As the statistician George E. P. Box wrote, “All models are wrong, but some models are useful.”90 What he meant by that is that all models are simplifications of the universe, as they must necessarily be. As another mathematician said, “The best model of a cat is a cat.”91 Everything else is leaving out some sort of detail. How pertinent that detail might be will depend on exactly what problem we’re trying to solve and on how precise an answer we require.

Nor are statistical models the only tools we use that require us to make approximations about the universe. Language, for instance, is a type of model, an approximation that we use to communicate with one another. All languages contain words that have no direct cognate in other languages, even though they are both trying to explain the same universe. Technical subfields have their own specialized language. To you or me, the color on the front cover of this book is yellow. To a graphic designer, that term is too approximate—instead, it’s Pantone 107.

[...]

A good model can be useful even when it fails. “It should be a given that whatever forecast we make on average will be wrong,” Ozonoff told me. “So usually it’s about understanding how it’s wrong, and what to do when it’s wrong, and minimizing the cost to us when it’s wrong.”

The key is in remembering that a model is a tool to help us understand the complexities of the universe, and never a substitute for the universe itself. This is important not just when we make predictions. Some neuroscientists, like MIT’s Tomasso Poggio, think of the entire way our brains process information as being through a series of approximations.

This is why it is so crucial to develop a better understanding of ourselves, and the way we distort and interpret the signals we receive, if we want to make better predictions.

Thus, everywhere in Disneyland the objective profile of America, down to the morphology of individuals and of the crowd, is drawn. All its values are exalted by the miniature and the comic strip. Embalmed and pacified. Whence the possibility of an ideological analysis of Disneyland (L. Marin did it very well in Utopiques, jeux d'espace [Utopias, play of space]): digest of the American way of life, panegyric of American values, idealized transposition of a contradictory reality. Certainly. But this masks something else and this "ideological" blanket functions as a cover for a simulation of the third order: Disneyland exists in order to hide that it is the "real" country, all of "real" America that is Disneyland (a bit like prisons are there to hide that it is the social in its entirety, in its banal omnipresence, that is carceral). Disneyland is presented as imaginary in order to make us believe that the rest is real, whereas all of Los Angeles and the America that surrounds it are no longer real, but belong to the hyperreal order and to the order of simulation. It is no longer a question of a false representation of reality (ideology) but of concealing the fact that the real is no longer real, and thus of saving the reality principle.

The imaginary of Disneyland is neither true nor false, it is a deterrence machine set up in order to rejuvenate the fiction of the real in the opposite camp. Whence the debility of this imaginary, its infantile degeneration. This world wants to be childish in order to make us believe that the adults are elsewhere, in the "real" world, and to conceal the fact that true childishness is everywhere - that it is that of the adults themselves who come here to act the child in order to foster illusions as to their real childishness.

[...]

Disneyland: a space of the regeneration of the imaginary as waste-treatment plants are elsewhere, and even here. Everywhere today one must recycle waste, and the dreams, the phantasms, the historical, fairylike, legendary imaginary of children and adults is a waste product, the first great toxic excrement of a hyperreal civilization. On a mental level, Disneyland is the prototype of this new function. But all the sexual, psychic, somatic recycling institutes, which proliferate in California, belong to the same order. People no longer look at each other, but there are institutes for that. They no longer touch each other, but there is contactotherapy. They no longer walk, but they go jogging, etc. Everywhere one recycles lost faculties, or lost bodies, or lost sociality, or the lost taste for food. One reinvents penury, asceticism, vanished savage naturalness: natural food, health food, yoga. Marshall Sahlins's idea that it is the economy of the market, and not of nature at all, that secretes penury, is verified, but at a secondary level: here, in the sophisticated confines of a triumphal market economy is reinvented a penury/sign, a penury/simulacrum, a simulated behavior of the underdeveloped (including the adoption of Marxist tenets) that, in the guise of ecology, of energy crises and the critique of capital, adds a final esoteric aureole to the triumph of an esoteric culture. Nevertheless, maybe a mental catastrophe, a mental implosion and involution without precedent lies in wait for a system of this kind, whose visible signs would be those of this strange obesity, or the incredible coexistence of the most bizarre theories and practices, which correspond to the improbable coalition of luxury, heaven, and money, to the improbable luxurious materialization of life and to undiscoverable contradictions.

