ONT Re: Information = Comprehension x Extension -- Discussion
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ICE. Discussion Note 41
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HT = Hugh Trenchard
WB = William Blake
Re: ICE Discussion 38. http://suo.ieee.org/ontology/msg05328.html
HT: Jon, I am still in the process of reviewing your many posts
leading up to this, so I cannot profess to understand to any
great degree of completeness the concepts you have presented.
You know how it is -- on a clear day you can see forever,
or think you can, but on days like this you have to move
on little cat feet. Some of the people who "catalyzed"
my current try at this question have moved on to other
harbors and cities, at any rate, for the time being,
but that's okay, I still keep up conversations with
lots of people that I haven't talked to in decades.
What happened this time was all in accord with the model of inquiry
as I understand it -- first the bold guess, next the teasing out of
its more secret consequences, and then the testing of those effects
against further brushes with reality. That's not to say the phases
do not overlap, nor that the cycle ends so long as we continue, but
that's the general drift of it. Right now I'm in the more middling
muddle of it all, though.
HT: Nevertheless, I think I have gleaned just enough to be able to ask a couple
of questions: When you say "symmetry invariant meaning", are you referring
to the equivalencies of the information increase as between comprehension
and extension referred to ICE Note 19 ("... in that way we increase the
comprehension of the 'dotted circle' and at the same time increase the
extension of 'crossed and dotted circle'")? Is the symmetry the
proportionate increases of extensions and comprehensions?
You are already racing ahead of me -- at the moment I'm backtracking
to try and get a clearer picture of what Peirce said the first time
out of the chutes -- but maybe I can make a generic comment about
the contemporary setting that pressed me to coin the acronym SIM.
The way we get at reality in mathematics and physics is through symmetries.
I deliberately made that statememt as sloganesque as I could, but the more
accidental connotations of bumper stickers can cause mishaps in traffic if
we can't guess what the other guy is driving at, so let me explain further.
There is the reality that we are trying to describe, and then there are the
"frames of reference" (FOR's), the assembled masses of signs that we bring
to bear on describing the bare reality. There's always a big gap between
the reality and any of the FOR's, which lack we try to supply, or cover,
by using multiple FOR's. This tactic raises a host of issues, not to
mention a cloud of dust, in its own right, but the immediate problems
are (1) characterizing compatible collections of FOR's, (2) relating
their members to each other, and (3) relating the whole system of
FOR's to the object reality.
The main catch with using a FOR to address a reality,
no matter whether we have one or many, is being able
to tell what's a property of the reality in question
and what's an artifact of the FOR, or the particular
host of FOR's that is used at the moment in question.
One way to deal with this problem is to try and analyze what we mean
by "objective reality" or "real object", and this analysis typically
results in our identifying properties of objects that can be defined
on the grounds of any FOR in the class of FOR's that we have in mind.
The way that this sort of technique usually works out, the FOR's are
related by collections of transformations that actually or virtually
turn each one into any other, and so the objects and properties that
we commonly dignify with the honorific title "objective" ate usually
the objects and properties that are invariant under those symmetries.
At any rate, that's the best that
I can see or say it at the moment.
I'll probably need another cup of coffee ---
to cut the fog a little before moving on ...
Jon Awbrey
HT: My second question relates to the analogy of particulars and properties to
particles and waves, which question arises more at this point from a lack
of a full appreciation of what is meant by particulars and properties.
But despite my lack of understanding of properties and particulars,
are you suggesting some sort of coexisting duality of particulars
and properties -- or are you employing that analogy only to say
that the implications of Peirce's formalisms are far beyond
what people may have initially thought?
HT: My third question then relates to the PHU. Here again I don't pretend to
possess any in depth understanding of Heisenberg's Uncertainty principle,
but if it is essentially that both the position and the velocity of certain
sub-atomic particles cannot be known simultaneously with certainty (i.e. to
measure one is to displace the other), then are you saying there is a quality
to properties and particulars and/or comprehensions and extensions, by which
they are not both known or determinable at the same time? It seems to me
this would run counter to the notion of symmetry invariancy.
HT: In any event, I have this funny feeling you have been
preparing to unleash a tour de force that will answer
these questions and many more.
HT: I know you like to quote the odd bit of poetry to add color to your theses.
So in that vein:
WB: | Tiger, Tiger, burning bright,
| In the forests of the night,
| What immortal hand or eye,
| Dare frame thy fearful symmetry?
|
| -- William Blake
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http://www.cs.bsu.edu/homepages/mighty/history.html
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