fact it induced them. That is, once it had been decided that these two notions
were to be fused, it became a matter of looking at them on a level where
analogous parts emerged into view, then going ahead and mapping the parts
onto each other, and so on, recursively, to any level that was found desir-
able. Here, for instance, "voice" and "character" emerged as corresponding
slots when "crab canon" and "dialogue" were viewed abstractly. Where did
these abstract views come from, though? This is at the crux of the
mapping-problem-where do abstract views come from? How do you make
abstract views of specific notions?Abstractions, Skeletons, AnalogiesA view which has been abstracted from a concept along some dimension is
what I call a conceptual skeleton. In effect, we have dealt with conceptual
skeletons all along, without often using that name. For instance, many of
the ideas concerning Bongard problems could be rephrased using this
terminology. It is always of interest, and possibly of importance, when two
or more ideas are discovered to share a conceptual skeleton. An example is
the bizarre set of concepts mentioned at the beginning of the Contra factus: a
Bicyclops, a tandem unicycle, a teeter-teeter, the game of ping-ping, a
one-way tie, a two-sided Mobius strip, the "Bach twins", a piano concerto
for two left hands, a one-voice fugue, the act of clapping with one hand, a
two-channel monaural phonograph, a pair of eighth-backs. All of these
ideas are "isomorphic" because they share this conceptual skeleton:a plural thing made singular and re-pluralized wrongly.Two other ideas in this book which share that conceptual skeleton are (1)
the Tortoise's solution to Achilles' puzzle, asking for a word beginning and
ending in "HE" (the Tortoise's solution being the pronoun "HE", which
collapses two occurrences into one), and (2) the Pappus-Gelernter proof of
the Pons Asinorum Theorem, in which one triangle is reperceived as two.
Incidentally, these droll concoctions might be dubbed "demi-doublets".
A conceptual skeleton is like a set of constant features (as distinguished
from parameters or variables)-features which should not be slipped in a
subjunctive instant replay or mapping-operation. Having no parameters or
variables of its own to vary, it can be the invariant core of several different
ideas. Each instance of it, such as "tandem unicycle", does have layers of
variability and so can be "slipped" in various ways.
Although the name "conceptual skeleton" sounds absolute and rigid,
actually there is a lot of play in it. There can be conceptual skeletons on
several different levels of abstraction. For instance, the "isomorphism"
between Bongard problems 70 and 71, already pointed out, involves a
higher-level conceptual skeleton than that needed to solve either problem
in isolation.
Artificial Intelligence: Prospects 669