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

boggling at first. A couple of pictures may help (Figs. 83, 84). Figure 83 is a

picture which can be interpreted on two levels. On one level, it is a sentence

pointing at itself; on the other level, it is a picture of Epimenides executing

his own death sentence.

FIGURE 83.

Figure 84, showing visible and invisible portions of the iceberg,

suggests the relative proportion of sentence to processing required for the

recognition of self-reference:

cognitive processes

required for understanding

the self-reference in the

Epimenides sentence

waterline

English language sea

FIGURE 84.

It is amusing to try to create a self-referring sentence without using the

trick of saying "this sentence". One could try to quote a sentence inside

itself. Here is an attempt:

The sentence "The sentence contains five words" contains five words.

But such an attempt must fail, for any sentence that could be quoted

entirely inside itself would have to be shorter than itself. This is actually

possible, but only if you are willing to entertain infinitely long sentences,

such as:

(^496) Self-Ref and Self-Rep