Monthly Archives: October 2014

The Royal Dutch Academy of Sciences (and formerly Arts) KNAW in Amsterdam had a session on both cancer and math. The issue of cancer is of general importance while math may require a bit more patience.

Roland Kanaar and 42° Celsius

From Douglas Adams and his Hitchhikers’ guide to the Galaxy we know that the number 42 is important. Roland Kanaar cs have discovered that 42º Celsius hinders cancer cells to maintain their wrong DNA. Heating cancerous cells makes them vulnerable to additional treatment that can cause their cell-death. It is a medical and complex story and I should not try to repeat it. Here is a page in wikipedia that I perhaps should not refer you to because it is not clear what their medical standards are.

My reason to mention the issue is rather something for general awareness. A review in (meta) epidemiology – I lost the reference, shame on me – showed that three factors are most important for cancer – apart from many others like genetics of course:

  • time: thus, when you grow older then cells have more chance to go wrong
  • number: thus, when you have more cells (you are bigger), then there is more chance that some cells go wrong
  • non-specialisation: thus, cells that are specialised don’t change much, while non-specialised cells that still have to find a specialisation may make a wrong turn.

A key example is breast cancer. Women in the West are larger than women in the East, and thus run greater risk. Diet of fish rather than meat, and oil rather than butter, would not be so relevant, and mainly size is important. Looking for an example I came across this somewhat commercial “Double Dutch” crowdfunding video that argues that women in Holland would tend to have larger cup sizes. It is on record that the French philosopher Descartes and the painter Monet already had an issue with this, which eventually contributed to them leaving the country. Subsequently, there is also the specialisation of the breast cells. For mothers who have breast-fed, the cells have specialised to a function. For other women the cells are waiting what to do, and thus run greater risk that DNA transcription causes some error. One remedy to prevent breast cancer thus would be that women also without child still participate in breast feeding, or have equivalent hormone treatment. One would have to set up a (randomised controlled) trial to work out the parameters and verify this idea.

This session at KNAW also reminded me of my 2004 discussion of an STI passport, which may be an exercise in logic but which at least clarifies some of the points to consider.

Amsterdam Nieuwmarkt October 27 2014 (four couples and a backpack)

Amsterdam Nieuwmarkt October 27 2014 (four couples and a backpack)

Jan Bergstra and division by zero

Subsequently Jan Bergstra presented his ideas on calculation on the computer. Data types determine how numbers are handled. A crucial issue is how to deal with “division by zero”. This division is an error but it may not clear how to handle that error. Computer programs may make different choices. Apparently Intel might turn 1 / 0 into 0 but Wolfram Mathematica has 1 / 0 become Indeterminate. Professor Bergstra wonders what would be the best mathematical answer to this issue – which answer may also be seen as a transcription of 1 / 0. I wonder whether it wouldn’t be better to approach the issue from the angle of computer algebra – like Mathematica – so that the issue actually is already solved, and see this paper of almost 15 years ago about some technology choices. But perhaps the mathematical problem remains to select the criteria for deciding “that it is solved”.

Professor Bergstra was helpful with advice on this paper of mine: Education, division & derivative: Putting a Sky above a Field or a Meadow (September 2014). In some respects he might be regarded as a co-author since the paper develops along his objections and explains how those can be dealt with. We still disagree on various points, but I regard my paper as finished so it is up to him to indicate what his view is. I suppose that an academic can always find a new question – that is what academics are for, except when they abuse their leisure to ask silly questions. The main issue is what works for education, and here KNAW and the Ministry of Education are in an awkward dance. It is better that Parliament starts to enquire the issue. For Dutch readers: see the petition. For the rest of the world: see the idea of academic schools like academic hospitals. It is much better to talk to Roland Kanaar who has researched his issue than to Jan Bergstra who has little idea about education but thinks that he does.

Overall, readers must be aware of the paradox that I am a teacher of mathematics but not a (research) mathematician. I am willing to go along in a lot of theory but my bottom line is that students should benefit in understanding and competence. An issue like 1 / 0 must be solved in highschool this very instant and we don’t have the luxury that some seem to suggest.

At KNAW, a dove looks for some sunlight, Monday October 27 2014

At KNAW Amsterdam, a dove in search of some Autumn sunlight, Monday October 27 2014


After the lectures, it was fortunate that there was an opportunity for a longer discussion, that I can report upon, between me, Jan Bergstra and Bas Edixhoven (Leiden, KNAW). There were various topics, but let me now concentrate on this issue:

  • See is this memo of mine to Jan and Bas on Cantor’s “diagonal proof” for the power set
  • Bas follows Cantor & Hilbert and produces a theorem and proof, that I deconstruct, so that my book ALOE applies,
  • Jan is caught in the middle, since I had been discussing the derivative and “division by zero” with him, and now there is a whole range of new issues to deal with.

Overall, though, the key issue remains the education of mathematics. I have reported that the integrity of science is at stake here. Jan Bergstra happens to be the secretary of the mathematics section of KNAW Royal Academy of Sciences of Holland. Let us hope that he can handle this issue without getting distracted by my other analyses on the derivative and Cantor and the Liar paradox and such.

Thomas Robert Malthus (1766-1834) recently visited Maastricht, known for the creation of the European Monetary Union and the establishment of national debt and deficit ceilings. Sitting at the bank of the Meuse river and watching the ghosts of long departed salmon splashing in the stream and its gentle vortices, Malthus allowed for some soul searching as well. It appears that he always used the name Robert so that our intention to link him up with Tomas Sedlacek and Thomas Piketty collapses.

Malthus and Darwin

Malthus set Charles Darwin on the path of the theory of evolution. Darwin records in his autobiography:

“In October 1838, that is, fifteen months after I had begun my systematic inquiry, I happened to read for amusement Malthus on Population, and being well prepared to appreciate the struggle for existence which everywhere goes on from long- continued observation of the habits of animals and plants, it at once struck me that under these circumstances favourable variations would tend to be preserved, and unfavourable ones to be destroyed. The results of this would be the formation of a new species. Here, then I had at last got a theory by which to work”. (Taken from this weblink.)

Malthus and Keynes

Malthus set John Maynard Keynes on the parth of the theory of effective demand. Keynes in his Essays in Biography:

“If only Malthus, instead of Ricardo, had been the parent stem from which nineteenth-century economics proceeded, what a much wiser and richer place the world would be to-day!” (Keynes 1961 [1933], p. 120) (Quoted by John Pullen in HETSA here)

Relevant is also this archive of the History of Economics Review, and in particular Steven Kates on JMK and TRM and then also on JMK and McCracken,or see the longer discussion by Kates in HER 48, 2008.

“Thus, at the very time that he has commenced writing the book that will become the General Theory, the single most influential book on the business cycle written during the past century, Keynes states in no uncertain terms that the most fruitful approach to dealing with the economic issues raised by the cycle ought to be set within an analytical framework that descends from Malthus.” (Kates HER 48, 2008)

Note that David Ricardo isn’t kicked out of the window. His method of mathematical modeling is retained, of course. His arguments are duly weighted too. The only thing is that Malthus’s argument on the lack of demand finds proper recognition. What was counter-intuitive to Ricardo is rephrased so that it becomes the proper intuition that we enjoy today. Merely putting money in the bank doesn’t help: it are the real investments that determine income.

“The Keynesian Revolution, which swept the economics world in a matter of less than a decade, had its origins in Keynes’s reading of Malthus’s letters to Ricardo in late 1932. It was from these letters that Keynes discovered the issue of demand deficiency. Reading Malthus’s letters in the midst of the Great Depression infused within him the be­lief that demand deficiency was the cause of recession and mass unem­ployment. The essay on Malthus, found in Keynes’s Essays in Biography and published in February 1933, makes plain the extent to which he had absorbed Malthus’s economic views while reading Malthus’s writings. Malthus had been the leading advocate of demand deficiency in the nineteenth century. It was this message that Keynes’s carried into the twentieth.” (Kates 2010, History of Economic Ideas, xviii/2010/3)

The Keynesian revolution is still relevant. There is criticism whether the model still applies, but see the About page for my amendments to Keynes and Tinbergen so that there is a sound manner to tackle the economic crisis. See my memo in the Royal Economic Society Newsletter October 2014 for the need for an Economic Supreme Court per nation.

