# things pondered

Ideas related to science, math, technology, engineering, and society

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## Things to read about

### Review - “The Last Days of Socrates”

### Review - “Anthem”

### Excerpt from "The Man Who Loved Only Numbers" - The difference between physicists and mathematicians

"The Man Who Loved Only Numbers" by Paul Hoffman is a biography about the memorable personality that is Paul Erdős, the prolific mathematician, who published with over 500 collaborators. Erdős, who is well-known for his contributions to number theory, set theory, probability theory, graph theory, and more, as well as the invention of the Erdős Number, a measure of one's proximity to having collaborated with him, is of course a subject himself. That said, in Hoffman's biography of him, there is a bit about the behavior of mathematicians and a lone physicist that does well to embody the spiritual and cognitive differences between the two groups, both of which share a passion for mathematical thinking but nevertheless are separable beasts.

The excerpt of interest tells of a mathematics conference in which a group of mathematicians return to the coffee table after a talk only to find a puzzle.

### Review - "The Strangest Man: The Hidden Life of Paul Dirac, Mystic of the Atom"

### Review - “Sapiens: A Brief History of Humankind”

### Introducing didacticful: a live textbook about physics

I have recently launched a new venture: didacticful, a live blog-style textbook that is devoted to topics in physics. Currently, I am writing a textbook on particle physics, which you'll find on the blog. Along the way, you'll also find posts related to interesting topics in physics.

Continue reading to find topics on mechanics and special relativity

### Lorentz invariance of the relativistic dot product

It turns out that there is an analog to the dot product with regards to four-vectors. That is, there is a quantity that we can calculate that is unaffected by a certain kind of transformation. We call this quantity the "relativistic dot product" and this transformation the "Lorentz transformation." This form of invariance is often referred to as "Lorentz invariance."

**Continue reading on didacticful**