He who refuses to do arithmetic is doomed to talk nonsense


The above slogan came to my attention once again from the excellent Cosma Shalizi comments on Krugmans book ‘Pop Internationalism’. In the book review
The great Computer Scientist has a slogan which Shalizi extends from merely arithmetic to algebra.
This short essay will be looking at this issue. It is often said by politicians for instance that Mathematical literacy is important. I can’t disagree with this comment, yet Mathematics is a deep subject and I doubt everyone needs to know for instance ‘Sheaf Theory’.,
The question could be stated: ‘What is essential knowledge from Mathematics so that one doesn’t speak nonsense’.
I can only propose a provisional list, and clearly its worthwhile writing some articles on this.
Probability I feel is essential, since so many things in our world involve calculation probabilities. For instance it is more likely that Mary is an investment banker than Mary is an investment banker AND a Feminist.
Rather than reinvent the wheel, allow me to link to Steve Strogatz writing about probabilties and conditional probabilities:

The comments on the cognitive problems involved in calculating probabilities (our brains are bad at dealing with such things) is fascinating. I think its excellent reading on the limits of our cognition, and how Mathematics can be used to stop us talking nonsense, and to better understand the risks involved in our every day lives. From Cancer diagnosis, to catching those who have broken the law, to accessing the risks involved in building Nuclear Power Plants, if we fail to learn probability we are doomed to talk nonsense.
So Algebra, Arithmetic AND Probability, are all essential skills. Would anyone care to disagree?