Allin Cottrell has the nice argument that the Ricardo-Malthus discussion used money as a veil, and that Keynes showed that Say’s Law only breaks down when money isn’t a veil: so that Malthus was wrong and so that it is curious that Keynes selects him as a hero. I have “always” been somewhat intrigued by the historical use of the tally stick, and wonder whether analysts like Hume and Smith and thus also Ricardo and Malthus could really regard money as only a veil, certainly after the creation of the Bank of England in 1694. Even more amazing is that Jean-Baptiste Say himself wrote letters to Malthus too, see the pdf at the Von Mises institute. But I am not a historian and all this leads too far.

I had thought that I could leave the matter at that, so that this would be a rather short section, but the ghost or google of Robert Malthus alerted me to an issue.

Sanjeev Sabhlok 2012 claims that Keynes plagiarized Malthus and McCracken. Sabhlok himself copies this 2010 article by Kates. However, Kates denies this plagiarism on some points and merely asks pointed questions on other points.

Thomas Robert Malthus 1766-1834 (Source: wikimedia commons)

Thomas Robert Malthus 1766-1834 (Source: wikimedia commons)

Kates provides statements from the Rymes lecture notes in Autumn 1932 that show Keynes referred to Malthus and a failure of effective demand. Keynes biography of Malthus of early 1933 would make clear that he came to this view independently.

Keynes can only plagiarize McCracken in that biography of Malthus if he would have used earlier articles by him without proper reference. But currently there is only evidence about an exchange in 1933, after the publication of the Essays in Biography.

The picture is diffuse, since Kates in this other text refers to John R. Commons (1862-1945) who apparently already wrote on Ricardo and Malthus around 1920, and whom Keynes wrote to in 1927. McCracken wrote his Ph. D. thesis with Commons, and there is a joint article in 1922 on the business cycle. There is for example also William Trufant Foster (1879-1950), apparently a precursor to Keynes too, but eclipsed by the impact of the General Theory. Thus, Keynes had ample impulses to look into the Ricardo-Malthus controversy, after the 1929 Wall Street Crash made that issue urgent again. But it seems that the Ricardo-Malthus controversy was part of general knowledge amongst researchers like Pigou and Keynes anyway.

Kates shows that McCracken in early 1933 sent a copy of his 1933 book to Keynes. Kates suggests that it is to Keynes as a person, but it may also have been for a review, since Keynes was editor of the Economic Journal. There is a review by (if I understand it correctly) James Meade, EJ, Vol 47 no 186 (June), p 337-339, 1937 – somewhat late for such an important book from 1933. Correction 2015-01-01: Keynes’s 1933 letter to McCracken clearly states: “Having now read your book, I must again thank you for having sent it to me.” Thus it must have been sent directly, and note the “again”. I thank Kates for correcting me on this, and his additional comment is: “if it is not a personally sent copy, there is no reason for Keynes to have written to McCracken at all.”

One supposes that Harlan McCracken (1961) “Keynesian Economics in the Stream of Economic Thought” would explain the situation himself. Kates quotes McCracken stating that Commons developed the theory of expectations (“futurity”) twenty years before Keynes. Common’s 1934 book that further develops that issue would almost certainly have drawn the attention of Keynes, who already admired him in 1927. (Addendum 2015-01-01: I now have a copy of McCracken (1961) and should return to the issue later on.)

However, did Commons put all the pieces of the puzzle together to create the General Theory ? One additional piece on Say’s Law was provided by McCracken himself, but there are also the issues of liquidity preference, the internal rate of return (a.k.a. marginal efficiency of capital), and the Knightian “uncertainty” related to the ‘animal spirits‘ (Aristotle’s spiritus animalis).

One point is that, when McCracken was writing on the history of economic thought in 1930, he might have tried to contact James Bonar, editor of Malthus, or Piero Sraffa, editor of Ricardo, and thus have indirectly caused Keynes to look at the Ricardo-Malthus correspondence. Malthus’s letters were rediscovered, but how exactly ? It is up to historians to see whether more evidence on this can be recovered.

The proper point to consider is:

“One could, of course, decide Keynes had found someone else who had come to the same conclusion as he had on Ricardo and Malthus. Coincidence possibly or parallel development of ideas.” (Kates 2010)

“The fortuitous arrival of McCracken’s Value Theory and Business Cycles in early 1933 was a prime example in the parallel development of thought. Keynes immediately recognised the strong similarity of view. How much Keynes already understood of the context of the Malthus-Ricar­do correspondence or the General Glut debates is difficult to know. But McCracken, being as he was a specialist in the history of thought, would have added to Keynes’s understanding of the issues at stake, and pro­vided an appreciation of what was needed to refute Say’s Law.” (Kates 2010)

Kates shows that Keynes took the summary of Say’s law as “supply creates its own demand” from McCracken rather than the common “supply and demand are in equilibrium”. Keynes had considerable literary talent and will have recognised the value of that formulation. His letter of August 1933 to McCracken therefor seems disingenious. Rather than thanking McCracken for his phrase, he suggests that both reached the same kind of insight at the same time. At best, perhaps Keynes realised only in 1934 that McCracken’s phrasing of Say’s Law was a very effective way to put the argument, but then, why not refer to McCracken in the General Theory ?

The term “insight” should not be overworked. Concluding that Ricardo was wrong and Malthus was right is important as an insight but doesn’t generate the very mechanism for 1933 how to tackle the Wall Street Crash of 1929.

A key question is: why the delay from 1933 to 1936 ? Why didn’t Keynes publish a recommendation in the Economic Journal for the world to read McCracken’s analysis ? In McCracken’s book some elements are already available, of what took Keynes three years to write himself, though in different words:

“If Aftalion [in 1913] has succeeded in establishing the possibility of a voluntary failure of demand by those who have purchasing power but insufficient keenness of desire, when facing expanded production under the influence of the principle of diminishing utility, then it constitutes one of the greatest contributions to economic theory in a generation. Say’s Law of Markets, according to which production financed consumption and supply generated adequate demand is in serious need of modification.” (Kates 2010 quoting McCracken 1933)

Of course, McCracken’s book did not contain other elements that Keynes was concerned about. He however could have said that too. This however would have put Keynes in the position of a reporter. Keynes did not see himself as a reporter. Correction 2015-01-01: I wrote this too fast, since I did not read McCracken (1933), and it might be guesswork what “Keynes was concerned about” (except trying to find clarity). Dr. Kates writes me that McCracken (1933) may be seen as “a preliminary version of The General Theory”. Thus, indeed, historians must read McCracken (1933) and tally the overlap and differences. But my idea that Keynes did not see himself as a reporter would hold. There could have been a choice in recommending the book to others or developing “his own argument”.

His focus was on being a scientist and develop his own theory. Apparently, Keynes was focused on the Einstein’s distinction between the special and the general theory of relativity. The special theory is Say’s Law, the general theory allows this law not to hold as well. He might use what was available in the literature, but his own contribution would be the complete picture. In that complete picture the elements changed their role because of that complete picture. In this, I merely rephrase Kates’s observation:

“However, in showing that savings might grow as a proportion of in­come as income increased, it would have been clear to Keynes that less than half the task in demonstrating the possibility of demand deficien­cy was complete. What was still needed was a theory to explain why the additional savings made available because of a proportionate drop in consumption would not be channelled into investment through adjustments in the rate of interest. The elements that went into this part of the story were, in essence, the theory of liquidity preference, the mar­ginal efficiency of capital and the related notions of expectations and economic uncertainty. These were, however, concepts that in early 1933 Keynes had not yet appreciated the significance of. As he noted in an oft-quoted passage in his letter to Harrod (cw, xiv, 85), these concepts would be assembled one by one. Each of these concepts had already been discussed in depth in the contemporary economic literature by leading economists but in each case with a different purpose in mind. Moreover, each of these econo­mists had had a book published during the early 1930s while Keynes was preparing the General Theory. Two of these works were published in 1933 and two in 1934, the years of greatest intensity in the development of Keynes’s core ideas.” (Kates 2010)

Keynes referred to Ricardo and Malthus but generally not to others. This modus operandi is totally unacceptable today.

