Universal

SATURDAY, JUNE 7, 2008

    

What is Universal?

What is universal?    

Nothing is. (rather, there does not exist something which is universal).

Universality is a partial order (see previous post), which orders according to ability to be translated without significant loss of meaning. The statement “I am hungry” is more universal than the statement “Mayor Madison manufactured a million magnesium missiles” for a variety of reasons. First of all, the context of the second statement demands an understanding of what a mayor is. We’ve had similar town officials in most civilized regions and times, but the meaning changes significantly if we go far enough back, or far enough away. Next, Madison is a name. This is more or less arbitrary; unless of course you know that the Madisons are a particular family with a particular public standing. “Manufactured” cannot exactly translate to “made,” so context requires understanding of post-industrial revolution production. Similarly with “missiles.” “Magnesium” will not translate easily to a society without a periodic table of the elements, and even “million” is inexplicable to a primitive tribe with a number system consisting of the four quantities {1, 2, 3, many.} Et cetera. Furthermore, the sentence strikes any English speaker as having been concocted to alliterate. Therefore, it can be argued that this is part of its meaning, so that translation to a foreign language becomes much more difficult. On the other hand, every society on earth has a word (or hand signal) for “hungry” and in particular some way to declare being in this state (regardless of whether the subjective pronoun is explicitly used). (Think, also, of different ages of individuals, or different levels of accessibility: an uneducated child has a way of saying the first sentence, no way of even understanding the second).

Context, in the above paragraph, is at the scale of societies of humans. We also can speak of the context of certain species. “I am hungry” can be translated to the lexigram language of the bonobo monkeys, whereas we doubt that it’s even meaningful to consider translating this to something a tree would understand (“understand”?!). We can go in the other direction too, of specificity. I can create words I never share with anyone, which refer to complex memories or particular synesthetic experiences such as a smell which reminds me of a shade of brown. Now the problem of translation is between individuals and not societies or species. 

We can arrange academic disciplines according to this partial order. I contend that physics and mathematics are more or less at one end and poetry and film theory are at the other. Not that there couldn’t be personal theories which are significantly less universal than film theory, I believe there are. Nor that there might not be some way of understanding the universe which is more universal than mathematics, but this is much harder to conceive of, indeed an example would most illuminating!

Here I must warn myself that things are not as easy as a partial order, exactly. Advanced mathematics is not very universal in the context of the human race. So here what appear to be most universal are simple statements, referencing basic animal desires. Still if we are to find any common ground with an alien species, especially one that can traverse great distances of intergalactic space, we assume they have a language for expressing “a^N+b^N=c^N, a,b,c,N positive integers, has solutions only for N=1,2”, (which neither the bonobo nor the hobo do (though the hobo could be taught, which is a form of translation)) before we assume they can relate to “hunger.” I.e., on a grand scale, universality is not about accessibility, but about the ability to be translated between contexts which arose more independently. 

(I am willing to admit this may not be the best definition of universal. It seems there are qualities and states such as pain and pleasure, experience, and desire that are arguably more universal than particle physics. There is probably a lot more to say here, but I haven’t thought it out).

I am interested in the common ground which is necessary for translation–those suppositions which some discipline is predicated on–as a measure of that discipline’s universality. Literary theory, for example, requires not only experience with the texts but also the cultural and historical context to parse what has been written. Chemistry, on the other hand, is predicated on the identification of elements and distinguishing elements from the molecules they form. Mathematics is predicated on the notion of a collection of things and on the simplest possible relationships and patterns common to different situations: number, order, position.

How then could I claim mathematics is not universal? the child/monkey/homeless man example is one direction to go. We could even conceive of an alien race who appear to be technological but who have no explicit mathematics, surely. A more interesting direction to substantiate this claim: we can consider mathematics a tool to compensate for weakness. In this way we can argue that mathematics belongs only to the context of beings that need to recognize common patterns in different situations. 

This point is subtle but worth investigating. Nor does it make mathematics very context-dependent. But it does suggest “universal” may not be a quality at all (in that nothing can posses universality), but necessarily only some sort of partial order.

How could mathematics be a tool to compensate for weakness? It can be argued that a great deal of our faculty for analysis originated in the survival mechanism of thinking something out, conceiving of a plan, understanding the nature of animals and plants and ourselves. Also of communicating the results of thinking things out. Of having language for any and all thoughts. If there was never a necessity of survival to communicate we wouldn’t have theories, as we do. Could a creature evolve such that it was able to perform seemingly mathematical or technological feats without having a theory of same? well of course! the birds have no theory of flight, yet to us this is a feat requiring great skill in mathematics and physics. Could the equivalent of flying birds exist, but instead as interplanetary flight? There is no reason why not. Even more so, could it be possible that a creature exists not merely born with an instinct to perform a specific, highly skilled action, but with a subconscious mind that does all the learning and processing and inventing, while a conscious mind observes only desires and suffers a very limited vocabulary, much like a child? This is entirely conceivable. One such creature builds the first space shuttle and upon being asked the question “why?” it says “well tommy built an airplane, it flies, so I wanted one too, but one that goes out into space.” Upon being asked the question “how?” I suppose it says something like “well it has to be able to go fast, and made from really good stuff,” all other details being obvious and trivial, and interpolated with the advanced instinct these creatures have.

So perhaps it is not as simple as a partial order, after all. My theory of consciousness as a partial order may have fallen apart, as well, though I have an idea to resurrect both, in new and more robust form! That’s for next post, but now I’ll conclude with God’s lack of mathematics.

It seems reasonable to talk about God as some sort of limit (in the mathematical sense) of the partial order of consciousness. Little omega, a limit ordinal. Still the singularity of God’s mental capacity puts God in a completely solitary context. I don’t buy the model of God and humans as actors with free will, capable of interacting and learning from each other. It makes no sense to me. An omniscient being has no need for communication, does not answer questions. I don’t know, this area is difficult because the concept of omniscience isn’t even comprehensible, may not even make sense at all. Still, to the extent it does make sense, recognizing patterns is not a necessity of such a creature. That is, if you know everything, you have no need to identify the commonalities between different atoms and classify them all according to a model atom and call them “atoms.” Instead you have every possible nuanced difference of matter available to your imagination, and you observe the universe without any reason to compare atoms, since no two are alike anyway. Interestingly, I imagine a sequence of creatures which converge to this God, and each has more and more theories and levels of mathematics and abilities to identify patterns, yet in the limit all these dissolve. Though, as I’ve suggested here, there are probably other sequences of creature which converge to the same God, without language or theories. At some point you have to know all the theories of mankind, possibly all the possible theories, since this is arguable anything in the universe which can be known.

Advertisements

Leave a Reply

Fill in your details below or click an icon to log in:

WordPress.com Logo

You are commenting using your WordPress.com account. Log Out / Change )

Twitter picture

You are commenting using your Twitter account. Log Out / Change )

Facebook photo

You are commenting using your Facebook account. Log Out / Change )

Google+ photo

You are commenting using your Google+ account. Log Out / Change )

Connecting to %s

%d bloggers like this: