28 November 2010

Creationist mathematics

I wrote a couple of days ago about creationists and the like. Today I want to give an example of their scientific stupidity by pointing out one of their latest articles on infinity. I first read it in Recursivity.

Creationists have a presence on the Internet via the site "Uncommon Descent". People like Dembski often write stupid articles trying to prove that gods (they call them intelligent designers) exist. In this article, Robert Sheldon writes:
For example, take the number line from 1 to ∞. It’s infinite of course. But now divide every number by the largest number on the line, and we have mapped the entire number line into the fractions between 0 and 1. 
What the hell does he mean by "divide by the largest number"? He may have heard that the transformation x → 1/x maps (0,1] onto [1, ∞) but he hasn't quite understood this high school concept.
So the rational numbers contain the entire integer number line between 0 and 1, and the rational numbers go up to infinity too. 
Excuse me? The rational numbers contain what? The... integer (?) line? And how does this follow from the above?
Then the rational numbers are at least ∞2 bigger. (Yup, I’m being sloppy, because Cantor also showed how to map x2–>x, so instead of calling it ∞2, he called it ℵ0 cardinality where integers and rational numbers have the same size infinity.)
Here he is, again, completely off. So much so that it smells from quite far.
[The cardinality of the irrrationals] really is bigger [than the cardinality of the rationals], and Cantor called it ℵ1 cardinality.
Mr Sheldon, go do your homework before you write anything on infinities.
Now if you are like Cantor's left wing critics, then arbitrary things must be random. It is a peculiar property of atheists that they all worship the god of Chance. It would seem possible that they might worship Lady Luck instead, but no, Xaos, Random Chance, must remain the king of the modernist pantheon. So this contingency drives them bonkers.
This is so funny! Left wing critics of Cantor? Atheists worshipping the god of Chance? What about communists? Homosexuals? Liberals? Punks? People with tattoos? (I think the latter folk don't like Cantor either.)

This is the kind of "mathematics" typically used by creationists. The religious folk will, at the same time, applaud them because, in their eyes, they are oh so sophisticated!

For another example of creationist maths look here.

Creationists and similarly-minded religious imbeciles should leave mathematics for mathematicians and scientists. Instead, they should just go to their church to light a candle or whatever their particular religion tells them to do.

26 November 2010

A blog's purpose OR creationism: a recurring theme

I couldn't decide which of the two titles I wanted to have on this posting today. I wanted to express my belief that a blog can help see another point of view and, indeed, show that some things that would never see the light of Earth can surface and be discussed. I am talking about an idiotic movement, mainly in the US, but with branches in the UK and elsewhere, called creationism. It is also called intelligent design. It is nothing new. People, from ages ago, wanted to have their holy texts the only ones that they would read (out of laziness, for instance). They said that you don't need science, just the bible is enough. Some are more radical than others claiming that the Earth is flat or that the Earth is the center of the Universe, some get pimples when they hear the word (Darwinian) evolution, and some do accept science, but get irritated when someone tells them that gods are not a necessary ingredient in any mathematical or physical theory. The latter type of creationists have call themselves intelligent designers and try to "prove" that some intelligence (a.k.a. god) is needed.

Mention these things to an average person in Sweden, a country I live in, and we'll have a laugh and then a beer (if we can afford it--it's too expensive here). But mention these things to an average US-person and you're in for a big surprise. More to the point, it is almost impossibe for a European who has not lived in the US to understand why those people over there are so fanatic about religion and creationism. Vice versa, your average US creationist or religious person has hard time understanding a secular, plain rational, point of view. (Be careful: I said "average", in the common sense of the term. There are people on the other side of the Atlantic who are much more sophisticated than those one meets on this side of the Ocean on a daily basis.)

Some blogs' purposes is to speak openly about these things. The average creationist can (although I doubt it it will happen any tie soon) realize that his/her beliefs are idiotic and that all this intelligent design hoopla has purposes and roots that have nothing to do with science.

It is interesting to take a look at Jeff Shallit's blog. He often writes about creationism. And he gives very good answers to many intelligent design desperate attempts to (ab)use science/mathematics in their arguments. A very good example of the abuse of mathematics in creationism is William Dembski, the leading member (founder?) of a certain theological institute called Discovery Institute whose purpose is to prove that a certain god (called intelligent design) is necessary in Physics. Dembski was a PhD student of Patrick Billingsley with a PhD in Probability Theory. But he didn't do much with mathematics. Having failed in his field he turned to theology.