A negative interpretation is intellectual theft. I am not convinced of this yet. I wonder whether a historian can give more information about the conventions in those days.

About Alfred Marshall writing his Principles of Economics it is known that he first developed an argument and then threw away the formula’s and references since the argument should be convincing by itself, and a reader should not be burdened by the need to look up the references. Marshall taught his students to work in that fashion. It seems that Keynes worked in that fashion indeed.

A positive interpretation is as follows:

  • Given the manner how arguments were settled in the academia and government circles in those days, nothing would do, except the formulation of the General Theory.
  • A reference would draw attention away from the General Theory. Reference would occlude the new role assigned to the particular piece in the puzzle. Such reference would cause discussion whether a definition was applied correctly, and whether it could indeed be put to such new use.
  • Since this applied to various authors who provided various pieces of the puzzle, the discussion would fragment over all these authors, instead of focus on the point that the puzzle was finally completed.
  • The book was about Keynes making up his mind, it wasn’t a report about how others contributed to the solution to the puzzle.

Kates asks:

“It is thus an interesting question why Foster and Catchings, worthy heretics in 1933, had been dropped from the list by 1936. Indeed, why McCracken is not on this list, and perhaps Commons as well, are questions that might well be asked.” (Kates 2010)

An answer is – of course unacceptable in our days:

  • References to Foster and Catchings and Commons and McCracken might weaken the General Theory, for, all arguments that had been waged in the past to those authors would then be wielded against the General Theory.
  • A reference would cause a discussion of particulars, refutation of old arguments, and only then the introduction of the new application.
  • The General Theory might require more than double its present pages.
  • Reference would not be necessary for the connaisseurs (who also read the Wall Street Journal) and who would recognise the relevant authors anyway.
  • Keynes did not mind referring to some authors that clearly differed from the General Theory so that there would be little discussion about overlap.

Compare Keynes’s argument why he did not refer to Fisher originally and only did so after some urging by others:

“My definition of the marginal efficiency of capital is quite different from anything to be found in [Marshall’s] work or in that of any other classical economist (except for a passage which he makes little subsequent use of in Irving Fisher’s latest book).” (Kates 2010 quoting Keynes cw, xiii, 549)

It is a convoluted statement that indeed is rather disingenious. Why not clarify Marshall’s method of exposition ? Marshall might say: Why waste time on discussing Fisher’s use of that definition if it doesn’t pertain to the role that the notion has for the General Theory ?

A key question: Did the General Theory settle the various disputes or did it create more dispute ?

One may suppose that there would have been much earlier discussion about references and priorities w.r.t. Kahn, Commons, McCracken, Schumpeter, Fisher, Knight, Foster & Catchings, and the Swedes, if the Harrod, Hicks & Meade IS-LM model hadn’t surfaced soon and shown the usefulness of the complete picture. There has been ample discussion of the precursors to the General Theory, but Kates’s inclusion of McCracken and the subsequent deconstruction indeed is a new twist to the story.

PM 1. On the use of the words “uncertainty” and “risk” see this discussion. PM 2. See how consumer durables would be investments that satisfy Say’s Law. PM 3. The wikipedia article on effective demand Oct 26 2014 is deficient. Effective demand is the actual production occurring in the present short period, following the decisions that entrepreneurs have made, based upon their expectation of what people will demand and they will be able to sell. PM 4. My analysis on unemployment continues from that of Keynes and Tinbergen, see the About page. I am willing to defend that theory and have no vested in interest in Keynes’s ethics w.r.t. his references. PM 6. Perhaps the best introduction to the GT is Fanning & O Mahony (1999) “The General Theory of Profit Equilibrium: Keynes and the Entrepreneur Economy“. PM 7. See Coleman’s review of Kates’s earlier book on Say’s Law. Kates is a bit in danger of suggesting “Keynes stole, but from crackpots”. The true story would be that Malthus and others weren’t crackpots and that Keynes might have reasons, seemingly defensible at that time in the Marshall way, for not referring to all. Kates seems a fine scholar to me, but in his IEA weblog he attacks a rather vulgar ‘keynesianism” that is very remote from the real Keynes, as if this Steve Kates here is a quite different person. PM 8. See my protest against plagiarism in the research in mathematics education.

Malthus and McCloskey

Deirdre McCloskey (1942) invokes Malthus to maintain that homo sapiens sapiens (but rather, with Darwin, the little bit more intelligent version born circa 65,000 years ago, perhaps in the wake of the Toba volcanic eruption) lived on $3 a day until 1800 AD, after which income exploded 30-fold. Her theory is that the latter income explosion derived from respect for the individual, such that ideas & innovation, that normally occur in 10% of the population but that are suppressed by tyrants and priests, finally got the chance to work their wonders. She tends to state that the process started in Holland, see our earlier weblog text on the Dutch World Empire.

A hypothesis concerns the influence by Geert Groote (1340-1384), from the Hanseatic towns of Deventer and Zwolle. The Wikipedia article is lackluster on him, for it doesn’t emphasize that Groote started elementary schools and that his convents were factories that produced hand-written bibles for common people to read. Johannes Gutenberg was inspired to invent the printing press in 1455 only because there was already a big market for people reading the bible because of Geert Groote. See this weblog text on the Scottish Enlightenment and Adam Smith, and this CPB research paper.

There is an instructive Nebraska 2014 video in which McCloskey wiggles her finger to illustrate Malthus’s law of population from 250,000 years ago (this should rather be 65,000) to 1800 AD and then the woosh take-off. Perhaps you must know that she has a small speaking disorder that might take to get used to. Overall she makes a lot of sense. The spoken presentation is simpler than Rostow’s theory of stages but her analysis is rather more involved, which you can discover by trying her books – thanking Gutenberg. Unfortunately, McCloskey hasn’t grasped the analysis of this website yet. E.g. she gives the advice of a basic income, and see my reply to that.

The reference to J.R. Commons is not without relevance for McCloskey. Commons, in his stages of economic development, distinguished stages (1) scarcity / feudal, (2) abundance / individual, (3) stabilisation / modern, see Skidelsky “John Maynard Keynes: The Economist as Saviour, 1920-1937”, Macmillan 1992, p229-231.

Capitalism, wild or tamed

Rostow already asked: “where is compound interest taking us? Is it taking us to communism; or to the affluent suburbs , nicely rounded out with social overhead capital; to destruction; to the moon; or where?”

Interviewer Evan Davis, The Spectator May 24 2014, who compares Piketty and McCloskey, summarizes:

“Wealth, by whatever means it is originally created, thus begets more wealth; successful entrepreneurs, through their initial accumulation of capital, go on to ‘become more and more dominant over those who have nothing but their labour’. In Piketty’s excellent phrase, it is through capital that ‘the past devours the future’.

(…) She enthuses about the Great Enrichment of the 19th century. ‘What happened, understand, is not 100 per cent growth, but anywhere from 2,900 per cent growth to 9,900 per cent growth. A factor of either 30 or 100.’ That jump in incomes came about not through thrift, she says, but through a shift to liberal bourgeois values that put an emphasis on the business of innovation. In place of capitalism, she talks of ‘market-tested innovation and supply’ as the active ingredient of our economic system. It is incidentally a system ‘drenched’ in values and ethics overlooked by economists.

(…) Bill Gates or Liliane Bettencourt? They co-exist, of course, and have both had a pretty good time of it in recent decades. The question is which one better characterises the very rich. And also which risk you would rather take: taxing the Bills at the risk of deterring them from creating Microsofts? Or not taxing the Lilianes, at the risk of letting them become ever wealthier and more powerful while sitting at home doing nothing?

(…) I know that the 99 per cent of the population have no difficulty coming to a view. I’m in the sad 1 per cent, who can see both sides.”

Speaking about Bill Gates: recall Malcolm Gladwell on Outliers, and the specific turns in technology that make some people rich, like also Carnegie and VanderBilt. See my earlier discussion of Piketty’s case.

