This is an interesting, if brief look back at historical computing mechanisms. It is interesting for two reasons. First, that it focuses exclusively on tools for logical reasoning, and not on numerical tools like a slide rule or abacus. Second, it was written at the dawn of the electronic computing era, before even one-at-a-time transistors were used, and long before the earliest integrated circuit.
It briefly describes Lull's rotating disks, a little like the child's toy that can put a lion's head on a turtle's body. Lull used dozens of variants (up to 14 disks, in one case) to explore combinations of theological and moral ideas, but not for reaching conclusions from basic premises. Gardner goes on to describe set-inclusion diagrams pioneered by Euler and popularized by Venn, Pierce's arcane "existential diagrams", and a few other pencil and paper notations. He describes a few clever tools based on different cards with windows cut into them, so that the alignment of windows in overlapping cards represents joining of logical statements. He also mentions mechanical, electrical, and relay-based gadgets, as well as one based on rotating, counter-rotating, and jammed gears.
For some reason, he chose not to mention a once-popular tool based on stacks of cards, with holes punched or notches cut in the edges. Stack the cards, slide a pin through the aligned holes representing (for example) male subjects, and shake loose all the cards with notches that don't snag the pin. Repeat the process on the male or female stack of cards, using other holes representing different traits, and the desired subset of subjects (if any) remain. Although used for filing, this tool could easily have handled dozens of logical variables, not just the four or five seen in other mechanisms.
The second facet of this book gives it a quaint feeling. Gardner ends the book with a set of predictions about the future of logic machines. He dismisses programmable computers as unwieldy and inefficient. Still, he hopes for inference engines to be sped up electronically, perhaps using analog computation. Other predictions sound equally odd - some because they did not come to pass, others (like H. G. Wells' World Brain) because they did in some way.
This book is an interesting bit of modern history, and a worthwhile collection of visual tools for representing logical concepts. If nothing else, it gives insight into how complex problems of four logical variables were once thought to be - much simpler than the computer circuits and even logic puzzles of today.
//wiredweird
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