Small-souled Men, Beware!I can't help but recall, at this point, a horribly elitist but very droll remark by
one of my favorite writers, the American "critic of the seven arts", James
Huneker, in his scintillating biography of Frederic Chopin, on the subject of
Chopin's etude Op. 25, No. 11 in A minor, which for me, and for Huneker,
is one of the most stirring and most sublime pieces of music ever written:
"Small-souled men, no matter how agile their fingers, should avoid it."
"Small-souled men"?! Whew! Does that phrase ever run against the
grain of American democracy! And yet, leaving aside its offensive, archaic
sexism (a crime I, too, commit in GEB, to my great regret), I would suggest
that it is only because we all tacitly do believe in something like Huneker's
shocking distinction that most of us are willing to eat animals of one sort or
another, to smash flies, swat mosquitos, fight bacteria with antibiotics, and
so forth. We generally concur that "men" such as a cow, a turkey, a frog,
and a fish all possess some spark of consciousness, some kind of primitive
"soul", but by God, it's a good deal smaller than ours is - and that, no more
and no less, is why we "men" feel that we have the perfect right to extinguish
the dim lights in the heads of these fractionally-souled beasts and to gobble
down their once warm and wiggling, now chilled and stilled protoplasm with
limitless gusto, and not to feel a trace of guilt while doing so.
Enough sermonizing! The real point here is that not all strange loops
give rise to souls as grand and glorious as yours and mine, dear reader.
Thus, for example, I would not want you or anyone else to walk away from
reading all or part of GEB, shake their head and say with sadness, 'That
weird Hofstadter guy has convinced himself that Russell and Whitehead's
Principia Mathematica is a conscious person with a soul!" Horsefeathers!
Balderdash! Poppycock! G6del's strange loop, though it is my paragon for
the concept, is nonetheless only the most bare-bones strange loop, and it
resides in a system whose complexity is pathetic, relative to that of an
organic brain. Moreover, a formal system is static; it doesn't change or grow
over time. A formal system does not live in a society of other formal systems,
mirroring them inside itself, and being mirrored in turn inside its "friends".
Well, I retract that last remark, at least a bit: any formal system as powerful
as PM does in fact contain models not just of itself but of an infinite number
of other formal systems, some like it, some very much unlike it. That is
essentially what G6del realized. But still, there is no counterpart to time, no
counterpart to development, let alone to birth and death.
And so whatever I say about "selves" coming to exist in mathematical
formal systems has to be taken with the proper grain of salt. Strange loops
are an abstract structure that crops up in various media and in varying
degrees of richness. GEB is in essence a long proposal of strange loops as a
metaphor for how selfhood originates, a metaphor by which to begin to
grab a hold of just what it is that makes an "I" seem, at one and the same
time, so terribly real and tangible to its own possessor, and yet also so vague,
so impenetrable, so deeply elusive.
Twentieth-anniversary Preface P-