On Exactitude in Science

"On Exactitude in Science" or "On Rigor in Science" (the original Spanish-language title is "Del rigor en la ciencia") is a one-paragraph essay written in 1946 by Jorge Luis Borges, about the map–territory relation, written in the form of a literary forgery. 

This is a short and marvelous essay about the value of abstractions (in scientific knowledge) by the Argentine writer Jorge Luis Borges. Though written in the 20th Century, Borges cleverly styled it as an extract from a historic travel book dating from 1658 entitled "Travels of Well-Behaved Young Gentlemen", by the fictitious author Suarez Miranda. 

The Plot..

The Borges story, credited fictionally as a quotation from "Suárez Miranda, Viajes de varones prudentes, Libro IV, Cap. XLV, Lérida, 1658", imagines an empire where the science of cartography becomes so exact that only a map on the same scale as the empire itself will suffice.

The Original Essay..

Cartography reached such perfection that the map of a single province occupied the whole of a city, and the map of th empire took up an entire province. With time, those exaggerated maps no longer satisfied, and the Colleges of Cartographers came up with a map of the empire that had the size of the empire itself, and coincided with it point by point. Less addicted to the study of Cartography, succeeding generations understood that this extended map was useless, and without compassion, they abandoned it to the inclemencies of the sun and of the winters. In the deserts of the west, there remain tattered fragments of the map, inhabited by animals and beggars; in the whole country there are no other relics of the geographical disciplines.

Suárez Miranda: Viajes de varones prudentes, libro cuarto, cap. XLV, Lérida, 1658.

(Translation updated by Nikos Salingaros)

The Influence..

The story elaborates on a concept in Lewis Carroll's Sylvie and Bruno Concluded: a fictional map that had "the scale of a mile to the mile." One of Carroll's characters notes some practical difficulties with this map and states that "we now use the country itself, as its own map, and I assure you it does nearly as well."

"What a useful thing a pocket-map is!" I remarked.

"That's another thing we've learned from your Nation," said Mein Herr, "map-making. But we've carried it much further than you. What do you consider the largest map that would be really useful?"

"About six inches to the mile."

"Only six inches!" exclaimed Mein Herr. "We very soon got to six yards to the mile. Then we tried a hundred yards to the mile. And then came the grandest idea of all ! We actually made a map of the country, on the scale of a mile to the mile!"

"Have you used it much?" I enquired.

"It has never been spread out, yet," said Mein Herr: "the farmers objected: they said it would cover the whole country, and shut out the sunlight ! So we now use the country itself, as its own map, and I assure you it does nearly as well."

 Lewis Carroll, Sylvie and Bruno Concluded Chapter XI, London, 1895

The Legacy ..

Umberto Eco expanded upon the theme, quoting Borges's paragraph as the epigraph for his short story "On the Impossibility of Drawing a Map of the Empire on a Scale of 1 to 1." It was collected in Eco's How to Travel with a Salmon and Other Essays.

Jean Baudrillard cites the short story as the "finest allegory of simulation" in his treatise Simulacra and Simulation, describing how "an aging double ends up being confused with the real thing", covering the very thing it was meant to represent. In this way the story contributed to developing the semiotic concept of the hyperreal.

I read the above Essay a few years back & then re read it recently.

Surprisingly, I found myself drawing some inferences this time.

- If a system, such as the geography of a country - is irreducibly complex, then any representation must necessarily be an abstraction, approximation or simplification of the original. Hence True models don't exist.

 - At the same time - if a reductionistic representation is too abstract to adequately describe the system -  a representation that is just as complex as the system itself is equally impractical and redundant (as in the absurd example described by Borges).

Hence the scale of abstraction, reduction, approximation becomes a key factor in representation of any complex system, be it large numbers, impossible graphs or complex drawings of complex buildings.

A Temple Elevational View and its abstract representation

A Literary forgery is writing, such as a manuscript or a literary work, which is either deliberately misattributed to a historical or invented author, or is a purported memoir or other presumably nonfictional writing deceptively presented as true when, in fact, it presents untrue or imaginary information or content.