Umberto Eco
Scuola Superiore di Studi Umanistici
Via Marsala 26, Bologna
Italy
Dear Professor Eco:
I read with great interest your seminal "On the Impossibility of Drawing a Map of the Empire on a Scale of 1 to 1". I can, of course, find no flaw in your logic. From consideration of the initial requirements, which I shall list presently, surely can come no other conclusion than the assertion of the nonexistence of the Empire, and that the 1:1 Map then be a map not of the empire, but of a nonexistent empire.
Requirements for a 1:1 Map
1) That map be, in fact, one to one, and 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 maius cogitary 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 tose 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 reliefs of the territory 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 maxium existential graph.
excerpted from How to travel with a Salmon, by Umberto Eco
From careful consideration of these premises, you eventually arrive at the conclusion that any such fulfilling map, which, of course, must exist above the empire it represents, instead of below, would modify the empire so completely that it would not longer be a representative map. And indeed on this theoretical basis I can find no quarrel.
On a practical consideration, though, I believe your criteria to be nearly fulfillable. First, one must realize that, if a fulfilling map existed, it would be perceivable only within in a certain radius of where the perceiver stood; that is to say, standing at point X, I would only have the perception of the map in a radius R around me. Given this undisputable physical truth, and given the fact that your requirements establish no criteria on a minimal R, I conclude that R can be minimized to the very extent that I wish; if I could design a map that fulfilled the requirements but had R to be the distance from my elbow to my second knuckle, a fulfilling map we would have.
One of the dull and inastute might of course object that, though they couldn't see the map at a distance greater than R, they could indeed perceived it by tugging on it, beating on it to send a sort of primitive and vibrationally conducted morse code, or calling a relative (named "Cletus" no doubt, or, in the Italian, "Balduccio") and asking them to affirm that they were indeed perceiving the map. However these objections may be countered in the following sequential (former to latter) manner: the map is many sections of width R sutured together with interceding metal rods, the same, and that all he has proven is that the map is perceptible in both radii of R. Clearly these objections do not the argument refute.
To continue, we have established that such a map need be perceptible at a finite radius R, and no further. The next logical step is to realize that this means the map need only present itself to the human senses within a finite radius R. Its existence at radii outside R is of course necessary, but it need not be perceptible to a human mind.
Furthermore, because of the great size of such a map as you posit in your essay, it's clear that it is not a requirement that it be viewable from one position; that is to say, viewing a city a hundred miles (162 chilometri) away might in fact involve a travel of a hundred miles.
From these observations one may conclude that a fulfilling map may be constructed from a video camera pointed at the feet of the wearer, and a viewing module near her head. Not only is this precise, it fulfills the requirements, as well as being quite practical and epistemologically non-contradictory! If the Professor likes, it could even be contrived to produce excessively contrasted colors and have a poor legend, to enhance the feel of a petrol-station-1500-lire-special.
I'm now working on my next project: a 5:1 map. And as soon as I have the means to purchase a zoom lens for the camera, I'll have one.
Sincerely,
VelourFabric
[8D]