On Philosophy

September 15, 2007

Finding Patterns

Filed under: Mind — Peter @ 12:00 am

I don’t think the hard problem in the philosophy of mind is defining conscious or explaining the nature of experience. Such questions may appear difficult, but their difficulty is a product of our stupidity; answering them involves mainly abandoning faulty intuitions and learning to ask the right questions (the wrong questions being puzzles about the nature of experience; although the contents of experience are transparent to us the nature of experience itself is mostly closed to introspection). The real hard problems lie in the details, in making more concrete claims about which systems are conscious. Today I am going to address a part of one of those hard problems, namely that of how to connect an abstract functional description to actual physical events, or perhaps it is better to say that I will lay the foundation for such a solution.

The problem actually is not drawing a connection between an abstract functional description and parts of the world, but preventing ourselves from going overboard and drawing too many such connections. As a first approach we might consider something to be a manifestation of the appropriate functional properties if we can simply construct a correspondence between what actually exists and the abstract functional description. The problem with that approach is that it is possible to draw such a correspondence between nearly anything and a set of abstract functional properties, if we allow any kind of correspondence. In principle there is nothing stopping us from drawing a correspondence between a single particle and an entire set of functional properties, except common sense that is.

Obviously we didn’t mean to admit such ad-hoc correspondences, but it is not immediately obvious how to rule them out. Well, functional properties are essentially causal properties of the parts of the system. And causation essentially boils down to the existence of patterns. Our problem is to determine then when one pattern (the functional properties) can be said to hold of some part of the world. And the goal is to find out which patterns really are there (to discover them), but not to impose new patterns. We can do that by taking a subset of the world and applying some kind of transformation. If that part of the world can be transformed into the desired pattern then we say that the pattern does exist there, that we have discovered an instance of it. The remaining challenge then is to say which transformation rules count as discovering patterns and which count as imposing them.

But first, an illustration:

This picture represents some world. And in it we are trying to find a pattern, one example of which is labeled A. The key features of this pattern is that there are five elements that form a half circle, and each is rotated 45 degrees more than the previous. And I would claim that B, C, and D are all examples of ways we can legitimately find this pattern.

But first, back to the issue of finding the pattern versus imposing it. Ultimately it comes down to whether the pattern is there to find or whether we are creating it in our minds via over-interpretation. And to determine that we can ask whether our transformation rules are adding any new information. If our transformation rules are working with what is already there then they are finding a pattern, but if they add new information then we are imposing a pattern where none existed before.

Let’s first consider spatial transformations. If we have a collection of objects then, spatially at least, what matters is their relationships to each other. One way of creating information would be to transform the same spatial relationship into different ones. If objects A and B have a 5 inch horizontal separation and objects C and D also have a 5 inch horizontal separation then our transformation, whatever it does to their relationships, should keep them the same. Otherwise we have added new information, that there is a difference between these two relationships, where there was none before. Thus, spatially, the transformations are limited to stretching, rotation, and translation if we want to keep the amount of information the same. And, given that, we can see how the arrangements labeled B and C can be transformed into A, if we allow a one-to-one substitution of lines for Xs and arrows, respectively.

To explain why D can be transformed into A is more complicated. Obviously we must allow the rules for transformation from one shape to another be more complicated than one-to-one, but allowing many-to-one (any number of original objects to be converted to a single destination object) is equally unacceptable, because then we could transform any half-circle arrangement, so long as it was made of five different shapes, into A, and that is clearly unacceptable (clearly an example of creating a pattern where none existed before). The problem with it is that such a transformation is adding information too, this time of a similarity where none existed before. What is allowable is using the features of the object to be transformed to make the determination into which shape (and which size and orientation) it is to be transformed into, but we must stipulate that this determination is to be made on the basis of a single set of features (such as the shared general arrow shape in D), and that all transformations into a single destination shape must be based on the same set of features.

Obviously more could be said about these rules, but since we are not really interested in transforming one set of shapes into another there is no need, since we are not genuinely interested in such transformations. What is key is that our transformation rules may not add information. What exactly means depends exactly on how we decide to formalize functional properties (a project for another time). In most cases it will be simply a matter of forbidding transformations between identical things into different final products, but sometimes it will mean disallowing the transformation of totally unrelated things into the same final product. Our transformations, we might say, are to bring to our attention existing relationships, not create new ones.

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