Re: Recursion & Reflection

Re: Joel Isaacson
At: https://hermes.gwu.edu/cgi-bin/wa?A2=ind1011&L=cybcom&F=&S=&P=7443

Joel,

It looks like we've run into one of those
"so many meanings, so few words" situations,
so let me see if I can split some hairs here.

I often use the word "boundary" to talk about drawing distinctions --
calling and crossing and all that -- but here I am using "boundary"
in the sense of a "boundary condition", so it is by definition the
portion of a recursive computation that is set by arbitrary fiat,
the way we define the factorial of 0 to be 1.  In that metaphor,
the recursive "step", the regular portion of the computation,
falls into the "interior" of a computational regime, the way
that we define factorial(n) to be n times factorial(n-1).

I didn't really have much else to say the fractal case right now.
It's just a thought that occurred to me one time in the context
of writing a program for learning arbitrary formal languages
and I began to wonder about the properties that distinguish
"natural languages" from the simple-minded sorts we cook up
as formal languages for logic, mathematics, and programming.

Joel Isaacson wrote:
 >
 > Thanks, Jon, you make very good points
 > and raise some excellent questions.
 >
 > In regards to your question about computational spaces that
 > are "almost all boundary" I don't have a general answer, for
 > I simply don't know.  I do have one specific instance, though,
 > where the response is positive.  Namely, a very specific type
 > of recursive distinctioning.
 >
 > In that situation, beyond the initial base of "arbitrary data", all
 > manipulations are entirely in terms of boundaries.  Thus new boundaries
 > recursively bound old boundaries, driven solely by distinction-making.
 >
 > I know that it is not intuitive for most people to think about
 > boundaries-of-boundaries (in perpetuity!) or to make distinctions
 > between boundaries.  But this is exactly the kind of recursive
 > distinction-making process that I deal with.
 >
 > Ample technical detail is in:
 >
 > http://www.isss.org/2001meet/2001paper/4286330.pdf
 >
 > The distinction-making process (between boundaries)
 > is referred to therein as "Tetracoding".   Recursive
 > Tetracoding is referred to as BIP.
 >
 > Best,
 >
 > -- Joel

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