The Maastricht Treaty question

Phillip Longman in his May 2 WSJ review of Robert J. Mayhew (2014) Malthus. The life and legacies of an untimely prophetdistinguishes the young and old Malthus. One might find it a bit surprising that the old Malthus provides exactly the position of this weblog, see the About page:

“To accommodate such anomalies to his original theory, Malthus developed the concept, later reformulated by Keynes, of effective demand. The main cause of poverty, Malthus gradually conceded, was not that there were too many people or too few natural resources; rather it was that society was organized in such a way that too few people had a way to earn the money necessary to buy the resources they needed. Give them a job or some other way to make money, Malthus concluded, and the problem would be solved. As Keynes summarized Malthus’s intellectual journey, which was one that Keynes himself followed: “Just as the young Malthus was disturbed by the facts of population as he saw them round him and sought to rationalise that problem, so the older Malthus was no less disturbed by the facts of unemployment.”” (Longman, WSJ 2014)

We are thus left with the final question in this musing with Robert Malthus on the banks of the Meuse river that flows through Maastricht:

What to do with the economic crisis in the European Union ?

Alas, a chilly October breeze touches Malthus and he drifts off, solving in fragments, evaporating over the Meuse’s waters.

On November 5, Thomas Piketty will inform Dutch Parliament in The Hague and then continue to Amsterdam for the evening. While he is busy in The Hague – and likely will be grilled on the French economy – there will be a small symposium on inequality at the University of Amsterdam so that the students are prepared for the evening. Then in the evening Piketty will be interviewed by Joris Luyendijk (Dutch, The Guardian), who we can see already praising Tomas Sedlacek and his book on the economics of good and evil in this video from Belgium.

For some curious reason – probably to exploit the library budgets – there will also be a Dutch translation of Piketty’s book on October 30, even though it is a scientific book and English is the language of science. But, rationality and consistency are hard to maintain in an international hype. Also, for Dutch translators it is easier to translate from English to Dutch than to translate from Dutch to English. Translators paradoxically are a major cause for maintaining the Dutch language sinkhole.

My objection is that Piketty’s bookcase doesn’t have copies of my books DRGTPE and CSBH.

Thomas Piketty in Amsterdam 2014-11-05, Announcement (Source: Screenshot Paradiso)

Thomas Piketty in Amsterdam 2014-11-05, Announcement (Source: Screenshot Paradiso)

Overall, I seem to be one of the few economists who hasn’t read Piketty’s book yet. I intend to keep it so, not for lack of interest but because of lack of logical necessity. Piketty’s summary does not indicate that it is essential reading unless you are involved in economic statistics.

There are two papers w.r.t. Piketty’s work that I can recommend:

  • James K. Galbraith, Unpacking the first fundamental law, RWER 69download pdf
  • David Colander,  Piketty’s policy proposals: How to effectively redistribute incomeRWER 69, download pdf

I am happy to observe that inequality was large before 1900 and that labour unions, mass education and the welfare state contributed to a much more equal society. The economic analyses of Keynes (1883-1946) and Tinbergen (1903-1994) provided a framework such that natural human desires for democracy and social care could be combined with sensible economic policy. The problem is that this fortunate combination broke down since 1970. The explanation is provided in these sources:

Unfortunately, Holland appears to be a rather sick country that doesn’t mind censorship of economic science.

In that symposium at the University of Amsterdam there is econometrician David Hollanders, who in 2004 wrote a curiously convoluted analysis on the ‘death of politics because of the technocracy by said CPB’, but it may be that he also asserted the opposite because his analysis is rather inconsistent. Hollanders rejected to look into the censorship at the CPB. The magazine De Groene that published his convoluted article did not print my protest against his gibberish, see this 2004 protest here, and see also my 2012 protest against the Dutch “young Turks” who are so-called critical but who are intellectually lazy (and, indeed, try to find a translator for these Dutch texts). Fact-checking De Groene, we find that they put Thomas Piketty on their cover twice. Apparently they will use anything that sells, hypes included.

That symposium is also organised by AMCIS, and one click away is AIAS where we find professor Paul de Beer, who we discussed before on the basic income issue. Holland remains a small country.

My own work that relates to inequality, apart from full employment:

Thomas Piketty twice on the cover of De Groene (Source: website screenshot)

Thomas Piketty twice on the cover of De Groene (Source: website screenshot)


Tomáš Sedláček (1977) (henceforth without accents) will be giving the 32nd Van der Leeuw lecture in Groningen, November 7 2014. The title of the lecture isEconomics as an Unorchestrated Orchestrator“. This reminds of Adam Smith’s Invisible Hand or modern-day recourse to The Great Divinator of “the financial markets”. Since the lecture is held in the Groninger Martini church the religious notion that God himself creates order comes to mind as well. In this RSA video Sedlacek refers to economics as the modern religion indeed. However, his lecture in Groningen will be refereed only by professor Barbara Baarsma (1969), CEO of SEO in Amsterdam.

Actually, the Foundation that organizes the lecture has as its main purpose to use that church for other cultural or social events rather than the dwindling religious services. Especially when the heating costs in November must be bridged before the uptake around Christmas, it is useful to organise some event to get people into the building. Since the building concerns a church, they found a theologian to name the lecture series after, even though Gerardus van der Leeuw (1890-1950) isn’t so remarkable compared to other Groningers Daniel Bernoulli (mathematician), Johan Huizinga (historian), Heike Kamerlingh Onnes (discoverer of superconductivity) or Hendrik Willem Mesdag (painter). Every human being is important and should be remembered however, so we can only hope that more cities take the opportunity to dedicate their lectures to those who are in danger of being forgotten especially when the weather turns cold.

Announcement 32nd Van der Leeuw Lezing (Source: screenshot website)

Announcement 32nd Van der Leeuw Lezing (Source: screenshot website)

That Sedlacek gives the lecture fits the confusion of location and purpose. Sedlacek does history and philosophy but uses the label of economics. Listeners in a church and partaking in a non-religious event should not mind another and lesser distortion. Unless we have returned to the historical situation that everything is religion anyway.

Sedlacek is known internationally for his 2011 book Economics of Good and Evil: The Quest for Economic Meaning from Gilgamesh to Wall Street, see this review by Samuel Brittan in the FT. The book is his thesis that was rejected by the Charles University, and his website mentions that he is still registered there as a Ph.D. student. I haven’t read that book but have read some reviews and watched also this video recorded in Amsterdam June 11 2013.

I know about Evil, since I wrote about the pure evil of the basic income. I know about Good since I wrote The simple mathematics of Jesus (2012). I know about Economics, see the About page. I still don’t know whether Sedlacek’s book is good or evil but it doesn’t look like economics to me, whatever Deirdre McCloskey says about it. A term used is “meta-economics” but that might be comparable to sociology perhaps. I settle for “history and philosophy while trying to focus on economic thought”.

The publisher “describes” the book as:

“Tomas Sedlacek has shaken the study of economics as few ever have. Named one of the “Young Guns” and one of the “five hot minds in economics” by the Yale Economic Review, he serves on the National Economic Council in Prague, where his provocative writing has achieved bestseller status. How has he done it? By arguing a simple, almost heretical proposition: economics is ultimately about good and evil.

[Comment by TC: Surely, since economics is not about good and evil, it is ground-shaking to turn economics into theology indeed. Doing so is not heretical but quite fitting in church. It is quite a miracle: to be at an economics department, stop doing economics, but convince other people that you are still doing economics. As people can believe that Jesus walked on water, they can also believe that you are doing economics. The same miracle was performed by mathematicians who said that they were doing economics but in fact continued doing mathematics.]

In The Economics of Good and Evil, Sedlacek radically rethinks his field, challenging our assumptions about the world. Economics is touted as a science, a value-free mathematical inquiry, he writes, but it’s actually a cultural phenomenon, a product of our civilization. It began within philosophy–Adam Smith himself not only wrote The Wealth of Nations, but also The Theory of Moral Sentiments–and economics, as Sedlacek shows, is woven out of history, myth, religion, and ethics.

