultures of C.P. Snow.

Italy has developed a complex system to allocate seats with the intention to enhance stability. That system now seems to enhance instability. It might be that it works out okay, as we hope above, but that would be by chance or wisdom, and the electoral system remains a disaster.

Of the many people who have been sleeping, a great responsibility falls on the politcians who voted this system into action. There is also a responsibility for the mathematicians who have been advising in the background. The fundamental problem is they can help to design systems, but run away from criticism, do not acknowledge error, and thus do not learn from mistakes. With their structurally erroneous advices these mathematicians destroy huge democracies.

We need a disciplinary board for mathematicians. When a medical doctor gives a wrong advice then there is such a board. A mathematician who doesn’t study reality but still advises that abstract notions apply to reality, is condemnable in the same manner.

In a short Dutch article Pas op met wiskunde over verkiezingen I explain the issue at a level for highschool students. Its appendix also contains a list of some 10 mathematicians who run away from criticism on their work on voting and democracy. In 1990 I observed that serious errors were being made, and the list gives that experience of denial since then. The list contains only mathematicians who are supposed to have an ethic of ‘definition, theorem, proof’ and who sin against that, even when the error is pointed out to them. It is no use to make a list of economists and political scientists who repeat the errors of the mathematicians, since that list would be much longer, and they would tend to refer to the mathematicians anyway (as if that would be proper).

The story turns into horror. I do not know whether I should refer to the dancing and waving of Eleni Bitali and her song about her life (zoi mou). Beware: first it seems as if she is the blond lady but later the camera switches position and it appears that she is the lady with red hair. I offered above Dutch article to the journal of the Dutch Association for Mathematics Nieuw Archief voor Wiskunde (NAW). One would think that the editors would be delighted with a short exposition of the major errors by mathematicians on voting theory and democracy. At that, a discussion that high school students should be able to understand, and that reviews which mathematician better corrects which misunderstanding. One would expect that the editors would desire to advance better mathematics. But no. Editor Barry Koren of the University of Leiden answers that he has studied the short article, fails to understand it, doesn’t specify what passage he doesn’t understand, rejects the paper and closes the discussion, in one grand sweep. I have included his name on the list of failing mathematicians because of this event, though as far as I know he hasn’t written on voting theory. But the horror is that this concerns criticism on the math profession and that a journal blocks that criticism.

Perhaps professor Koren of Leiden didn’t understand that the article was targetted at a level of exposition for highschool students, though it was explained to him. Perhaps he mistook the easy language with sloppy thinking. Perhaps he wanted to see complex mathematics though he could have found these in the references. We can imagine various misunderstandings. The fundamental point is that he presents a closed mind. An econometrician is not allowed to criticize mathematicians when they don’t study reality but still give advice on that.

Do the mathematicians fail only on democracy and election methods ? No, they do so too in the education of mathematics, when they have been trained for abstract thought and suddenly encounter real life pupils. They do so too when they are ‘rocket scientists’ and develop financial products that do not account for real risks. They do so too in the study of logic when they exclude nonsense while that is the most nonsensical thing to do. I only mention areas that I have studied myself and where I have established this. Perhaps other people have other examples.

My advice for a disciplinary board for mathematicians thus is dead serious.

We end with Eleftheria Arvanitaki and a sirtaki in the studio. Listen especially from minute 37 onwards, when the guests have unpacked their presents, and Eleftheria enchants all hearts, with all eyes becoming watery and proud men holding on to their sigaret, and with Haris Alexiou in full rapture.

When Greek singers and their musicians would travel over Europe and would teach us to sing and dance then they have another export product with great potential, alongside with those earlier ideas about democracy and mathematics.

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