If people do not believe that mathematics is simple, it is only because they do not realize how complicated life is.
We do not know where in the physically viewed nervous system a memory resides; we do not know whether it is a separate organ or a collection of specific parts of other already known organs, etc.
Apart from all other considerations, the main limitation of analog machines relates to precision. Indeed, the precision of electrical analog machines rarely exceeds 1:10^3, and even mechanical ones achieve at best 1:10^4 to 10^5... On the other hand, to go from 1:10^12 to 1:10^13 in a digital machine means merely adding one place to twelve; this means usually no more than a relative increase in equipment (not everywhere!) of 1/12 = 8.3 percent, and an equal loss in speed (not everywhere!) — none of which is serious.
Thus all sorts of sophisticated order-systems become possible, which keep successively modifying themselves and hence also the computational processes that are likewise under their control.
Any computing machine that is to solve a complex mathematical problem must be 'programmed' for this task. This means that the complex operation of solving that problem must be replaced by a combination of the basic operations of the machine.
In an analog machine each number is represented by a suitable physical quantity, whose values, measured in some pre-assigned unit, is equal to the number in question.
