30 May 2010

Interview with Gromov

In the March 2010 issue of the Notices of the American Mathematical Society, there is a very good interview with Mikhail Gromov, prominent mathematician and the recipient of the 2009 Abel Prize of the Norwegian Academy of Science and Letters. I would like to quote just a couple of little excerpts from this interview, leaving aside the majority of it for future comments which will appear on this blog.
As you know, in the UK, in some
of the universities, there are faculties of homeopathy
that are supported by the government. They
are tremendously successful in terms of numbers
of students. And anybody can learn that nonsense.
It is very unfortunate.
Alas, this is true. However, it is easy to spot fake university programmes, like those offering courses on homeopathy. What is harder is to spot university programmes that hide themselves under the guise of science. Indeed, imagine, for instance, a university offering a course on the Mathematics of Homeopathy, say, luring students who aspire to learn applied mathematics. Such a hoax would be harder to spot.

A second excerpt, from the same interview, goes as follows. (It is a reply to the question on how education should change to get better adapted to very different minds.)
Look at the number of
people like Abel who were born two hundred
years ago. Now there are no more Abels. On the
other hand, the number of educated people has
grown tremendously. It means that they have not
been educated properly because where are those
people like Abel? It means that they have been
destroyed. The education destroys these potential
geniuses—we do not have them! This means that
education does not serve this particular function.
The crucial point is that you have to treat everybody
in a different way. That is not happening
today. We don’t have more great people now than
we had one hundred, two hundred, or five hundred
years ago, starting from the Renaissance, in spite
of a much larger population. This is probably due
to education. This is maybe not the most serious
problem with education.
What he says is absolutely true: Despite the fact that the population has grown by almost an order of magnitude in 200 years, despite the fact that the majority of people are able to (and do) enter a "higher education establishment", the number of thinkers like Abel has not grown in proportion to the world population. Education, says Gromov, is responsible for this. Indeed, many universities nowadays offer vocational training instead of university education. There is nothing wrong with vocational training: we need car mechanics, accountants, paramedics, fire-fighters, etc. What is wrong is to substitute university education with vocational training. And what is much worse is to claim that we are not doing so; that we are still offering "high quality" education, whereas, in reality, we are training people to do a specific job. This is were the problem lies. And this is why Gromov, in the first excerpt above, gave the homeopathy example as an example of what is happening in universities nowadays.

23 May 2010

Martin Gardner dies

Martin Gardner has died at the age of 95, according to a report in *The Seattle Times*. See
for details. James Randi also makes the announcement on his blog at

Martin Gardner played a key role in promoting mathematics education, through his numerous columns and books. He had an uncompromising attitude toward pseudoscience, he was critical of organized religion, and was regarded as a hard-core Platonist. Through his work, he promoted the thought process at all levels. Donald Knuth refers to the 15 volumes of collected Martin Gardner's columns from Scientific American as "the Canon".

22 May 2010


This is a wonderful video, it's about friendship. Between members of the order Primates, in fact between members of the family Hominidae, more specifically between members of the subfamily Homininae.

How little is the difference between its members!

21 May 2010

A paper with 2789 authors

I came across this physics paper by browsing the arXiv.org e-Print archive tonight. It is titled
"Readiness of the ATLAS Liquid Argon Calorimeter for LHC Collisions"
and has 2789 authors! Yes, that's right:
Two thousand seven hundred and eighty nine authors!

The papers is 31 pages long. Seven of these pages are devoted to the listing of the authors' names. Actually, all letters of the alphabet are there: there is at least one author whose family name starts with any given letter. It takes another 4 pages to list the authors' affiliations. One of the authors is marked as deceased at the time of submission of the paper. (Considering their number, this must be a not-so-unlikely event.)

I wish I knew whether this is a world record.

12 May 2010

Don't talk to aliens

I'm spending a few months at Cambridge. I couldn't miss it therefore but be informed of the latest announcement of Professor Stephen Hawking, namely:
“To my mathematical brain, the numbers alone make thinking about aliens perfectly rational. The real challenge is to work out what aliens might actually be like.”

