Thursday, 12 June 2008

Studying infinity

I was shattered last night and watched The Apprentice (see below) and a programme about infinity, called Dangerous Knowledge. Fascinating it was too.

Apparently, infinity comes in different sizes. If you imagine a circle, it is possible to draw an infinite number of lines from the centre to its edge. However, if you then draw another, bigger circle round that circle and extend the lines then you will have gaps beteen the (extended) lines.

But more interesting was listening to how great minds like Cantor, Turing and Godel found that there are limits to maths and science. That the ultimate conclusion of logic, was illogical. Turing died trying to prove unprovability.

This surely cuts to the heart of many academic issues, not least the realisation that maths and science are both an art is surely one. But second, it shows how all the academic disciplines from philosophy to maths are grounded in humanity. They are all flawed, all illogical. And our attempt to understand the world and impose order on it is ultimately doomed.

This gave me hope for psychology, as by studying the human directly in 'real life' circumstances, one imposes order through science and yet acknowledges the limits of doing this. This is the scientist practitioner approach, which is at the heart of Bloom Psychology.

1 comment:

Reed Burkhart said...

The arguments of Georg Cantor are in error. Correction is available in a new paper introduced below and also at http://limitstomaths.com/.

The father of Taoism, Lao Tzu (aka Lao Tse or Laozi and many other translations) introduces Taoism with the following opening introduction in his book “Tao Teh Ching” (“The Classic Book of the Way and its Power”):

“The way that can be spoken is not the real Way. The name that can be named is not the real Name.”

A new paper, “Limits to Maths”, explains precisely why this is true from the scientific viewpoint. I look forward to reading more on your BLOG about your career shift -- something I am working through myself at the moment -- and welcome any interest you have in the clarifications offered about the foundations of math and human language, generally.