Symbols and topology

In Douglas Hofstadter's book, Gödel Escher Bach an Eternal Golden Braid he goes into great detail on how inanimate matter can become conscious without the coexistence of some higher metaphysical entity such as the soul. His argument boils down to a relatively simple, if highly non-intuitive concept. It goes as follows: given a set of objects (say, for example, ants, or birds, or slime mold cells, or neuron cells, you get the picture...) there exists a set of interactions between the objects that allows them to organize themselves spontaneously. This is similar to some of the arguments presented by Steven Strogatz in his popular novel Sync, and I sort of eluded to it earlier in the post Order for Free. Once these objects organize spontaneously symbols can be encoded in patterns within these objects. These symbols are usually higher order phenomenon that are represented in the way in which the objects orient themselves in space and time. Hofstadter writes a clever interlude about a bunch of ants, where each ant is mindlessly going about its business, but the collective of ants is able to perform complicated interactions at a different level than the individual ants. A symbol is a tough object to define because it is highly dependent upon the context in which it resides. Random noise could be described as a pattern of sorts, but random noise does not have a few essential features that makes it symbol-like. A symbol has to be robust, insomuch as that it can have a variable response to similar inputs or parameters in its environment, but the variable response can not exceed a critical threshold such that the behavior of the system can not be distinguished from random behavior. This is very likely a very subtle point which may take some serious further investigation.

What do symbols do? Well that is a very good question. In my last post (The Adjacent Possible) I talked about the extra flaps of skin on the squirrel from Kauffman's book. This is a symbol of sorts, because it is a pattern among the spatio-temporal distribution of squirrel cells. The devil is in the details of course, because there are any number of other "patterns" in the spatio-temporal distribution of squirrel cells, but the key question is what patterns are important and which ones exist but do not serve any purpose. This begins to border on philosphical (and therefore there could be less opportunity to dissect analytically) for a few reasons. First of all, the idea of purpose is a little strange here, because the flaps of skin do not know anything about their greater purpose. Very likely they are the result of some random mutation or series of random mutation in a growth plan of the skin along the sides of the squirrel. There is probably a complicated network or series of networks of cellular signaling that determines the orientation, density, and type of epidermal cells that span this extra flap of skin. It seems unlikely but not necessarily impossible that a single mutation could produce such a pattern, but the point is that because of some change in the overall system of the squirrel, a new robust phenomenon has arisen. This new pattern, or symbol as it were, leads to a whole new functionality, which opens up an entire new region in the phase space of possible "spatio-temporal orientations" for not only the skin cells in the flaps of the flying squirrel, but also for future generations of squirrels. Yet this new functionality could quite possibly never be discovered without the occurence of a totally different event (the hawk!). And this is where the layers of stochasticity become coupled to the symbol (pattern). Mutation initially creates this pattern by feeding variation into the bottom of the system. This variation percolates up through the layers of organization and through some very likely complicated series of causes and effects (that probably are impossible to predict ab initio) which produces the new pattern or symbol. Yet at the top layer, the hawk has to come swooping in so that the squirrel can jump out of the tree and fly. If the squirrel never deviates from its normal behavior than it will never discover the greater functionality, or new region of phase-space that has opened up, and future generations of squirrels will be less likely to benefit from this beneficial pattern.

Symbols are usually used in a more abstract way than flaps of skin on a small furry mammal. Yet, this circles back to the original idea. The squirrel example adds a lot of added complexity, what with selection, additional stochastic processes, the the phenomenon of skin flaps being at such a high level in organization that the transition between the very basic level (say the genes) and the phenotype (the flaps) is anything but transparent. Yet going back to Hofstadter's ants, or an even more general example, with some even more boring agents, it seems possible that there exists any number of interesting behavior or symbols given the right rule set between the ants. The question becomes, can such rule sets be found such that the behavior of the ants (or agents) is something both interesting and useful in some manner? And by interesting I mean that it is robust, it responds to various inputs or initial conditions in dynamic and sometimes unpredictable ways, and that there is also something novel about the behavior.

