Recursion and Infinity

According to Chomsky, a fundamental property of language is that any grammar can produce infinitely many sentences. However, an ethnographic study on the Piraha tribe of Brazil reveals that there is a grammar which lacks recursion, and is thus only capable of producing a finite number of possible utterances. My first reaction to this was: impossible! As I read through the article I noticed some things, and I basically want to sketch out a few of the things that I noticed.

The essence of human language is, according to Chomsky, the ability of finite brains to produce what he considers to be infinite grammars. By this he means not only that there is no upper limit on what we can say, but that there is no upper limit on the number of sentences our language has, there's no upper limit on the size of any particular sentence. Chomsky has claimed that the fundamental tool that underlies all of this creativity of human language is recursion: the ability for one phrase to reoccur inside another phrase of the same type. If I say "John's brother's house", I have a noun, "house", which occurs in a noun phrase, "brother's house", and that noun phrase occurs in another noun phrase, "John's brother's house". This makes a lot of sense, and it's an interesting property of human language.

http://www.edge.org/3rd_culture/everett07/everett07_index.html

On this level, we have the last output of "John's" being re-entered into the meaning, so that we know it isn't John we're talking about, but his brother's house.

Let's contrast this to what the Piraha would say:

So in the case of Pirahã, the language I've worked with the longest of the 24 languages I've worked with in the Amazon, for about 30 years, Pirahã doesn't have expressions like "John's brother's house". You can say "John's house", you can say "John's brother", but if you want to say "John's brother's house", you have to say "John has a brother. This brother has a house". They have to say it in separate sentences.

On the level of the sentence, there is no possibility of chaining possessives, but the overall meaning of one sentence is carried over into the next and in fact it would make no sense to say "this brother" without the preceding sentence. "This brother" in fact refers back (self-refers, calling itself...) and is therefore fundamentally recursive. Because the chunking system does not allow recursion within sentences, it must allow recursion between sentences. "This" is an earmark of recursion because it is infinitely various, it refers to "the last thing" and is still built on LISP-like linked list principles which are different from "Infinite Language" that "uses recursion" only insofar as the rules which allow it to be employed.

Recursion is not permitted on the level of the sentence, because the sentence, like a word in English, conveys a single thought. On some level, every language is finite. Containing a finite set of agreed upon meanings regardless of articulation. The finitude in fact allows us to define. Without it, everything would remain undefined.

The endlessness with which such a culture could string their sentences together shows me that the set of all things described in tandem is up to the author's attention to detail, and does not limit the possibility of what things can be described. It may refuse certain possibilities but (Infinity - Any number), does not mean that number is finite.

At any rate, my only knowledge of this culture is from the aforementioned article so I take it on faith that these people have violated one of Chomsky's laws. However, we can still say that recursion occurs within this language, so Chomsky's law can be relaxed without causing a cascade failure of Chomskyan linguistics. My only point in making this argument is to corrupt previously held ideas about finite-ness and recursion. The idea of referencing back is necessarily recursive, in fact "this" is a tell tale sign of recursion. But perhaps not the kind Chomsky is talking about.

The Opening of Closure II

In any one single statement, the implications of the fact of its capacity to be stated, is implicit in the meaning of the statement. A single statement means the entire reality in which it is produced, there are layers upon layers overlain in a sequence of causes which extends back to the beginning of time.

Closure is an effect of separation. There is no such thing as a discontinuity between an single individual and everything else.

The Opening of Closure

The first time I read The Rejection of Closure I had a very emotional reaction to it. Perhaps because I am a naturally irate person, or perhaps because I felt there was an advocacy for something I couldn't abide. I haven't read Lyn Heijinian's text in a very long time, but I'm always struck with the same problem: closure can not be opened by rejection. Rejection is a kind of closure. Closure turned on closure. When we reject something we deny its possibility. The very fact that could be "true".

The target is closure. The strategy is closure. The system is rejection. When we think about closure, we can think of it along an isomorphic echo as encasement, encapsulation, containment, envelopment, often in terms of human affect as being "closed off", or "not open", or "not-openminded." And it's really there that we get stuck.

In the end you're left with another kind of closure. A tacit acknowledgement in the reality/possibility of a "closure" and the rejection of part of that reality. I have in my lifetime found it far more liberating to reject the possibility of a closure. There is always a veritable regress of information implicit in even the simplest of utterances.

Self-Similarity

Throughout the course of my work, I've implicitly made reference to a type of similarity which also different, giving numerous interpretive schema along the way that was capable of at least tacitly accounting for this repetition. The foundation for this has been a thorough investigation into fractal geometry in which each part of a whole is more or less an exact copy of the whole. That is to say, if you take a look at a fractal, and then proceed to zoom in at various scales of magnification, the fractal will keep its overall shape, or you will be able to see little copies of the whole as you zoom in. This is known as self-similarity.

The sort of logic that can be drawn out of such a shape is one of scale invariance. To use a social sciences example, the same laws that apply to individuals, would apply en masse to societies, cultures, groups and so on.

During the course of my work, I have tried to point out the fractal nature of self-referential utterances such as $This Sentence is False$ which relies on a specific kind of recursion. That is to say, the last output becomes the next input into the function. This sort of recursion is implicit to fractality and is also a prevalent motif in Hofstadter's great work _Godel, Escher, and Bach_.

The eternal golden braid is the helicoid acid and holomorphic structure of none other than the bodies that constitute life. They too have an image of the whole present at each indivisible unit known as the cell.

The implications of this self-similarity resound within a new geometry in which each of the parts reflect each of the other parts within a reflexive and undifferentiable matrix of re-entry.

This (to a certain extent) can resolve the paradox of Western Ontology which was discussed in the Lossy Compression post.

