[FOM] mathematics as formal

[Steven Ericsson-Zenith]

On Mar 25, 2008, at 2:00 PM, Timothy Y. Chow wrote:
> Here is a way to approach the question of the "mathematics of  
> aliens" that
> is (perhaps) not entirely speculative.
>
> ... 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.

Yet our species has a clear structural advantage given the opposable  
thumb. We are able to place detailed records in the world that are  
identifiable and accessible to future generations. We construct vast  
legacies of these records. I will argue that this is not simply  
because we are "intelligent" in the sense that we have an  
extraordinary brain.

Dolphins, for example, have brains that seem much more sophisticated  
than ours, yet they lack the structural capacity to record and  
preserve for future generations. With our new technological capacity  
we could actually put this to the test by providing a community of  
dolphins with that capacity.

So there does appear to be a structural requirement that would forbid  
the type of intelligence that our species manifests in species without  
that structure, aside from any requirement to actually develop a  
nervous system.

> 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.)

Memory of some kind seems an obvious requirement (and some form of it  
may be pervasive). However, I have come to believe that our own  
physiological capacity for memory is really very primitive/poor (and  
ultimately inadequate for our intellectual goals) and should likely be  
something that is improved upon in more advanced species.

It is feasible, perhaps, that a species could develop such an extreme  
and vivid memory capacity and the mechanisms to transmit such memory  
to others (in ways different from our own) under pressure of natural  
selection. Those circumstances do not exist here but may elsewhere,  
and if they existed could circumvent the structural requirement I  
mention above.

> But
> whether the aliens would necessarily have "mathematics" is less  
> clear to
> me.

Arithmetic and Geometry seem to be necessary precursors to a broader  
"mathematics" and they are the necessary product of reference.  
Assuming that all communications among species members require an  
increasingly refined response to the questions "Where?" and "How  
many?" I do expect mathematics to be a universal characteristic of  
higher forms of intelligence.

Now whether or not they find prime numbers at all interesting really  
depends upon how useful it is perceived to be to investigate the  
matter. We have discovered, it seems, that apparently idle pursuits  
(such as deep inquiry) occasionally produce remarkable insights into  
the world, and that the discovery of these insights provides the  
species with some equally remarkable benefits.

> 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.

I agree.

With respect,
Steven

--
Dr. Steven Ericsson-Zenith
Institute for Advanced Science & Engineering
http://iase.info
http://senses.info