July 16, 2010


ME + me : Merely mathematical & psychological


The files from July 14 and July 15 have been again uploaded, albeit with few changes, because I was so wasted yesterday I managed to upload the last but one version of July 15 instead of the last.

I am still not well physically at all and it still feels hot and humid where I am, so I restrict myself today to two brief remarks having to do with mathematical and psychological matters - and in fact the first is mostly linguistic and logical and the second is mostly of interest to psychologists.

Tomorrow there may be another translation, namely from another Amsterdam mafiosi in the garb of civil servant, but in case you had hoped for this today, my message is to look again the coming days, about which I cannot say much, because I am quite PEM'ed (*)

1. What does "reading Feferman" mean?

I have repeatedly said the last week that I was "reading Feferman" or intended to do so, which let to questions what I possibly might have meant.

Here is the answer: It has nothing whatsoever to do with ME but a lot with me, for Solomon Feferman is a well-known (among those who know mathematical logic, to be sure) mathematical logician whose papers I always liked, but often could not afford, apart from photocopies, because they were published in books or journals I could (and can) not afford and it so happens that I discovered about two weeks ago that he has had the kindness to put a large amount of his papers, mostly in excellent pdf editions, on line.

Feferman is at Stanford, and his papers are here:

Since I mentioned logic and psychology, here are links to two fine papers of his that may be of interest to psychologists (with some mathematical logic)

So now this riddle has been solved.

2. Professor Freudenthal also read professor Piaget

I studied psychology for three reasons: (1) I'd read William James, and hoped for more of that quality (no such luck); (2) my wife wanted to study psychology, because she had been a psychological assistant in a lunatic asylum, giving tests of various kinds to inmates, and wanted to understand what these tests were based on, and I thought that this study could not be a difficult one (and indeed); and (3) I was and am most interested in the very broad field of human reasoning of all kinds since I was 15 and found out for myself that was a really interesting subject, so I was curious what the study of psychology could teach me about it (nothing that isn't in James, that wasn't in the courses I took, because that would have been far too difficult for 95% of the students, who moreover didn't want any of that, but clear, simple, easily summarizable coursebook summaries of things).

But what has this to do with Freudenthal and Piaget? Well... to start with, I have linked their names with the Wikipedia entries for them:

Hans Freudenthal was a German-Dutch mathematician, who started as an admirer and assistant of Brouwer, one of the founders of intuitionism in mathematics, but got into a quarrel with Brouwer (many did: real geniuses are often not the friendliest of persons), and then more or less went his own way as professor of mathematics in Utrecht (Holland).

I read several of Freudenthal books, notably one about Lincos, which is - mathematical subject, readers! - a language designed to communicate as easily as is possible with extra-terrestrial intelligence (which means that it also is about the foundations of mathematics and logic, whatever extra-terrestrial intelligence there is or fails to be (**)), and a very fine one about probability. He also wrote about mathematical education, where I will arrive in a moment, after briefly introducing the other person I mentioned.

Jean Piaget was a Swiss developmental psychologist, who was quite famous both inside psychology, because of his radical new ideas about learning, especially in children, and who wrote a large number of books, that have several characteristics that are deplorable, in spite of his deserved fame: For one thing, he preferred a truly awful grandiose terminology, that makes his theories a lot more difficult to understand than they would be otherwise.

His ideas are interesting though, and gave rise to rather a lot of experimental psychology, which is a subject that is not close to my heart, for which reason I only mention it in passing. (***) He also wrote a number of mostly theoretical books, notably about mathematics and learning, and I'd read some of these before studying psychology, and they had lodged the strong conviction in my mind that Piaget when writing about mathematics (i) did not really umderstand his subject (Piaget on "transformation groups" is certainly not what Sophus Lie had in mind, when he wrote about it!) and (ii) had a very personal understanding of many expressions written in precisely the same letters in the same sequence in mathematics.

It so happened that the few psychologists I met who were truly intelligent were also much taken by Piaget, and I could never really clarify why I personally was not very much impressed by Piaget at all, while also liking some of his results.

Well... it so happens that today I opened a thick volume that Hans Freudenthal wrote late in life, "Mathematics as an Educational Task", that I read about half of in 1980, and found today that it has an Appendix I "Piaget and the Piaget school's investigations on the development of mathematical notions". (p. 662-677)

I was very pleased to find that professor Freudenthal had just the same impressions as I had, for which reason I have listed it here, in case it might enlighten some. In fact, I could quote rather a lot, but will restrict myself to one single subject, that of the empty set (link to my Philosophical Dictionary).

In brief, the empty set is a name for nothing at all: The set of square circles, the set of even prime numbers greater than 2, and the set of legally married elephants are all precisely the same set of things: the empty set, there being in either case no such things as mentioned at all.

Not so for professor Piaget: He did experiments with children with cards on which there were various pictures, about which Piaget wrote (in Freudenthal's translation)

(..) it is easy to observe the reactions of the subject, whether he is struck by the absence of pictures on certain cards, or whether he restricts himself to all elements positive characters, say of shape. (p. 675, op. cit)

For Piaget supplied his "subjects" - young children in which he wanted to study what he called "the genesis of mathematical concepts" - with cards with pictures and cards without pictures.