In Shallit's blog you will also find a recurring theme, called Miranda. This person, apparently a creationist, tries to attack each and every posting of Jeff's that has to do with intelligent design. As an example, read the posting on Harun Yahya (a creationist of Muslim type--yes, they are not necessarily Christian) and read Miranda's replies here. Shallit wrote
Yahya isn't much different from the theocrats at the Discovery Institute, who want to link Darwin to both fascism and communism. 
Miranda, in her replies, wrote that
Richard Evans, historian at Cambridge University, has explained, "The real core of Nazi beliefs lay in the faith Hitler proclaimed in his speech of September 1938 in science--a Nazi view of science--as the basis for action. Science demanded the furtherance of the interests not of God but of the human race, and above all the German race and its future in a world ruled by ineluctable laws of Darwinian competition between races and between individuals."
I asked to explain what she meant. She replied:
My conclusion is that Jeff's charge: "the theocrats at the Discovery Institute, who want to link Darwin to both fascism and communism" is shared by reputable historians.
Miranda attempts here to obfuscate the dialog:
  • Jeff mentions that the Discovery Institute theocrats link Darwin to fascism.
  • Mirand replies that, in her understanding, Hitler also linked Darwin to his ideology.
So what? Even if the latter is true, what does this tell us about the Discovery Institute and its attempts to show that gods are needed in science?
Miranda, I'll tell you this: it's so nice to live in a country (Sweden) where almost nobody--as far as my limited experience has been--cares about creationism/intelligent_design/religious crap. It's so refreshing not to have the crowds around you who want to explain science through the bible and holy texts. I feel happy I can look at these idiocies from a distance and have a laugh at them. But I do care about people who live on the other side of the Atlantic and have to constantly put up with all this nonsense, sometimes on a daily basis. 
 Perhaps, with the help of blogs or otherwise, Miranda can see that her fellow creationists are a largely American phenomenon. A phenomenon which, in other civilized countries of this world, fortunately does not exists (in such a scale). If creationists could broaden their horizons, perhaps they could embrace a more rational standpoint. Instead, they shelter themselves from everybody else, they build fairy taile-like theme parks (creationist museums), and live with false beliefs. The apotheosis of all is the so-called Holy Land Experience, a Disney-like theme park in Orlando Florida (next to DisneyWorld), where, instead of Mickey Mouse and Donald Duck, the pious creationists, intelligent designers, religious folk, can experience the reenactment of Jesus' crucifixion, on a daily basis:

Now some creationists/inteligent designers may complain that Jesus has nothing to do with their efforts. True, for instance, Yahya's version of creationism is different. Nevertheless, they're all the same in spirit: in that they abuse science and mathematics and make claims that are completely irrational

24 November 2010

Galileo was wrong. Vive la Bible!

Damn! I missed the conference. It took place on 6 November 2010. Just a couple of weeks before my visit to the U.S. Otherwise I would have gone to learn the truth: the Earth is at the center of the Universe, as proven by scientific experiments (e.g., reading the Bible carefully in ancient Hebrew).

According to Dr. Robert Sungenis,

Scientific evidence available to us within the last 100 years that was not available during Galileo's confrontation shows that the Church's position on the immobility of the Earth is not only scientifically supportable, but it is the most stable model of the universe and the one which best answers all the evidence we see in the cosmos.

The consequences are amazing. One of them is, surely, that aliens will reach us soon, since we are the center of the Universe and they surely are looking for it too.

23 November 2010

The monetary value of a professor

According to this Wall Street Journal article, Texas wants to assign a monetary value to each of its university faculty members. For example, Carol Johnson (Biology) is worth minus $279,617,  a colleague of hers, Charles Criscione is worth minus $45,305, history professors are worth minus a lot more, and so on.

Students are customers, and as such, they have every right to receive royal treatmement that goes all the way to assigning a value to each of their lecturers.

The logic is simple: If a professor is worth plus something, then keep them. If a professor is worth minus something, then fire them. And the savings can be used for increasing the other professors' salary.

So what's gonna happen? There will be a university with no languages, no history, no biology, no mathematcs, none of these subjects which generate negative profit. The university will comprise of Business, Marketing, Media--whatever it generates immediate profit.

Performance metrics they say, and they mean it in Texas. Texas wants it BIG. No small potatoes, but big bucks.

The article above mentions, in particular, Chester Dunning, a history professor, has won several teaching awards. According to a report by the chancellor, he also loses money for the university, though his department is in the black overall.

What is the solution? I propose one, Texas-style: Get in his office and shoot him!

5 November 2010

The fear of OMEGA

A few weeks ago I finished teaching (yet another time) a sort-of upper division undergraduate probability course. What I want to talk about is the beauty and fear of Ω.

As everybody knows, many undergraduate texts in probability start (pompously so) by putting the subject in its proper basis: A probability space is a triplet (Ω, F, P), where Ω is a set, F is a sigma-algebra of subsets of Ω and P is a countably additive function from F to the nonnegative real numbers such that P(Ω)=1.

