I read The Joy of X by Steven Strogatz on Jan 7th, 2024

I rate a two-star for this book, not due to the absence of scientific merit, but rather I encountered it in the wrong time. Had I encountered this book in my childhood, this book might inspire and motive me to explore the uncharted realms. The act of reading is akin to a relationship, you need to meet the right book in the right time.

Here are some hidden gems.

The Snell’s law

The Snell’s law follows Fermat’s principle of least of time: the light always takes the minimum time to travel from A to B. When the light travels between medias, the refraction happens. I learned this in my college physics studies, but wonder why lights or waves exhibit a preference to travel in a straight line in the vacuum to comply to the Fermat’s principle?

Here is a Quora answer: the interferences cancel out the circular waves.

Wasted seats

In a cinema open only to couples, if all the couples insist to sit together, and the seats are randomly assigned, there will be 1e2\frac{1}{e^2} seats wasted.

I just run the seated-couples.py to evaluate the 2-seat row to 1000-seat row with 1000 experiments, and get the following chart.

The chart shows the correlation of number of seats vs. vacancy rate
The chart shows the correlation of number of seats vs. vacancy rate

The average vacancy rate for the number of seats varies from 800 to 1000 is 0.1355669756, very close to 0.1353352832366127.

Beyond the complex numbers

The complex number facilitates the vector computations within 2D space, which leads to Quaternion introduced by William Hamilton. The eureka moment is celebrated annually through the Hamilton Walk.

Romeo and Juliet

If affection between Romeo and Juliet are defined as:

dRdt=αJdJdt=−βR\begin{align} \frac{dR}{dt} &= \alpha J \\ \frac{dJ}{dt} &= -\beta R \end{align}

the tug-of-war relationship would oscillate as:

The tug-of-war relationship
The tug-of-war relationship