One more misleading image of Pythagoras Theorem

One more misleading image of Pythagoras Theorem

Structures, Learning and Ergosystems

A wonderful text by Michael Gromov: http://www.ihes.fr/~gromov/PDF/ergobrain.pdf

Obsessive Compulsive Disorder

From The Guardian:

One of our first patients, just 17 years old, was brought to us in a wheelchair,” says Professor Christer Lindquist,  a pioneer in the use of a brain surgery technique for people with Obsessive Compulsive Disorder   (OCD),  known as Gamma Knife. “This boy would set himself maths problems, which he had to solve before he could eat. His OCD had become so severe, and the maths problems he set himself so complex, that he couldn’t solve them any more, so he couldn’t eat.

(With thanks to muriel)

AN: A childhood story

As for the limits, we were told to imagine an animal getting closer to point on the plane but not really arriving at it.  This is a very poor discription and gave me many years of unnecessary pain while dealing with limits.  The things is this animal might actually decompose itself into many different animals who have nothing to do with the first one and whoever acts more dramatically close to a certain point will guide the limit close to that point.

The anthropology of meaning

L. Radford,  The anthropology of meaning. Educational Studies in Mathematics 61 (2006), 39–65:

Meaning is one of the recent terms which have gained great currency in mathematics education. It is generally used as a correlate of individuals’ intention and considered a central element in contemporary accounts of knowledge formation. One  important question that arises in this context is the following: if, in one way or another, knowledge rests on the intrinsically subjective intentions and deeds of the individual, how can the objectivity of conceptual mathematical entities be guaranteed? In the first part of this paper, both Peirce’s and Husserl’s theories of meaning are discussed in light of the aforementioned question. I examine their attempts to reconcile the subjective dimension of knowing with the alleged transcendental nature of mathematical objects. I argue that transcendentalism, either in Peirce’s or Husserl’s theory of meaning, leads to an irresolvable tension between subject and object. In the final part of the article, I sketch a notion of meaning and conceptual objects based on a semiotic-cultural approach to cognition and knowledge which gives up transcendentalism and instead conveys the notion of contextual objectivity.

Childhood stories from TE

I found your blog via the entry on women and mathematics.

I know that this is not exactly what you are searching for with your demand for stories, but I have to comment on the “intrinsic competitiveness” of mathematics.

In mathematics olympiads and in professional mathematics, competitiveness is ritualized and contained by ethical rules. In my olympiad training session, you were expected to explain things to newer participants even though they might well be better than you at the competition. In olympiads and real life, I have found that this kind of ethics almost always corresponded to mathematical capability.

So here is my anecdote on competitiveness:

In primary school (age 6-10), I had about half the running speed of any other child. On the other hand, I understood everything in maths immediately and was very quick with mental calculations. In sports, we had weekly running competitions of groups by four, where my group never had a chance at all.  In maths, we had weekly speed calculating competitions where each pair of students were posed a question and the quicker one would remain standing until one student was left and got a little prize. I won every time and was only allowed to participate every other week.

The lesson that good performance in math is bad for your social standing with your peers could not have been more evident.

More anecdotes on learning:

Age: 3
Gender: female
languages involved: German
Brother aged 5

My brother and I had learned (presumably from our parents) how counting goes on and on without an end. We understood the construction but we were left with some doubt that you could *really* count to high numbers, so we decided to count up to a million by dividing the work and doing it in the obligatory nap time in kindergarten in our heads. After a couple of days, we had to admit that it took too long, so we debated whether it was ok to count in steps of thousands or ten-thousands, now that we had counted to thousand many times. We ended up being convinced that it is possible to count to a million but slightly unhappy that we could not *really* do so ourselves.

Age: 14
Gender: female
languages involved: German

I participated in a mathematical competition where an inequality had to be proven by induction. I adhered strictly to a ”one-line-format” where you start with the left-hand-side of the desired inequality, apply induction hypothesis etc until you arrive at the right-hand-side.

When I afterwards saw someone at some step adding the desired right-hand-side and manipulating the unproven inequality, I understood the advantage immediately and felt stupid for not considering this possibility, but I could never have asked a question about this because I was not aware of any restriction in my thinking. My teachers also could not notice any problems because my proofs were correct.

Motherlode: Math’s Too Hard for a Parent’s Help

SUNDAY MAGAZINE | October 30, 2009 Motherlode: Math’s Too Hard for a Parent’s Help By Lisa Belkin Many parents would rather talk to their kids about sex and drugs than math and science.

