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.
- 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.
We have overlooked the possibility of a suspended map capable of being folded and unfolded in a different orientation. This solution would no doubt eliminate many of the difficulties discussed above, but, even if technically different from the folding map of the third category, it would prove physically more cumbersome. It would in any case involve the same paradoxes of folding that arise with this third type of map, and would be open to the same objections.
2.3 Transparent Map, Permeable, Extended, and Adjustable
Let us imagine that such a map, drawn on transparent and permeable material (gauze, for example), is spread out over the surface and is adjustable.
In any case, once the map has been drawn and spread out, either the subjects remain on the territory beneath it, or they climb on top of it. But if the subjects were to prepare the map while it is above their heads, not only would they be unable to move, because every movement would alter the positions of the subjects that the map describes (unless we have recourse, once again, to an impoverished map), but further, in moving, they would cause tangles in the very fine membrane above them, resulting in serious discomfort and once more making the map unfaithful: it would assume a different topological configuration, producing disaster areas not corresponding to the planimetry of the territory. It must therefore be supposed that the subjects have produced and extended the map while remaining on top of it.
In this case we can adduce numerous paradoxes already considered in connection with the previous maps: the map would represent a territory inhabited by subjects who in reality inhabit the map (unless it is a summary, or impoverished, map); the map could not be consulted because each subject could examine only the part corresponding to the territory on which subject and map lie; the map’s transparency would eliminate its semiotic function, since it would be functional as sign only in the presence of its own referent; residing on the map, the subjects could not tend the territory, which would deteriorate, making the map unfaithful….It is necessary, then, for the map to be capable of being folded and then reopened with a different orientation, so that every point X of the map representing a point Y of the territory can be consulted when the point X of the map lies on any point Z of the territory, where Z ≠ Y. Folding and unfolding, finally, permit long periods of time when the map is not being consulted and does not cover the territory, and thus allow the cultivation and maintenance of territory necessary to keep its actual configuration always the equivalent of the one depicted on the map.
2.4 Folding and Unfolding the Map
Certain preliminary conditions must be postulated: (i) that the reliefs of the terrain allow the free movement of those subjects assigned to folding; (ii) that a vast central desert exist, where the folded map can be stored and where it can be turned when it must be unfolded again in a different orientation; (iii) that the territory have the form either of a circle or of a regular polygon, so that the map, however oriented, will not exceed its boundaries (a 1:1 map of Italy, shifted ninety degrees, would be spread out over the Mediterranean); and (iv) that, as an inevitable consequence, the map will have a central point, lying always on the same portion of the territory that it represents.
Once these conditions have been satisfied, the subjects can move en masse towards the farthest boundaries of the empire to avoid the map’s being folded up with subjects inside. To avoid potential over-crowding when the subjects are all clustered at the edges of the map (and of the empire), we must postulate an empire inhabited by a number
