Time to get to work on producing fifty book reviews for this year. Book Review No. 1 is Jordan Ellenberg's How Not to Be Wrong: The Power of Mathematical Thinking. Pick it up. Read it. Understand it. I'm not kidding. No equations, lots of illustrations, and plenty of intuition. You. Have. To. Develop. Your. Intuition.
The book appealed particularly to me as many of the mathematical pitfalls trap people who traffic in statistical inference or political economy. I used to make a good living at those endeavors, and still pay attention to a few of the controversies. Thus, the material on statistical significance, conditional probability, uncertainty, and voting had a lot I could either nod my head at or flag for future reference. My slime mold reference alludes to experimental research, in which slime molds revealed preferences that the irrelevance axiom of choice theory would rule out a priori, something that human beings often do (to provide material for mathematicians and psychologists to analyze at length.) Fun stuff; even when Professor Ellenberg goes along with the coastal Democrat prejudices in his examples. And yes, there's more on his nurture everybody, not the geniuses alone, in his book.
But "not to be wrong?" Sorry. "Wrongness is like original sin; we are born to it and it remains always with us, and constant vigilance is necessary if we mean to restrict its sphere of influence over our actions." Put another way, develop your jive detector. And be aware of the many situations in which there's an impossibility theorem at work, something that often happens where choice, particularly collective choice, is concerned.
You. Have. To. Develop. Your. Intuition.
(Cross-posted to 50 Book Challenge.)