1. 'Map' means, according to the OED, a representation of the earth's surface, or more generally, a 'diagram representing the spatial distribution of anything or the relative positions,' and 'a mental conception of the arrangement.' Also it has the meaning of an 'embodiment or incarnation,' and, 'to map' means to 'establish relative positions.'  Thus, a map is the mental and conceptual organization or representation; it is the representation of the world under symbolic order of humans.
Historically, map was not always a product of scientific measurement of the world as it is nowadays; map found its position in the middle between science and art . The motivation to draw a map, in both senses, is an idea of 'utopia': in a map, every object, all the artifacts of men and nature surrounding them are never in defective or defunct state. 'Looking through them, one might well conclude that all is well with America' . As a medium of science-and-art, thus reason-and- aestheticism, a map is the medium of two very distinct yet closely related human mentalities. A map as a medium, representing land rather in mathematical exactness or in aesthetic pleasantness, carries two messages; firstly the apparent depiction of land, and secondly, the very utopian idea of man in relation to the world.
Talking about today's typical maps drawn to scale with well-defined set of symbols, the bodily interaction of subject and his/her experiential limitation is subdued; the map appears as a neutral representation and pure icon of natural world just as a mathematical order of scientific knowledge. Since this science as an ideology of Cartesian rationalism has been well accounted for by Martin Heidegger through his argument of 'world picture,' it'll be useful to discuss it as a map's second-level message. He claims that the whole system of science and knowledge is based on actively projecting the 'fixed ground plan' and binding to it, rather than being essentially neutral itself. Moreover, for him, 'only within the perspective of this ground plan does an event in nature become visible as such an event'. Even (scientific) 'explanation', he says, 'accounts for an unknown by means of a known, and at the same time it verifies that known by means of the unknown'. Now, the objectiveness is also a 'setting-before, a representing, ... in such a way that man who calculates can be sure, and that means be certain, of that being'. Along this scheme, Heidegger interprets 'world picture [Weltbild]' not as a copy of world in literal sense, but as an 'entirety of what is ... set up by man, who represents and sets forth'. Further, he extends his accounts of world picture as the 'conquest of the world as picture', a symbolical overview and ruling .
Taking Heidegger's idea discussed above, 'mapping' should be interpreted and located within the wider philosophy of rationalism, which dominated every social, cultural, political, and economical sphere of modern worlds. Map of Texas [Fig. 1] could be an example here. In it, the straight lines that divide counties do not reflect any events, activities, or exchanges which take place in accordance with geographical topology of nature; whatever represented here is the 'mapping' of Texas itself, and as a medium, this map carries the ideas, such as conceptual organization and arrangement done on this land, and presupposition of land as infinite and flat object. As a result of mapping, now the land is actively manipulated, exploited, and controlled by the map. 2. Is any other kind of mapping possible? At the other extremity from modern scientific cartography, old worlds were always divided in accordance with geographical forms, such as rivers, ridges, or plantations. In this mapping, the relationship between human and nature is more tactile and bodily rather than conceptual; the boundary lines are human boundaries of economical and cultural reach, thus also the limits of cognitive grounds. That is why oceans surrounding lands in ancient maps are sometimes decorated with mythical creatures; distant oceans were the 'beyonds' of cognitive limitations.
As for today, we notice this primitive mediation between land and human reemerging in the new technological territories such as the internet and metropolises. Ironically, as McLuhan's famous term of 'global village' suggests, these spaces are full of tactile and intimate interactions, even for the fact that this metaphorical online 'space' has nothing to do with physical or material land.
A user sitting in front of a glass panel with keyboard endlessly searches, writes, chats, views, or just surfs around. More or less, the interaction in this space resembles that of metropolitan spaces like New York. Built on the technology, yet full of uncontrolled desires. The navigation in it is also immediately guided like following arrow-signs from a place to another in underground or large buildings of urban spaces, where as in internet, navigation is performed by clicking through hyper-links which appears on the screen one after another. In this navigation, traditional cartography based on geometric grid inevitably fails. There have been attempts to 'map' the network of the internet, as shown in [Fig 2], but without doubt, this does not reflect our practical experience, nor could it be useful for the navigation.
