29 January 2011

Ok, more of the Rah-Rah, Winning the Future (I know…WTF) but hey it is ok.

Stupidity: Recursivity points us to this article:

Mathematics tends to be both misunderstood and credited with magic powers, especially by those who are intelligent but not mathematically inclined. Arising from this, there is a perennial temptation for mathematicians to play to the gallery and to assume the role of magicians and, even more temptingly, high priests.

The late Bernard Scott, founding professor of mathematics at the University of Sussex, wrote a paper in the 1960s deploring the tendency in some schools to treat mathematics as juju. This, if left unchecked, leads to people acquiring a blind faith in mathematics and mathematical formulae, a faith that bears little relation to their true logical powers.

We know that a major cause of the financial crash of 2008 was the blind faith invested in certain mathematical risk models by managers in the financial institutions. They thought they had covered the risks, but the mathematics and financial reality were, it turned out, miles apart. The problem was exacerbated by the fact that few senior managers in the banks understood the mathematics.

Scott warned against the dangers of letting mathematical educators adopt attitudes that tacitly encouraged their pupils to interpret mathematics the “blind faith” way. It is a warning we need to heed now more than ever.

Groan. The problem is that the models didn’t apply and NOT that the mathematics was bad. Example: ordinary differential equations with constant coefficients do a good job at modeling some classical mechanics problems (harmonic motion) but don’t deal with, say, quantum behavior.

But there is even more crackpot stuff here:

We have seen blind faith in mathematics in action recently. In addition to the contribution of mathematical models to the great credit crunch of 2008, take physicist Stephen Hawking’s claim that philosophy is dead. The reason he gave was that philosophers have stopped bothering trying to understand modern mathematical cosmology. This cosmology is based on current mathematical physics, most of which has been in place for less than 100 years. It is an impressive edifice of concepts and mathematical models, but one that has not yet built up a track record for reliability over a thousand years, let alone a million years.

Well, duh: really understanding cosmology requires a background in things like differential geometry and few have the combination of the ability and the time to learn it on that level.

Let’s skip to mathematics

So how has it happened that for a hundred years, the mathematical establishment has swallowed the idea of transfinite sets? Georg Cantor produced an argument that seemed to point to transfinite immensities, but that was before we realised that mathematics was incompletable. In effect Cantor’s argument showed that the set of real numbers was incompletable. It did not (could not) show that there were more mathematical objects than an ordinary infinity.

No: he showed that there were more than a countable number of real numbers. This clown is confusing the incompleteness theorem with uncountable cardinals. The incompleteness theorem shows that any system will have logically true statements that will remain unprovable within that system; the uncountability of the real numbers is a different matter entirely.

Why the mainstream press publishes the writings of cranks is beyond me.

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