Today, 21 May 2011, is the end of the world

I mentioned this again last year. Brief review: Mr Harold Camping "proved", using "mathematics", that the world is scheduled to end today. Indeed (Camping claims), Jesus was crucified on 1 April 33, and, since then, there have passed 722500 days. But 722500=(5 x 10 x 17) x (5 x 10 x 17). And, according to Camping and the Bible, 5=Atonement,  10=Completeness and 17=Heaven. This argument allowed him to draw the conclusion that the world ends today.

So, hurry up and do your shopping before it's too late. I have to finish a presentation on Lévy processes, but I'm not too motivated.

As for the last picture, my readers will probably recall that Stephen Hawking is not always right. I had pointed out that Pierre Brémaud's scientific predictions differ from those of Hawking when it comes to serious matters, like aliens contacting humans.

Think before you condemn

I found this brilliant article on "a Nadder!" about Afghanistan, based on a Foreign Policy photo essay. Most of us tend to think of Afghanistan as a county of bearded mullahs, religious fanatics. terrorists, uneducated people, etc. We also adopt a point of view that the present is always better than the past and so, if Afghanistan is the way it is now, imagine what it was 50 or 100 years ago. Probably people living in caves. But we are wrong. The following photo is from a biology class in a university in Afghanistan:

And this is from the Radio Kabul transmitter. The radio could be heard as far as South Africa.

Is this the image we have about this country? Certainly not. Look at the sources above for more details and more pictures. And, most of all, think and look around before you form an opinion based on what the media tell you or what the person down the road thinks. And think, also, how fragile the current system you live in may be. This is an advice for me too.

The Pope is more influential than any scientist

"Like it or not, the Pope is more influential than any scientist", says the New Scientist (December 2010).

In an article about the Pope's tacit approval of condom use to prevent the spread of HIV, it is also mentioned that prominent scientists have urged the Vatican's Pontifical Academy of Sciences to endorse genetically modified (GM) crops.

The Catholic Church has yet to officially back GM. But if it does, it would be a welcome shift away from a gimlet-eyed obsession with sexual morality into areas that could genuinely improve the lives of billions. Like it or not, the Pope is more influential than any scientist. Supporters of GM should hope he sees the light.

 A quick search in New Scientist's archives shows how often scientists try to get the Pope's endorsement:

• Three prominent US scientists have asked Pope Benedict XVI to clarify the Roman Catholic church's view on Darwinism.
• Could it be that the Vatican is about to enter the age of enlightenment?  
• Will the papacy ever come to terms with progress in reproductive science, or will the new pope follow in his predecessors footsteps?
• The Catholic church's demonising of the technologies that facilitate test-tube babies is making it look out of touch and irrelevant.

The Pope's opinion matters for millions of people in the world. They would rather listen to him, a scientifically-illiterate individual, about all kinds of important things, rather than listen to scientists. Religion is interfering with so many important things in this world and this is a really sad state of affairs.

Intelligent designers: move to Texas!

Texas on the news again: They are considering a bill to protect creationists from discrimination. I heard about it last Friday from a postdoctoral student of our department and checked it out. There is an article about it in Mother Jones. Using the language and rationale of political correctness, the author of the bill, Republican state representative Bill Zedler proposes:

HB 2454, Section A51.979.A:
A PROHIBITION OF DISCRIMINATION BASED ON RESEARCH RELATED TO INTELLIGENT DESIGN.
An institution of higher education may not discriminate against or penalize in any manner, especially with regard to employment or academic support, a faculty member or student based on the faculty member's or student's conduct of research relating to the theory of intelligent design or other alternate theories of the origination and development of organisms.

Texas is the state where the major proponent of creationism/intelligent design, William Dembski, teaches: He is professor at the Southwestern Baptist Theological Seminary in Ft. Worth, he conducts research in theology by means of creationism/intelligent design, and desperately tries to use pseudo-mathematics in support of his theological claims. Dembski did a PhD in mathematics but he immediately switched to theology. He is not alone in Texas. There are many creationist pseudoscientists there who can find lots of money by religious fundamentalists; the latter will happily fund the former in order that they use pseudo-science and pseudo-mathematics to "prove" theological claims, ranging from denial of evolution to belief that the Earth is a few thousand years old.

Now the state of Texas is trying to pass the aforementioned bill. In my opinion, this will have at least two effects:

1.  If a faculty member in a Texas university cannot do serious mathematics or science then he or she can turn to creationism and publish papers in pseudo-scientific creationistic journals.  He or she then will ask to be tenured and, based on the above law, he or she should not be discriminated against.
2.  Funding for creationism will have to be considered as academic funding. The law justifies creationism as an academic field of study.
3. Academics with creationistic tendencies will seek jobs in Texas universities.

I have served in Texas as a faculty member and know the mentality. Although there are many academics who will be angry at such a bill, there are several others, academics or not, religious fundamentalists, who will espouse this bill and use it for theological purposes.

A new very short proof of the fundamental theorem of algebra

I've always been intrigued by the fundamental theorem of algebra (every nonconstant polynomial with complex coefficients has a root), not least because I don't know any proof which uses algebra only. Earlier, I posted an easy proof in this blog, one that uses Cauchy's theorem.There is a recent proof (Oswaldo Rio Branco de Oliveira, Mathem. Intellig., March 2011), which is almost trivial. It goes as follows (and this is a chance for me to see if the embedded LaTeX script works...):

Let $P(z)$ be a polynomial of degree $n$. Since $|P(z)|$ is a nonnegative continuous function, tending to $\infty$ as $|z|$ tends to $\infty$, it has a minimum at some point $z_0$:

$|P(z)| \ge |P(z_0)|$, for all $z$.

By division of $P(z)-P(z_0)$ by $z-z_0$, write

$P(z) = P(z_0) + (z-z_0)^k Q(z-z_0),$

where $Q(0) \not = 0$. Since $P(z)$ is nonconstant, the integer $k$ is $\ge 1$.
Therefore

$|P(z_0) + (z-z_0)^k Q(z-z_0)|^2 \ge |P(z_0)|^2$, for all $z$,

and, expanding the square,

$|z-z_0|^{2k} |Q(z-z_0)|^2 + 2 \Re \{ (z-z_0)^k Q(z-z_0) \overline{P(z_0)}\} \ge 0$, for all $z$.

Let $z=z_0 + r e^{i \theta}$, divide by $r^k$, and let $r$ tend to $0$. We obtain

$\Re \{ e^{i k \theta}  Q(0) \overline{P(z_0)}\} \ge 0$,  for all real $\theta$.

It is an easy exercise in algebra that, if $\alpha$ is a complex number such that $\Re \{ e^{i k \theta} \alpha\} \ge 0$ for all $\theta$, then $\alpha=0$. Hence $Q(0) \overline{P(z_0)}=0$. Since $Q(0) \neq 0$, we obtain $P(z_0)=0$.