The Prehistory of Computing, Part II
In part I of this two-part series we covered lookup tables and simple devices with at most a handful of moving parts. This time we’ll pick up in the 17th centuries, when computing devices started to became far more complex and the groundwork for later theoretical work began to be laid.
Pascal
We enter the era of mechanical calculators in 1642 when Pascal invented a machine, charmingly called the pascaline, which could perform addition and subtraction:
The primary problem that must be solved to build a working adding machine, mechanical or electrical, is the carry. Yes, I’m talking about that operation you learned in elementary school, where you “carry the 1” when the digits in a column add up to more than 10. This problem is far less trivial than it sounds; even today, chip designers must decide to implement either a simple ripple-carry adder or one of many competing designs for a carry-lookahead adder depending on their transistor budget and logic depth. Carry, it turns out, is the very soul of the adding machine.
That’s why the pascaline represents such a crucial breakthrough: it featured the world’s first successful mechanical carry mechanism.
Still, the machine wasn’t very useful - adding and subtracting aren’t particularly hard, and the time spent fiddling with the dials to input the numbers easily dwarfed the time saved. The real prize would be a machine that could multiply and divide, and that was the problem that Gottfried Wilhelm von Leibniz set out to solve.
Leibniz
Leibniz, if you’ve only heard of him as a philosopher, may seem like an unlikely person to tackle this problem. In philosophy he’s chiefly remembered for his incomprehensible theory of monads and for stating that this was the best of all possible worlds, a point of view that was caricatured by Voltaire as the thoroughly unworldly and deeply impractical Dr. Pangloss in his novel Candide.
But of course he also helped invent Calculus, proved that kinetic energy was a conserved quantity distinct from momentum, designed hydraulic fountains and pumps, and generally produced an enormous body of work that was original, practical, and rigorous. If luminaries such as Voltaire viewed him as ridiculous, it was perhaps because he was too logical; or rather that he kept trying to apply rigorous logic to theology and the humanities, which is rarely a recipe for success.
... continue reading