the BlooP-like language above, using the given self-rep as a model.) Would
this funny program count as a self-rep? Yes, in a way, because a trivial
transformation performed on its output will restore the original program.
It seems fair to say that the output contains the same information as the
program itself, just recast in a simple way. Yet it is clear that someone might
look at the output and not recognize it as a program printed backwards. To
recall terminology from Chapter VI, we could say that the "inner mes-
sages" of the output and the program itself are the same, but they have
different "outer messages"-that is, they must be read by using different
decoding mechanisms. Now if one counts the outer message as part of the
information-which seems quite reasonable-then the total information is
not the same after all, so the program can't be counted as a self-rep.
However, this is a disquieting conclusion, because we are accustomed
to considering something and its mirror image as containing the same
information. But recall that in Chapter VI, we made the concept of "intrin-
sic meaning" dependent on a hypothesized universal notion of intelligence.
The idea was that, in determining the intrinsic meaning of an object, we
could disregard some types of outer message-those which would be uni-
versally understood. That is, if the decoding mechanism seems fundamental
enough, in some still ill-defined sense, then the inner message which it lets
be revealed is the only meaning that counts. In this example, it seems
reasonably safe to guess that a "standard intelligence" would consider two
mirror images to contain the same information as each other; that is, it
would consider the isomorphism between the two to be so trivial as to be
ignorable. And thus our intuition that the program is in some sense a fair
self-rep, is allowed to stand.Epimenides Straddles the ChannelNow another far-fetched example of a self-rep would be a program which
prints itself out, but translated into a different computer language. One
might liken this to the following curious version of the Quine version of the
Epimenides self-ref:"est une expression qui, quand elle est precedee de sa traduction,
mise entre guillemets, dans la langue provenant de I'autre cote de
la Manche, cree une faussete" is an expression which, when it is
preceded by its translation, placed in quotation marks, into the
language originating on the other side of the Channel, yields a
falsehood.You might try to write down the sentence which is described by this weird
concoction. (Hint: It is not itself-or at least it is not if "itself" is taken in a
naive sense.) If the notion of "self-rep by retrograde motion" (i.e., a pro-
gram which writes itself out backwards) is reminiscent of a crab canon, the
notion of "self-rep by translation" is no less reminiscent of a canon which
involves a transposition of the theme into another key.
Self-Ref and Self-Rep 501