Books written for a different audience are hard to read. I don’t belong to the wide audience of Hamming’s “The Art of Doing Science and Engineering.” I admit parts of the book cost me way too much time. So you can imagine the comfort I felt when I read that I could skip the maths:
Later sections will be understandable […]. General results are always stated in words […]”
I kept on reading. The book is about “style”, after all. I am interested in his general results. It did, however, hurt a bit to read:
“Later sections will be understandable provided you are willing to forgo the deep insights mathematics gives into the weaknesses of our current beliefs.”
The first chapter of the book is titled “Orientation.” and it gives a good taste of Hamming’s style: a delightful mix of a mathematically clear mind, self-help (for researchers) a la The Art of Manliness, and eloquently delivered life advice.
A quick online search led me to the conclusion that many are attracted to one of the latter. In most instances, academically oriented people seemed to have cherished the self-help. Interestingly, I also came across Andrew Gelman expressing unfulfilled career desires, and one person who asked a question about one of Hamming’s examples.
I’ll consider the following self-evident: cherishing motivational quotes from a book on “style” won’t have great returns. Gelman’s discovery seems useful to him, and prospective students of him. I’ll focus on the question on StackExchange. (A message to the writer of the question: I hope this helps you enjoy it more the next time. My purpose is not to discourage you from picking up the book again, or cause any other emotional distress.)
One of the examples from this chapter is an illustration of how to quickly evaluate two well-specified hypotheses. This is an important example, because, again, “Style of thinking is the center of the course.” and it is the style that allows the evaluation. It is the style that is on display.
The style is elaborate enough for 227 pages from Hamming, I won’t even try to summarise it. Here’s an example, though:
“I will take […] two statements, knowledge doubles every 17 years, and 90% of the scientists who ever lived are now alive, and ask to what extent they are compatible. The model of the growth of knowledge and the growth of scientists assumed are both exponential, with the growth of knowledge being proportional to the number of scientists alive. We begin by assuming the number scientists at any time t is \(y(t) = ae^{bt}\)
You may feel like you’re missing something obvious, I know this person did: “What’s a? What’s T? I assume e is this guy.” Then you need to listen to Hamming a bit more closely: This is a back of an envelope example. If you read his passages prior to the mathematical formulation of the example, and rely on your common sense while playing with the example, these questions may be easier to answer. I recommend you make sure you can parse the paragraph into the formula with the help of a pen and a paper. (And yes, the e is that guy, as it will very, very frequently be. Consider making it a habit to try to full in that guy each time you see e in math before asking it. You may end up thinking faster.)
It may seem like too much effort, and remember “[…] the technical content is […] only illustrative material.” Consider the potential pay-off, though. You may be able to evaluate two statements dense with information with high confidence. You could even be able to express it in half a page, in a language that’s legible to thousands of people, like Manning does.
Welcome to the journey!