Why Jaynes's book "The Logic of Science" is wonderful
I am still diligently working through E.T. Jaynes’ book (Probability Theory: The Logic of Science) and the content keeps astonishing me. Just when I think that I got the most out of his book, this “thousand-year-old vampire” (Jaynes) presents me with yet another awe-inspiring chapter. There are also two meta things I learned from the book:
One doesn’t need complex, abstract maths for arriving at far-reaching results. Jaynes’ ability to investigate the hell out of a subject using only simple equations1, plain English (as opposed to set-theoretic) formulations with a wealth of references across various fields spanning work developed throughout several centuries is incredibly remarkable and such analysis is a breath of fresh air. Jaynes waded through original manuscripts of famous mathematicians, read their correspondence with peers and understood in depth their view-points. There’s an entire history-of-maths book hidden inside this gem, but not full of irrelevant trivia, full of the ways grand mathematicians tackled problems that are still important today.
We are teaching Statistics wrong. Mathematicians taking stats courses across universities proudly declare that they hate stats shortly after dabbling in it. I don’t blame them: right now we teach stats as a bunch of vaguely related techniques and often say “use your own judgement” when people ask which technique really is appropriate for the task at hand. Except mathematicians don’t want to use their judgement: that’s why they like maths after all. They want a bunch of rules to follow to arrive at the conclusion. Turns out such rules have existed for the last 30-60 years, but we kept them hidden from “the mainstream”. As for the field of Statistics, it really isn’t that different to maths as one can derive all the important results from just a few axioms.
which don’t always have simple solutions, but Jaynes tackles them with well-established techniques rather than clever tricks ↩