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Categories
Category Archives: Mathematics
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
Real magecraft
In a fantasy setting with magic, one finds the enjoyable trope of characters taking what we would consider aweinspiring to be routine and boring. An example in mind would be from the Harry Potter universe, where students at a school … Continue reading
Posted in Mathematics, Technology