Such is simulation, insofar as it is opposed to representation. Representation stems from the principle of the equivalence of the sign and of the real (even if this equivalence is Utopian, it is a fundamental axiom). Simulation, on the contrary, stems from the Utopia of the principle of equivalence, from the radical negation of the sign as value, from the sign as the reversion and death sentence of every reference. Whereas representation attempts to absorb simulation by interpreting it as a false representation, simulation envelops the whole edifice of representation itself as a simulacrum.

Such would be the successive phases of the image:

it is the reflection of a profound reality;
it masks and denatures a profound reality;
it masks the absence of a profound reality;
it has no relation to any reality whatsoever;
it is its own pure simulacrum.

In the first case, the image is a good appearance - representation is of the sacramental order. In the second, it is an evil appearance - it is of the order of maleficence. In the third, it plays at being an appearance - it is of the order of sorcery. In the fourth, it is no longer of the order of appearances, but of simulation.

If once we were able to view the Borges fable in which the cartographers of the Empire draw up a map so detailed that it ends up covering the territory exactly (the decline of the Empire witnesses the fraying of this map, little by little, and its fall into ruins, though some shreds are still discernible in the deserts - the metaphysical beauty of this ruined abstraction testifying to a pride equal to the Empire and rotting like a carcass, returning to the substance of the soil, a bit as the double ends by being confused with the real through aging) - as the most beautiful allegory of simulation, this fable has now come full circle for us, and possesses nothing but the discrete charm of second-order simulacra.

Today abstraction is no longer that of the map, the double, the mirror, or the concept. Simulation is no longer that of a territory, a referential being, or a substance. It is the generation by models of a real without origin or reality: a hyperreal. The territory no longer precedes the map, nor does it survive it. It is nevertheless the map that precedes the territory - precession of simulacra - that engenders the territory, and if one must return to the fable, today it is the territory whose shreds slowly rot across the extent of the map. It is the real, and not the map, whose vestiges persist here and there in the deserts that are no longer those of the Empire, but ours. The desert of the real itself.

In fact, even inverted, Borges's fable is unusable. Only the allegory of the Empire, perhaps, remains. Because it is with this same imperialism that present-day simulators attempt to make the real, all of the real, coincide with their models of simulation. But it is no longer a question of either maps or territories. Something has disappeared: the sovereign difference, between one and the other, that constituted the charm of abstraction. Because it is difference that constitutes the poetry of the map and the charm of the territory, the magic of the concept and the charm of the real. This imaginary of representation, which simultaneously culminates in and is engulfed by the cartographers mad project of the ideal coextensivity of map and territory, disappears in the simulation whose operation is nuclear and genetic, no longer at all specular or discursive. It is all of metaphysics that is lost. No more mirror of being and appearances, of the real and its concept. No more imaginary coextensivity: it is genetic miniaturization that is the dimension of simulation. The real is produced from miniaturized cells, matrices, and memory banks, models of control - and it can be reproduced an indefinite number of times from these. It no longer needs to be rational, because it no longer measures itself against either an ideal or negative instance. It is no longer anything but operational. In fact, it is no longer really the real, because no imaginary envelops it anymore. It is a hyperreal, produced from a radiating synthesis of combinatory models in a hyperspace without atmosphere.

By crossing into a space whose curvature is no longer that of the real, nor that of truth, the era of simulation is inaugurated by a liquidation of all referentials - worse: with their artificial resurrection in the systems of signs, a material more malleable than meaning, in that it lends itself to all systems of equivalences, to all binary oppositions, to all combinatory algebra. It is no longer a question of imitation, nor duplication, nor even parody. It is a question of substituting the signs of the real for the real, that is to say of an operation of deterring every real process via its operational double, a programmatic, metastable, perfectly descriptive machine that offers all the signs of the real and shortcircuits all its vicissitudes. Never again will the real have the chance to produce itself - such is the vital function of the model in a system of death, or rather of anticipated resurrection, that no longer even gives the event of death a chance. A hyperreal henceforth sheltered from the imaginary, and from any distinction between the real and the imaginary, leaving room only for the orbital recurrence of models and for the simulated generation of differences.