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Pick a number at random number, any number. When we think of mathematics and mathematicians, we tend to think of proofs, solving a problem, and getting the right answer. Our intuition would tell us that randomness wouldn’t come into play into any of these things. Actually, randomness does play a role in the instructions for much of problem solving, whether in mathematics or other fields such as game theory and software engineering.
Let’s use the simple example of long division. Let’s say the problem is to divide one big number by a smaller number. Let’s specify and say that this particular long division begins with how many times does 39 go into 6. How do you start? Well, the instruction is to pick a random number, any number between zero and nine. Let’s say we start out with the number four. Well it turns out, it’s too small, and since it’s too small, we have to pick a bigger number. So we try the number eight, and as it turns out, the number eight is too big. What’s happened is that we’ve narrowed our range quite a bit. And by continuing this process of picking a random number, keeping track and narrowing down the choices, we can perform a long division that gives us the one correct answer to as many significant digits as required.
Simple procedures such as alphabetizing a list of names could not be accomplished if we did not start somewhere. Sometimes, we are forced to make random choices. And as we proceed, we store a temporary result that is subject to refinement. The temporary result is modified as we incorporate the next randomly selected name in the list.
It is simple instructions and procedures such as these that form the foundation of much of the functionality of computer software. These simple instructions and procedures also are the basis of macro-economic models that make sense of billions of transactions and also form the basis of the mathematical models that forecast the path of hurricanes.
