Book review - 重讀蓋莫夫的“從一到無窮大”

重讀蓋莫夫的“從一到無窮大”

One Two Three . . . Infinity: Facts and Speculations of Science by George Gamow

http://www.amazon.com/One-Two-Three-Infinity-Speculations/dp/0486256642/ref=cm_cr_pr_product_top

我以前為這本書寫過的一個書評：

I bought a new copy of this book online and read through it again. I’m delighted to “re-discover” this book.

I have to admit I was inspired by this great book when I was a high-school boy and happened to read a copy of its Chinese translation in the era of “the March towards Science” at the time then that China just started to open her door to the outside world in the late 1970s.

I’d read this book many times and lost two copies of its Chinese translation. My father bought the first one for me when I was in high school. I left the copy home after I went to universty. It went missing and I forgot this book since. After I went to the graduate school, I came across the book and had the second copy myself. I read it again and kept it with me until I went to a remote mountainous area for my MSc project (It was a 50-hour journey with train and bus!). I left a lot of books in the graduate school and after I got back many books went missing. Unfortunately, this second copy was one of the casualties.

I was studying cryptography during that period. This book introduced and clarified many basic concepts to me, such as entropy, big numbers and randomness. I applied one example of the book, the drunkard’s walk, for Random Number Generator test in my first job in High-Tech Vanguard (我的第一個工作 – 不小心幹了一趟測試員). Another example, the birthday paradox, helped me to understand the Birthday attack against the Data Encryption Standard (DES). Topics on prime numbers, especially Prime Number Theorem, are very useful for understanding public key cryptosystems such as RSA. I was amazed by the Buffon’s needle to calculate the Pi. In addition, the four-color problem, the Fermat’s Last Theorem, non-Euclidean geometry, and treasure hunting in the island  are very entertaining.

One thing I admire the book so much is its writing style – its explanation on quantam mechanics and relativity is so clear that a high school student would have no trouble to understand.

During this re-reading, I’d like add one remark regarding the imaginary number described in Figure 10 for the treasure hunting. Although the answer to the treasure hunting in Figure 11 is correct but its presentation is inconsistent with Figure 10 where a point is counterclockwise turned 90 degrees after times i with regard to (0, 0). The explanation in Figure 11 appears discussing turning a vector which may make inexperienced readers hard to grasp.

I would like to offer my explanation in another way to make Figure 11 consistent with Figure 10.

Let G be the location of the gallows. The location of the spike with respect to the pine can be found by following steps:
1. Move the G left by 1 to the location of (G – 1).
2. Right rotate the point (G -1) 90 degrees to (G – 1) * (-i) = -G*i + i
3. Move the point (-G*i + i) right by 1 to -G* + i + 1.

Similarly, the location of the spike with respect to the oak can be found at G*i + i – 1.

The location of the treasure is at (1/2)*[( -G*i + i + 1) + (G*i + i - 1)] = i, the same answer as the book.

A very enjoyable book. I highly recommend it.