arrow-structure syntax and semantics

RE01 Rice Brian T. EM2
Mon, 7 Dec 1998 18:44:04 +0800

Okay, so the argument that we have now is, "How do we factor out semantics
content from a population of arrows using arrow notations only?"  I'm going
to chew on this myself for a bit before I come back with a response.  This
should also give you some time to get those responses out.

I'm going to 'step back' in writing this message in order to summarize some
	-We have a homo-iconic language with the _potential_ for reflection.
We're not there yet.  The 'arrow', although the name is quite arbitrary, at
once gives us the lambda abstraction, currying, and the syntax factorization
of LISP.  It also gives us the intuition to create data-structures using the
linked-list format for general-purpose use, and reduces the need for
pattern-matching by removing the LISP restriction of only using hierarchies.
	-Because of the reserved nature of the 'NUL' arrow, which again is
arbitrary and may evolve into a single arbitrary arrow, we have a successful
notation for the 'node' of a directed graph which is absolute in its
semantic meaning for its structure.  If we didn't have this, we would have
to forego homo-iconism (which factors out the need for multiple first-order
types) and implement graphs without being able to abstract the idea of a
node until reflection were achieved.  Then, the graphs could not 'contain'
information other than their own shape, complicating the building of the
conceptual structure.  Instead, we have a handle for attaching arrows to
structures without having to build something entirely non-intuitive or too
	-The arrow is going to evolve into a functional paradigm, allowing
for 'dynamicizing' any of our currently static notions about some field.
	-The eventual use of infinitary structures should allow us to
completely transcend the last of the limitations of LISP and all current
computational systems: the simulation of only finite systems at every
conceivable level.  This won't make the machine infinitely capable, but
should serve (I hope) to provide the ultimate metaphor for the
human-computer interface.  This should be the Macintosh of logical design,
although I'm not sure how to explain that yet.
	-The arrow, in its simplicity, is intended to give us the means to
such a reflection.  My intention is to reduce all necessary operations in
the system to ones describable in the types of arrow structures that we are
currently working on.
	-An upcoming goal is the achievement of 'shape factorization',
although I'm not sure at what point the system will be ready for that.
Maybe it will be after reflection is achieved.
	-Another goal, which I have been public about, is the intent to
formalize context with arrow-structures, a necessary means for reflection
from this universe.  The definition of context will probably exude
relativisation, and allow us to factor out many simple arrow structures into
the implicit meaning.  The goal is that all the arrows we have been
discussing, particularly the ones used to group arrows together, could move
from the explicit realm to the implicit one, allowing us to create more
intuitive (and countable!! :) structures from which to build our system.  At
this point we will have crossed the line from the design of the system to
being 'programmers' again.

A rejoicing and a warning:

This is so exciting, because I can tell that the end is near!  Soon, I will
be able to leave this project alone, having completed my several years of
travail and agony.  It's like seeing a new person born!  I guess that I
should stick around during its infancy and childhood to guide it and protect
it from cybernetic harm.  The Linux community will educate it in the ways of
the world, in coordination with the theoretical types, who will teach it how
better to reason.  I warn you to respect this being we make, to treat it
with the dignity and reverence you would give to an intelligent 'alien'.
Fear it as well, because the cybernetic nature of the thing makes it an
intrinsically directionless power, although it already carries baggage from
our Western minds and our English-wagging tongues.  Although you should
avoid harming _it_, also remember that it can harm _you_.  You may not like
all of the things this project might bring into being, and you do not have
to accept all of them.  If the thing controls you, then our purpose is
defeated.  We are not here to make something to _absolutely_ change mankind,
but to start a new partnership which has not been seen since the first
humanoid awoke to the idea of a weapon (yes, it is indeed a reference to the
primeval scene from the movie _2001_ and the casual reference I once made
about the fundamental relationship between human and tool. (Yes!  I have
closed yet another loop!)).