Birkhoff believed that the intuitive appreciation stemmed from an uncon-
scious application of the mathematical aspects of his formulas.
If I were to hazard a guess, the complexity of aesthetic factors is highly
likely to serve as a barrier to any sort of aesthetic predictability. Evi-
dence for this is the total inability of husbands to predict what their
wives will appreciate; as against that, wives often seem to have an un-
canny ability to know what their husbands will like. If there’s a theorem
in here somewhere, it wouldn’t surprise me in the least if it is a woman
who finds it.
The Ultimate Questions
Is it possible for mathematics to come up with a way to know where the
dead ends are, or what we cannot know? This book is filled with specific
examples of dead ends that we have circumvented and things we have
found that we cannot know, but is it conceivable that there exists a meta-
theorem somewhere that delineates some of the characteristics of math-
ematical or scientific ideas that are beyond the reach of knowledge? Or is
there a meta-theorem that says it is impossible for a meta-theorem as de-
scribed in the previous sentence to exist?
I think that results in this area are unlikely to be so grandiose, and
that the dead ends and limits to knowledge will arise only in specific
circumstances rather than as the result of an ultimate meta-theorem
about the limits of knowledge. Mathematics can only discuss mathe-
matical objects; although the scope of what constitutes mathematical
objects is continually expanding. As great a mathematician as Gauss
was, he did not foresee the possibility of treating infinities as completed
quantities, and infinities are clearly something he could have consid-
ered to have the potential for being mathematical objects. We do not yet
have the mathematical objects needed to discuss art, or beauty, or love;
but that does not mean they do not exist, only that if they exist, we
haven’t found them. Indeed, if we exist in Tegmark’s Level 4 multiverse,
which consists of realizations of mathematical objects, then since art,
beauty, and love exist, they are mathematical objects; we just have not
found the way to describe them mathematically. Maybe Keats really was
right about beauty being truth, and vice versa; most mathematicians
believe at least half of it, that truth is beauty. If some future Kurt Gödel
manages to construct a mathematical theory of interpersonal relation-
ships, and in so doing proves that there are aspects to love that we can-
not know, how deliciously ironic it would be that mathematics could
Through a Glass Darkly 247