Alan Turing’s genius as a mathematician was recognized in his day for his ability to solve the most sophisticated encryption algorithms of the Second World War. The team at Bletchley Park known as “the Codebreakers” created fake messages so perfectly that the Axis forces did not realize that the Allies were intercepting and faking crucial messages within the Nazi military communications system. Many historians consider Turing’s contribution as the single most important accomplishment toward the success of the Allied Forces.
None could foresee that Turing’s invention would change the face of technology forever. The immediate problem of code decryption was reduced to a machine that read the individual letters in a linear string and inferred the code that was superimposed over the real message. Turing’s starting point as a mathematician was to propose that any code generating machine could be modeled by reducing it to a series of algorithms that are solved using zeros and ones. The Turing method further assumes that a generalized or universal problem solving machine can ultimately be constructed using his methods and that any problem can be solved in a finite period of time.
By itself this was a novel concept in mathematics, but the implications were quickly grasped by Turing and others and the race for what would later turn out to be modern computing began. The earliest working computer, built as a proof of concept, had a 32 bit by 32 bit memory (1K bits) and processed calculations at just over 1,100 instructions per second. The first program was a 17 line algorithm to solve for the largest divisor of 2 to the 18th power. Solving the problem using an algorithmic approach required 3.5 million operations which is why humans don’t do math using algorithms. The fact that an electrical “machine” could execute 3.5 million instructions in 51 minutes is why humans use machines that can “think”. (I use the term advisedly)
Time in relation to the process of solving problems was simply not a concern. The problems were abstract in nature and required programming to be input, run time on the machine and an output was provided some time later. The result was an answer to a problem, not a means of controlling machinery in the real world. Speed was only a concern to the extent that mankind found more and more problems for which coding the zeros and ones was an acceptable tradeoff for creating answers that were previously difficult or altogether impractical for a human to undertake. Like calculating the distance and trajectory for canon fire for all size of munitions at all possible ranges.
Now multiply the performance of the computer in 1948 time 1 billion.