[Comment by TC: Economics as a science ought to be value-free, but its application is in society and thus its application is immersed in values. Yes, there have been and still are many influences on the development on economic thought, but that does not take away that former distinction.]

“Even the most sophisticated mathematical model,” Sedlacek writes, “is, de facto, a story, a parable, our effort to (rationally) grasp the world around us.”

[Comment by TC: There is nothing new in this, that a mathematical model can be seen as a story or parable – except that it would tend to be consistent and more precise. So what is the point ? Can philosophy be set equal to mathematics, since both are “just stories” ?]

Economics not only describes the world, but establishes normative standards, identifying ideal conditions. Science, he claims, is a system of beliefs to which we are committed. To grasp the beliefs underlying economics, he breaks out of the field’s confines with a tour de force exploration of economic thinking, broadly defined, over the millennia. He ranges from the epic of Gilgamesh and the Old Testament to the emergence of Christianity, from Descartes and Adam Smith to the consumerism in Fight Club. Throughout, he asks searching meta-economic questions: What is the meaning and the point of economics? Can we do ethically all that we can do technically? Does it pay to be good?

[Comment by TC: (1) Economics does not establish normative standards. Economics enlightens such choices. Check e.g. Pareto Optimality: Economic models don’t impose this but elucidate the notion. (2) The latter quoted questions are useful for the talk between an economic scientist and a policy maker. (3) The inner value of economics lies in increased knowledge, as for any science. Like pure number theory in mathematics. (4) The outer value of economics lies in its application. Like using number theory for cryptography for secure bank accounts.]

Placing the wisdom of philosophers and poets over strict mathematical models of human behavior, Sedlacek’s groundbreaking work promises to change the way we calculate economic value.”

[Comment by TC: If philosophers and poets can do without bread and butter, they can be excluded from the economic calculation, and we indeed have something novel. Overall though, economics was developed to get away from those unscientific story-tellers.]

Sedlacek in Dutch VPRO "Tegenlicht" program, June 11 2013 (Source: screenshot)

Sedlacek in Dutch VPRO “Tegenlicht” program, June 11 2013 (Source: screenshot)

Let us conclude with the following points:

  1. Dutch VPRO and professor Baarsma do not report about the censorship of economic science by the directorate of the Dutch Central Planning Bureau since 1990.
  2. Dutch VPRO and professor Baarsma do pay attention to Tomas Sedlacek’s story that isn’t economics and that is at points unscientific.
  3. We can enjoy various points in Sedlacek’s tale. The history of economic thought and its precursors is interesting and it would require a worse author to destroy this. For example the analogy between Christianity and the calculation of sin and redemption is nice. Hopefully he included the invention of Purgatory for the collectors of interest too. But the book should be rewritten before it can be advised.
  4. Check my books DRGTPE and SMOJ referred to above, for the full story on getting an Economic Supreme Court, for a better orchestra.

PM. Since Sedlacek is from the Czech Republic and advised Vaclav Havel, he might take an interest in the point that my analysis in 1990 originated from the Fall of the Berlin Wall in 1989, and was targetted at handling the economic fall out, see this text. The history of Eastern Europe and Russia would have looked quite different when the directorate of the Dutch CPB had respected science – or others in the surrounding had made a correction.

It turns out that Cressida Cowell has been writing her dragon books for years and that the box offices of the films are approaching $1 billion, while this weblog was rather oblivious of that. I only noticed these elementary facts from watching with my youngest son and hugely enjoying How to train your dragon 1 on television and How to train your dragon 2 in the theatre. See the official website for the trailers. The films establish that mankind is destined to fly.

While the Harry Potter films were never convincing with their crude suggestion of broomsticks and overall tendency to neglect humour, the relationship of Hiccup and Toothless not only engages us, reminding of other stories of boy & horse or boy & dolphin, but also makes us want to fly along, dive, loop, plunge, and what you have, and share this close bonding of body and mind. Now that Google is developing robots, the obvious suggestion is to concentrate on flying robots and then notably in the form of dragons, so that the phantasy is just a premonition.

How to Train Your Dragon - And flying it (Source: Trailer Screenshot)

How to Train Your Draghi – And flying it (Source: Trailer Screenshot)

That future is already with us, in that Mario Draghi, the president of the European Central Bank, is yet untrained, and takes us and the world economy diving, looping, plunging, and what you have.

Europe needs someone like Hiccup who neglects danger and is convinced that feeding Draghi some fish will gain the monster’s trust, so that it will let itself be put into a harness and be controlled.

How to Train Your Dragon (Source: Trailer Screenshot)

How to Train Your Draghi – Using a big fish (Source: Trailer Screenshot)

Angela Merkel (in the film called “Astrid”) finds the house on fire and gets a bucket to extinguish it. Obviously, she will not succeed.

Angela Merkel discovers that the house is on fire and picks up a bucket to extinguish it (Source: Trailer Screenshot)

Angela Merkel fnds the house on fire and gets a bucket to extinguish it (Source: Trailer Screenshot)

Read more about this story in these links:

(A) Thomas Colignatus,An Economic Supreme Court“, a piece in the Royal Economic Society Newsletter, issue 167, October 2014, see above “About“.

(B) Still in the dark, not seeing the evidence:

This weblog warned about Frans Timmermans who is intended to play a key role in the new EU Commission. After this warning I deemed it wiser to be silent on him and focus on the math, statements, book, film and interviews by mathematics professor Edward Frenkel of the University of California at Berkeley.

This Friday Timmermans – henceforth T, rather than FT since that is the Financial Times – passed his responsibilities as Foreign Secretary of the Kingdom of the Netherlands on to Bert Koenders who ought to be able to do a better job. It remains amazing that policy can depend upon the Department of Personnel so much.

Let me explain that T has committed social suicide in Holland. He essentially has no political credibility anymore on the world stage. When I meet Jean-Claude Juncker this weekend at one of the farewell parties for José Manuel Durão Barroso then I can explain the situation to him over a few good drinks. Hopefully Jeroen Dijsselbloem will not be there to tell Juncker that he shouldn’t be drinking. This issue would be hard to swallow for most people.

The sentiment in Holland has turned against T and this is indicated, apart from my verdict, by:

  1. The satyrical column “the pin” prints a “speech” by “T” in which he lauds himself.
  2. The site prints an exchange on twitter, in which (a) someone criticizes T at his farewell party, and (b) T reacts remarkably rudely, shooting himself in the foot as a diplomat. holds that T is a “walking mine field between citizen Frans and minister Timmermans”.
  3. Columnist Bas Heijne in the leading newspaper in Holland criticizes T on his mentioning of the oxygen mask: C’est pire qu’un crime, c’est une faute. (It is worse than a crime, it is a mistake.)
  4. Columnist Jonathan van het Reve in a column of October 11 (Vonk p13) in the 2nd newspaper precisely states what I thought myself too, when I noticed that oxygen mask incident.

