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The following applies to elections for Parliament, say for the US House of Representatives or the UK House of Commons, and it may also apply for the election of a city council. When the principle is one man, one vote then we would want that the shares of “seats won” would be equal to the shares of “votes received”. When there are differences then we would call this inequality or disproportionality.

Such imbalance is not uncommon. At the US election of November 8 2016, the Republicans got 49.1% of the votes and 55.4% of the seats, while the Democrats got 48% of the votes and 44.6% of the seats. At the UK general election of June 8 2017, the Conservatives got 42.2% of the votes and 48.8% of the seats while Labour got 39.9% of the votes and 40.3% of the seats (the wikipedia data of October 16 2017 are inaccurate).

This article clarifies a new and better way to measure this inequality or disproportionality of votes and seats. The new measure is called Sine-Diagonal Inequality / Disproportionality (SDID). The new measure falls under descriptive statistics. Potentially it might be used in any area where one matches shares or proportions, like the proportions of minerals in different samples. SDID is related to statistical concepts like R-squared and the regression slope. This article looks at some history, as Karl Pearson (1857-1936) created the R-Squared and Ronald A. Fisher (1890-1962) in 1915 determined its sample distribution. The new measure would also be relevant for Big Data. William Gosset (1876-1937) a.k.a. “Student” was famously unimpressed by Fisher’s notion of “statistical significance” and now is vindicated by descriptive statistics and Big Data.

The statistical triad

Statistics has the triad of Design, Description and Decision.

  • Design is especially relevant for the experimental sciences, in which plants, lab rats or psychology students are subjected to alternate treatments. Design is informative but less applicable for observational sciences, like macro-economics and national elections when the researcher cannot experiment with nations.
  • Descriptive statistics has measures for the center of location – like mean or median – and measures of dispersion – like range or standard deviation. Important are also the graphical methods like the histogram or the frequency polygon.
  • Statistical decision making involves the formulation of hypotheses and the use of loss functione to evaluate that hypotheses. A hypothesis on the distribution of the population provides an indication for choosing the sample size. A typical example is the definition of decision error (of the first kind) that a hypothesis is true but still rejected. One might accept a decision error in say 5% of the cases, called the level of statistical significance.

Historically, statisticians have been working on all these areas of design, description and decision, but the most difficult was the formulation of decision methods, since this involved both the calculus of reasoning and the more complex mathematics on normal, t, chi-square, and other frequency distributions. In practical work, the divide between the experimental and the non-experimental (observational) sciences appeared insurmountable. The experimental sciences have the advantages of design and decisions based upon samples, and the observational sciences basically rely on descriptive statistics. When the observational sciences do regressions, there is an ephemeral application of statistical significance that invokes the Law of Large Numbers, that all error approximates the normal distribution.

This traditional setup of statistics is being challenged in the last decades by Big Data – see also this discussion by Rand Wilcox in Significance May 2017. When all data are available, and when you actually have the population data, then the idea of using a sample evaporates, and you don’t need to develop hypotheses on the distributions anymore. In that case descriptive statistics becomes the most important aspect of statistics. For statistics as a whole, the emphasis shifts from statistical decision making to decisions on content. While descriptive statistics had been applied mostly to samples, Big Data now causes the additional step how these descriptions relate to decisions on content. In fact, such questions already existed for the observational sciences like for macro-economics and national elections, in which the researcher only had descriptive statistics, and lacked the opportunity to experiment and base decisions upon samples. The disadvantaged areas now provide insights for the earlier advantaged areas of research.

The key insight is to transform the loss function into a descriptive statistic itself. An example is the Richter scale for the magnitude of earthquakes. It is both a descriptive statistic and a factor in the loss function. A nation or regional community has on the one hand the cost of building and construction and on the other hand the risk of losing the entire investments and human lives. In the evaluation of cost and benefit, the descriptive statistic helps to clarify the content of the issue itself. The key issue is no longer a decision within statistical hypothesis testing, but the adequate description of the data so that we arrive at a better cost-benefit analysis.

Existing measures on votes versus seats

Let us return to the election for the House of Representatives (USA) or the House of Commons (UK). The criterion of One man, one vote translates into the criterion that the shares of seats equal the shares of votes. We are comparing two vectors here.

