Analog is the nu-digital
Whether is a slide rule or the Nordsieck's Differential Analyser (image above); analogue computers differ from digital ones inthe same way as analogue sound synthesis differs from the digital. Digitalised data and so processes are descrete, data is sampled and processed and outputted in an all be it fast stream of individual items. There is always a delay inbetween one sample and the next, however fast the processor is running. These factors either, and I have never been sure which, lenditself to or are a natural outcome of the concept of a CPU; a central processing unit that sequentially performs a single operation on an indivual snapshot of data at a time. Either way the requirement that the CPU or even a series of CPU be able to perform an ever increasing number of operations is a natural progression.
Analgue computers fascinate me in the same way as organic systems (or simulations of organic systems or weak AI) do. The processing intelligence is spread through the system and each element works concurrently to everything else, there is no sample rate it all just seems to, well, happen.
The next thing that I love about analogue computing is that you don't need a computer. Nordsieck's Differential Analyser was based on World War II surplus to simulate/run in realtime, complex systems of "engineering, rocketry, physics, economics, and other disciplines that needed to model complex real world conditions" (http://www.computerhistory.org); and that is what analog computing does best : model real world systems.
The final thing that I love about analog computers is that you don't need electricity, weights, water, compressed air, or even (much to our Owl Project delight) wood, wheels and wire.