We can represent representations of representations
I love this book: This Explains Everything (Edited by John Brockman).
It's a compendium of short articles where people we all know and love like Dennett and Diamond and Pinker and Turkle and many others briefly describe ideas that they think are really great. An article by Hugo Mercier on page 116 caught my attention titled; Metarepresentations Explain Human Uniqueness. At least the proposal is bold enough :-)
Let's try as a simple way of talking about what a representation is. If I say "It's raining outside" that sentence represents a situation outside. What's happening outside might be thought of as a presentation; a state of affairs presented by reality. So the sentence "It's raining outside" takes that presentation and re-presents it.
I know! I know! Lots of philosophers think that the whole issue of representation is very very murky and hard to understand. And let's leave them to their fun and see how far we can get with this clearer idea. A metarepresentation is a representation about a representation. If Mary believes that is going to rain that might be called a representation to her self of the present state of affairs with her. If she says that she believes it's going to rain she is representing that to state of affairs to someone else. If she says "I think Paul think's it's going to rain." First we have the representation, "to rain" Then a metarepresentation - Paul believes the representation. Then there is the metametarepresentation - Mary represents Pauls representation of his own state which contains a representation of the state of reality.
Mercier points to Dan Sperber as a good thinker about metarepresentations.
Here's a page with an article by Sperber dealing with this topic:
"Humans have the ability to represent representations. I would argue that this metarepresentational ability is as distinctive for humans and as important in understanding their behaviour, As echolocation in bats."
In the past 20 years or so I've become aware of a lot of meta-systems like this. Reality is extremely complex - I'm not thinking of the complexity of the details of the grains of sand on a beach. I'm thinking instead of the sort of complexity found in ecosystems, or cultures, or brains. In all these circumstances we see a sort of fractal complexity - the apparent complexity is generated by the recursive interactions of various systems that themselves are relatively simple.
I've used this example of what I mean about complexity being generated by recursive operations of systems that are simple. This example is of a drawing system called an L-System (after Arastide Lindenmeyer) that has been used to model bilogical forms. An L-system has these components. You need a "turtle" - a software structure that draws according to simple instructions. This is how the figures are made visible. You need a a seed string of commands for the turtle to follow. And finally, you need a system that rewrites the string of commands according to a set of rules.
Say you have three commands; f, l, and r.
f means "draw a line 100 pixels long from where you are in the direction you are pointing r means "turn right 90 degrees" l means "turn left 90 degrees"
We might start with the seed "frfrfrfr" This draws a square.
We might apply a rule to that seed:
f becomes flfrfrflf
That is - I replace each f with flfrfrflf
Our seed becomes:
Which draws a square that has square blocks on its sides
Which is a square with blocks with blocks on them
Iterating this seed even a 5 or 6 times creates a tremendously long string, that draws an extremely complex fractal figure.
You can see from my illustration below how the resulting drawing quickly becomes bewilderingly complex.
This figure is a fractal and it displays a wierd sort of order. This suggests an interesting idea for me - it's sort of an easy to see example how you can complex but lawful systems. It's just that at the level of seeing the whole the simple law: f becomes flfrfrflf is hard to see. So we need these sorts of tools to help us comprehend that it's possible. What do you think?