“We only have to look at ourselves to see how intelligent life might develop into something we wouldn’t want to meet. I imagine they might exist in massive ships, having used up all the resources from their home planet. Such advanced aliens would perhaps become nomads, looking to conquer and colonise whatever planets they can reach.”

“If aliens ever visit us, I think the outcome would be much as when Christopher Columbus first landed in America, which didn’t turn out very well for the Native Americans.”

However, today, another fact became known to me which, surely, and beyond any doubt, provides the definitive explanation about aliens:
The Gwizls, an alien species far more advanced than humans, missed their invasion of planet Earth and all disappeared in the depths of sea by lack of knowledge of the basic properties of water (H2O)
The announcement was made by Professor Pierre Brémaud (visiting fellow of the Newton Institute for Mathematical Sciences). Proof below:

As much as you can


As Much As You Can

And if you can’t shape your life the way you want,
at least try as much as you can
not to degrade it
by too much contact with the world,
by too much activity and talk.

Try not to degrade it by dragging it along,
taking it around and exposing it so often
to the daily silliness
of social events and parties,
until it comes to seem a boring hanger-on.

(C.P. Cavafy, Collected Poems. Translated by Edmund Keeley and Philip Sherrard. Edited by George Savidis. Revised Edition. Princeton University Press, 1992)

For another translation in English, by Charles Bryant, click here.

10 May 2010

What is Enlightenment?

The motto of the Enlightenment is not a thing of the past. It is modern and will always be so:
Aufklärung ist der Ausgang des Menschen aus seiner selbst verschuldeten Unmündigkeit. Unmündigkeit ist das Unvermögen, sich seines Verstandes ohne Leitung eines anderen zu bedienen. Selbstverschuldet ist diese Unmündigkeit, wenn die Ursache derselben nicht am Mangel des Verstandes, sondern der Entschließung und des Muthes liegt, sich seiner ohne Leitung eines anderen zu bedienen. Sapere Aude! Habe Muth dich deines eigenen Verstandes zu bedienen! ist also der Wahlspruch der Aufklärung.
Enlightenment is man's release from his self-incurred tutelage. Tutelage is man's inability to make use of his understanding without direction from another. Self-incurred is this tutelage when its cause lies not in lack of reason but in lack of resolution and courage to use it without direction from another. Sapere aude! "Have courage to use your own reason!" - that is the motto of enlightenment.
So the message of the Enlightenment is not, simply, the lack of reason but the lack of ability to use one's reason. Reasoning independently and with courage is what the motto of the enlightenment is. "Sapere aude" means "dare to know" and, by extension, dare to use your own reason, independently, without the guidance of somebody else, free of external influences even (or, perhaps, especially) when these influences are part of an established "tradition".

The message of the Enlightenment should be read and understood by all, even people working in the Academia (teachers and administrators alike).

Here is the original first page from Imanuel Kant's essay "Beantwortung der Frage: Was ist Aufklärung? -- Berlinische Monatsschrift, Bd. 4, 481-494, 1784".

6 May 2010

Neanderthal genes 'survive in us'

A fascinating report:

