Re: Recursion & Reflection

Amending and extending Friday's remarks a little bit more ---

| In language used for inductive proofs -- of which recursive programs are
| the computational cousins -- the Base is the arbitrary or irregular data,
| the aggregate of which makes up a data base, and the Step is the regular
| procedure repeated up the ladder, the code that forms the program proper.
|
| When we come to interactive programs, whose bases encompass data that is read
| from the environment on a recurring basis, our initial notion of a base as an
| initial condition becomes broadened to a base as a boundary condition that is
| open-ended and extends forward in time.

It may seem like a trivial shift in terminology from the inductive proof language
of Base and Step to the topological language of Boundary and Interior, but it has
a couple of interesting consequences, just at first sight.

1.  It keeps us from getting mired in various brands of "fundamentalism" --
     also known as "foundationalism" or even "objectivism" in some circles --
     the notion that there is anything absolute and unproblematic about the
     "immediate givens" of experience.

2.  It opens up the question of how the Boundary and the Interior are related.
     For example, are there computational spaces that are "almost all boundary",
     like certain fractals we know?

Jon Awbrey

cc: CYBCOM, Inquiry

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