ONT Re: Information = Comprehension x Extension -- Discussion
o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o
ICE. Discussion Note 43
o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o
HT = Hugh Trenchard
Re: ICE Discussion 38. http://suo.ieee.org/ontology/msg05328.html
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.
Let me "try" to tell you where I'm "at" with this,
in spite of the fact that it risks waylaying where
I may be going with it. My own understanding of all
these quantum quandaries is nowhere near as clear as
I could wish it to be. The first time I told the not-
altogether-joke above, I was a freshperson in physics,
as you can tell from the fact that people were still
using the phrase "where it's at" and its derivatives.
It struck me, upon my "moment's incidental reflection"
(MIR), that trying to figure out where I was at, exactly,
would frequencely interfere with where I was going, exactly,
and so I relaxed and gave up the quest to figure out either,
exactly, though not entirely, of course, as that is the duty
of reflection for a semio-intelligent and pragmatic creature.
I view "Heisenberg Uncertainty" (HU), like many other folks do,
as a mathematical principle first and foremost, that applies to
certain formal domains that may or may not afford us good models
of our favorite physical reality, and thus it is only secondarily
and contingently to be treated and tested as a physical principle.
The way physics goes, tomorrow afternoon or the day after we could
all find out that the whole thing was nothing but a dream, pleasant
or unpleasant depending on one's particular aesthetic predilectrons --
the token law would continue being taken as the coin of the realm in
just those undying lands where it's minted, even if the wide world of
human beings will likely lose interest in its purely formal credibility.
I didn't say that I was betting on it, 'cause I'm not, not by a long shot.
At any rate -- of interest or otherwise -- as a formal principle the last
formal statement of HU that I can remember reading, if a bit uncertainly,
went a bit like this: "The mumble-mumble density of the state vector and
its conjugate dual cannot both be concentrated on sets of small measure".
I just barely get that we have to pass from thinking of states, like position,
to thinking about whole mumble-mumble probability densities (or distributions)
that give us some vertical amplitude of mumble-mumble probability values along
some horizontal dimension that corresponds to the domain of possible positions.
Then the momentum must be the dual conjugate whatever to the position variable.
But to make a continuous story more-or-less discreet,
where I more-or-less went from where I more-or-less
was at, more-or-less then, to where I more-or-less
am at, more-or-less now, is that I redistributed
my quanta of attention less from physics and
more to logic. And so now I have a whole
new set of problems to worry about, that
have to do with the sorts of analogies
that one can push through from the
quantitative realm of physics to
the qualitative realm of logic,
and where they break, because
they always do, if you push
them hard enough.
Speaking of breaks ...
Jon Awbrey
o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o
http://www.cs.bsu.edu/homepages/mighty/history.html
o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o