NIMROD: Don't worry. It could never happen here. Not in Babel.
1991
On the Impossibility of Drawing a Map of the Empire on a Scale of 1 to 1
"...in that Empire, the Cartographer's art achieved such a degree of perfection that the Map of a single Province occupied an entire City, and the Map of the Empire, an entire Province. In time, these vast Maps were no longer sufficient. The Guild of Cartographers created a Map of the Empire, which perfectly coincided with the Empire itself. But Succeeding Generations, with diminished interest in the Study of Cartography, believed that this immense Map was of no use, and not Impiously, they abandoned it to the Inclemency of the Sun and of numerous Winters. In the Deserts of the West ruined Fragments of the Map survive, inhabited by Animals and Beggars; in all the Country there is no other Relic of the Geographical Disciplines."
(from Viajes de Varones Prudentes, Suárez Miranda, book IV, chap. XIV, Lérida, 1658. Quoted by Jorge Luis Borges, Historia universal de la infamia "Etcetera," Buenos Aires, 1935).
1. Requirements for a 1:1 Map
Herein is discussed the theoretical possibility of a map of the empire on a scale of 1 to 1, assuming these postulates:
1. That the map be, in fact, one to one, and therefore coextensive with the territory of the empire.
2. That it be a map and not a plaster cast; in other words, dismissing the possibility of covering the surface of the empire with a malleable material reproducing every relief, even minimal. In this case the project would be considered, not cartography, but rather the packaging or paving of the empire, and it would thus be more appropriate legally to decree the empire a map of itself, with all the consequent semiotic paradoxes.
3. That the empire in question be that X than which nihil mains cogitari possit, and hence that the map cannot be produced and spread out in a desert area of a second, separate empire X2 such that X2 > X (as if a 1:1 map of the Principality of Monaco were to be spread out in the Sahara). In this case the project would lose all theoretical interest.
4. That the map be faithful, depicting not only the natural reliefs of the empire but also its artifacts, as well as the totality of the empire's subjects (this last is an ideal condition, which may be discarded in the production of an impoverished map).
5. That it be a map and not an atlas with partial pages. In theory there is nothing to prevent the realization, over a reasonable amount of time, of a series of partial projections on separate sheets, to be used individually for reference to different portions of the territory. The map may be produced on separate sheets, but only on condition that they be sutured in such a way as to construct the overall map of the entire territory of the empire.
6. That the map, finally, be a semiotic tool—that it be capable, in other words, of signifying the empire or of allowing references to the empire, especially in those instances when the empire is not otherwise perceptible. This last condition means that the map cannot be a transparent sheet in any way fixed over the territory on which the reliefs of the territory itself are projected point by point; for in that case any extrapolation carried out on the map would be carried out at the same time on the territory beneath it, and the map would lose its function as maximum existential graph.
It is therefore necessary that (i) the map not be transparent; or that (ii) it not lie on the territory; or, finally, that (iii) it be adjustable in such a way that the reference points of the map lie on points of the territory that are not the ones they indicate.
It will be demonstrated that each of these three conditions involves insuperable practical difficulties and theoretical paradoxes.
2. Methods of Production of the Map
2.1 Opaque Map Spread Out Over the Territory
As it is opaque, this map would be perceptible while perception of the underlying territory would be obscured, but by creating a membrane between the territory and the sun's rays or any atmospheric precipitation, it would alter the ecological equilibrium of the territory itself. Such a map would therefore depict the territory differently from its actual state. The constant correction of the map, theoretically possible in the case of a suspended map (cf. 2.2), is in this case impossible: the alterations of the territory could not be perceived through the opacity of the map. Thus the observer would make inferences about an unknown territory from an unfaithful map. If, finally, the map must include the inhabitants as well, it would for this same reason prove once again unfaithful as it would represent an empire inhabited by subjects who, in reality, inhabit the map.
2.2 Suspended Map
On the territory of the empire stakes would be erected, of a height equal to its highest relief points, and over the upper ends of the stakes would be extended a cartaceous or linen surface on which, from below, the features of the territory would be projected. Such a map could be used as a sign of the territory, since, to inspect it, one must raise one's eyes, turning one's gaze away from the corresponding territory. In practice, however (and this is a consideration that would apply also to the spread-out, opaque map, if it were not made impossible by other, more cogent arguments), since each portion of the map could be consulted only by those residing in the corresponding portion of the territory, the map would not allow the reception of information about parts of the territory different from those where the map is being consulted.
The problem could be overcome by surveying the map from above: but (apart from [i] the difficulty of emerging with kites or guided balloons from a territory entirely covered by a cartaceous or linen surface; [ii] the necessity of making the map equally legible from above and from below; and [iii] the fact that the same cognitive result could easily be achieved flying over a territory without a map) any inhabitant who flew over the map, abandoning for this purpose the territory itself, would automatically make the map inaccurate, because it would then represent a territory having a number of inhabitants superior, at least by one, to that obtaining at the moment of the aerial observation. Such a solution would thus be possible only with an impoverished map that did not depict the subjects.
Finally, if the suspended map were opaque, the same objection raised for the extended map would be valid: preventing the penetration of solar rays and atmospheric precipitation, it would alter the ecological equilibrium of the territory and thus become an unfaithful representation of it.
The subjects could obviate this problem in two ways: either (i) by producing every single part of the map, once all the stakes were in place, in a single moment of time at every point in the territory, so that the map would remain faithful at least in the instant when it is completed (and perhaps for many successive hours); or else (ii) by arranging for ongoing correction of the map based on the modifications of the territory. But in this second case, the corrective activity of the subjects would involve them in migrations that the map could not record, and unless it were an impoverished version, it would become unfaithful once more. Furthermore, occupied in constant revision of the map, the subjects could not deal with the ecological decline of the territory; the activity of map revision would lead to the extinction of all the subjects—and therefore of the empire.
A similar situation would arise if the map were of transparent and permeable material. It would be impossible to study in the daytime, because of the glare of the sun's rays, and any colored area that reduced the glare would inevitably diminish the action of the sun on the territory below, provoking at the same time ecological transformations of lesser extent but of equal theoretical impact on the fidelity of the map.