This is a very hard idea to explain, but here it is worded differently: how does one distinguish mutliple levels in the system of ants. Obviously there is the base level, where the ants (or agents or whatever) go about mindlessly, doing whatever they do, not really thinking on a higher level. Then above the ants, because of their interactions is a much more subtle phenomenon. In Hofstadter's example, the patterns that the ants produce enable it to hold a conversation with other fictious characters. The patterns are having the conversation though, not the ants. Its as if by magic because of the interactions between the ants an entirely new level of organization and "symbols" is created. Within this higher level of organization there are new rules, new capabilities, and new constraints. The new capabilities come from the opening up of phase space that the interactions produce. This means that the ants, who as a disconnected uncoordinated mob, would not be able to accomplish much of anything (such as gather resources, create a suitable living environment, protect themselves) with any great success, are able to accomplish both new and greater things. For example, a single ant could never build a complicated colony in which to live, work, and propogate. But a colony of ants can. Also, a single ant could not protect itself from certain predators, but a colony of ants just by virtue of it being composed of many ants has a natural buffer against predation, because a predator would have to wipe out the entire colony...and the analogies go on. Colonies of ants can cover more distance, forage more efficiently, etc...But there is also more constraints for this higher level of organization. The colony can only grow so big, based upon the available resources and the environment in general. The colony is more adaptable than a single ant...it can respond almost like a super organism, if say a predator destroyed part of the ant mound, the ants could work in concert to repair the broken area, but there are limits to this adaptability. Also, ants who live by the colony, die by the colony.

Anyway, the whole point of this long rambling, is that interactions between agents in a system can produce very interesting behavior...behavior that can be described as being a symbol even. Now, the natural extension of this that Hofstadter goes into in great detail, is that the mind is essentially many many levels of these kinds of symbols, chugging along doing their thing, whether programmed in from birth, or whether acquired through interactions with the environment. Here is the key idea: the patterns created by the interactions between the base units (or the symbols on the first level above the bottom) can also interact with one another to produce higher level patterns above them. In terms of programming language this is sort of like the jump from machine language to assembly language, and then from assembly language to a higher level language like C++.

There is something very important to notice about the mind though. This is the fact that these levels of symbols can talk to one another. It is not like they are completely seperated from each other, not affecting the behavior of each other running like they are completely independent of one another. No, it is in fact very important to recognize the recursive relationsip between the levels of the system. Hofstadter's most controversial and contentious point is the idea that consciousness is the highest level symbol the mind has. He argues this because when someone become conscious, they become more aware of themself. In terms of the symbol analogy, all the different symbols that make up you, from every purely physical experience you have had, to every emotional experience you have had, to every thought and internal model you have built to try and reconcile the world in your head to the world outside of you starts to realize something. What all these symbols start to realize is that they exist. Whereas most other things that we know of, from the simplest to the most complex organisms, go about doing things for whatever reason, we are one of the only entities that we know of that can look aback upon ourselves and say AHA! I am a thing that thinks about other things, that feels things, and that has symbols for other things. It is as if all the symbols that flow through your mind do a doubletake, and realize that they are there in the first place. Hofstadter describes this as the top level of the mind looking down at the layers beneath it. This is one of the most amazing occurences in the history of life on earth, because by gaining the power to look down upon the symbols that make up ourselves we essentially bootstrap ourselves into consciousness and all the wonders of being conscious entities...(e.g. complex emotions, from love to hate, a sense of humor, the appreciation of beauty, and perhaps even a soul).

Now what I want to know is why isn't there a way to be able to both create such systems that build layer after layer of symbols on top of each other, each new layer adding some sort of new phenomenon or ability to the system. I have a hunch that there are a variety of factors that are very important in generating such systems. One such factor is the topology both within and between levels. The topology, or connectivity between both the base units or agents, as well as the symbols in each level above the base level, is probably highly correlated with the corresponding functionality. Also, I am pretty sure that the cross-talk between levels is also very important in gaining certain higher level functionality that is beyond the scope of isolated levels of symbols working independently of one another. Finally, the biggest mystery is the types of interactions between elements that are necessary to construct such elaborate systems of symbols and patterns.

These ideas drive to the very core of what I believe are some of the most interesting questions out there at the moment. I truly hope to develop a general framework for creating such systems of multiple levels of symbols, and maybe even developing an entirely new language or something! to deal with such systems.

I sincerely hope to write that C++ program ASAP so I can start posting actual results including graphical representations of some interesting systems.