The reason why the shares of seats and votes do not match is because the USA and UK use a particular setup. The setup is called an “electoral system”, but since it does not satisfy the criterion of One man, one vote, it does not really deserve that name. The USA and UK use both (single member) districts and the criterion of Plurality per district, meaning that the district seat is given to the candidate with the most votes – also called “first past the post” (FPTP). This system made some sense in 1800 when the concern was district representation. However, when candidates stand for parties then the argument for district representation loses relevance. The current setup does not qualify for the word “election” though it curiously continues to be called so. It is true that voters mark ballots but that is not enough for a real election. When you pay for something in a shop then this is an essential part of the process, but you also expect to receive what you ordered. In the “electoral systems” in the USA and UK, this economic logic does not apply. Only votes for the winner elect someone but the other votes are obliterated. For such reasons Holland switched to equal / proportional representation in 1917.

For descriptive statistics, the question is how to measure the deviation of the shares of votes and seats. For statistical decision making we might want to test whether the US and UK election outcomes are statistically significantly different from inequality / proportionality. This approach requires not only a proper descriptive measure anyway, but also some assumptions on the distribution of votes which might be rather dubious to start with. For this reason the emphasis falls on descriptive statistics, and the use of a proper measure for inequality / disproportionality (ID).

A measure proposed by, and called after, Loosemore & Hanby in 1971 (LHID) uses the sum of the absolute deviations of the shares (in percentages), divided by 2 to correct for double counting. The LHID for the UK election of 2017 is 10.5 on a scale of 100, which means that 10.5% of the 650 seats (68 seats) in the UK House of Commons are relocated from what would be an equal allocation. When the UK government claims to have a “mandate from the people” then this is only because the UK “election system” is so rigged that many votes have been obliterated. The LHID gives the percentage of relocated seats but is insensitive to how these actually are relocated, say to a larger or smaller party.

The Euclid / Gallagher measure proposed in 1991 (EGID) uses the Euclidean distance, again corrected for double counting. For an election with only two parties EGID = LHID. The EGID has become something like the standard in political science. For the UK 2017 the EGID is 6.8 on a scale of 100, which cannot be interpreted as a percentage of seats like LHID, but which indicates that the 10.5% of relocated seats are not concentrated in the Conservative party only.

Alan Renwick in 2015 tends to see more value in LHID than EGID: “As the fragmentation of the UK party system has increased over recent years, therefore, the standard measure of disproportionality [thus EGID] has, it would appear, increasingly understated the true level of disproportionality.”

The new SDID measure

The new Sine-Diagonal Inequality / Disproportionality (SDID) measure – presented in this paper – looks at the angle between the vectors of the shares of votes and seats.

  • When the vectors overlap, the angle is zero, and then there is perfect equality / proportionality.
  • When the vectors are perpendicular then there is full inequality / disproportionality.
  • While this angle variates from 0 to 90 degrees, it is more useful to transform it into sine and cosine that are in the [0, 1] range.
  • The SDID takes the sine for inequality / disproportionality and the cosine of the angle for equality / proportionality.
  • With Sin[0] = 0 and Cos[0] = 1, we thus get a scale that is 0 for full inequaliy / disproportionality and 1 for full equality / proportionality.

It appears that the sine is more sensitive than either absolute value (LHID) and Euclidean distance (EGID). It is closer to the absolute value for small angles, and closer to the Euclidean distrance for larger angles. See said paper, Figure 1 on page 10. SDID is something like a compromise between LHID and EGID but also better than both.

The role of the diagonal

When we regress the shares of the seats on the shares of the votes without using a constant – i.e. using Regression Through the Origin (RTO) – then this gives a single regression coefficient. When there is equality / proportionality then this regression coefficient is 1. This has the easy interpretation that this is the diagonal in the votes & seats space. This explains the name of SDID: when the regression coefficient generates the diagonal, then the sine is zero, and there is no inequality / disproportionality.

Said paper – see page 38 – recovers a key relationship between on the one hand the sine and on the other hand the Euclidean distance and this regression coefficient. On the diagonal, the sine and Euclidean distance are both zero. Off-diagonal, the sine differs from the Euclidean distance in nonlinear manner by means of a factor given by the regression coefficient. This relationship determines the effect that we indicated above, how SDID compromises between and improves upon LHID and EGID.

Double interpretation as slope and similarity measure

There appears to be a relationship between said regression coefficient and the cosine itself. This allows for a double interpretation as both slope and similarity measure. This weblog text is intended to avoid formulas as much as possible and thus I refer to said paper for the details. Suffice to say here is that, at first, it may seem to be a drawback that such a double interpretation is possible, yet, on closer inspection the relationship makes sense and it is an advantage to be able to switch perspective.