(with thanks to muriel)

RAE/REF and the ‘economic and social impact’ of research

Most likely you have heard about HEFCE’s proposal that in the REF (a

replacement for the RAE) 25% of future research funding would be

allocated according to the ‘economic and social impact’ of submitted

research. Many of our colleagues believe that this ‘impact’ proposal

represents an attack on the knowledge process and constitutes a threat

to the existence of basic research activity in the UK.

What appears to be missing from the increasingly intensive discussion is

that the REF proposal provides not just the poison to kill independent

academic research, it offers a syringe for injection, too. The latter is

described in a few innocuous lines about the aims of the exercise:

“We will be able to use the REF to encourage desirable behaviours at

three levels:

*  THE BEHAVIOUR OF INDIVIDUAL RESEARCHERS WITHIN A SUBMITTED UNIT [...]“

[http://www.hefce.ac.uk/pubs/hefce/2009/09_38/09_38.pdf , page 8]

The emphasis on inducing change in the behaviour of “individual

researchers” is the result of a slow evolution of the RAE/REF. In 1996

and in 2001, the RAE  went to great lengths to ensure that individual

researchers could not be identified in the panels’ responses. This

changed in 2008, when the percentages of the submission with each number

of stars were published. So it was possible, in the case of a small

unit, to work out exactly how many papers were internationally

excellent, etc., and make a fairly good guess which papers they were.

The passage in the REF proposal concerned with “individual researchers”

is much more worrying, especially since this time “the overall

excellence profile will combine three sub-profiles – one for each of

output quality, impact and environment – which will also be published.”

If “behaviour” just meant “doing good/bad/no research”, it would not be

so terrible, but since extraneous things like “impact” now loom large,

HoDs will be able to use this to warn staff off doing their preferred

research and onto more “impactful” projects. There is a danger that, at

department level, the REF might be translated into unheard of levels of

bullying and harassment.

Please sign the Number 10 Petition:

http://petitions.number10.gov.uk/REFandimpact/

Please also sign the UCU petition STAND UP FOR RESEARCH (even if you are

not an UCU member; signing is open to everyone):

http://www.ucu.org.uk/standupforresearch

Most likely the readers of my blog have heard about HEFCE’s proposal that in the REF (a replacement for the RAE) 25% of future research funding would be

allocated according to the ‘economic and social impact’ of submitted

research. Many of our colleagues believe that this ‘impact’ proposal

represents an attack on the knowledge process and constitutes a threat

to the existence of basic research activity in the UK.

What appears to be missing from the increasingly intensive discussion is

that the REF proposal provides not just the poison to kill independent

academic research, it offers a syringe for injection, too. The latter is

described in a few innocuous lines about the aims of the exercise:

“We will be able to use the REF to encourage desirable behaviours at

three levels:

*  THE BEHAVIOUR OF INDIVIDUAL RESEARCHERS WITHIN A SUBMITTED UNIT [...]“

[http://www.hefce.ac.uk/pubs/hefce/2009/09_38/09_38.pdf , page 8]

The emphasis on inducing change in the behaviour of “individual

researchers” is the result of a slow evolution of the RAE/REF. In 1996

and in 2001, the RAE  went to great lengths to ensure that individual

researchers could not be identified in the panels’ responses. This

changed in 2008, when the percentages of the submission with each number

of stars were published. So it was possible, in the case of a small

unit, to work out exactly how many papers were internationally

excellent, etc., and make a fairly good guess which papers they were.

The passage in the REF proposal concerned with “individual researchers”

is much more worrying, especially since this time “the overall

excellence profile will combine three sub-profiles – one for each of

output quality, impact and environment – which will also be published.”

If “behaviour” just meant “doing good/bad/no research”, it would not be

so terrible, but since extraneous things like “impact” now loom large,

HoDs will be able to use this to warn staff off doing their preferred

research and onto more “impactful” projects. There is a danger that, at

department level, the REF might be translated into unheard of levels of

bullying and harassment.

Please sign the Number 10 Petition:

http://petitions.number10.gov.uk/REFandimpact/

Please also sign the UCU petition STAND UP FOR RESEARCH (even if you are

not an UCU member; signing is open to everyone):

http://www.ucu.org.uk/standupforresearch

A wonderful blog

Apparently, by a woman mathematician:

http://ideafoundlings.blogspot.com/

A comics novel about Bertrand Russell

http://www.logicomix.com/en/

(with thanks to Jean-Michel Kantor).