Let me refer to the BBC report on the T – oxygen mask incident. I hope that Jonathan van het Reve doesn’t mind that I relate his analysis that was precisely mine too:

  1. His tears at the UN Security Council did not achieve anything but turned him into an international celebrity.
  2. When Jeroen Pauw questioned his inconsistency that the explosion was instantaneous and that the passengers and crew had suffered, T was irritated and defended himself with the mask.
  3. But he may well have abused the happenstance that such masks fly around and may land around some passenger’s neck. This aspect of the research has not been completed yet.
  4. T gave priority to his irritation and public standing and new status as a celebrity, above the families of the victims and the political impact.
  5. Families now worry that their relatives have been suffering the 10 km drop.
  6. Commentators in Russia hold that there wasn’t an instant explosion but machine guns from an Ukrainean fighter plane.
  7. T is narcissistic and will meet destiny at one time. Well, in addition to that, my own point is that he comes from Limburg, alike Wilders, see my earlier warning. This Catholic province has an inferiority complex because of 300 years of domination by the Protestant provinces of Holland. We shouldn’t label all people from Limburg or from anywhere in the world, but we should take heed of the facts, and ask the Department of Personnel to do so too.
Frans Timmermans versus oxygen masks (Source: Wikimedia commons)

Frans Timmermans versus oxygen masks (Source: Wikimedia commons)

In the 9-minute Numberphile interview Why do people hate mathematics? – see yesterday’s discussion – professor of mathematics Edward Frenkel states, in minute three:

“Georg Cantor said: “The essence of mathematics lies in its freedom.” But I would like to augment this with the following: Where there is no mathematics there is no freedom. So mathematics is essential to our freedom, to the functioning of our democracy. (…) Our ignorance can be misused by the powers that be. And for us … as citizens in this Brave New World … we have to be more aware of mathematics, we have to know and appreciate its power – to do good but also to do ill.” (Edward Frenkel, Jan 19 2014)

We can only applaud this. In my Elegance with Substance (EWS)(2009):

“Mathematics is a great liberating force. No dictator forces you to accept the truth of the Pythagorean Theorem. You are free to check it for yourself. You may even object to its assumptions and invent non-Euclidean geometry. Mathematical reasoning is all about ideas and deductions and about how far your free mind will get you – which is amazingly far. But you have to be aware of reality if you say something about reality.” (EWS p9)

“Democracy is an important concept. The mathematics of voting is somewhat complex. It would be beneficial for society when its citizens understand more about the mathematics behind election results. Students in the USA have a Government class where such aspects can be indicated. Political Science as a subject has not reached highschool in general. Much can be said in favour of including the subject in economics, since the aggregation of preferences into a social welfare function is a topic of Political Economy. See page 59 and Colignatus (2007b) Voting theory for democracy (VTFD) for details and other references. Most economists will be unfamiliar with the topic and its mathematics though and thus it may well be practical to include it in the mathematics programme.” (EWS p48)

However, let us also look at key criticism:

  1. Mathematician Kenneth Arrow presented his “impossibility theorem” in his 1951 thesis. It holds, in his own words: “there is no social choice mechanism which satisfies a number of reasonable conditions”  Palgrave (1988:125) and quoted in Voting Theory for Democracy (VTFD)(2014) 4th edition p240. Thus collective choice would require us to be unreasonable. Mathematician Arrow continued in economics and got the Nobel Prize in economics for this and other work.
  2. Mathematicians, political scientists and economists have tried since 1950 to debunk Arrow’s result, but did not find real solutions. These areas of science have become a force against democracy. Collective choice would require us to be unreasonable, and this would be scientifically proven.
  3. When I showed in 1990 that Arrow’s words do not fit his mathematics, and a bit later that his result was either inconsistent or incomplete, hell broke out. My paper was suppressed from discussion and publication. A mathematician who was supposed to review VTFD (3rd edition) started slandering. See the journal Voting Matters (April 2013). See my point however that there is a distinction between “voting” (counting ballots) and “deciding”. And see VTFD for the more involved presentation (starting with matricola).
  4. It has been impossible to find someone in Holland to discuss this issue rationally. Here is a report in English on a working group in social choice theory. Here is a page in Dutch. On a website for highschool students,, deluded mathematician Vincent van der Noort, who did not properly study the issue, claims that “democracy isn’t entirely fair“, thus encouraging highschool students to use their ellbows. The editors refuse to correct this falsehood and selective use of sources (or mystery, since Vincent doesn’t define fairness).

I suppose that professor Frenkel discusses democracy in general, without thinking specifically about Arrow’s “Theorem”. Perhaps he doesn’t know about it, and would be surprised that it would be “mathematically proven” that some degree of dictatorship would be necessary. However, to some extent we can agree with him. Good education in mathematics will do wonders for liberty and democracy. But, my point again: the definition of “good education in mathematics” is subtle. See these quotes from EWS too:

“With respect to logic and democracy, Colignatus (2007ab, 2008b), updated from 1981 / 1990, considers statements by mathematicians that have been accepted throughout academia and subsequently society on the basis of mathematical authority. It appears however that those statements mix up true mathematical results with interpretations about reality. When these interpretations are modelled mathematically, the statements reduce to falsehoods. Society has been awfully off-track on basic notions of logic, civic discourse and democracy. Even in 2007, mathematicians working on voting theory wrote a Letter to the governments of the EU member states advising the use of the Penrose Square Root Weights (PSRW) for the EU Council of Ministers. See Colignatus (2007c) on their statistical inadequacy and their misrepresentation of both morality and reality.

Over the millennia a tradition and culture of mathematics has grown that conditions mathematicians to, well, what mathematicians do. Which is not empirical analysis. Psychology will play a role too in the filtering out of those students who will later become mathematicians. After graduation, mathematicians either have a tenure track in (pure) mathematics or they are absorbed into other fields such as physics, economics of psychology. They tend to take along their basic training and then try to become empirical scientists.

The result is comparable to what happens when mathematicians become educators in mathematics. They succeed easily in replicating the conditioning and in the filtering out of new recruits who adapt to the treatment. For other pupils it is hard pounding.” (EWS p10)

PM. See where Georg Cantor went wrong: Contra Cantor Pro Occam (2012, 2013).

In 2009 I wrote Elegance with Substance (EWS), discussing both better education in mathematics and the political economy of the mathematics industry. See the available PDF. Check also Steven Krantz Through a Glass Darkly at arXiv 2008.

The dismal state of mathematics education is generally acknowledged, essentially since Sputnik 1957. People have tried all kinds of solutions. Why do those solutions not work ?

The answer: because of barking up the wrong tree. The finding in EWS is:

  1. Mathematicians are trained to think abstractly.
  2. Education is an empirical issue.
  3. The courses for becoming a math teacher don’t undo what has gone wrong before.
  4. When abstract thinking math teachers meet real life students, those math teachers solve their cognitive dissonance by sticking to tradition: “School Mathematics” (SM).
  5. School mathematics isn’t clear but collects the confusions and wreckages of math history.
  6. Thus we need to re-engineer math education and reorganise the mathematics industry. One idea is that education would use the form of the Medical School: both practice and research.

EWS contains various examples where traditional math is crooked instead of clear. One example is that “two and a half” means addition and should be denoted as 2 + 1/2, but is denoted as multiplication or “two times a half” or 2½.

2009 + 5 = 2014

Now five years later in 2014, this explanation can be enhanced by including:

  1. There is a collective failure w.r.t. the integrity of science, in that Research Mathematicians step outside of their field of expertise (RM) and make all kinds of unwarranted claims about Education in Mathematics and its research (EM). This aggravates the observation above that the conventional EM is lopsided to SM.
  2. It is also a breach of research integrity that the warning in EWS is not responded to. When it is shown that the brakes of some kind of car don’t work properly, it should be recalled – and the same for EM.
  3. This especially holds in Holland. In Holland there is even explicit fraud in EM
  4. For the UK there is some worry, see my 2014 paper Pierre van Hiele and David Tall: Getting the facts right.
  5. For the USA there is now the worry concerning professor Edward Frenkel.

Pierre van Hiele (1909-2010) was the greatest analyst on mathematics education of the last century, with his main thesis in 1957, coincidentally with Sputnik. However, his analysis was maltreated by Hans Freudenthal (1905-1990), who stole Van Hiele’s ideas but also corrupted those – partly claiming his “own” version but without proper reference. Van Hiele looked at the angle of abstract versus concrete, while Freudenthal turned this into model versus reality, which is didactically rather absurd, but which apparently appealed to policy makers after Sputnik 1957. Holland now has a 95% dominant “Freudenthal Institute” that rather should be called the “Freudenthal Head in the Clouds “Realistic Mathematics” Institute”. Apparently, the Dutch RM and EM community is unable to resolve the issue. Internationally, IMU / ICMI (see my letter) has a “Freudenthal Medal” honoring the fraudster.

A leading analyst in the UK is David Tall (b. 1941) who rediscovered the importance of the Van Hiele analysis, but erroneously thinks that Van Hiele was not aware of what he was doing, so that Tall claims the discovery for himself. Part of Tall’s misunderstanding of the situation is the consequence of Freudenthal’s abuse of Van Hiele. Professor Tall should however quickly bring out a revised 2nd edition of his 2013 book to set the record straight.