Weber – Fechner sensitivity, factor 10, sign

In human psychology there appears to be a distinction between actual differences and perceived differences. This is called the Weber – Fechner law. When a frog is put into a pan with cool water and slowly boiled to death, it will not jump out. When a frog is put into a pan with hot water it will jump out immediately. People may notice differences between low vote shares and high seat shares, but they may be less sensitive to small differences, while these differences actually can still be quite relevant. For this reason, the SDID uses a sensitivity transform. It uses the square root of the sine.

(PM. A hypothesis is that the USA and UK call their national “balloting events” still “elections”, is that the old system of districts has changed so gradually into the method of obliterating votes that many people did not notice. It is more likely though that that some parties recognised the effect, but have an advantage under the present system, and then do not want to change to equal / proportional representation.)

Subsequently, the sine and its square root have values in the range [0, 1]. In itself this is an advantage, but it comes with leading zeros. We might multiply with 100 but this might cause the confusion as if it would be percentages. The second digit might give a false sense of accuracy. It is more useful to multiply this by 10. This gives values like on a report card. We can compare here to Bart Simpson, who appreciates low values on his report card.

Finally, when we compare, say, votes {49, 51} and seats {51, 49}, then we see a dramatic change of majority, even though there is only a slight inequality / disproportionality. It is useful to have an indicator for this too. It appears that this can be done by using a negative sign when such majority reversal occurs. This method of indicating majority reversals is not so sophisticated yet, and at this stage consists of using the sign of the covariance of the vectors of votes and seats.

In sum: the full formula

This present text avoids formulas but it is useful to give the formula for the new measure of SDID, so that the reader may link up more easily with the paper in which the new measure is actually developed. For the vectors of votes and seats we use the symbols v and s, and the angle between the two vectors give cosine and then sine:

SDID[v, s] = sign 10 √ Sin[v, s]

For the UK 2017, the SDID value is 3.7. For comparison the values of Holland with equal / proportional representation are: LHID 3, EGID 1.7, SDID 2.5. It appears that Holland is not yet as equal / proportional as can be. Holland uses the Jefferson / D’Hondt method, that favours larger parties in the allocation of remainder seats. At elections there are also the wasted vote, when people vote for fringe parties that do not succeed in getting seats. In a truly equal or proportional system, the wasted vote can be respected by leaving seats empty or by having a qualified majority rule.

Cosine and R-squared

Remarkably, Karl Pearson (1857-1936) also used the cosine when he created R-squared, also known as the “coefficient of determination“. Namely:

  • R-squared is the cosine-squared applied to centered data. Such centered data arise when one subtracts the mean value from the original data. For such data it is advisable to use a regression with a constant, which constant captures the mean effect.
  • Above we have been using the original (non-centered) data. Alternatively put, when we do above Regression Through the Origin (RTO) and then look for the proper coefficient of determination, then we get the cosine-squared.

The SDID measure thus provides a “missing link” in statistics between centered and non-centered data, and also provides a new perspective on R-squared itself.

Apparently till now statistics found little use for original (non-centered) data and RTO. A possible explanation is that statistics fairly soon neglected descriptive statistics as less challenging, and focused on statistical decision making. Textbooks prefer the inclusion of a constant in the regression, so that one can test whether it differs from zero with statistical significance. The constant is essentially used as an indicator for possible errors in modeling. The use of RTO or the imposition of a zero constant would block that kind of application. However, this (traditional, academic) focus on statistical decision making apparently caused the neglect of a relevant part of the analysis, that now comes to the surface.

R-squared has relatively little use

R-squared is often mentioned in statistical reports about regressions, but actually it is not much used for other purposes than reporting only. Cosma Shalizi (2015:19) states:

“At this point, you might be wondering just what R-squared is good for — what job it does that isn’t better done by other tools. The only honest answer I can give you is that I have never found a situation where it helped at all. If I could design the regression curriculum from scratch, I would never mention it. Unfortunately, it lives on as a historical relic, so you need to know what it is, and what misunderstandings about it people suffer from.”

At the U. of Virginia Library, Clay Ford summarizes Shalizi’s points on the uselessness of R-squared, with a reference to his lecture notes.

