Patterns and lumps

Many people, both philosophers and AI proponents, talk about patterns.  They typically suggest that we start by finding patterns in the world.  We then build up perception and knowledge based on the patterns that we find.

Sometimes people talk of “regularities” rather than of “patterns”.  The term “regularity” implies some sort of rule following.  And that fits with our ordinary idea of pattern.

So let’s examine the idea of starting with patterns or regularities

Patterns

What’s a pattern?

I’m stumped already.

I know what’s a pattern in mathematics.  I know what’s a pattern in a drawing.  But I don’t know what’s a pattern in the world.

We often find patterns in representations, whether those representations be descriptions or pictures.

If by “pattern” people mean the patterns that we find in representations, then fair enough.  But in that case we need to start with representations before we can begin to look for patterns.  Typically, when people talk of starting by finding patterns, they are trying to suggest a starting point for making representations.  And I don’t see how that works.

If I look at an atlas, then I may see a pattern of flatness.  We can call that the “flat earth” pattern.  If, instead, I look at a globe map, then I see a pattern of curvature.  Call that a “curved earth” pattern.

The problem with finding patterns in representations, is that the patterns we find are dependent on how the representation is constructed.

The Ptolemaic astronomers found that the planets moved in a system of cycles and epicycles.  That’s based on their geocentric representation system.  Using a heliocentric representation system, Kepler instead found a pattern of planets moving in confocal ellipses.  This is an historical example where the patterns found depend on the way that representations are constructed.

If we look at it in terms of regularities, we run into the same problem.  Perhaps it would be okay to start with rule making.  People who try to describe using regularities often have something in mind such as Newton’s .  Inventing that rule and discovering that it works might be permissible from that perspective.  But we could not possibly come up with that rule until we already have a concept of force and a concept of mass.  So we already need to be representing some aspects of the world in terms of mass and force before we could hope to find that Newtonian regularity.  So it still cannot qualify as a starting point.

What we would need is some definition of “pattern” or of “regularity” which is completely independent of any human decisions on how to form representations.  And I am not aware of any way of doing that.

Lumps

Talking of patterns, let’s suppose that the world is as highly patterned as possible.  Let us suppose that the world is homogeneous.  That would make the world the same in every direction.  That’s about the strongest pattern that I can think of.

If we were such in a homogeneous world, we would not be able to see anything.  If we had a vision system, everything would look the same in every direction.  We would not be able to make out any distinctions at all.  That could not possibly work.

Fortunately, we live in a lumpy world.  It is not homogeneous.  There are parts that stand out as different from others.  And we use those lumps to guide us.

If we warm up water, it expands as we heat it.  That’s a kind of pattern.  But at the freezing point of water (or melting point if ice) that pattern is badly broken.  The water changes state between solid and liquid.  That’s an example of a lump that interrupts the pattern.  And we use that lump to calibrate our thermometers.  We set the freezing point of water to be zero degrees on the Celsius scale.

I suggest that it isn’t the patterns that guide us, it is the lumps.  Yes, the patterns are useful.  And making use of patterns helps us make predictions.  But the lumps are the starting point that we need to begin to form representations of the world.

Tags: representations