Definition and Motivation of Simulacra

Simulacra are copies without originals. This seems incoherent; any reasonable definition of a “copy” operation requires a target to reproduce. Let S be a set of similar objects, and consider the following game.

1. Alice is given access to S and must produce new object, x.
2. Bob is given S′ = S ∪ x, the original set with x included.
3. Bob is paid $1 if he can identify which element of S was synthesized by Alice. Alice is paid $1 if Bob guesses incorrectly.

If Alice can win by adding noise to an existing object y in S, then x is simply a noisy copy of y and no problem arises in identifying an original. However, what if this “prototype+perturb strategy” fails with high probability? Suppose the structure of S-members is delicate, meaning that randomly selecting a single y ∈ S and performing an efficient modification is likely to produce an object that Bob can easily distinguish from the original members of S.

Suppose further that there is a winning strategy for Alice, but she must inspect at least k objects from the set S to synthesize an x with good chance of fooling Bob. Under these conditions, we call x a Simulacrum for S. Intuitively, x is a copy of something “about” of S, but we cannot identify a particular object as the original for x.

One could object to using the word “copy” to describe such x. But, because x must imitate existing elements of S, we feel that it is justified.

So, this is what makes the term ‘Simulacrum’ useful: it picks out successful imitations of an existing concept that are too complex to be produced by randomized mockery of a single original prototype. A pseudo-S would include the simple imitative objective, and we wish to make this distinction, especially in iterative applications of imitation games.