Since the cosine is symmetric, the R-squared is the same for regressing y given x, or x given y. Shalizi (2015, p18) infers from the symmetry: “This in itself should be enough to show that a high R² says nothing about explaining one variable by another.” This is too quick. When theory shows that x is a causal factor for y then it makes little sense to argue that y explains x conversely. Thus, for research the percentage of explained variation can be informative. Obviously it matters how one actually uses this information.

When it is reported that a regression has an R-squared of 70% then this means that 70% of the variation of the explained variable is explained by the model, i.e. by variation in the explanatory variables and the estimated coefficients. In itself such a report does not say much, for it is not clear whether 70% is a little or a lot for the particular explanation. For evaluation we obviously also look at the regression coefficients.

One can always increase R-squared by including other and even nonsensical variables. For a proper use of R-squared, we would use the adjusted R-squared. R-adj finds its use in model specification searches – see Dave Giles 2013. For an increase of R-adj coefficients must have an absolute t-value larger than 1. A proper report would show how R-adj increases by the inclusion of particular variables, e.g. also compared to studies by others on the same topic.  Comparison on other topics obviously would be rather meaningless. Shalizi also rejects R-adj and suggests to work directly with the mean squared error (MSE, also corrected for the degrees of freedom). Since R-squared is the cosine, then the MSE relates to the sine, and these are basically different sides of the same coin, so that this discussion is much a-do about little. For standardised variables (difference from mean, divided by standard deviation), the R-squared is also the coefficient of regression, and then it is relevant for the effect size.

R-squared is a sample statistic. Thus it depends upon the particular sample. A hypothesis is that the population has a ρ-squared. For this reason it is important to distinguish between a regression on fixed data and a regression in which the explanatory variables also have a (normal) distribution (errors in variables). In his 1915 article on the sample distribution of R-squared. R.A Fisher (digital library) assumed the latter. With fixed data, say X, the outcome is conditional on X, so that it is better to write ρ[X], lest one forgets about the situation. See my earlier paper on the sample distribution of R-adj. Dave Giles has a fine discussion about R-squared and adjusted R-squared. A search gives more pages. He confirms the “uselessnes” of R-squared: “My students are often horrified when I tell them, truthfully, that one of the last pieces of information that I look at when evaluating the results of an OLS regression, is the coefficient of determination (R2), or its “adjusted” counterpart. Fortunately, it doesn’t take long to change their perspective!” Such a statement should not be read as the uselessness of cosine or sine in general.

A part of history of statistics that is unknown to me

I am not familiar with the history of statistics, and it is unknown to me what else Pearson, Fisher, Gosset and other founding and early authors wrote about the application of the cosine or sine. The choice to apply the cosine to centered data to create R-squared is deliberate, and Pearson would have been aware that it might also be applied to original (non-centered) data. It is also likely that he would not have the full perspective above, because then it would have been in the statistical textbooks already. It would be interesting to know what the considerations at time were. Quite likely the theoretical focus was on statistical decision making rather than on description, yet this for me unknown history would put matters more into perspective.

Statistical significance

Part of the history is that R.A. Fisher with his attention for mathematics emphasized precision while W.S. Gosset with his attention to practical application emphasized the effect size of the coefficients found by regression. Somehow, statistical significance in terms of precision became more important than content significance, and empirical research has rather followed Fisher than the practical relevance of Gosset. This history and its meaning is discussed by Stephen Ziliak & Deirdre McCloskey 2007, see also this discussion by Andrew Gelman. As said, for standardised variables, the regression coefficient is the R-squared, and this is best understood with attention for the effect size. For some applications a low R-squared would still be relevant for the particular field.

Conclusion

The new measure SDID provides a better description of the inequality or disproportionality of votes and seats compared to existing measures. The new measure has been tailored to votes and seats, by means of greater sensitivity to small inequalities, and because a small change in inequality may have a crucial impact on the (political) majority. For different fields, one could taylor measures in similar manner.

That the cosine could be used as a measure of similarity has been well-known in the statistics literature since the start, when Pearson used the cosine for centered data to create R-square. For the use of the sine I have not found direct applications, but its use is straightforward when we look at the opposite of similarity.

The proposed measure provides an enlightening bridge between descriptive statistics and statistical decision making. This comes with a better understanding of what kind of information the cosine or R-squared provides, in relation to regressions with and without a constant. Statistics textbooks would do well by providing their students with this new topic for both theory and practical application.

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Mathematicians can be seen as lawyers of space and number.

