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Complexity, relations, and systems

  
 
6opow
22:05 / 18.07.02
Not wanting to disrupt the Wolfram thread, and never having read him, I thought I'd start a new thread to talk about something that cusm says over there:

...complex systems can be reduced to simple relations and algorythms, and that intelligence can be contained in self-referencing systems.

I tend to think along these lines as well. But I wonder if we are looking at this in the right way? I mean, is it not possible that what we perceive as a "complex" system is really a simple system with "complex" relationships amongst a meagre few fundamental bits?

I am not trying to be facetious here, but am drawing attention to words that hook up in a binary pairing of "simple / complex." (Big surprise, right?) But seriously, it seems to me that the system (complex or not) shares an identity with its relations; that is, the system and the relations within the system are the same thing. We could consider any system as being itself a unit(y). Hmm...this isn't as easy to write about as I'd hoped.

With respect to algorithms, I wonder if such things would exist if there was not a system in which they could be computed. This sorta' carries over from the thread about mathematical truth. The connection, to me anyway, is that algorithms do not exist in some emptiness, but within a world which is populated by objects (these objects can be taken here as numbers or something similar): I do not see how we can isolate the algorithm from its instantiations; that is, the system, the rules, and the parts are a cohesive unit which arises together--not one before or after the others, but all together.

Um...to get back to the quote, I see it maybe as more like complex systems are complex relations seen as such, and the same for simple systems are simple relations. It is a matter of the scope of the observer perhaps?

Also, it seems to me, more and more, that self-referencing is what generates anything. It is a driver because self-referencing generates the possibility of an infinite feed-back loop: self references self, self references self referencing self, self references self referencing self referencing self,... It appears to me that within such a cycle of “almost there but not quite” there is room for anything. What is that quote about there being more in heaven than your_____(insert discipline here) dreams of?

So to get back to Wolfram, it seems to me that anyone who thinks that they've come up with a view that can provide all the answers hasn't. They are only deluded by their own siren song. Haven't we learned yet, from years of paradigmatic turmoil, revolution, and modification, that our arrogance is larger than any allegedly all-encompassing theory?
 
 
Annunnaki-9
14:14 / 19.07.02
I haven't read the Wolfram thing either, but I have read a bit of Douglas Hofstetter (sp). His work on A.I. is based (or was so the last I heard) on this self-referencing notion you bring up above. In fact, I think in 'Godel, Escher, Bach,' he argues that any living system, be it a work of vibrant art, a solid and sustaining philosophy, or a sound mathematical theory is indeed self-referencing.
 
 
cusm
20:32 / 19.07.02
Well, for starters, the terms "complex" and "simple" in regards to systems are inherently flawed as what makes a system "complex" or "simple" is the subjective understanding of the observer. While still useful descriptors, this should be kept in mind and not treated as any sort of definitive description of a system. All systems have a certian level of complexity. The key issue here, is that the basic algorythm or relation that gives rise to the system of many elements may indeed be of a "simple" nature, and by that one of few elements or relations.

I like to think of it in terms of an equation. An equation is a relation between elements, consisting of variables. Say, ax^2+by+c=0. A fairly simple relation in that I can express it in so few terms. Yet, when data is entered into the system (for values of a b and c), values of x and y (as relative to each other) are generated forming what can be a rather complex graph. When you look at just the graph alone, you see a complex set of data, or a system of data. But in examination of that system, you may be able to determine its patterns and reduce the data down to an equation to represent it through mathmatical abstraction. I think this is much the same process Wolfram is suggesting.

As a real work example, DNA. At its basic level (if I remember correctly) it has something like 4 bits in a series of 23 cromosomes. Yet, this strand of 23x4 elements can expand to a data set so complex as to give rise to a system as myself, capible even of examining the system which brought it to be or even making changes to that system for the sake of improvement of the whole. There's some deep self-referencing for you.

So we've mapped the genome of DNA, we understand (to a certain degree) what the data in the DNA strand represents. What we do not understand is how to use the data to create the system it represents, the rather complicated algorythm encoded in RNA used to translate this data. But if we understand the ways in which the chemical elements relate on the basic level, we find a set of rather simple rules and relations which governs the entire system. We do not understand the system, but we understand that if the data is subjected to interaction according to this algorythm, the data in DNA and RNA interact to create the data system that is ourselves.

Its like the example of the neural net. We can build large ones due to the basic function of the neuron being simple, but we can't understand how they function on higher levels. But one may argue that we don't have to understand how the system works if we know how to build and use it. Empowering, if not enlightening. Certainly a different approach, and a valid one, though hardly a reason to abandon attempts at understanding the system itself. A little from column A, a little form column B.
 
  
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