What was the purpose of cards without pictures? Professor Freundenthal explains, with professor Piaget again in smaller type:

In classifying the subjects neglect the set of empty cards:

... the child refuses to construe the empty set.

The set of empty cards is, according to Piaget, an empty set. After what we have quoted from [J. Piaget & Barbel Inhelder, La génčse de l'espace chez l'enfant, Paris 1948] this is not shocking anymore.

Here professor Freudenthal refers to 5 pages he has translated from that text, with such clarifying notes of his such as the following, which concerns a topic I had torn my hair out when reading it first ca. 1977 (with a link to the Wikipedia article on "group" in the mathematical sense):

In Piaget's work the transformation group is never properly understood. Displacements need not form a group and those displacements considered by Piaget cannot even be extended to constitute a group, and anyhow do not have anything to do with the group of motions.

Justified at last! He really didn't know what he was talking about, but he did it in such awful jargon that this was hard to find out for non-specialists!

It may be feared that I've just logically destroyed the scaffolding of several thousands of Ph.D.s in the science of psychology, but then most of these doctors will never know this, and will happily continue their careers.

In case you ever seriously puzzled about Piaget's texts though, you now may know why.

P.S. Anyway... as you see my texts are not always satirical or about ridiculous, phony, lying, deceiving, falsifying and/or sadistic pseudos, politicos or bureaucrats, and in fact my texts have to be about what happens to interest me to get written at all. (And I may have today saved at least one career of at least one at least fairly intelligent budding psychology student. And the title of Freudenthal was given above; the publisher is D. Reidel, the year published 1973, and the ISBN 90 277 0322 1.)

Tomorrow there may be more on the subject of sadistic pseudos, politicos or bureaucrats, that may astonish many who do not know the Amsterdam ways as they really are, but I make no promises in view of being quite PEM'ed. (*)

P.P.S. It may be I have to stop Nederlog for a while. The reason is that I am physically not well at all. I don't know yet, but if there is no Nederlog, now you know the reason.

As to ME/CFS (that I prefer to call ME):

1. Anthony Komaroff

Ten discoveries about the biology of CFS (pdf)

3. Hillary Johnson

The Why

4. Consensus (many M.D.s) Canadian Consensus Government Report on ME (pdf)
5. Eleanor Stein

Clinical Guidelines for Psychiatrists (pdf)

6. William Clifford The Ethics of Belief
7. Paul Lutus

Is Psychology a Science?

8. Malcolm Hooper Magical Medicine (pdf)

Short descriptions:

1. Ten reasons why ME/CFS is a real disease by a professor of medicine of Harvard.
2. Long essay by a professor emeritus of medical chemistry about maltreatment of ME.
3. Explanation of what's happening around ME by an investigative journalist.
4. Report to Canadian Government on ME, by many medical experts.
5. Advice to psychiatrist by a psychiatrist who understands ME is an organic disease
6. English mathematical genius on one's responsibilities in the matter of one's beliefs:
   "it is wrong always, everywhere, and for anyone, to believe anything upon
     insufficient evidence
7. A space- and computer-scientist takes a look at psychology.
8. Malcolm Hooper puts things together status 2010.

"Ah me! alas, pain, pain ever, forever!

No change, no pause, no hope! Yet I endure.
I ask the Earth, have not the mountains felt?
I ask yon Heaven, the all-beholding Sun,
Has it not seen? The Sea, in storm or calm,
Heaven's ever-changing Shadow, spread below,
Have its deaf waves not heard my agony?
Ah me! alas, pain, pain ever, forever!
     - (Shelley, "Prometheus Unbound") 

    "It was from this time that I developed my way of judging the Chinese by dividing them into two kinds: one humane and one not. "
     - (Jung Chang)

See also: ME -Documentation and ME - Resources

P.P.S. ME - Resources needs is a Work In Progress that hasn't progressed today.

(*) "PEM" = "Post Exertional Malaise". This the key symptom of ME in the Canadian Definition, which is the best, and precisely what I have complained most about since 1979 in these terms:

"Whatever I do physically, it turns out that I always have to pay back afterward, in terms of more tiredness, more muscle agues, more night sweats etc. Moreover, apart from that fact, it is unpredictable, apart from having to pay back: How much and how long may vary considerable, for what seems the same expenditure of calories on a task."

The reason I complained most about this is that while I did not even know the first ten years of my disease (1979-1988) what ME is - which is not odd for a non-medical person, though it is a lot more odd that many tens of professors and doctors of medicine my ex wife (also ME, also started with Epstein Barr) saw also seem never to have heard from it or read about it, though they should have - both my wife and I studied from study loans and had to make so many course points every year to get the loan renewed for the next year. Therefore, she and I were out and about a fair amount, usually more than was good for us, and were also often asked what was the matter with us, since we did not look ill, and were both excellent students.

(**) Extra-terrestrial intelligence is spmething I personally was never much interested in, after I realized at 16 that Einstein's finite speed of light made communications which such intelligence, if it was outside the solar system the earth belongs to, a very tedious exchange, and anyway I am not one who easily takes a considerable interest in issues it is hard to get good evidence about.

(***) Well, I make two possibly enlightening remark: Too many possibly relevant variables! Too many statistical distributions accepted as panaceas!

Maarten Maartensz

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