Euclid wrote about 300 BC. Much earlier, Hammurabi wrote his legal code around about 1792-1749 BC. It is an interpretation of history: Hammurabi might have invented all of his laws out of thin air, but it is more likely that he collected the laws of his region and brought some order into this. Euclid applied that idea to what had been developed about geometry. The key notions were caught in definitions and axioms, and the rest was derived. This fits the notion that Pierre de Fermat (1607-1665) started as a lawyer too.

Left Codex Hammurabi, right a piece of Euclid 100 AD. Wikimedia commons

Left: codex Hammurabi. Right: a piece of Euclid 100 AD. Wikimedia commons

The two cultures: science and the humanities

In Dutch mathematics education there is a difference between A (alpha) and B (beta) mathematics. B would be “real” math and prepare for science. A would provide what future lawyers can manage.

In the English speaking world, there is C.P. Snow who argued about the “two cultures“, and the gap between science and the humanities. A key question is whether this gap can be bridged.

In this weblog, I already mentioned the G (gamma) sciences, like econometrics that combines economics (humanities) with scientific standards (mathematical models and statistics). Thus the gap can be bridged, but perhaps not by all people. It may require some studying. Many people will not study because they may arrogantly believe that A or B is enough (proof: they got their diploma).

Left and right hemisphere of the brain

Another piece of the story is that the left and right hemispheres of the brain might specialise. There appears to be a great neuroplasticity (Norman Doidge), yet overall some specialisation makes sense. The idea of language and number on the left hemisphere and vision on the right hemisphere might still make some sense.

“Broad generalizations are often made in popular psychology about certain functions (e.g. logic, creativity) being lateralized, that is, located in the right or left side of the brain. These claims are often inaccurate, as most brain functions are actually distributed across both hemispheres. (…) The best example of an established lateralization is that of Broca’s and Wernicke’s Areas (language) where both are often found exclusively on the left hemisphere. These areas frequently correspond to handedness however, meaning the localization of these areas is regularly found on the hemisphere opposite to the dominant hand. (…) Linear reasoning functions of language such as grammar and word production are often lateralized to the left hemisphere of the brain.” (Wikipedia, a portal and no source)

For elementary school we would not want kids to specialise in functions, and encourage the use of neuroplasticity to develop more functions.

Pierre Krijbolder (1920-2004) suggested that there is a cultural difference between the Middle East (Jews), with an emphasis on language – shepherds guarding for predators at night – and the Indo-Europeans (Greeks), with an emphasis on vision – hunters taking advantage of the light of day. Si non e vero, e ben trovato.

There must have been at least two waves by Indo-Europeans into the Middle-East. The first one brought the horse and chariot to Egypt. The second one was by Alexander (356-323 BC) who founded Alexandria, where Euclid might have gotten the assignment to write an overview of the geometric knowledge of the Egyptians, like Manetho got to write a historical overview.

Chariot spread 2000 BC. (Source: D. Bachmann, wikimedia commons)

Chariot spread 2000 BC. (Source: D. Bachmann, wikimedia commons)

It doesn’t actually matter where these specialisations can be found in the brain. It suffices to observe that people can differ in talents: lawyers would deal much with language, and for space you might turn to mathematicians.

Pierre van Hiele (1909-2010) presents a paradox

The Van Hiele levels of insight are a key advance in epistemology, for they indicate that human understanding itself is subjected to some structure. The basic level concerns experience and the direct language about this. The next level concerns the recognition of properties. Another level is the recognition of relations between these properties, and the informal deductions about these. The highest level is formalisation, with axiomatics and formal deduction. The actual number of levels depends upon your application, but the base remains in experience and the top remains in axiomatics.

Learning goes from concrete to abstract, and from vague to precise.

Thus, Euclid with his axiomatic approach would be at the highest level of understanding.

We arrive at a paradox.

The axiomatic approach is basically a legal approach. We start with some rules, and via substitution and reasoning we arrive at other rules. This is what lawyers can do well. Thus: lawyers might be the best mathematicians. They might forget about the intermediate levels, they might discard the a-do about space, and jump directly to the highest Van Hiele level.

A paradox but no contradiction

A  paradox is only a seeming contradiction. The latter paradox gives a true description in itself. It is quite imaginable that a lawyer – like a computer – runs the algorithms and finds “the proper answer”.

However, for proper mathematics one must be able to switch between modes. At the highest Van Hiele level, one must have an awareness of applications, and be able to translate the axioms, theorems and derivations into the intended interpretation. In many cases this may involve space.

