Ignorance as Science

The new book Ignorance: How it Drives Science by Stuart Firestein gives an interesting report from the inner secret life of scientists well hidden to the public:

• Scientists don’t concentrate on what they know, which is considerable but minuscule, but rather on what they don’t know…. Science traffics in ignorance, cultivates it, and is driven by it. Mucking about in the unknown is an adventure; doing it for a living is something most scientists consider a privilege.

This is contrary to the facade of science as a temple of knowledge solidly built stone by stone from the foundation to the top by using logical deduction, mathematics and careful experimental observation according to the model of physics as the King of Sciences assisted by mathematics as the Queen.

But is it true that physicists and mathematicians cultivate ignorance as an expression of their royal stature?  

Yes, I think so. A physicist/mathematician may say that in principle the World is governed by Newton's laws of motion and thus a physicist/mathematician in a certain sense "knows everything" by knowing the  equations expressing Newton's laws. On the other hand, Newton's laws of motion cannot be solved by analytical mathematics, not even for three interacting bodies, and if the equations cannot be solved the physicist/mathematician cannot make any prediction and in this sense "knows nothing". 

This is the clash between a facade of knowing everything and a truth of knowing nothing which the physicist/mathematician has to handle somehow every day. 

If you still believe that a physicist/mathematician knows if not everything for sure a lot, ask about the physics of the CO2 greenhouse effect which is supposed,  to determine the future of humanity, and if you get a sensible answer, send it to me. I have tried myself many times without success.

Another example is Calculus: The mission of a Calculus course/book is to convince the student that all problems can be solved by a proper use of Calculus, for example that all integrals can be computed analytically by a proper combination of tricks, by forcing the student to compute so many integrals that there hardly could be any left which could not also be computed. A Calculus teacher would thus be expected to give the impression to "know everything" while at the same time knowing that there are many more analytically uncomputable integrals than computable.

Similarly, as pointed out by Firestein, the standard academic course seeks to overwhelm the student with facts in order to convince the student that with so much known not much unknown can remain.

Elementary school mathematics fills the student with simple reguladetri problems to give the impression that all problems can be solved if not reguladetri by proper mathematics. Teachers are not used to be confronted with unsolvable problems and thus tend to stick to reguladetri problems all solvable.