Gödel, Escher, Bach An Eternal Golden Braid by Douglas R. Hofstadter

(Dana P.) #1
C ontracrostipunctus Molecular Biology
phonograph ¢:=> cell
"Perfect" phonograph ¢:=> "Perfect" cell
record ¢:=> strand of DNA
record playable ¢:=> strand of DNA
by a given phonograph reproducible by a given cell
record unplayable ¢:=> strand of DNA
by that phonograph unreproducible by that cell
process of converting ¢:=> process of transcription
record grooves into sounds of DNA onto mRNA
sounds produced by ¢:=> strands of messenger RNA
record player
translation of sounds ¢:=> translation of mRN A
into vibrations of phonograph into proteins
mapping from external ¢:=> Genetic Code
sounds onto vibrations (mapping from mRNA triplets
of phonograph onto amino acids)
breaking of phonograph ¢:=> destruction of the cell
Title of song specially ¢:=> High-level interpretation of
tailored for Record Player X: DNA strand specially tailored
"I Cannot Be Played on for Cell X: "I Cannot Be
Record Player X" Replicated by Cell X"
"Imperfect" Record Player ¢:=> Cell for which there exists at
least one DNA strand which it
cannot reproduce
"Todel's Theorem": ¢:=> Immunity Theorem:
"There always exists an "There always exists an
unplayable record, given unreproducible DNA strand,
a particular phonograph." given a particular cell."

The analogue of Codel's Theorem is seen to be a peculiar fact, proba-
bly little useful to molecular biologists (to whom it is likely quite obvious):

It is always possible to design a strand of DNA which, if injected
into a cell, would, upon being transcribed, cause such proteins to
be manufactured as would destroy the cell (or the DNA), and thus
result in the non-reproduction of that DNA.

This conjures up a somewhat droll scenario, at least if taken in light of
evolution: an invading species of virus enters a cell by some surreptitious

(^536) Self-Ref and Self-Rep

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