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.

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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