I had a discussion lately with someone who told me that her father used to punish her for making math mistakes in the childhood… This is probably the silliest thing one could do. I can write a long post about parenting but this is not the point. The point is I am looking at my posts here and I see they are full of typos, I also had some typos in the papers I submitted but I am sure I’ll have the occasion to correct them. The thing I want to insist upon is the relevance of mistakes. Take a simple paper, with little or no new ideas in it. Mistakes there are as common as in any other paper but their effect will be disastrous. The same is valid for theoretical physicists trying to figure out things about nature by performing long and complicated mathematical calculations (note, I am not talking about math, but about mathematical calculations). While they have no other idea except the set of calculations they wish to perform, any mistake in these calculations can ruin the whole result. Empty papers with no ideas are extremely sensitive to mistakes too… imagine you publish a new numerical result that has some typos in it… The use will be greatly diminished and the results false. But now, try having a new idea, independent of calculations, one that is based on theorems and gives results in terms of new ideas. The mathematical calculations become simple verifications. Mistakes in them cannot affect the true value of the idea. Even using different branches of mathematics cannot affect the correctness. It is more or less like topological computations: small errors cannot affect the global structure. The way of thinking you introduce is new and correct and this or that typo can not harm it in any way! Take for example dirac and his use of anticommutators in order to quantize fermions and his solution to the negative energy problem. It was a brilliant idea and no matter how many mistakes one could make while doing the calculation one simply cannot avoid the main idea, that fermionic fields need anticommutation relations to be quantized. There are lots of other examples where ideas are unaffected by possible mistakes. But what about the oppozite? Take a student’s homework… this is certainly a piece of idea-less work… so completely devoided of any kind of intuition, inspiration or thinking by that matter that a simple mishandling of a calculator would ruin it completely. Axiom: the more a piece of work is affected by mistakes the less relevant it is.

# mistakes and topology…

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