When Is a Program Original?This issue of a program outdoing its programmer is connected with the
question of "originality" in AI. What if an AI program comes up with an
idea, or a line of play in a game, which its programmer has never
entertained-who should get the credit? There are various interesting
instances of this having happened, some on a fairly trivial level, some on a
rather deep level. One of the more famous involved a program to find
proofs of theorems in elementary Euclidean geometry, written by E.
Gelernter. One day the program came up with a sparklingly ingenious
proof of one of the basic theorems of geometry-the so-called "pons
asinorum", or "bridge of asses".
This theorem states that the base angles of an isosceles triangle are
equal. Its standard proof requires constructing an altitude which divides
the triangle into symmetrical halves. The elegant method found by the
program (see Fig. 114) used no construction lines. Instead, it considered
AP '--____ ...l P'
FIGURE 114. Pons Asinorum Proof
(found by Pappus [-300 A.D.] and
Gelernter's program [ -1960 A.D. ]). Prob-
lem: To show that the base angles of an
isosceles triangle are equal. Solution: As the
triangle is isosceles, AP and AP I are of
equal length. Therefore triangles PAP I and
P'AP are congruent (side-side-side). This
implies that corresponding angles are equal.
In particular, the two base angles are equal.the triangle and its mirror image as two different triangles. Then, having
proved them congruent, it pointed out that the two base angles matched
each other in this congruence-QED.
This gem of a proof delighted the program's creator and others; some
saw evidence of genius in its performance. Not to take anything away from
this feat, it happens that in A.D. 300 the geometer Pappus had actually
found this proof, too. In any case, the question remains: "Who gets the
credit?" Is this intelligent behavior? Or was the proof lying deeply hidden
within the human (Gelernter), and did the computer merely bring it to the
surface? This last question comes close to hitting the mark. We can turn it
around: Was the prooflying deeply hidden in the program? Or was it close
to the surface? That is, how easy is it to see why the program did what it
did? Can the discovery be attributed to some simple mechanism, or simple
combination of mechanisms, in the program? Or was there a complex
interaction which, if one heard it explained, would not diminish one's awe
at its having happened?
It seems reasonable to say that if one can ascribe the performance to
certain operations which are easily traced in the program, then in some
sense the program was just revealing ideas which were in essence hidden-
though not too deeply-inside the programmer's own mind. Conversely, if
(^606) Artificial Intelligence: Retrospects