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

Note the base-pairing of A and T (Arithmetization and Translation),
as well as of G and C (Gode) and Crick). Mathematical logic gets the purine
side, and molecular biology gets the pyrimidine side.
To complete the esthetic side of this mapping, I chose to model my
Godel-numbering scheme on the Genetic Code absolutely faithfully. In
fact, under the following correspondence, the table of the Genetic Code
becomes the table of the Godel Code:

(odd) 1 ¢:~

(even) 2 ¢:~

(odd) 3 ¢:~

(even) 6 ¢:~

A

C

G

U

(purine)

(pyrimidine)

(purine)

(pyrimidine)

Each amino acid-of which there are twenty-corresponds to exactly one

symbol of TNT-of which there are twenty. Thus, at last, my motive for

concocting "austere TNT" comes out-so that there would be exactly

twenty symbols! The Godel Code is shown in Figure 100. Compare it with

the Genetic Code (Fig. 94).

There is something almost mystical in seeing the deep sharing of such

an abstract structure by these two esoteric, yet fundamental, advances in

knowledge achieved in our century. This Central Dogmap is by no means a

rigorous proof of identity of the two theories; but it clearly shows a pro-

found kinship, which is worth deeper exploration.

Strange Loops in the Central Dogmap

One of the more interesting similarities between the two sides of the map is

the way in which "loops" of arbitrary complexity arise on the top level of

both: on the left, proteins which act on proteins which act on proteins and

so on, ad infinitum; and on the right, statements about statements about

statements of meta-TNT and so on, ad infinitum. These are like heterar-

chies, which we discussed in Chapter V, where a sufficiently complex

substratum allows high-level Strange Loops to occur and to cycle around,

totally sealed off from lower levels. We will explore this idea in greater

detail in Chapter XX.

Incidentally, you may be wondering about this question: "What, ac-

cording to the Central Dogmap, is Gildel's Incompleteness Theorem itself

mapped onto?" This is a good question to think about before reading

ahead.

The Central Dogmap and the Contracrostipunctus

It turns out that the Central Dogmap is quite similar to the mapping that
was laid out in Chapter IV between the Contracrostipunctus and Godel's
Theorem. One can therefore draw parallels between all three systems:

(^534) Self-Ref and Self-Rep