From Russia with math and confusion

I have discussed some of Frenkel’s ideas. As he hasn’t studied math education empirically, he is not qualified to judge, but he follows the RM arrogance to think that he is. Well, hasn’t he passed through the educational system himself ? Isn’t he teaching math majors now ? These are hard fallacies to crack.

Numberphile has a 9-minute interview with Frenkel, asking him: Why do people hate mathematics?”  I leave it as an exercise to the viewer to identify the amazing number of delusions and fallacies that Frenkel mentions in this short time. Perhaps shortness invites imprecision. However, check this weblog’s texts of the last week, and see that these delusions and fallacies are systematic. Just to be sure: debunking those delusions and fallacies may not be easy. If it were easy, the state of math education would not be as dismal as it is now.

To help you getting on the way, check some of these delusons or fallacies:

  • The beauty of art is abused again. Math education would teach you painting fences but not the appreciation of the great results of mathematics. To some extent one can agree. Math history and some encyclopedia of math are very useful to have. But art education is not intended to get people to make masterpieces. Mathematics education is intended to help students develop their understanding and competence. These are different settings.
  • Frenkel claims that everything is based upon the language of mathematics. “In a way one can survive without art. No one can survive without mathematics.” Since abstraction means leaving out aspects, it should not surprise that if you start with the world and then abstract from it, then your results may indeed be relevant for “everything”. But you cannot infer from such an abstract position that people should love their math education.
  • He again is in denial of the role of mathematics in causing the economic crisis.
  • The problem is often stated in the terms of “people hate mathematics” in a manner that is not linked to mathematics education. As if there are two kinds of  people, mathematicians and other – the elite versus the peasants. But the true problem is mathematics education. Math teachers have their students for some 12 years as their captive audience, and manage to turn human innate interest into said hate. By stating the problem in terms of some vague “general audience” it becomes easier to run away from the responsibility staring you in the face, and the destruction of human lives going on in the classrooms around the world.

Taking a blame without any consequence

There is no doubt that Frenkel respects education – though it is from personal experience and without empirical research of a national curriculum:

“Now that I’ve had students of my own, I appreciate even more what (… my teachers …. have …) done for me. It’s hard work being a teacher! I guess in many ways it’s like having children. You have to sacrifice a lot, not asking for anything in return. Of course, the rewards can also be tremendous. But how do you decide in which direction to point students, when to give them a helping hand and when to throw them in deep waters and let them learn to swim on their own? This is art. No one can teach you how to do this.” (“Love & Math p129)

The major point is this: Asked who is to blame for the dismal appreciation for mathematics (minute five) he offers himself as the scape-goat:

“If I really were to assign the blame, … I would assign the blame to myself. And my colleagues, professional mathematicians. We don’t do nearly enough, in exposing these ideas to the public.”

Okay, so, Frenkel takes the blame. But there is no consequence. No reduction in salary. No prison term – with use of the library to start studying mathematics education. Just the burden to go out into the public and become a media star by comparing mathematics to Van Gogh, Picasso, and what other artist that can be abused and intimidated into an admiration for mathematics that they don’t understand but generally hate.

In minute six he says that the math teachers are not to blame. “They are overworked and underpaid” and “products of the same flawed system”. Thus, the idea that grown-ups should take responsibility for what they are doing, and that professional educators have an ethic to live up to, is flushed down the drain. Jesus absolves the sins of those who believe in him. The topic of discussion is reduced to “beauty”. This will generally concern topics that require an advanced university degree to understand – and that conventionally are presented in a confused manner to the general public (see yesterday).

About the improvement of education, Numberphile properly aks (minute seven-and-a-half): “Why has that not happened ? It seems so obvious. What you said is not like a huge conceptual link. Why isn’t it not already happened ?”

Since he has no clue about empirical science, the world turns into a conspiracy:

“Sometimes I am wondering myself why it hasn’t already happened. It is almost like a conspiracy. I mean, honestly. It is almost like there is this system of mirrors that has been created which distorts reality, that does not allow people to see what is out there.”

His closing statement turns failure on scientific integrity, fraud and dismal negligence into “irony”:

“This is the coolest stuff in the world. And yet everyone hates it. Isn’t it ironic ?”

Left: Dali's "Crucifixion" on a hypercube. Right: Edward Frenkel teaching (Source: wikipedia commons, Dali, Eget værk, Søren Fuglede Jørgensen)

Left: “Crucifixion” on a hypercube, Salvador Dali. Right: Edward Frenkel teaching (Source: wikipedia commons, Dali, Eget værk, Søren Fuglede Jørgensen)

PM. The link of Jesus to a scape-goat is no coincidence. December 25 falls in the sign of Capricorn and Jesus was sacrificed as the Lamb of God. See The simple mathematics of Jesus for a discussion that the Bible is an astrological book – and, if you didn’t know, that astrology isn’t science.

There is a curious argument that 1 + 2 + 3 + 4 + … = -1 / 12  (New York Times February 3 2014).

Some pronounce this as “minus one over twelve” but this weblog proposes “min per ten-two” or “negative per ten-two”. On occasion we employ H = -1, to be pronounced as “eta”. Thus “eta per ten-two” is okay as well. We can also use 1 / 12 = 12H, pronounced as “per ten-two”. (The Germans would pronounce H as “Ha” and we would not want them to be laughing all the time.)

The NY Times article and Numberphile video was debunked by other mathematicians and physicists on the internet, see some links below. However, this weblog looks at issues from the angles of both econometrics and the education of mathematics. From these angles we find:

  1. The article and video do not satisfy the conditions of didactics.
  2. There appears to be a large mathematical industry to confuse people.

Mathematics professor Edward Frenkel is part of the mêlée. He is quoted in above article (and can be heard in some video’s saying similar things):

“This calculation is one of the best-kept secrets in math.”
“No one on the outside knows about it.”

The article states:

In modern terms, Dr. Frenkel explained, the gist of the calculations can be interpreted as saying that the infinite sum has three separate parts: one of which blows up when you go to infinity, one of which goes to zero, and minus 1/12. The infinite term, he said, just gets thrown away.

The latter is rather curious. Why are you allowed to throw infinity away ? If you take something from infinity before you throw infinity away, why would you select -12H and not something else ?

Let us consider the situation, and start with Grandi’s Series. Personally, I was reminded about an approximation to -12H found last year, but since it is only an approximation this comment has been put into Appendix A.

An unwarranted deduction

In Numberphile, Thomsons’s Lamp, there is this video discussion about “Grandi’s SeriesG. That discussion (and on wikipedia retrieved today, see Appendix B) is unwarranted. The proper deduction is:

G = 1 – 1 + 1 – 1 + …. = (1 + 1 + 1 + ….) – (1 + 1 + 1 + …) = ∞ – ∞ = undefined

It is an altogether different question that we can look at the average of the series of partial sums. The Lamp mentions this (to their credit) but uses the same plus-sign which is unwarranted. We should use a different plus sign. Then we find:

G’ = 1 ⊕ H ⊕ 1 ⊕ H ⊕ ….  = 1 – G’    so that   G’ = 2H

Partial sums of G:  1, 0, 1, 0, 1, 0, ….

Summing (again !) those into a series: 1 + 0 + 1 + 0 + 1 + ….

Averaged series G’:   1 / 1,   (1 + 0) / 2 = 2H,   (1 + 0 + 1) / 3 = 2/3,   2 / 4 = 2H, …

The mystery completely disappears.

Divergent series can be operated upon, with differences, sums, averages, until you find something that converges. You might use this to catalog them.

That Lamp video discusses turning on and off an actual lamp, in ever smaller fractions 2^(-n) of a minute, starting at zero, such that the process should stop after two minutes (we can calculate that period mathematically): and then the question is whether the lamp is on or off. This is a badly defined problem. It is the same as the Zeno paradox of Achilles and the hare. A mathematical story using terms from physics doesn’t make it proper physics.

