Arrow System -- Rationale?

[RE01 Rice Brian T. EM2]

> 	If not, I don't understand how an arrow can 'DO' anything.  An arrow
> 	system appears (to me) to have no defined means of changing itself;
> the
> 	changes have to come from without.  (That's a good thing, as I see
> it,
> 	but it's counterintuitive if you're used to thinking of traditional
> imperative languages.)
> well, if i postulate a group of arrows which is every arrow in the system
> (the current set of postulated arrows), and use it in a mapping like {the
> set of all arrows} -> {the set of all arrows} U some new arrow satisfying
> X, Y, and Z requirements in terms of the original systems, then i have
> information updates and such.  yes, the theory needs work.  and if anyone
> uses the word 'paradox', i'll have to slap them with a wet fish!! :)
> 
ok. now, i'll deal with the 'paradoxical' aspect of the previous example.
obviously, the introduction of new atoms to this system, as an iterative
procedure atom, yields an infinite amount of new information, mostly
concerning recursive applications of abstractions and such.  for instance,
if i say that for every arrow, the results of the abstraction operator
(previously discussed) for that arrow yields the three new arrows (one node
and two arrows denoting the ordered pair of references), then we see that
there are 1,4,10,28, and so forth number of arrows, which by recursion
yields an infinite amount (probably uncountable).  this is one reason why
such a system should understand its limitations for iteration at a level
which precludes following such lines of reasoning like 'counting the number
of arrows generated by indefinitely-terminated abstraction on every arrow'.

this concept can be generalized to a view of the system where all
information (and resulting arrow structures) possibly derivable exists
already in first-order form, and the system calculates the structure of such
information 'on demand'.  this view would not necessarily be useful, of
course.  however, the principle of demand could form our ontology of
user-interface which corresponds to the standard ones used in todays
interfaces via commands, messages, and such.

this also suggests an answer to the question of how to represent infinitary
structures.  the idea would be to show the iteration atom and the resulting
structure in some special interface flavor (like a color highlight in a
visual representation), and to apply it as necessary to achieve the desired
structure as a result.  of course, if one wants the number 13635654786, then
one defines an interface to the natural number iteration atom which feeds a
string of digits vice the entire number (which is the number itself, and so
makes the calculation redundant).  but then, it seems logical to extend this
interface to include the function which generates this number, as in
f(3478).