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Before I forget: there's a moment in life of a category when functions have to become functors, and vice versa. We can think about it as if an object is being "expelled" from its mother category and has to become its own category. Alternatively, a category can be "sucked" into another category and become an object. (the video below describes how hermits became monks in a monastery).

Probably this is not new, but it's useful to think about such transitions.

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The [Roman] empire is a constant presence in our evidence from this period, and it enters mathematical discourse in several ways. Managing an army, collecting taxes, keeping a census on such a vast scale implied centralized administrative practices (accounts, tax rolls, land surveys). Mathematics was also used to articulate views about politics, society and morals. It would be impossible to describe our period in a few words: let us just say that the world had become even larger than after Alexander’s expedition, exchanges of all types increased; and the textual past kept accumulating in the form of books and libraries.

S.Cuomo. Ancient Mathematics.

As the scale increases, what can't be mapped can't be governed or reflected upon.

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Although estimates vary, military history experts generally agree that the average GI who served in Europe from D day to the end of the war had sex with about twenty-five women. By the time Germany surrendered, the US occupying army had to ration condoms to four per soldier per month, something an army official complained was “entirely inadequate.”
When the American military occupied Italy, it was estimated that 75 percent of all soldiers had sex regularly with Italian women.

Screen Shot 2016-11-27 at 6.18.33 PM
-- Aine Collier, The Humble Little Condom: a History.
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The merchants of Amsterdam at the end of the ixteenth century-a hundred years after the great flow f silver had started-were the recipients of a notably diverse collection of coins, extensively debased as to gold or silver content in various innovative ways. A manual for money changers issued by the Dutch parliatnent in 1606 listed 341 silver and 505 gold coinS.
Within the Dutch Republic no fewer than fourteen rUnts were then busy turning out money;

For each merchant to weigh the coin.. he received was a bother; the scales were also deeply and justifiably suspect.dam Smith told. 170 years later. of the solution: "In order to remedy [the aforemenhoned] inconveniences, a bank was established in 1609 l1I1~er_ the guarantee of the City. This bank received oth foreign coin, and the light worn [and other de>ased] coin of the country at its real intrinsic value in the good standard money of the country, deducting lly so much as was necessary for defraying the eJl!" lease of coinage, and the other necessary expense 01 lanagement. For the value which remained, after thi! imall deduction was made, it gave a credit on its books."12 Thus appeared, to regulate and limit abuse of he currency, the first notable public bank.
p. 19-20
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Human nature lay be an infinitely variant thing. But it has constants. )ne is that, given a choice, people keep what is the ,est for themselves, i.e., for those whom they love be most.

With numerous coins in circulation variously aduIera ted, clipped, filed, sweated, trimmed, and with he worst being offered first, coins became a probm. The path was now open for the next great rcorm, which was to go back to weighing. This decilve step was taken by the City of Amsterdam in 1609 -a step that joins the history of money to the history if banking. It was a step especially occasioned by the arge trade of Amsterdam. That, in turn, was assoated with one of the most pervasively influential :vents in the history of money-the voyages of Columbus and the effect on Europe of the ensuing conluest and development of Spanish America.

Discovery and conquest set in motion a vast low of preciou~ metal from America to Europe, and the re~ult was a huge rise in prices-an inflation occasioned by an increase in the supply of the hardest of hard money.
p. 13


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