A string theory mystery

I am no physicist and know nothing about string theory, but am a bit perplexed when this other Numberphile video shows that page 22 for 1 + 2 + 3 + 4 + … ⇒ -1 / 12. Note the arrow rather than the equality sign. It remains a question: are they really taking the limit ? Hopefully the deduction in string theory is more to the point than the deduction given in the video. The deduction in that video clearly is not sound. It uses G = 2H but we have shown that only G’ = 2H. Indeed, see below for some links to physics websites that show that the video is crooked.

Page 22 of Joseph Polchinski, “String Theory" (Source: Numberphile video)

Page 22 of Joseph Polchinski, “String Theory” (Source: Numberphile video)

The Numberphile video uses three series. Confusingly it uses the normal plus sign but let us consider the idea that these would concern averages of a series of partial sums (with ⊕ instead of +). Series S1 = G and S2 is another form of ∞ – ∞ = undefined.

Read (+) and (+ H) instead of plus and minus (Source: Numberphile video)

Read (+) and (+ H) instead of plus and minus (Source: Numberphile video)

Let us repeat above procedure for S. Since there are no negative values involved, the series merely explodes, and obviously the outcome cannot be negative.

S’ = 1 ⊕ 2 ⊕ 3 ⊕ 4 + ….  

Partial sums of S:  1, 3, 6, 10, 15, ….

Summing (again !) those into a series: 1 + 3 + 6 + 10 + 15 +  ….

Averaged series S’:   1 / 1,   (1 + 3) 2H = 2 ,   10 3H = 3 + 3H,   16 4H = 4  ….

The Numberphile team has a longer video on the sum of the natural numbers that uses the Euler-Riemann Zeta function to argue their point, supposedly in “proper fashion”. However, they do not discuss the paradoxes here, and thus leave the reader confused. For example, they also refer to the basic geometric series, differentiate this, and then substitute r = -1 to create S2 (calling this “analytic continuation”), but, if the original geometric series is undefined for r = -1 (and then actually generates the Grandi Series again): why do you think that you can do this ?

Geometric series converges for -1 < r < 1 (Source: wikipedia)

Geometric series converges for -1 < r < 1 (Source: wikipedia)

See some physics links

The 1 + 2 + … = -1/12 video got 1.5 million hits and a fair amount of reactions from physicists. Their point is that Riemann and they are doing their job. See Steven Corneliussen in Physics Today and Phil Plait at Slate, for example. Plait has this quote from Jordan Ellenberg:

“It’s not quite right to describe what the video does as “proving” that 1 + 2 + 3 + 4 + …. = -1/12. When we ask “what is the value of the infinite sum,” we’ve made a mistake before we even answer! Infinite sums don’t have values until we assign them a value, and there are different protocols for doing that. We should be asking not what IS the value, but what should we define the value to be? There are different protocols, each with their own strengths and weaknesses. The protocol you learn in calculus class, involving limits, would decline to assign any value at all to the sum in the video.  A different protocol assigns it the value -1/12. Neither answer is more correct than the other.”

This is not entirely correct. Once you have defined “addition” and “equals” then you are stuck with it. Yes, you are free to find another protocol, but, beware of using “addition” and “equals” in general publications and education in another sense than people understand, because then your create confusion.

It seems to me that Physics Buzz is the most enlightening on what the real intention is.

Some nice quotes however

However, to soften our conclusion, the NY Times article by Dennis Overbye provides some nice quotes:

The problem with infinity is that you can’t stop. You never get there. It’s more of a journey than a destination.

Niels Henrik Abel, whose notion of an Abel sum plays a role here, once wrote, “The divergent series are the invention of the devil, and it is a shame to base on them any demonstration whatsoever.”

Of course there is also Wigner again:

To him and others, this is just another example of what the eminent physicist Eugene Wigner called the “unreasonable effectiveness of mathematics.” Why should such woolly and abstract concepts as zeta functions or imaginary numbers, the products of a chess game in our minds, have such relevance in describing the world?

However, as mathematics = abstraction, and abstraction = leaving out aspects, it should not be surprising that if you start with the world and leave things out then you still have something. See here for complex numbers, and check the steps in turning around a circle:

1,  i,  H = i²,  H i, 1  (start at 1 = {1, 0}, quarter turn, half turn, three-quarters turn, back to 1)

Appendix A:   φ² / Θ ≈ 5 / 12

Remember that we found that φ2 / Θ ≈ 5 / 12 with an error of 6 per million, where ‘phi’ φ = 1.618033989… is the golden ratio, and where ‘archi’ Θ = 2 π = 6.283185307….

φ2 / Θ   =   0.416673050492137…

5  / 12   =    0.4166666…

φ2 / Θ  –  5 / 12  =  0.00000638382547060161…

φ2 / Θ  –  2H   ≈    -12H                                                    (with the same error)

Thus, the suggestion is that when some physics formula generates the number –12H, look whether this kind of thing might be involved. We came upon this from an application. The relation holds by approximation only, however, and might be abused again to confuse people.

Appendix B:  Wikipedia 2014-10-15 on Grandi’s series contributes to confusion

Wikipedia's discussion today on Grandi's series (Source: wikipedia)

Wikipedia’s discussion today on Grandi’s series (Source: wikipedia)

The complex number i = √has a danger that some people may not be aware of. We use H = -1, see here.

For, consider:

-1 = i²  = (H) (H) = (H H) = 1 = 1

Professor of mathematics Edward Frenkel states in his book, intended for the general audience, and thus giving false information to that general audience:

“Note that it is customary to denote √-1 by i (for “imaginary”), but I chose not to do this to emphasize the algebraic meaning of this number: it really is just a square root of -1, nothing more and nothing less. It is just as concrete as the square root of 2. There is nothing mysterious about it.” (E. Frenkel, “Love & Math”, p101-102)

Observe the factual error and the error in didactics:

  1. The factual error is to say that the symbol √ has the same meaning in √-1 as in √2.
  2. Didactically, it is writing that conveys the algebraic meaning better, not writing √-1.

It took William Rowan Hamilton (1805-1865), the hero of Irish mathematics, a major part of his time to discover that = {0, 1}, i.e. the point in the two-dimensional plane where x = 0 and y = 1. Stepping into another dimension is not the same as staying in the same dimension. If you treat those at the same then you get above deduction that -1 = 1. The conclusion is that i is an operator and not a common number. The step (√H) (√H) = (H H) is forbidden since it concerns an operator, with a different rule for √. We can only call i a “(complex) number” if we adapt the notion of “number” to include it.

Let us look a bit more at the reason why i was mysterious and imaginary. Consider the quadratic equation, and let us “complete the square” on the left hand side

a x²  + b x + c = 0                                                  (formula for a vertical parabola)

x²  + b aH x       = – c aH                 (bring c to the right and multiply by aH= 1 / a)

b aH 2H) ²  = (b aH 2H) ²  – c aH                                    (using  2H 2H =  1)

+ b aH 2 =  ±  √ ((b aH 2H) ²  – c aH )                 (discriminant = √(b² – 4 a c) )       

(– b  ±  √ (4 a c ))  (2 a)H                            (the quadratic formula)

From wikipedia: this formula covering all cases was found by Simon Stevin in 1594, who also gave us the decimal dot. The present form was given by Descartes in 1637. In the past people were calculating every step. Having the final formula allows you to reduce the actual number of calculations you have to do.

There will be an intersection with the horizontal axis (above equation has a root) only if D ≥ 0. Otherwise there is no intersection.

It is an option to interprete i = √H as a number too. In that case the problem is redefined to have existed in the complex plane all along, and then there is always a solution. This explains where the mystery comes from: you have to grow aware that your original problem was not one-dimensional but two-dimensional.

Frenkel’s approach “there is nothing mysterious about it” kills this last insight. He claims to draw you to the beauty of mathematics, comparable to masterpieces of art, but at the same time he says that you should not be worried since it is as common as bread and butter. There is a difference between admiring a masterpiece and making one yourself. The professor is seriously confused. It is better that students understand the quadratic equation and the complex plane, and then admire their own understanding too.

Parabolic jump (Source: Jarek Tuszynski, wikimedia commons)

Parabolic jump (Source: Jarek Tuszynski, wikimedia commons)