# ðŸ’¡ Algorithms and hairdressers

In the process of writing any book, many ideas and stories fall by the wayside. Not because they arenâ€™t insightful or emotive but because the thesis veers from its original course. A favoured tale may become a detour.

And so, I wanted to share with members of Exponential View** one of the cuts from my book ****Exponential ****(****The Exponential Age ****in the US and Canada)**. To celebrate the release of my book tomorrow, I decided to open this post to all readers of EV (if you decide to get a membership, welcome!). It is a tale about one of the first computing machines built, and helps us think about the nature of many of the AI systems of today.

This is a fantastic story that has currency in todayâ€™s contemporary debates, even if I couldnâ€™t squeeze it into the book.

### The coiffeurs of revolutionary France

The French Revolution was in full swing. Two years after the mob had stormed the Bastille, carrying out the head of governor Bernard RenÃ© Jourdan on a pike, the rulers of the nascent Republic needed to finance the state. And to pay for that public machinery, the government coffers needed filling. But tax reform had been a key pillar of the French Revolution. Out went the tax exemptions from the nobility and clergy and much of the punishing monetary load on commoners. The former revolutionaries, now governors, introduced less regressive taxes levied on the wealthy owners of land.

Of course, to raise such cadastral taxes would demand detailed knowledge of who owned what parcels of property across the Republic. Compiling an accurate database of estates for the Land Register was an arduous task that fell to the Republicâ€™s renowned chief engineer, Gaspard Clair FranÃ§ois Marie Riche de Prony. (Although, rumour has it that De Prony took on this Sisyphean mandate so that he could stay in Paris. Otherwise, he may have been forced to take up the role of Chief Engineer to Perpignan, in the outlying region of the Oriental Pyrenees.)

Figuring out the taxable area of each estate from geographic surveys would require a lot of geometry and, in particular, trigonometry. Fortunately, de Prony was an accomplished statistician, with a fondness for trigonometry.

In the days before electronic calculators, trigonometric calculations would be completed using mathematical tables of â€˜logarithmsâ€™. A logarithm is a mathematical function that describes the number of times you need to multiply a number to get a given number. How many twos multiply to get 16? The answer is four (two times two times two times two) so the logarithm to base two of 16, in this case, is four.

There is a particular set of logarithms called natural logarithms which were relevant for De Prony. In the case of natural logarithms, the question you are asking is how many times do you need to multiply the mathematical constant, *e *(which is approximately 2.718281828...) to get a particular number.

Logarithms do speed up trigonometric calculations but calculating those natural logarithms was difficult. The full set of logarithmic tables De Prony needed was too large and complex for a single person, however talented, to complete.

### Divide and conquer

De Prony was also a student of the Scottish economist, Adam Smith. Some years earlier, Smith had published *The Wealth of Nations*. The Scot had detailed his ideas of organizing work and breaking hard problems into simpler, more basic, steps: the division of labour.

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