RE01 Rice Brian T. EM2 BRice@vinson.navy.mil
Sat, 2 Jan 1999 13:17:26 +0300

> >arrows are abstract objects with N slots, the "default" being 2.
> iteration
> >on the default arrow type yields multi-dimensional arrow types.  each
> slot
> >is a reference to an arrow.  all arrows are available for reference.
> I'm looking for more specifics.  Here are some.
>  - what's an abstract object?
a logical atom is something in a system which is not a construct, although
statements can be made about them and constructs are made from them.  in our
system, logical atomicity is relative, so i don't want to stick with one

however, this is what an 'abstract object' is not:
	a Self object
	an execution object
	a black box (this is contradictory. i know this.)
	something with a 'clean' definition (why would we want to reflect on
something with a clean definition, since we know that multiple ontological
perspectives annihilate this attempt?)

>  - what's a slot?
(see the below explanation on the difference between a reference and a

>  - how is the number of slots significant?
it signifies positive statements that we make about what the abstract object
"is" (which is, of course, relative even within the system).

>  - what is "iteration on the default arrow"?
do you remember the Lisp-style linked list metaphor that i used for an arrow
grouping mechanism, where {tail, head} becomes (car cdr)?  This is the same
idea.  The way that you make a 3-slot arrow from a two-slot arrow is by
combining the first arrow with a second whose tail points from the entire
first arrow to the third slot.  Here it is in formal terms: an arrow of type
(or dimension or order) N is an (N-1) type arrow and a primitive arrow (type
2) which leads from the whole (N-1) type arrow to the Nth slot.  a type 2
arrow is a primitive type with respect to this iteration.  none of this
means that the size of an arrow is limited to the counting numbers (the
ordinals / natural numbers) vice infinitary cardinals.

this last statement suggests my attitude towards iteration: it is NOT a
computation to be processed by a von Neumann architecture which calculates
each iteration in some finite time interval with only as much time span
available as the number of counting numbers.  neither is it equivalent to
such a process in any way.  said attitude toward iteration which i just
distinguished my viewpoint from does not truly understand abstraction.

all of the arrow system will be reflected upon eventually, of course.

>  - what's a reference?  How does it differ from a slot?
a reference is just a way to specify the connections between arrows in
"arrow space", if you will.
a slot is just a term that i picked up from Self which is misapplied here,
since the object-slot ontology is not the issue.  i apologize.  i guess that
a slot could be distinguished as the potential of an object for a positive
statement of connection with another arrow.

>  - what's the use?
well, i could mention object-orientation and lambda-abstraction, but those
uses (i believe) are obvious to you.  the main new benefit is arbitrary
cross-cutting of ontologies _without_ the invocation of any special
reflection method.  in other words, this language reflects "right out of the
box", so to speak.  aspect-orientation will emerge as a property of the
kinds of systems that Tunes requires.  (obviously this last statement begs
explanation.  this will follow soon.)

> You may have done a lot of study to get this theory, but I wonder whether
> you've ever tried writing it down before.  You're using terminology from
> diverse fields in ways which are not directly related to the original
> field -- it's a healthy guess that the meanings have changed, but it's
> _hard_ to guess how.  Your so-called specification won't be complete until
> it contains all of the things I mentioned in my last post, with all of the
> possibly ambiguous terms de-ambiguized.
sorry.  i guess that i've messed with my mind a bit too much.  on the other
hand, i could be quite irrititated by your apparent insatiable desire for
terminological strictness.  i personally don't give a damn about Western
thought about language.  i do indeed see it as destructive, for reasons
which should not find their voice here, although they are far more complex
than the things with which this project is directly concerned.

[statement i made which turned out to be quite esoteric :)]
> Very Zen.  As such, I can't argue with it -- viewed as a koan, it holds
> too much truth in its own contradiction.  Viewed as anything else, of
> course, I have to call it rubbish.
yes.  one of my central mental excursions is throught the complex infinitely
dimensional manifolds of human (and otherwise) thought.  i have to admit,
then, that mathematics is in a way my "religion" of sorts for transcending
the Eastern ideas of Zen and the Western ideal of the Overman.  it's a shame
for you that i don't canonize my ideas into dogma so that you can reduce my
thoughts to a controllable item.

> Western logic isn't the only way to view the world, and I've become decent
> at using other means.  But Logic isn't wrong just because it's not
> omnipotent.
you'd be surprised at some of the results that i've reached, in that case.