And then they go on by giving the reader (only) some trite (silly) examples of probability spaces (such as the set {1,2,3,4,5,6}). After going throuh this rite, the quickly forget Ω.

Poor Ω, you seem to be condemned to death right away, from the start. We talk about you, we make you appear stupid, and then we tell the students: We shall not use this from now on.

What makes things worse is that when we speak of random variables, we immediately tell our students that we shall never write X(ω), but, simply, X. There are, of course, very good reasons for doing so, and, indeed, many times, we need not think of random variables as functions, but, simply, be able to handle probabilities associated with them.

In doing so, we immediately destroy the power of Ω, and tell the student that it's not really there. We condemn it to death. We make students fear of them. Some students graduate, they go to get a Master's, maybe a PhD later, and they reach the professorial levels, all the way having the fear of Ω. So much so, that they often miss a huge part of Probability because they are unwilling to delve into Ω and see that it is there and exists!

I am starting a campaign: Re-introduce Ω and keep it up to the surface, by giving, right from the beginning, meaningful examples where the construction (rather than the axiomatization) of Ω is used.

It took people long time to talk about Probability correctly and now what? Should we pretend we don't know what it is? And keep going on teaching the subject as if it were not understood?

No, I am NOT claiming we should teach it a la Bourbaki. No. I am just saying that, while we do speak of Probability in terms of dice, coins, coincidences, noise, etc., let us not forget that it lives on some Ω which can be used, whenever convenient.

1 November 2010

Language fashions

I called a friend in Greece yesterday but the connection was not possible due to technical problems. A recorded message announced:
Η τηλεφωνική σύνδεση που καλέσατε δεν είναι εφικτή για τεχνικούς λόγους.
(The telephone connection that you called is not possible due to technical reasons.)
I've been hearing this message for a few years: it has been the standard recorded message of the Greek telecommunication company during the last, say, 6-7 years. What's wrong with this? Well, we do not call a telephone connection. We either call a telephone (number) or we establish a telephone connection. To call a telephone connection is, simply, an absurd expression.

So I will make a prediction: because this message has been on for many years, and because nobody has bothered to change it, this will become a de facto expression in the Greek language: "to call a telephone connection". I don't complain when a language changes (like nite instead of night or gonna instead of going to), but, nevertheless, it seems peculiar when a language changes due to a stupidity. The example above is a change witnessed in action.

Here is another example, a phonological change this time: The double consonant 'γγ' in Greek is sometimes pronounced as 'ng' (i.e. nasalised hard g), as in αγγελος (a'ŋgelos), and sometimes as 'ŋγ' (i.e. nasalised soft g) as in the word
συγγραφέας (writer)  :   siŋγraféas
The reason is simple: the latter word is formed by joining a prefix (συν) with a word derived from the verb γραφω (to write):
συν + γραφέας = συγγραφέας
The nasal consonant ν becomes γ in front of the (soft) consonant γ. While the writing changes, the pronunciation remains unaltered. Nevertheless, many younger Greeks pronounce the word as
i.e. (i) they drop the nasal sound completely and (ii) the harden the γ. So the 'υγγ' in 'συγγραφέας' sounds like the 'ig' in 'dig'. The result sounds both funny and ridiculous.

How did this come about? It appears that several years ago some illiterate TV news broadcaster, or some other popular TV personality, started pronouncing the word as 'siGraféas'. Probably, this became the cool thing to do. And, lo and behold, we have a generation of Greeks pronouncing the word in a funny way. (Please don't ask me for references; this is, simply, my guess...)

Again, it is silly to complain about changes in language (it changes all the time), but it does sound a bit funny when the changes are due to errors that can be witnessed in action.

My final example, again of phonological nature, is the triplet of months
Οκτώβριος,  Νοέμβριος, Δεκέμβριος (October, November, December).
They derive from the latin words octo, novem, decem, meaning eight, nine, ten, respectively. Notice that the nasal consonant 'm' appears at the end of only two of these numerals. Therefore 'October' is not pronounced 'octoMber'. However, modern (i.e. the last 5 years or so) Greeks, and learned ones, supposedly (such as politicians and lawyers), say
Why? Well, I don't know. Apparently, Since Νοέμβριος and  Δεκέμβριος are pronounced as NoéMvrios and DekéMvrios, some not-so-cautious Greeks started inserting a nasal consonant in Οκτώβριος as well, making it, effectively, Οκτώμβριος. And since people like to behave as the ones whom they consider superior to them, the latter pronunciation of our second autumn month has been accepted.

Well, October (or should I say Octomber to be cool too) ended up yesterday. We're already in November and I need to do get some work done....

(Besides, my problem, now, is pronouncing Swedish, which is tougher than Finnish, and, oh boy, how much I have to learn (but can't face it yet).)


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