[FOM] mathematics as formal
Timothy Y. Chow
tchow at alum.mit.edu
Tue Mar 25 17:00:30 EDT 2008
Steven Ericsson-Zenith <steven at semeiosis.org> wrote:
>It seems to me that whatever their appreciation of prime numbers, they
>are at least as likely as we to evolve a genuine curiosity about the
>nature of apprehension and logic, and to arrive at some conception of
>it. Indeed, the simply observation of prime numbers and that they
>possess a universal quality absent in other conceptions is due to such
Here is a way to approach the question of the "mathematics of aliens" that
is (perhaps) not entirely speculative.
Our popular understanding of aliens has been strongly influenced by
science fiction literature and film. Although I enjoy science fiction,
there is a danger in relying too much on it when thinking about actual
aliens. For a work of art to be widely successful, it must appeal
emotionally, and this economic fact forces artists to develop aliens that
are very much human, in the sense that they typically communicate with
human beings using human languages, share the same sorts of concerns that
human beings have, and so forth.
The environment on real planets is not constrained by the need to entice
human beings to open their wallets, so it seems to me that if there is
extraterrestrial life, it will more likely resemble bacteria or plants or
possibly insects than humans.
The fact that terrestrial bacteria/plants/insects are not "intelligent"
according to our usual notion of the term shouldn't, in my mind, preclude
us from imagining that there might be extraterrestrial life that is
"structurally" similar to bacteria/plants/insects but that is still
"intelligent" in the sense of having the ability to manipulate the
environment in sophisticated ways in order to promote its own existence.
I think it's an interesting question whether the development of advanced
*technology* requires the development of advanced *science*. That is,
suppose we discover some alien life that has what we regard as advanced
technological means of building machines to aid in transportation,
nutrition, weaponry, etc. Suppose further, just to help break old habits
of thought, that these aliens resemble terrestrial bacteria more than they
resemble any other terrestrial life form, and that we cannot figure out
how to "talk" to them (perhaps because they seem completely uninterested
in communicating with us). Do we expect that such aliens necessarily have
"science" and "mathematics" that enable their technology?
It seems intuitively to me that some form of *memory* would be necessary
for advanced technology. (By using the word "memory" I don't want to
imply that the aliens are necessarily "conscious" (whatever that means);
the storage medium could take on any of a wide variety of forms.) But
whether the aliens would necessarily have "mathematics" is less clear to
The reason I believe that these questions are not entirely speculative is
that one might, in principle, be able to build such "alien life forms"
here on earth. The question of whether "aliens" with advanced
technological capabilities could be constructed without slavishly
mimicking human (or for that matter, any known biological) systems then
becomes an empirical question.
We are probably a long way off from being able to perform such
experiments, but it seems to me that if we could, we might learn some
truly foundational facts about mathematics and science that are not
currently apparent to us.
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