I’ve been reading this book on and off for the last week or so, a biography by Andrew Hodges of Alan Turing, who was the one responsible for the ideas of how a computer should be designed. He wrote the thesis On Computable Numbers which explained the Turing Machine, the basis for the design of computers. The book is not highly technical, but there is quite a bit of mathematics, logic, and philosophy in it. The term Entscheidungsproblem is often used, a term with which I’m unfamiliar.
Later in the book Turing’s thesis Intelligent Machinery is discussed. On page 384 the author stated
He showed that in a job taking more than 101017 steps, a physical storage medium would be virtually certain to jump into the ‘wrong’ discrete state, because of the ever-present effects of random thermal noise.
I started to think about how incredibly large that number is (but that was not the largest number he used!). Written on paper, that’s one with ten to the 17th zeroes after it! For example, let’s use 10101 steps as an example. That’s 1010 steps, or one with ten zeroes after it, a very large number.
I got my scientific calculator out and started poking away at the keys. I entered the 10 to the 17th into the calculator. Then I reckoned that text would have about ten zeroes per inch in some fonts. I divided it by ten and the number came down to 10 to the 16th power inches of zeroes. Then I divided it by 12 inches per foot, and then by 5280 feet per mile. The number was still huge. I then thought, if I have a wheel with ten zeroes per inch around the circumference, and it was mounted on a handle, I could print zeroes on a very, very long paper strip. I decided that I would print the zeroes at the speed of light, 186,000 miles a second(!). I divided the number by 186,000, then by the number of seconds in a minute, and then by the number of minutes in an hour. The number was now down to about 235, or in other words nearly ten days of printing zeroes at the speed of light, to get to the end of the paper. Whoa!!
Thinking about it, any physically conceivable thing with that many discrete steps would have to have exceedingly minute steps, so these discrete steps would have to be easily disturbed by their environment. For example, the number of particles in the universe is generally considered to be less than 10 to the power 100 (a googol), so this huge number of discrete steps far, far exceeds the number of particles in the universe. If we used every particle in the whole universe to emulate this system of discrete steps, we would fall far short of the number needed, and I assume that it’s impossible to subdivide these particles any further.
In the last chapter of the book titled The Greenwood Tree the author gets into Turing’s essays on “How to build a brain”. At the time when there were only one or a few working computers in the whole world, journalists were wildly speculating that a computer could think like a human. Of course this was just their imagination gone wild, for today, sixty some years after the first computer, we still haven’t made a machine that comes close to human intelligence.
See my next blog for more mental flights of fancy.
