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  A Logical Calculus of the Ideas Immanent in Nervous Activity

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A Logical Calculus of the Ideas Immanent in Nervous Activity (1943)

Published by Warren McCulloch and Walter Pitts, a significant influence on the modern digital computer, as well as on the memex and artificial intelligence. McCulloch and Pitts examined the behavior of neurons. They reported the actual observations of neuronal function, and then showed how, by making certain simplifying assumptions, one could treat a neural network (i.e., the brain) as a logical machine. Independently of Claude Shannon, they applied Boolean algebra to the operations of a neural net and considered nets containing cycles and synaptic delays.

McCulloch and Pitts described how the most complex and magical processes—ideas—arise from the accumulation, the calculus, of the simplest possible particles of logic. They believed that the essential nature of neurons was that they could be either quiescent or excited. Intelligence and consciousness were just the complex interaction of simple logical switches.

To understand McCulloch and Pitts's vision, imagine a checkerboard of alternating light and dark squares. Now imagine the squares are connected by logical rules so that flipping one square, say, from dark to light, changes the colors of other squares, and so on. Even with only the sixty-four squares of the checkerboard, the patterns that can arise are unimaginably varied. Now imagine a cloud of a billion checkerboards, all interconnected. The unfathomable structure of the cloud is illuminated by lightning flashes of the tiny light squares flickering and streaking among the dark squares. If we delve into the cloud and regard a single checkerboard, we can follow the rules that flip dark to light, zero to one, false to true, quiescent to excited. But the behavior of the entire cloud is beyond comprehension. That is the logical calculus of the ideas immanent in nervous activity.

Any machine that, like the checkerboard cloud, calculates using discrete processes can be emulated by a Turing machine. If the human brain is a discrete calculating machine, then the brain is a computer. Since all computers are essentially equivalent, it should be possible to construct a computer to emulate the brain. McCulloch and Pitts were guided by this reasoning even before anyone had successfully built a digital computer.

A Logical Calculus, inspired by Turing and Wiener, went on to inspire all the cyberneticists in the 1940s and 1950s.

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