15 May 2012

Arithmetica Universalis

Staffan Rodhe's office door was open today, I was passing by, so I dropped in. I was admiring the collection of ancient mathematical texts on his shelves. I first picked up a book by Lagrange, then one by Euler, and then the Arithmetica Universalis by Newton. I opened it somewhere in the middle and found a square piece of paper  (size around 10 cm) with some equations on one side and a couple of geometric drawings on the other. Clearly, it belonged to an careful reader of some past century. Most likely, Staffan explained, it was written some time in the 18th c. I took a couple of photos of both sides, as well as a copy of the title page of the book because they are, in my opinion, like pieces of art. It also makes me wonder how people thought back then, how similar to us they were, etc.
Note that this edition of Arithmetica Universalis was published in 1732 in Lugdunum Batavorum, i.e., Leiden. There is a free version on the internet from a 1752 copy from Amstelodamum (Amsterdam). The original edition dates from 1707.

14 May 2012

The Dawn and the Golden Dawn

As well-known, in the latest parliamentary elections (6 May 2012) in Greece, the parties Coalition of the Radical Left (ΣΥΡΙΖΑ) and Golden Dawn (Χρυσή Αυγή) came, respectively, 2nd and 6th,  receiving 16.78% and 6.68% of the votes,

The somewhat curious coincidence is that the newspaper of the first party is called Dawn (Aυγή), while that of the second one is called Golden Dawn (Χρυσή Αυγή). This is true, albeit curious. It should also be mentioned that the online newspaper of the latter party was hosted by wordpress until 10 May 2012, when it was taken down by wordpress for alleged violations of the host organization's policies, which include spamming, defamation and copyright violation. Golden Dawn folks allege that any resemblance of their symbol to the nazi swastika is totally coincidental.

It is moderately funny that with the omission of an adjective one can swing from far right to far left.

9 May 2012

Obsession with gender

This blog is about rationality. So, when I spot things which are irrational, I write about them. Indeed, an offence to one's sense of logic should be one of scientists' concerns.

In my less-than-two-years sojourn in Sweden, I noticed that there is a certain obsession with the concept of gender. Much in the same way that there was (and still is) obsession with affirmative action in the U.S. So, much so, that the obsession often violates elementary logic.

I pointed out some of these gender-type of obsessions before. For example, here and here. Of course, there is nothing wrong about promoting equality, at all levels, for all people, all genders, all ethnicities. But to be obsessed about it so much so that you feel the need to theorize that "one's sex is not biologically determined but  rather something that is `socially constructed'" is a mere insult to elementary science and elementary logic. True, there are exceptions (as always) to the rule. There are people who may not feel comfortable with the gender they are born with and seek a change at some point in their lives. One should respect this. However, to say that everyone's gender is a social construct is not just absurd, but also idiotic.

Such things are pointed out in an article by Bo Rothstein, professor of Political Science at Gothenburg University. Rothstein refers to the Secretariat for Gender Research (sekretariat för genusforskning), formed several years ago, by the Swedish State. Again, having a body of the government interested in promoting equality of sexes, making sure that neither men are discriminated by women nor women by men, is laudable. But to have statements such as "analyze the need for gender research in all disciplines" is strange. I do not understand the meaning of the phrase. It is, to say the least, strange. It does not say "make sure that there is no sex discrimination in any job". The phrase above presupposes that there is a need for gender research in all scientific disciplines (analysera behovet av genusforskning inom alla vetenskapsområden). It is not unlikely that my Swedish (thanks to Google translate, to be honest) is not good enough, but "vetenskapsområden" means "scientific areas" (vetenskap = Wissenschaft = science). If, then, Physics is a scientific discipline, the phrase above implies that there is a need for gender research in Physics. Since it is true that Physics is a scientific discipline, we conclude that the sekretariat för genusforskning mandates that Physics should also be concerned with gender research. Now, this starts looking very irrational, doesn't it?

Pseudo-scientists who conduct gender research in Physics include a certain infamous philosopher, Luce Irigaray, who, among other things, argues that E=mc2 is a "sexed equation" because  "it privileges the speed of light over other speeds that are vitally necessary to us". She also concludes that fluid mechanics is a neglected discipline because it deals with fluids (duh!) which are feminine in contrast to rigid mechanics which are masculine. For more information on this kind of idiotic research, please take a look at the book "Fashionable Nonsense" by Alan Sokal and Jean Bricmont.

Perhaps the Secretariat for Gender Research do not really mean to be irrational. Perhaps the phrase above, taken from their Code of Statutes, means something else. (We should always give someone the benefit of the doubt.) But then it is a mystery what they might mean, if they don't really mean Irigaray-type of pseudo-research.

Last but not least, when we talk about under-represented gender, we may as well remember that such things are, unfortunately, so much embedded in people's minds that people (even the ones who promote gender equality) cannot think of the root of the problem. Rather, they touch upon these problems tangentially, on the surface. As an example, take, for instance, the four monotheistic religions (Zoroastrinism, Judaism, Christianity and Islam, in chronological order of their foundation). As soon as homo sapiens came up with the idea that there is one god, this god immediately assumed male gender. (Whether this has something to do with a male-dominated society, I'll leave it as an exercise.) Therefore, if the Secretariat for Gender Research want to do something about equality, they should go to the Swedish Church (for instance) and tell them to change, or eliminate, the gender of their deity. At least this is more rational than looking for gender research in Physics. I'm willing to bet, however, that they won't do it.

3 May 2012

New "Proof" of P=NP

Credit goes to Jeff Shallit again, for having found the most stupid "mathematical paper" of all times. It can be found here. After proving that the real numbers form a countable [sic] set, the author "establishes" the proof of a long-standing open problem.

It is a recommended read for those who suffer from insomnia and other maladies. As Shallit remarks, it is "a veritable garden of crankiness".

Oh yes, let us not forget the "proof" of Fermat's last theorem.


What measure theory is about

It's about counting, but when things get too large.
Put otherwise, it's about addition of positive numbers, but when these numbers are far too many.

The principle of dynamic programming

max_{x,y} [f(x) + g(x,y)] = max_x [f(x) + max_y g(x,y)]

The bottom line

Nuestras horas son minutos cuando esperamos saber y siglos cuando sabemos lo que se puede aprender.
(Our hours are minutes when we wait to learn and centuries when we know what is to be learnt.) --António Machado

Αγεωμέτρητος μηδείς εισίτω.
(Those who do not know geometry may not enter.) --Plato

Sapere Aude! Habe Muth, dich deines eigenen Verstandes zu bedienen!
(Dare to know! Have courage to use your own reason!) --Kant