An analog computer is one which can perform multiple calculations at once and can cope with infinite fractions of numbers. The term analog does not relate to how the computer is powered and it is possible to have electronic analog computers. The characteristics of an analog computer mean it can be better than a digital computer at particular tasks.
A computer is simply a machine which processes data in a set fashion or, to put it another way, calculates. Today most computers are digital and work by reducing all data to binary numbers before processing. Analog computers go back thousands of years but vary from digital computers in only two fundamental ways.
The first is that an analog computer works in parallel. This means it can carry out multiple tasks simultaneously. A digital computer, even though it may work considerably faster, can only perform one calculation at any one instant. The only way around this in a digital computer is parallel computing, where a single machine has multiple processors. Even then, programs must often be rewritten to take advantage of this.
The second difference is that an analog computer handles continuous variables, while a digital computer works with discrete numbers. The difference between these is that continuous variables can include every conceivable number, even irrational numbers. These are ones with infinite decimal fractions such as pi
Discrete numbers are those which are either whole numbers; those where the decimal fractions are either limited such as one-eighth being 0.125; or those which have sequences which repeat, such as one-sixth being 0.1666 recurring. The infinite nature of irrational numbers means they cannot be reduced to the binary figure needed for a digital computer. This means only analog computers can act as so-called “real computers” and solve some of the most complicated problems in mathematics.
An analog computer can work both mechanically and electronically. Mechanical analog computers have existed for thousands of years, with the oldest known example being the Antikythera. This is a Greek machine, thought to have been made around 100 BC, designed for calculating astronomical positions. A more recent and common mechanical analog computer is the slide rule.
The electronic analog computer works on the same principles, but uses electrical components to replace the physical parts. The big advantage is that the properties of these components can often being varied, whereas the physical parts would have to be replaced to change their properties. The downside is that the electronics are subject to noise, a type of interference caused by external physical factors.