Imagine, for a moment, that you are a member of a minor land-owning family in France in 1790. Your name is Gaspard Clair François Marie Riche de Prony. The Revolution began last year and it’s picking up steam. The Terror is a ways off, but it is still not the best time in the world to be connected, however remotely, with the old aristocracy. You are a mathematician and philosopher (we’d call you a “scientist”), and supposedly above all the turmoil of politics, but still…
To date, your career has been a howling success: You have just founded the Bureau de Cadastre (Land Registry), and gotten an assignment to remap France for tax purposes. And you have high hopes of taking over the École Nationale des Ponts et Chaussées (National School of Bridges and Roads).
But you must have stepped on someone’s toes. You suddenly learn that you are being reassigned, shipped off to the boondocks (actually the Oriental Pyrenees). Now, it might be safer out there, but your whole future lies in Paris. Besides, what decent Frenchman wants to leave Paris?
What are you going to do?
Well, you’ve heard that the Bureau des Longitudes is constantly plagued with the fact that the current mathematical tables are all too imprecise (only 7 places of accuracy) and full of errors. This is bad, not to say dangerous, for surveying and navigation, and catastrophic for astronomy. What France needs, you propose, is a completely new set of mathematical tables, made as accurately as possible. The work can obviously only be done in Paris and must be managed by a mathematician such as…yourself.
But how are you going to do it?
Traditionally, tables are generated by a team of low level mathematicians (called computers) tediously grinding out calculations by hand, under the supervision of highly skilled mathematicians who check them for errors.
All well and good, but how could you possibly find enough computers with the necessary mathematical knowledge, particularly in the chaotic conditions prevailing in France?
Then you read Adam Smith’s A Treatise on the Wealth of Nations and the solution becomes brilliantly clear: Hairdressers!
What? This is not intuitively obvious?
Let me explain.
In Wealth of Nations, Smith has a long discussion about how pins, traditionally made by specialists, can be mass produced by machines. The key, Smith said, was to break the production process down into small, simple steps that any machine could do.
This led you (de Prony) to revamp the whole process of making tables.
Suppose, you say, we had some highly skilled mathematicians to run the program, just as before. They could specify the equations that would be used. Below them we would have a smallish group of lesser mathematicians, who would break the equations down using mathematical series until the only steps left in the calculations would be simple additions and subtractions. Once that was done, any reasonably intelligent people could be trained to perform the additions and subtractions.
Enter the hairdressers.
Turns out that the Revolution, which had bettered some lives and damaged others, had been just awful for the hairdressers.
Not only had their favorite customers, the aristocracy, been driven off the streets (a grimmer fate awaited them), but their hairdos had become hated symbols of oppression. In short, nobody, but nobody, wanted any fancy do’s. All of a sudden, Paris’ hairdressers were going hungry.
So you put out the word that you’re willing to hire them and all they will have to do is simple addition and subtraction.
And it worked.
For the next five years about 80 of Paris’ hairdressers were retrained as “computers.” When the project was done, de Prony had the greatest set of mathematical tables ever generated before the dawn of the electronic computer. Nineteen volumes, with a standard precision of 14 places (for special cases, going up to 29). The logarithms went from 1 to 200,000.
It was a stupendous case of overkill, so large and complicated that they could never be commercially printed in their original form. They could only be directly consulted by scientists willing to go to the Paris Observatoire. The two original copies still exist, wonderfully precise, page after beautiful folio page.
So one could consider the whole project a waste. Except for a few facts. First, they were used, if only by specialists. Second, the project did indeed keep de Prony from being exiled to the Oriental Pyrenees. Third, it kept a bunch of hairdressers from starving (and turned some of them into permanent computers). But most importantly, de Prony pioneered a new way of thinking that would later be standard on electronic computers: break every job into smaller tasks that could be performed by extremely stupid machines that excel at simple, repetitive tasks.
And we shouldn’t forget those hairdressers. However unwittingly, they are the ancestors of all the inhabitants of Silicon Valley and all the other high-tech enclaves. They have reason to be proud.
Of course, I suspect the truth is that if those effete Parisian artisans could look on their long-haired, T-shirted, hygienically challenged descendants, they’d be something else.
They’d simply be appalled.