Unerkennbare Fehler, unauffindliche Wahrheiten ...
aus: Douglas R. Hofstadter: Gödel, Escher, Bach: an eternal golden braid. NY: Basic Books, 1979, p. 71
FIGURE 18. Considerable visual symbolism is featured in this diagram of the relationship between various classes of TNT strings. The biggest box represents the set of all TNT strings. The next-biggest box represents the set of all well-formed TNT strings. Within it is found the set of all sentences of TNT. Now things begin to get interesting. The set of theorems is pictured as a tree growing out of a trunk (representing the set of axioms). The tree-symbol was chosen because of the recursive growth pattern which it exhibits: new branches (theorems) constantly sprouting from old ones. The fingerlike branches probe into the corners of the constraining region (the set of truths), yet can neverfully occupy it. The boundary between the set of truths and the set of falsities is meant to suggest a randomly meandering coastline which, no matter how closely you examine it, always has finer levels of structure, and is consequently impossible to describe exactly in any finite way. (See B. Mandelbrot's book Fractals.) The reflected tree represents the set of negations of theorems: all of them false, yet unable collectively to span the space of false statements. [Drawing by the author.]