CHAPTE.R XIII
BlooP and FlooP and GlooP
Self-Awareness and ChaosBLOOP, FLOOP, AND GLOOP are not trolls, talking ducks, or the sounds
made by a sinking ship-they are three computer languages, each one with
its own special purpose. These languages were invented specially for this
Chapter. They will be of use in explaining some new senses of the word
"recursive"-in particular, the notions of primitive recursivity and general
recursivity. They will prove very helpful in clarifying the machinery of
self-reference in TNT.
We seem to be making a rather abrupt transition from brains and
minds to technicalities of mathematics and computer science. Though the
transition is abrupt in some ways, it makes some sense. We just saw how a
certain kind of self-awareness seems to be at the crux of consciousness.
Now we are going to scrutinize "self-awareness" in more formal settings,
such as TNT. The gulf between TNT and a mind is wide, but some of the
ideas will be most illuminating, and perhaps metaphorically transportable
back to our thoughts about consciousness.
One of the amazing things about TNT's self-awareness is that it is
intimately connected to questions about order versus chaos among the
natural numbers. In particular, we shall see that an orderly system of
sufficient complexity that it can mirror itself cannot be totally orderly-it
must contain some strange, chaotic features. For readers who have some
Achilles in them, this will be hard to take. However, there is a "magical"
compensation: there is a kind of order to the disorder, which is now its own
field of study, called "recursive function theory". Unfortunately, we will not
be able to do much more than hint at the fascination of this subject.Representability and RefrigeratorsPhrases such as "sufficiently complex", "sufficiently powerful" and the like
have cropped up quite often earlier. Just what do they mean? Let us go
back to the battle of the Crab and Tortoise, and ask, "What qualifies
something as a record player?" The Crab might claim that his refrigerator
is a "Perfect" record player. Then to prove it, he could set any record
whatsoever atop it, and say, "You see--it's playing it!" The Tortoise, if he
wanted to counter this Zen-like act, would have to reply, "No-your re-
frigerator is too low-fidelity to be counted as a phonograph: it cannot
reproduce sounds ·at all (let alone it~ self-breaking sound)." The Tortoise(^406) BlooP and FlooP and GlooP