Category Archives: Mathematics

Book Review: An Imaginary Tale

An Imaginary Tale: The Story of √-1 by Paul Nahin I’ve had this book for years, and have read the first few chapters several times but never actually finished it for some reason. I think I got bogged down in the … Continue reading

Posted in Mathematics, Reviews

Book Review: Approaching Infinity

Approaching Infinity by Michael Huemer “Infinity” is a concept that, if you’re not careful, can really bite you in the ass. In his latest book, Approaching Infinity, the philosopher Michael Huemer attempts to sharpen our idea of infinity to address … Continue reading

Posted in Logic, Mathematics, Reviews

Book Review: The Theory That Would Not Die

The Theory That Would Not Die: How Bayes’ Rule Cracked the Enigma Code, Hunted Down Russian Submarines, and Emerged Triumphant from Two Centuries of Controversy by Sharon Bertsch McGrayne If you have a passing familiarity with statistics, you’ve probably come across … Continue reading

Posted in Mathematics, Reviews, Science (general)

Huffman codes, language, and mythical creatures

Let’s say you’re a telegraph operator, and you can send bits of 0 or 1 down the line one at a time. Each bit has a cost associated with it; the longer the message the more you have to pay. To … Continue reading

Posted in Mathematics, Science (general)

The Legendre transformation in physics

In both classical mechanics and in statistical mechanics, at some point while you’re following the derivations, suddenly an expression like “and this is the Legendre transformation” will pop up. Now, in my experience that was it. I was so confused: … Continue reading

Posted in Mathematics, Physics

The reasoning robot, Jaynes’ desiderata, and Cox’s Theorem

I’ve been reading Probability Theory: The Logic of Science by ET Jaynes, and it’s worth sitting down with just for the first two chapters alone. Probabilities are typically introduced as obvious entities in and of themselves, where the chance of something … Continue reading

Posted in Logic, Mathematics, Rationality, Science (general)

Use the last significant digit to convey precision

Imagine you heard someone offhandedly say “The distance from London to Rome is about 1000 miles.” Now say you are more comfortable in SI units so you do a quick conversion in your head and think “So the distance from … Continue reading

Posted in Mathematics, Rationality