Just to be sure: the Van Hiele levels present conceptual divides. At each level, the languages differ. The words might be the same but the meanings are different. This also causes the distinction between teacher-language and student-language. Often students are much helped by explanations by their fellow students. It is at the level-jump, when the coin drops, that meanings of words change, and that one can no longer imagine that one didn’t see it before.

Thus it would be a wrong statement to say that the highest Van Hiele level must have command of all the lowest levels. The disctinction between lawyers and mathematicians is not that the latter have command of all levels. Mathematicians cannot have command of all levels because they have arrived at the highest level, and this means that they must have forgotten about the earlier levels (when they were young and innocent). The distinction between lawyers (math A) and mathematicians (math B) is different. Lawyers would understand the axiomatic approach (from constitutional law to common law) but mathematicians would understand what is involved in specific axiomatic systems.

Example 1

I came to the above by thinking about the following problem. This problem was presented as an example of a so-called “mathematical think-activity” (MTA). The MTA are a new fad and horror in Dutch mathematics education. First try to solve the problem and then continue reading.

2016-10-26-petervanwijk-smaller-englishDiscussion of example 1

The drawing invites you to make two assumptions: (1) the round shape is a circle, (2) the vertical x meets the horizontal x in the middle. However, why would this be so ? You might argue that r = 6 suggests the use of a circle, but perhaps this still might be an ellipse.

In traditional math ed (say around 1950), making such assumptions would cost you points. In fact, the question would be considered insoluble. No question would be presented to you in this manner.

In traditional math, the rule would be that the proper question and answer would consist of text, and that drawings only support the workflow. Also, the particular calculation with = 6 would not be interesting. Thus, a traditional presentation would have been (and also observe the dashes):

2016-10-26-petervanwijk-smaller-english-altA quick observation is that there are three endpoints, and it is a theorem that there is always a circle through three points. So the actual question is to prove this theorem, and you are being helped with a special case.

Given that you solved the problem above, we need not look into the solution for this case.

The reason for giving this example is: In mathematics, text has a key role, like in legal documents for lawyers. Since mathematicians are lawyers of space and number, they can cheat by using supporting drawings, tables and formulas. But definitions, theorems and proofs are in text (formulas).

(Potentially lawyers also make diagrams of complex cases, as you can see in movies sometimes. But I don’t know whether there are particular methods here.)

Example 2

The second example is the discussion from yesterday.

In text it is easy to say that a line has no holes. However, when you start thinking about this, then you must define what such a hole might be. If a hole doesn’t belong to the line, what does it belong to then ? How would you know when you would pass a hole ? Might you not be stepping over holes all the time without noticing ?

These are questions that lawyers would enjoy. They are relevant for math B but can also be discussed in math A.

See the discussion of yesterday, and check that the main steps should be acceptable for lawyers, i.e. math A.

These students should be able to master the symbolism of predicate logic, since this is only another language and a reformulation of common text.

Conclusions

Thus, a suggestion is that students in math A should be able to do more, when better use is made of the legal format.

Perhaps more students, now doing A, might also do B, if their learning style is better supported.

(Perhaps the B students would start complaining about more text though. Would there still be the same question, when only the format of presentation differs ? Thus a conclusion can also cause more questions. See also this earlier discussion about schools potentially manipulating their success scores by causing student underperformance.)

 

 

 

 

 

 

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

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

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

NWO Bessensap in Amsterdam

The invitation at the NWO website was:

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

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

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

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

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

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

Alice Dreger about “The scientist as activist”

Developing a hypothesis on the controversy

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

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

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

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

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

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

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

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

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

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

A background check on potential sources of bias

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

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

Adding to confusion and reducing it again

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

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

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

Insert of Tuesday June 14 2016

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

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

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

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

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

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

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

Conclusions

Given this hypothesis, some tentative conclusions are:

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

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

2016-06-10-NWO-outside

Listening to Izaline Calister “Mi Pais
“Atardi Korsou ta Bunita”, or Willem Hendrikse,
or Rudy Plaate “Dushi Korsou” or IC & CR “Mi ta stimabu“,
and Frank might also have liked Las Unicas “Ban Gradici Senjor” from Aruba

 

Frank Martinus Arion passed away yesterday in Curaçao. The English wikipedia site is a bit short, with his 1973 literary debut Double play. His important scientific work is his thesis: “The kiss of a slave”, that traces Papiamentu to Africa.

