Darwin's Dangerous Idea - Evolution and the Meaning of Life

130 THREADS OF ACTUALITY IN DESIGN SPACE Forced Moves in the Game of Design 131
explored this curious question, and his ingeniously reasoned answer is No. In
"Why Intelligent Aliens Will Be Intelligible," he offers grounds for believing
in something he calls the
Sparseness Principle: Whenever two relatively simple processes have products
which are similar, those products are likely to be completely identical!
[Minsky 1985a, p. 119, exclamation point in the original.]
Consider the set of all possible processes, which Minsky interprets a la the
Library of Babel as all permutations of all possible computers. (Any computer
can be identified, abstractly, as one "Turing machine" or another, and
these can be given unique identifying numbers, and then put in numerical
order, just like the alphabetical order in the Library of Babel.) Except for a
Vanishing few, the Vast majority of these processes "do scarcely anything at
all." So if you find "two" that do something similar (and worth noticing), they
are almost bound to be one and the same process, at some level of analysis.
Minsky (p. 122) applies the principle to arithmetic:
From all this, I conclude that any entity who searches through the simplest
processes will soon find fragments which do not merely resemble arithmetic
but are arithmetic. It is not a matter of inventiveness or imagination,
only a fact about the geography of the universe of computation, a world far
more constrained than that of real things.
The point is clearly not restricted to arithmetic, but to all "necessary
truths"—what philosophers since Plato have called a priori knowledge. As
Minsky (p. 119 ) says, "We can expect certain 'apriori' structures to appear,
almost always, whenever a computation system evolves by selection from a
universe of possible processes." It has often been pointed out that Plato's
curious theory of reincarnation and reminiscence, which he offers as an
explanation of the source of our a priori knowledge, bears a striking resemblance
to Darwin's theory, and this resemblance is particularly striking
from our current vantage point. Darwin himself famously noted the resemblance
in a remark in one of his notebooks. Commenting on the claim that
Plato thought our "necessary ideas" arise from the pre-existence of the soul,
Darwin wrote: "read monkeys for preexistence" (Desmond and Moore 1991,
p. 263).
We would not be surprised, then, to find that extra-terrestrials had the
same unshakable grip on "2 + 2 = 4" and its kin that we do, but we would be
surprised, wouldn't we, if we found them using the decimal system for
expressing their truths of arithmetic. We are inclined to believe that our
fondness for it is something of a historical accident, derived from counting
on our two five-digit hands. But suppose they, too, have a pair of hands, each
with five subunits. The "solution" of using-whatever-you've-got to count on
is a fairly obvious one, if not quite in the forced-move category. 3 It would not
be particularly surprising to find that our aliens had a pair of prehensile
appendages, considering the good reasons there are for bodily symmetry, and
the frequency of problems that require one thing to be manipulated relative to
another. But that there should be five subunits on each appendage looks like a
QWERTY phenomenon that has been deeply rooted for hundreds of millions
of years—a mere historical happenstance that has restricted our options, but
should not be expected to have restricted theirs. But perhaps we
underestimate the Tightness, the rationality, of having five subunits. For
reasons we have not yet fathomed, it may be a Good Idea in general, and not
merely something we are stuck with. Then it would not be amazing after all
to find that our interlocutors from outer space had converged on the same
Good Idea, and counted in tens, hundreds, and thousands.
We would be flabbergasted, however, to find them using the very symbols
we use, the so-called arabic numerals: "1," "2," "3" ... We know that right
here on Earth there are perfectly fine alternatives, such as the Arabic numerals,
" I," "v," " v," "i" ... as well as some not-so-viable alternatives, such
as roman numerals, "i," "ii," "iii," "iv" ... If we found the inhabitants of
another planet using our arabic numerals, we would be quite sure that it was
no coincidence—there had to be a historical connection. Why? Because the
space of possible numeral shapes in which there is no reason for choosing
one over the others is Vast; the likelihood of two independent "searches"
ending up in the same place is Vanishing.
Students often have a hard time keeping clear about the distinction between
numbers and numerals. Numbers are the abstract, "Platonic" objects
that numerals are the names of. The arabic numeral "4" and the roman
numeral "IV" are simply different names for one and the same thing—the
number 4. (I can't talk about the number without naming it in one way or
another, any more than I can talk about Clinton without using some word
3. Seymour Papert (1993, p. 90) describes observing a "learning disabled" boy in a
classroom in which counting on your fingers was forbidden: "As he sat in the resource
room I could see him itching to do finger manipulations. But he knew better. Then I saw
him look around for something else to count with. Nothing was at hand. I could see his
frustration grow. What could I do?... Inspiration came! I walked casually up to the boy
and said out loud: 'Did you think about your teeth?' I knew instantly from his face that he
got the point, and from the aide's face that she didn't. 'Learning disability indeed!' I said
to myself. He did his sums with a half-concealed smile, obviously delighted with the
subversive idea." (When considering using-whatever-you've-got as a possible forced
move, it is worth recalling that not all peoples of our Earth have used the decimal system;
the Mayans, for instance, used a base-20 system.)