[FOM] mathematics as formal

[Timothy Y. Chow]

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  
>a consideration.

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 
me.

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.

Tim