Kiss of a Slave, by Martinus Arion, Thesis Univ. of Amsterdam 1996

The Kiss of a Slave, by Efraim Frank Martinus (Arion), Thesis at the Univ. of Amsterdam 1996

Masha Danki !

Frank wouldn’t have wanted us to be sad. The best way to to thank him is to have the biggest party of all.

2013-curacao-carneval

Carneval 2013 (Source: Screenshot)

I met Frank in the bar of the then hotel Mira Punda in Scharloo. These are old pictures taken by its then-owner Jose Rosales in 2005. Nowadays it is refurbished, and you should check out Hotel Scharloo or see pictures, or see booking.com.

2006-Mira-Punda

Hotel Mira Punda 2005 before the refurbishment to Hotel Scharloo (Source: Jose Rosales)

A second time in 2005-2006 Frank came by to discuss the future of the Caribbean, and we sat there on the terras of Mira Punda. I was just getting my driver’s licence so it was impossible to drive up to his place.

Just a year later, in 2006, when I had returned to Holland, his book Double Play was presented as the Dutch liberaries book of the year, and I met him again in The Hague.

Here is my view on the future of the Caribbean, no doubt influenced by these brief but powerful meetings about national independence. Perhaps the Caribbean could develop a sense of nationhood ?

PENAFC

Listening to Roefie Huetng with Jamie’s Blues

 

Roefie Hueting (1929) is an economist and jazz piano player, or a jazz piano player and an economist, who cannot decide which of the two is most important to him. See this earlier report on his double talent.

Hueting’s first public performance was on stage on liberation day May 5 1945 at the end of World War 2, when he was dragged out of his home to play for the people dancing in the streets. He still performs and thus he has been 55+15=70 years on stage.

With the Down Town Jazzband (DTJB) Hueting recorded 250 songs, played on all major Dutch stages, five times at the North Sea Jazzfestival, while the 50th DTJB anniversity of 1999 was together with the Residence Orchestra in a sold-out The Hague Philips Hall.

Hueting was one of the founders of the Dutch Jazzclub from which sprouted The Hague Jazz Club. This HJC has its current performances at the Crowne Plaza Hotel, formerly known as the “Promenade”. This hotel is at the Scheveningseweg, the first modern road in Holland, created by Constantijn Huygens in 1653, connecting the area of the Peace Palace – the area where also Grand Duchess Anna Paulowna of Russia (1795-1865) had her Summer palace – to the sea. See also these pictures of the German Atlantik Wall – to stay with the WW 2 theme.

At the celebration last Sunday September 27 other performers were Joy Misa (youtube), Machteld Cambridge, Erik Doelman (youtube) and Enno Spaanderman.

The Hague Alderman Joris Wijsmuller (urban development, housing, sustainability and culture) came to present Roefie Hueting with a book containing a picture of Mondriaan‘s Victory Boogie-Woogie – also celebrating the end of WW 2. Wijsmuller observed the erosion of “sustainability” that in the opinion of Hueting rather should be “environmental sustainability”.

Roefie Hueting and alderman Joris Wijsmuller at Crowne Plaza Hotel 2015-09-27

Roefie Hueting and alderman Joris Wijsmuller at Crowne Plaza Hotel 2015-09-27

Roefie Hueting solo at the piano, 2015-09-27

Roefie Hueting solo at the piano, 2015-09-27

Hueting introducing a jam session 2015-09-27

Hueting introducing a jam session 2015-09-27

"Victory Boogie-Woogie" by Piet Mondriaan (Source: Wikimedia Commons)

“Victory Boogie-Woogie” by Piet Mondriaan (Source: Wikimedia Commons)

Now available

Elegance with Substance (2nd edition)

Mathematics and its education designed for Ladies and Gentlemen

What is wrong with mathematics education and how it can be righted

On the political economy of mathematics and its education 

Elegance with Substance (Cover)

Elegance with Substance (Cover)

National parliaments around the world are advised to have their own national parliamentary enquiry into the education in mathematics.

There is a failure in mathematics and its education, that can be traced to a deep rooted culture in mathematics. Mathematicians are trained for abstract theory but when they teach then they meet with real life pupils and students. They solve their cognitive dissonance by embracing tradition for tradition only. Instead, didactics requires a mindset that is sensitive to empirical observation which is not what mathematicians are trained for.

