![]() Initially, the string of symbols on the tape corresponds to the input, containing the data for the problem to be solved. The strip of tape is analogous to today’s hard drives that store bits of data. Each box contains a symbol (such as A,C,T, G for the letters of genetic code) or a blank space. His hypothetical device is now known as a “Turing machine.” The centerpiece of the machine is a strip of tape, divided into individual boxes. It took the genius of Turing to show that a very simple machine could in fact compute all that is computable. It seemed overwhelmingly difficult to build such machines. ![]() Some prominent mathematicians proposed elaborate designs for universal computers that would operate by following very complicated mathematical rules. For example, 6 can be expressed as the product of 2 and 3, but 7 cannot be factored into smaller integers and is therefore a prime number. Another example of a computable problem, important to modern encryption, is whether or not bigger numbers can be expressed as the product of two smaller numbers. ![]() For example, we can compute a car’s most energy-efficient route to a destination, and (in principle) the most likely way in which a string of amino acids will fold into a three-dimensional protein. In Turing’s time, mathematicians debated whether it was possible to build a single, all-purpose machine that could solve all problems that are computable. ![]()
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