It will be interesting to see how far self-similarity and fractal geometry can be taken as literary devices.

Cascade Failure

We've, I've begun to think, identified ourselves ideologically with our strategies. The strategy of more government, more “oversight”, more “supervision” or less of it. As a result, we've failed to see an important part of the overall picture.

Namely, the corporate controlled government is no better than a government controlled capitalism. In fact the two, coming from different directions as they do, amount to the same thing, the emergence of a surveillance based fascism where the activities of the individual are all dictated from a single source. The question that we need to sit down and consider is to what extent this isn't already the case.

The impulse of the corporation is in fact the same as the impulse of the government: to consolidate power. Mergers and buyouts are the name of the game. Amass as much of the market as you possibly can. The latest company to prove this true is Microsoft.

The only way to thoroughly separate the government from its market, is for it be regarded as a conflict of interest to represent both the interests of a corporation through the government. In fact, what you have now is corporate controlled capitalism, which is sliding into a state controlled capitalism.

By and large the reason that this happened was that we had a fiscal conservative in GWB who outspent his “liberal” predocesser while simultaneously lowering taxes. It was a deficit that could only cause one outcome: bankruptcy. I believe that Barak Obama inherited this deficit from Bush Era spending. Bush in fact is perhaps the worst president in American history. Here is a quick look at his resume: http://politicalhumor.about.com/library/blbushresume.htm.

It is ironic that his failure is so abolute in large part because he is a terrible businessman. The delicate balance achieved by former presidents was thrown completely out of wack. It could be argued that bankrupting the federal government is a really effective way to weaken it, and may very well have been intentional.

Now, if I'm philosophically committed to a decentralist impulse (which I am) how do I reconcile the fact that I think this is one of the worst catastrophes in American economic history with a weakened federal government teetering on the brink of death. On some level, we must face the fact, that this was by and large, a corporate orchestrated attack, and face down the realization that the oil companies have more government protections and personalized government influence than any other corporate power in America (other than perhaps banks).

So the real question becomes, what in pragmatic reality would happen if we allow the current federal government default on it's debt? The answer is something akin to an apocalypse (generally speaking) this is the terminology that has been used to describe it. The following results are probable:

1.The dollar would be worthless
2.Lending would stop
3....causing a large portion of the population to lose their jobs
4....businesses would shut down, collapse and the burden of unemployment benefits would fall on bankrupt companies, and the federal/state government
5.Mass bankruptcy
6.Famine
7.Most of our debt would fall to China

Many Republicans in congress have signed a pledge not to raise taxes, and this is primarily the reason why we cannot balance the budget, and why the debt ceiling keeps climbing. My sense of this is that while philosophically I'm opposed to it, the burden of higher taxes, must be borne in order to avoid a cascade failure of epic proportions. The New Deal is irrelevant if we don't have the money to borrow and our credit is worthless. There won't be any deal at all because there won't be anything to deal with. For the time being, the debt ceiling must rise, and if it is not going to rise again we must figure out to avoid an inevitable situation like this one from recurring, or else we won't face any more easy choices.

The Western Metaphysic of the End

Continuing from Lossy Compression

The issue then becomes not one of modeling, or mapping, but containing. The problem of the essence-that-contains is one of generality. Western Ontology is deeply rooted in the desire to set everything under a solitary system. The problem of the system is on the one hand a matter of properties becoming objects, and adjectives becoming nouns, it is also irresistably reconfigurable, and herein lies its redemption. The category is not a set containing objects, but a blueprint from which many models can be built. The category as an object of realism, a reality, objectifies each of its members by reducing it to a subset of qualities.

In the end of it all, you are left with a black hole signifier, that sucks everything under one sign. Even the qualativity of qualities, or an essence of the essence can begin to collapse this system, for its own externalization of this blueprint impresses it onto reality, and thus comes to manufacture reality. This is both “the Language of Eden” and the “Curse of Revelation.” What God would leave out of the Bible, is the fact that we are agents in our own creation. To a large extent, we've been making it up all along.

With our history mostly scripted by our mythologies, hurdling toward an apocalypse that even scientists are beginning to buy into, the majority of the resistance is ironically coming from a Christian dominated right.

Their arguments are based at least partially on science, citing a liberal usage of rate multipliers in producing projections.

At any rate, the multipliers do impact how the projections would pan out. The seemingly alarmless rate of one degree over the past 100 years has mollified the possibility of any consensus. The oil companies stand the most to lose and can no doubt afford to fund their own research projects. Since the oil companies have been a major target of environmentalists, one of the few government controlled industries within our sense of capitalism, the issue is on both sides politicized. The sense that one can take either side in earnest is intellectually dishonest. The speculations are all over the place for the projections. We could end up like Venus, or we'll kill off ourselves but life will continue. It's certainly possible that some tipping point will be reached triggering a chain reaction, which causes some sort of atmospheric cascade failure and kills off everything or most of everything. Maybe only insects survive, or bacteria. Certainly this is frightening to contemplate. And worse still it is all distinctly feasible.

So it's an interesting point for Western metaphysics. Will it have its apocalypse after all? Has our blueprint for disaster finally been realized? Never has it been more cleverly argued than by environmental scientists and perhaps never before has been felt the more pressing reality of an end that has been enacted several times before in history.

But the end is everywhere in every disaster, and apocalypses proliferate. Beasts are indeed everywhere, whores of all sorts, but no horsemen yet. We fantasize about it in movies and books. Two series in the last ten years dealt specifically with the apocalypse. Jericho and Jeremiah. Both were cancelled after showdowns with fascist police states. So we survive, perhaps, but suffer the death of our way of life.

But whatever the outcome, this will be remembered as a time when apocalyptic fears were very real.