How can we properly deal with this neo-primitiveness of the technological spaces? How should the notion of map and mediation be modified to do so? Surprisingly, contemporary philosophy has a very simple answer: for ?i?ek, who derives his theory from Lacan, there is no positive distinction between original and model, nor the thing and its sign. Subject is what constitutes the gap between the former and the latter. As for the questions posed above, the map is the internet itself. The land of the internet is not a medium, if mediation means the channeling between two distinct subjects: on the contrary, it is a medium as an environment, or rather a matrix, in which there are no subjects and media, but there are only subject-and-medium's. [see simulation-simulacrum, (2)]
If the land is its own map, if the original is its own model, if the thing is its own sign, then there is no positive, actual difference between them, though there must be some blank space which distinguishes the thing from itself as its own sign, some nonentity, which produces from the thing its sign - that "nonentity," that "pure" difference, is the subject. 
3. There is no map as medium representing land, but map is the land as a media of exchanges. To spell this out more clearly, and to deal with the qualities of mediation within the spaces, I would like to introduce the concept of map as shown by Deleuze and Guattari's A Thousand Plateaus.
In A Thousand Plateaus, one may find a whole different notion of map and topography contradicting scopic regime of rationalism and/or definition of the OED. To the authors, a map is 'entirely oriented toward an experimentation in contact with the real, ... [which] constructs the unconscious.'  Here, the usage of the word 'map' points to the real itself, which totally contests the OED's definition of it as the 'representation' of earth [see symbolic, imaginary, real]. Another formulation to be noticed might be that of 'smooth space.'
Space of contact, of small tactile or manual actions of contact, rather than a visual space like Euclid's striated space ... [which] can be explored only by legwork. They do not meet the visual condition of being observable from a point in space external to them. 
Some examples of smooth spaces includes sound, color, steppe, desert and sea, which are graduated rather than divided, open towards many directions, and not connected by artificial conduits, such as highways or aqueducts. If it is proper to take modern territories as smooth spaces, because of their tactility and navigational aspects, now it's clear why the mapping - in conventional meaning - of contemporary spaces as in above figure 2 is misguiding; the conventional mapping is exactly the observation from external space [see perspective], which smooth space won't allow. As navigation of the internet exemplifies, these spaces are not viewable from outside, and moreover, could be only be explored by 'legwork', in this case, 'clicking' through. Same could be said about metropolises, New York underground passages might never be able to be 'mapped'; one could only be guided by arrow-signs.
Last point to be noted here is their concept of land (territory) as medium. A 'plateau' is a middleness (milieu) without 'the beginning or the end,' a topographical feature on smooth space where 'multiplicity connected with other multiplicities' forms a 'circle of convergence.' Thus, the plateau is not the pan-optical viewpoint from above, where distant ground below would appear inert to politics. (Is this not the utopian vision of modern map, as discussed above?) Rather, it is a part of the real ground of praxis; within it are all the human exchanges, entailing those of signification, economics, and powers; these form micro- to macro- politics. Some examples might be the temporary gathering spots, the popular discussion forum, etc. In the sense, the 'territory' or land is the matrix of exchanges and politics.
What does all this imply? Why are they intentionally dismissing the gap between map as a signifier and land as its signified? Why are these relations especially set up around map and land? The territory is the basis of all powers and significations. Also it is the ground where the exchange takes place. But the signifiers, as manifestation of them, are the graspable objects by subjects. In the actual sense, or virtual sense, the signifier takes the power, it is the power, it is the discourse. Thus, we see here again, "Media (signifier) is the Message (power)" in philosophical terms. Now, what is at the stake is to discuss the proper orientation of powers, economy, etc., not in relationship with, but inside the physical and discursive 'ground'. There lies the philosophical importance of land and map.
In conclusion, the map, under their arguments, is the actual praxis. Any mediation through representation does not lie outside of this ground of praxis. Also, contemporary spaces exemplifies that it is impossible to be viewed from outside. Map is not inert. Map is the message.
Hong Kwan Lee
Department of Art History