Meaning and details of: Samson

On 14/10/2018 - 13:11

A computer does two things, and two things only: it performs calculations and it remembers the results of those calculations. But it does those two things extremely well. The typical computer that sits on a desk or in a briefcase performs a billion or so calculations a second. It’s hard to image how truly fast that is. Think about holding a ball a meter above the floor, and letting it go. By the time it reaches the floor, your computer could have executed over a billion instructions. As for memory, a typical computer might have hundreds of gigabytes of storage. How big is that? If a byte (the number of bits, typically eight, required to represent one character) weighed one ounce (which it doesn’t), 100 gigabytes would weigh more than 3,000,000 tons. For comparison, that’s roughly the weight of all the coal produced in a year in the U.S. For most of human history, computation was limited by the speed of calculation of the human brain and the ability to record computational results with the human hand. This meant that only the smallest problems could be attacked computationally. Even with the speed of modern computers, there are still problems that are beyond modern computational models (e.g., understanding climate change), but more and more problems are proving amenable to computational solution. It is our hope that by the time you finish this book, you will feel comfortable bringing computational thinking to bear on solving many of the problems you encounter during your studies, work, and even everyday life. What do we mean by computational thinking? All knowledge can be thought of as either declarative or imperative. Declarative knowledge is composed of statements of fact. For example, “the square root of x is a number y such that y*y = x.” This is a statement of fact. Unfortunately it doesn’t tell us how to find a square root. Imperative knowledge is “how to” knowledge, or recipes for deducing information. Heron of Alexandria was the first to document a way to compute the square root of a number.2 His method can be summarized as: • Start with a guess, g. • If g*g is close enough to x, stop and say that g is the answer. • Otherwise create a new guess by averaging g and x/g, i.e., (g + x/g)/2. • Using this new guess, which we again call g, repeat the process until g*g is close enough to x