When mathematicians deal with empirical issues then problems arise in general. Other examples are voting theory for elections, models for environmental economics and growth, and the role of ‘rocket scientists’ in causing the stock market crash in 2008 (Mandelbrot & Taleb 2009).

While school mathematics should be clear and didactically effective, a closer look shows that it is cumbersome and illogical. What is called mathematics thus is not really so. Pupils and students are psychologically tortured and withheld from proper mathematical insight and competence.

The mathematics in this book is at highschool level.

Listening to Theodorakis, The struggles of the Greek people

 

Last weblog referred to Pseudo Erasmus who referred to Graig Willy who referred to Thierry Medynski who referred to Emmanuel Todd.

Medynski uses a colour scheme for Todd’s categories that I find hard to remember. It also appears that Willy has given a colour to Russia while this is not available from Medynski. Thus, let me return to Medynski’s map and propose a colour coding that seems easier to remember (updated May 18).

My suggstion is: Green will be the authoritarian stem family structure that can live with inequality.  Gray blue will be the authoritarian family structure that wishes to see equality except for the patriarch. Red allows for inequality but because of liberal tendencies. Blue combines liberalism and equality. The blue-ish area identifies the region in which equality dominates.

“Todd identifies four premodern European family types according to two major criteria: Is an individual free upon adulthood or does he continue to live with, and under the authority of, his parents? Are brothers equal, notably in terms of inheritance, or are they unequal.” (Craig Willy’s summary of Todd)

My colour proposal Authoritarian Liberal (free from parents)
Unequal Stem (green) Nuclear (red)
Equal (inheritance)
Communitarian (gray blue)
Nuclear egalitarian (photon) (blue)

This gives the following map – in which the legend is also sorted from blue to red.

Traditional family systems of Europe (1500-1900) (Source: Todd - Medynski)

Traditional family systems of Europe (1500-1900) (Source: Todd – Medynski)

There is more cohesion between Germany and Norway and Sweden than commonly perceived.

Relation to the USA

My suggestion is based upon the USA Red and Blue, for the Republican versus Democratic states.

USA Red and Blue States, for Republican and Democratic party outcomes, purple mixtures (Source: Wikipedia)

USA Red and Blue States, for Republican and Democratic Party outcomes at Presidential elections. Purple: mixtures over elections (Source: Wikipedia)

The differences between red and blue states may not be quite comparable to Todd’s scheme, but it helps to develop the idea and identification. Still, the clue is that the USA apparently has been shaped predominantly because of the nuclear family structure.

“Les États-Unis et l’Europe n’ont pas le même projet de société du fait de leurs structures familiales. Structurés sur la famille nucléaire absolue, les États-Unis expriment une dérive du fondamentalisme protestant avec cette vision messianique et civilisatrice pour diriger le monde selon leurs propres intérêts. Du fait de sa mosaïque de structures familiales, l’Europe devrait favoriser l’émergence d’un monde polycentrique. Cependant, depuis l’Acte Unique, tout se passe comme si l’identité européenne était réduite aux valeurs véhiculées par la famille nucléaire absolue, à savoir la pensée unique du néo-libéralisme. D’où l’échec de cette conception de l’Europe.” (Medynski, my emphasis)

The differences between Republicans and Democrats thus may be linked to the differences between England and the Ile de France.

Consequences for Europe and the euro

Check out Todd’s 2013 Harper’s video on the euro – with thanks to Pseudo Erasmus for alerting us to this. See also Jamie Galbraith and perhaps also not so strong John Gray. And then see my paper Money as gold versus money as water.

PM

PM 1. For completeness and comparison, this is the colour scheme of Medynski’s image. We changed only red and yellow but it still makes a difference in reading.

Thierry Medynski Authoritarian Liberal
Unequal Stem (green) Nuclear (yellow)
Equal Communitarian (red) Nuclear egalitarian (blue)

PM 2. Never forget about the Heineken Eurotopia map.

PM 3. Check whether there is a relation with the other French intellectual, Thomas Piketty.

PM 4. Russia would have the gray blue too, which confirms Willy’s adaptation of Medynski’s image.

“Cette mosaïque de systèmes familiaux distingue l’Europe des Etats-Unis (structurés sur la famille nucléaire absolue) et de la Russie (structurée sur la famille communautaire exogame) où seul un des termes, l’individualisme ou le système communautaire, est privilégié.” (Medynski, my emphasis)