Kevin asked:

I received an answer from Steven Ravett Brown about how to understand Reflexivity. I understand
the answer that was given, but it was something that was unrelated to what I was referring to, which
is cool.

I am trying to complete Douglas R. Hofstadter Gödel, Escher, BachMetamagical Themas,
Section 1, 'Snags and Snarls'. Can you explain his concept of Reflexivity? where can I find out more
about it?

The title of this section conveys the image of problematical twistiness. The twist dealt with here are
those whereby a system (sentence, picture, organism, society, government, mathematical structure,
computer program etc.) twists back on itself and closes a loop. A very general name for this is
Reflexivity. When realized in different ways, this abstraction becomes a concrete phenomenon.
Examples are : self reference, self description, self documentation, self contradiction, self
questioning, self creation, self replication, self modification self amendment, self limitation, self
extension, self application, self self scheduling, and on and on. In the following four chapters, these
strange phenomena are illustrated in sentences and stories that talk about themselves, ideas that
propagate themselves from mind to mind, machines that replicate themselves, and games that modify
their own rules. The variety of these loopy tangles is quite remarkable, and the subject is far from
being exhausted. Furthermore, although their connection with paradox may make reflexive systems
seem no more than intellectual playthings, study of them is of great importance in understanding
many mathematical and scientific developments of this century, and is becoming ever more a central
of theories of intelligence and consciousness, whether natural of artificial.

Douglas R. Hofstadter Gödel, Escher, Bach

Whoops, sorry... but you weren't specific. "Reflexivity" in this sense refers to what might be termed
recursion, in the most general sense. He seems to be talking about any kind of referring backto a
starting point, an original position, a beginning state. So the "loop" he's talking about is a loop in the
time course of an action, where that action goes "out" to something, then comes "back" to oneself.
Self-reference is the act, let us say, of paying attention being "bent" back towards the self that is
paying attention. Self-description is the act of description being directed backtoward the person
actually doing the description. You see? The "loop" structure he's talking about is from you, your
"self", back into or towards your self. He refers, ultimately, to the idea of the "reflex arc", which is a
structural phenomenon in the nervous system in which a sensation like a pain activates spinal nerves,
which feed back, in an immediate reflex, to the muscles near the pain, to withdraw the limb. You can
read about that in texts about the nervous system.

Now, there is no place you can find more about the general concept of "reflexivity", as far as I know,
as a single unitary concept (except perhaps in other writings of Hofstadter), because "reflexivity" is a
word coined by him. You canfind out about the various subsets of that concept. There are, for
example, lots of places you can look at kinds of self-description, mainly in the literature of clinical
psychology, and in art, in, for example, self-portraits. If you want a neat story that talks about itself,
read Sophie's World, by Gaardner. If you want to learn generally about recursion, finish Hofstadter's
book, and then you have, I'm afraid, to learn some math. You might also look at the literature and
pictures of fractals, a relatively simple and interesting case of recursion.

Steven Ravett Brown