Nobel Prize-winning physicist Frank Wilczek explores the secrets of the cosmos. Read previous columnsMany summers ago, I discovered a book called “A Million Random Digits with 100,000 Normal Deviates” at a used bookstore I visit. That title being irresistible, I looked inside. It did not disappoint. The main table takes up 400 pages, each with 50 lines of 50 digits. Page after page, in neat columns, it makes parades of digits chosen from 0 to 9, guaranteed to be free of rhyme or reason.
The book, I learned, was published by the Rand Corporation in 1955. Rand generated the numbers physically, by spinning a series of wobbly electronic “roulette wheels” over and over and recording the results. Their classic book was widely used by engineers and scientists for years in the days before modern computers.
What does it mean for a series to look random? The simplest property is that each digit appears equally often—the digital die is not loaded. Each run of two digits also appears equally often. This means that each digit conveys no information about the next one. If no method works to use earlier digits to predict the values of later ones, our series has proven completely unpredictable—and it is fair to say that it looks random.
Sequences of such randomly generated numbers are useful for many purposes, such as what statisticians call unbiased sampling. To estimate average properties of a big data set, you sample a small subset. This is legitimate, provided that you choose the sample without any bias. A table of random numbers can help you do that.
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The mathematics is a amazing instrument for us, to think about the very nature of reallity
thanks
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