# Reading: ZMM

Several months later, I picked up this book again. During those several months, I had very brief bursts of productivity, but mostly I wasted time doing nothing.

I noticed that I didn't remember what the story so far was. One forgets things really fast. I remembered that I enjoyed reading this 'travel book' which is a philosophy book in disguise. He was talking about quality. In Chapter 22, he wrote about Mathematics. He first mentioned the Bolyai-Lobachevskian geometry (=hyperbolic geometry). I felt something was off when he said that Riemann geometry violated Euclid's first postulate. (I think he meant elliptic geometry. Riemannian geometry encompasses hyperbolic, euclidean and elliptic geometry. How names shift as time passes and we extend and reformulate...) I remembered that it violated only the fifth. Thus I looked up the first postulate on Wolfram and saw where the discrepancy was. The author thought the first postulate stipulates that exactly one straight line can pass through two given points whereas the version we are more accustomed to does not specify the upper limit of number of straight lines passing through two points. I thought, hey, you should check these facts with a mathematician before publishing the book, which is a very intricate precise book I liked so much. I noticed that I started to dismiss the book as a huge let-down just for this. Thus I stopped myself in the track. I was being too strict when it came to things concerning my domain knowledge. That was a minor misunderstanding which didn't really bear on topic. Even if it had erred severely on history of mathematics, it would not mar the rest of the writing. The author probably didn't have an easily accessible reference system at the time of writing. Checking everything along the way may hinder his chain of thoughts. It is fine to let this lapse, but I do make a note in my blog that there is a minor mistake. The two types of non-euclidean geometry have a difference number of parallel lines that one can draw through a point to a give line, one in excess (hyperbolic) and one in dearth (elliptic). I am not good with history of mathematics and I only know the basics of Riemannian geometry. Probably at the time of writing, mathematicians didn't have a clear presentation of the materials yet. We now benefit from all the good writings of the past generations.