Ethics and Second-Order Cybernetics - Understanding Understanding: Essays on Cybernetics and Cognition - page 292

cannot be too far away, “All even numbers can be composed as the sum of
two primes.” For example, 12 is the sum of the two prime numbers 5 and 7;
or 20 = 17 + 3; or 24 = 13 + 11, and so on and so forth. So far, no coun-
terexample to Goldbach's conjecture has been found. And even if all
further tests would not refute Goldbach, it still would remain a conjecture
until a sequence of mathematical steps is found that decides in favor of his
good sense of numbers. There is a justification for not giving up and for
continuing the search for finding a sequence of steps that would prove
Goldbach. It is that the problem is posed in a framework of logico-mathe-
matical relations which guarantees that one can climb from any node of this
complex crystal of connections to any other node.
One of the most remarkable examples of such a crystal of thought is
Bertrand Russell's and Alfred North Whithead's monumental Principia
Mathematica which they wrote over a 10 year period between 1900 and
1910. This 3 volume magnum opus of more than 1500 pages was to estab-
lish once and for all a conceptual machinery for flawless deductions. A con-
ceptual machinery that would contain no ambiguities, no contradictions and
no undecidables.
Nevertheless, in 1931, Kurt Gödel, then 25 years of age, published an
article whose significance goes far beyond the circle of logicians and math-
ematicians. The title of this article I will give you now in English, “On for-
mally undecidable propositions in the Principia Mathematica and related
systems.” What Gödel does in his paper is to demonstrate that logical
systems, even those so carefully constructed by Russell and Whitehead, are
not immune to undecidables sneaking in.
However, we do not need to go to Russell and Whitehead, Gödel, or any
other giants to learn about in principle undecidable questions. We can easily
find them all around. For instance, the question about the origin of the uni-
verse is one of those in principle undecidable questions. Nobody was there
to watch it. Moreover, this is apparent by the many different answers that
are given to this question. Some say it was a single act of creation some 4
or 5,000 years ago. Others say there was never a beginning and that there
will never be an end; because the universe is a system in perpetual equi-
librium. Then there are those who claim that approximately 10 or 20 billion
years ago the universe came into being with a “Big Bang” whose remnants
one is able to hear over large radio antennas. But I am most inclined to
trust Chuang Tse's report, because he is the oldest and was therefore the
closest to the event. He says:
Heaven does nothing, this nothing-doing is dignity;
Earth does nothing, this nothing-doing is rest;
From the union of these two nothing-doings arise all action
And all things are brought forth.
I could go on and on with other examples, because I have not yet told
you what the Burmese, the Australians, the Eskimos, the Bushmen, the