Arrows n=m+1 example

RE01 Rice Brian T. EM2
Mon, 26 Apr 1999 17:14:01 -1000

> > So it seems more intuitive to define an arrow as having two slots that
> > can reference either an arrow or an 'atom (or object)'. I guess this
> must be
> > wrong for you, since it would means to lose the homo-iconic property.
> > But I don't see by myself yet why it would be so bad.
> In a reflective system, what are "atoms" varies depending on the context.
> We can't have one set of atoms for the entire system, because we want to
> talk about what those atoms are defined by, which would necessitate
> something at the "sub-atomic" level.  Of course, once you have a system
> bootstrapped, you can use the atoms themselves in their own definitions,
> but you don't always want to do that.
> At a fundamental level, we don't like the concept of atoms.  In an
> intensional system, the meaning of any part of the system is entirely
> dependent on what other parts it is connected to.  So if you try to find
> definitions in the usual sense of the term (with atoms at the base level, 
> and more complex entities made of combinations of these atoms), you will
> end up with circularity sooner or later.  This same problem occurs when
> trying to write a dictionary.  You must describe language using language.
> People complain that to understand a word, they must look up other words
> recursively (ad infinitum).  In essence we are affirming that our world
> view no longer views such circularity as taboo.
> A more mundane answer is that you can use arrows that point back to
> themselves (or any other designated shape of arrow you wish) as atoms.
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.
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
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.
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.
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.
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.