As a retired college professor, I have been surprised by the fact that the implications of one of the most important intellectual ideas in the history of mankind, Gödel's theorem, has not yet penetrated very far into popular culture. In our society, most college educated individuals are generally aware of the implications of the ideas of Galileo (we do not live at the center of the universe), Darwin (humans are not as distinctly different from other animals as we previously thought), Freud (our behavior is often not guided by rational thinking), Einstein (some of our basic conceptions of space and time are wrong), Heisenberg (there are fundamental limits to what we can ever know about the properties of the physical universe). However, few individuals have any awareness of the implications of Gödel's theorem, which are as profound as any of the others enumerated in my short list. Thus, I greet with pleasant surprise the recent film scripts written by Andy Kaufman (Being John Malkovitch, Adaptation, Eternal Sunshine of the Spotless Mind). These films provide

So what are the implications of Gödel's theorem? To understand these implications consider a related example: attempts to build a perpetual motion machine. Schemes to accomplish this were worked on for centuries, but they have now completely stopped. Why? The reason is that once the laws of thermodynamics were understood it was realized that the entire enterprise of trying to build a perpetual motion machine was doomed to failure. It could be demonstrated, based on first principles, that the goal can never be achieved, so it is a waste of time to continue working on it.

Next consider an intellectual enterprise that had been embarked upon by human thinkers since before
the time of Euclid's geometry -- the enterprise of building, from the ground up, a formal mathematical/logical
system within which all mathematical/logical propositions could be demonstrated to be either true or false. The
pinnacle of this enterprise was *Principia Mathematica*, published in 3 volumes by Russell and
Whitehead in 1910, 1912, 1913. This
entire enterprise
has now been shutdown. Why? Because, Gödel, in his paper published in 1931, demonstrated that
this goal can never be accomplished so it is a waste of time to continue working on it. Gödel demonstrated
that within any formal system, it is possible to construct perfectly valid mathematical/logical propositions that
cannot be proven to be either true or false.
Attempts to try
to evaluate these propositions within the formal system can result in what
Hofstadter (D. R. Hofstadter, *Gödel, Escher, Bach*, Basic Books, 1979) calls strange loops.
Constructs
that lead to strange loops involve "self-reference". I do not know whether or not Charlie Kaufman
has embarked on a consciously explicit attempt to translate the implications of Gödel's theorem to film, but
in his previous screenplays (Being John
Malkovich and
Adaptation), he is obviously using the concept of "self-reference" to create cinematic strange loops.

In his
current film, Eternal Sunshine of the Spotless Mind, Kaufman goes a step further
in exploring the implications of Gödel’s theorem.
There is another puzzling property of Gödels theorem that I did not mention earlier. I stated
that it is always possible to construct
perfectly valid mathematical/logical statements that a formal system cannot evaluate in terms of whether the
statements are true or false. But what is in some ways even more surprising is that
humans/mathematicians can often evaluate these
same statements and come to agreement about whether they are true or false.
Some have argued that this proves
humans possess cognitive skills that are not based on following formal systems of rules.
Instead, humans can make use of
mysterious psychological faculties such as intuition. If correct, this
argument demonstrates that our brains do not operate by the same kinds of rules as formal systems.
Another implication is that it will
never be possible to build a computerized robot that can think the
way we humans think. The mathematician Roger Penrose constructed an elaborate
argument (R. Penrose, *The Emperor’s New Mind*, Oxford University Press, 1989)
that the mysterious human intuitive properties are enabled by
some characteristics of quantum physics operating in brain tissue. (Not
everyone one agrees with the assessment that humans possess mysterious
mental faculties impossible to duplicate in
any formal system but the counter-arguments would take way too much space to lay out here.
Some of these same issues are discussed, in a different context, in my own book (R Boothe,
*Perception of the
Visual Environment*, Springer-Verlag, 2002). This brings us to the current movie.

The Eternal
Sunshine of the Spotless Mind dramatizes a battle between a
formal system that is trying to wipe out memories located in brain tissue and psychological faculties
operating within this same brain tissue. The psychological faculties appear to be doomed, but wait! By employing
clever (human/mysterious ?) intuitive reasoning, these psychological faculties may be able to outwit
the formal system. To find out, you will have to watch the movie. I found watching this movie to be a fun ride
into and out of a strange loop.

I gave this movie a rating of 4 stars.

Ron Boothe