Arrows n=m+1 example

Fri, 30 Apr 1999 12:30:40 -0700 (PDT)

On Mon, 26 Apr 1999, RE01 Rice Brian T. EM2 wrote:
> i'll clarify on the issue of atomicity.  arrows are atoms of information (i
> posit), so that when i refer to atoms, i imply arrows with unknown
> semantics.  in other words, i am unconcerned with the arrow's references or
> with the graphs that reference that arrow.

But you can also reflect on the arrow, which means taking into account the
graphs that reference the arrow.  In this case you aren't considering that
arrow as an atom. Am I right?


I'm working on it!  It makes a lot of sense.  I'll have to follow up soon
with comparisons to my system.  For now, though, I'm positive each system
can be represented inside the other.  The main difference is that Arrow
makes no restriction on what arrow can point where, while (my unnamed
system) has a strong type system always in effect.  You can achieve
unrestricted combinations by defining a type that behaves that way.  I'm
sure it is easy to add type restrictions inside Arrow.  I'm not sure if
you would want to, though.

> what atomicity means for arrows is that they have no "internal" structure at
> all. this re-expresses the notion that the arrow system has no primitives.
> instead, all information is external to the arrow, in terms of graphs of
> arrows that refer to that arrow.  the current context merely decides which
> of that information is important to mention and which is to be left
> implicit.

I call the "graphs of arrows", expressions containing a reference to an
object.  But there isn't much practical difference.

> and, YES, the arrow system CAN be re-defined in terms of other types of
> atoms.  the paper outlines a few ideas for centering the arrow context
> around other ideas than the arrow construct and then interpreting arrow
> information into these new contexts.  in fact, the entire system could be
> implemented in other systems, given a certain meta-structure that is
> arrow-definable.  i will get to this soon in explanations.

Well, isn't that what you meant by model-level reflection, after all?  :)

> circularity of definition is NOT bad.  take a look at the notion of the
> relativism of ontologies.  an axiom of infinity _could_ be the ultimate
> protection against deadlocking due to infinite loops.

I agree it's not bad. That's what I said in my message.  How does the
axiom of infinity work?

> as for mathematical basis vice common-sense, i can see no other way to
> provide formalized semantics or even approach a proof of the system's value
> to Tunes.  natural language is just not going to provide you with the
> necessary concepts.  for instance, try explaining the ideas of general
> relativity to the laymen, and then compare his/her understanding to someone
> who understands the mathematical proofs and equations and the physical
> experiments behind the idea.

Or we could implement a system.  Demonstration is a good way to explain
things.  What code do you have so far?  I know you've worked a lot on this
paper, but you said you had modified my tunes.c a bit.

> i hope you all are getting the hint by now, because its obvious that you are
> still discussing the arrow idea on your own grounds, where only confusion
> and semantic arguments propagate.

What IS obvious is that a lot of people I have talked to (Fare included)
are having difficulty understanding the paper.  I might like to try to
write a guide to reading the arrow paper.  Would you support that?

David Manifold <>
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