Many people alive today possess some Neanderthal ancestry, according to a landmark scientific study.
The finding has surprised many experts, as previous genetic evidence suggested the Neanderthals made little or no contribution to our inheritance.
The result comes from analysis of the Neanderthal genome - the "instruction manual" describing how these ancient humans were put together.
The genomes of 1% to 4% of people in Eurasia come from Neanderthals.
But the study confirms living humans overwhelmingly trace their ancestry to a small population of Africans who later spread out across the world.
The most widely-accepted theory of modern human origins - known as Out of Africa - holds that the ancestors of living humans (Homo sapiens) originated in Africa some 200,000 years ago.
A relatively small group of people then left the continent to populate the rest of the world between 50,000 and 60,000 years ago.
While the Neanderthal genetic contribution - found in people from Europe, Asia and Oceania - appears to be small, this figure is higher than previous genetic analyses have suggested.
"They are not totally extinct. In some of us they live on, a little bit," said Professor Svante Paabo, from the Max Planck Institute for Evolutionary Anthropology in Leipzig, Germany.
Professor Chris Stringer, research leader in human origins at London's Natural History Museum, is one of the architects of the Out of Africa theory. He told BBC News: "In some ways [the study] confirms what we already knew, in that the Neanderthals look like a separate line.
"But, of course, the really surprising thing for many of us is the implication that there has been some interbreeding between Neanderthals and modern humans in the past."
John Hawks, assistant professor of anthropology at the University of Wisconsin-Madison in the US, told BBC News: "They're us. We're them.
"It seemed like it was likely to be possible, but I am surprised by the amount. I really was not expecting it to be as high as 4%," he said of the genetic contribution from Neanderthals.
The sequencing of the Neanderthal genome is a landmark scientific achievement, the product of a four-year-long effort led from Germany's Max Planck Institute but involving many other universities around the world.
The project makes use of efficient "high-throughput" technology which allows many genetic sequences to be processed at the same time.
The draft Neanderthal sequence contains DNA extracted from the bones of three different Neanderthals found at Vindija Cave in Croatia.
Retrieving good quality genetic material from remains tens of thousands of years old presented many hurdles which had to be overcome.
The samples almost always contained only a small amount of Neanderthal DNA amid vast quantities of DNA from bacteria and fungi that colonised the remains after death.
The Neanderthal DNA itself had broken down into very short segments and had changed chemically. Luckily, the chemical changes were of a regular nature, allowing the researchers to write software that corrected for them.
Writing in Science journal, the researchers describe how they compared this draft sequence with the genomes of modern people from around the globe.
"The comparison of these two genetic sequences enables us to find out where our genome differs from that of our closest relative," said Professor Paabo.

The results show that the genomes of non-Africans (from Europe, China and New Guinea) are closer to the Neanderthal sequence than are those from Africa.
The most likely explanation, say the researchers, is that there was limited mating, or "gene flow", between Neanderthals and the ancestors of present-day Eurasians.
This must have taken place just as people were leaving Africa, while they were still part of one pioneering population. This mixing could have taken place either in North Africa, the Levant or the Arabian Peninsula, say the researchers.
The Out of Africa theory contends that modern humans replaced local "archaic" populations like the Neanderthals.
But there are several variations on this idea. The most conservative model proposes that this replacement took place with no interbreeding between modern humans and Neanderthals.
Another version allows for a degree of assimilation, or absorption, of other human types into the Homo sapiens gene pool.
The latest research strongly supports the Out of Africa theory, but it falsifies the most conservative version of events.
The team also identified more than 70 gene changes that were unique to modern humans. These genes are implicated in physiology, the development of the brain, skin and bone.
The researchers also looked for signs of "selective sweeps" - strong natural selection acting to boost traits in modern humans. They found 212 regions where positive selection may have been taking place.
The scientists are interested in discovering genes that distinguish modern humans from Neanderthals because they may have given our evolutionary line certain advantages over the course of evolution.
The most obvious differences were in physique: the muscular, stocky frames of Neanderthals contrast sharply with those of our ancestors. But it is likely there were also more subtle differences, in behaviour, for example.
Dr Hawks commented that the amount of Neanderthal DNA in our genomes seemed high: "What it means is that any traits [Neanderthals] had that might have been useful in later populations should still be here.
"So when we see that their anatomies are gone, this isn't just chance. Those things that made the Neanderthals apparent to us as a population - those things didn't work. They're gone because they didn't work in the context of our population."
Researchers had previously thought Europe was the region where Neanderthals and modern humans were most likely to have exchanged genes. The two human types overlapped here for some 10,000 years.
The authors of the paper in Science do not rule out some interbreeding in Europe, but say it was not possible to detect this with present scientific methods.


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