Can you imagine a world without computers? You have Charles Babbage to thank in part for the computer that you are viewing this website on. He came up with the concept of the first computer, although it would not look anything like the computers that we are familiar with today.
Before calculators and computers, mathematicians would use complicated logarithmic tables to help them do long and complicated sums. Having used these tables, Charles Babbage decided to develop a machine to calculate them, using mechanical devices. He called it the Difference Engine. The name comes from the method that the engine used - a method that Newton had devised which he called the method of successive differences.
Babbage constructed a small prototype, and demonstrated its effectiveness by calculating answers for the sequence given by the formula: n^2+n+41
Such was the success of his engine that the British Government gave him substantial funding to construct a large Difference Engine. Unfortunately, the project took so long that it eventually ran out of funds, and was put on hold - permanently.
However, Babbage was not daunted by the lack of progress, and started to develop another, more ambitious machine in 1833.
This was the Analytical Engine, and is the grandfather of modern computers. Although it was never built, conceptually it is extremely similar to modern day computers. It consisted of five logical components: the store; the mill (our modern day CPU); the control (these were Jacquard punch cards which contained the ‘programme’ for a particular task); the input device and the output device.
The conceptual construction of modern computers has changed very little since Babbage’s original design.
But whereas his computers were based on mechanical parts - wheels with gears , levers and other moving mechanical parts - modern computers are based on electronic components in which electrons move.
Computers have not only changed the face of modern mathematics, but have actually changed the way we live our lives. All thanks to Charles Babbage and his engines.
Imagine you are given a sequence of numbers and asked to find the next term. You are given the sequence, 1, 3, 9, 19 , … You find the differences between the terms of the sequence, and then the differences between the difference, and so on…
We ‘guess’ that the next term of the difference of the differences is also 4; so the next term in the differences above it is 10 + 4 = 14; so the next term in the sequence itself is 19 + 14 = 33.
(The sequence is, in fact, given by the formula, 2n^2+1.)
You can see a Difference Engine, and parts of the Analytical Engine at the Science Museum in London. www.sciencemuseum.org.