3.230 uncertainty, etc. (204)
Willard McCarty (MCCARTY@VM.EPAS.UTORONTO.CA)
Mon, 10 Jul 89 21:32:24 EDT
Humanist Discussion Group, Vol. 3, No. 230. Monday, 10 Jul 1989.
(1) Date: Sun, 9 Jul 89 00:41:25 EDT (17 lines)
From: Don D Roberts (Philosophy) <ddrob@watdcs.UWaterloo.ca>
Subject: Goedel, Escher, Bach
(2) Date: Mon, 10 Jul 89 01:44 EST (20 lines)
From: EVENS@UTORPHYS
Subject: Goedel et al
(3) Date: Mon, 10 Jul 89 19:00 EDT (142 lines)
From: Peter D. Junger <JUNGER@CWRU>
Subject: More on the interpretations of quantum mechanics
(1) --------------------------------------------------------------------
Date: Sun, 9 Jul 89 00:41:25 EDT
From: Don D Roberts (Philosophy) <ddrob@watdcs.UWaterloo.ca>
Douglas de Lacey asks about GODEL, ESCHER, BACH. I think it is a
wonderful book (much better than THE MIND'S I (done with Dennett)
and METAMAGICAL THEMAS, in my estimation). I have used it 5 times
or so in seminars, and it has attracted bright students at UW which
made teaching enjoyable for me. I am aware that some people found
Hofstadter's punning and fooling around excessive, but for some
reason it doesn't bother me, in part, I suppose, because the book
provides such an unusual variety of excellent things--on the logic side,
for instance, the introductions to formal systems and to recursive
functions, and the treatment of Godel's incompleteness proof.
The dialogues are delightful. My students enjoyed the "games"
contained in the book, even the relatively hidden ones (for instance,
look up "ATTACCA" and "Hofstadter" in the index (add a reference to
page 702 for the latter)).
(2) --------------------------------------------------------------24----
Date: Mon, 10 Jul 89 01:44 EST
From: EVENS@UTORPHYS
Subject: Goedel et al
From: DEL2@phoenix.cambridge.ac.uk
>It is Douglas Hofstadter, *Goedel, Escher, Bach;
>an Eternal Golden Braid*, published (I think) by Harvester in UK and I
>don't know who in US. I would be interested to know what other
>HUMANISTs think of it.
Thank you for reminding me, it is long overdue that I reread
this book. I have enjoyed every attempt at it (about 4 or 5 now
I think) but never actualy finished it as I have always tried
to do all the "exercises" and it was taking weeks to the
chapter. Symbolic logic is not exactly my forte.
>And does anyone know how to transmit an umlaut over e-mail?
If you were using TeX it would be G\"oedel.
If you were using LaTeX then to get Goedel right it would be
G\"{o}edel.
My problem with G\"{o}edel is how to pronounce it.
(3) --------------------------------------------------------------146---
Date: Mon, 10 Jul 89 19:00 EDT
From: Peter D. Junger <JUNGER@CWRU>
Subject: More on the interpretations of quantum mechanics
The discussion of the Copenhagen 'interpretation' of the 'formalism' of
quantum mechanics--or is it the 'formalism' of the uncertainty principle?--
and the somehow consequent charges of anti-intellectualism have me very
confused.
Perhaps my confusion supports the position that humanists should not
talk--or read--about quantum mechanics, but I would still like to know
where I have gone wrong.
In the first place, as I understand it, the so-called Copenhagen
interpretation is an interpretation of quantum mechanics (or quantum
dynamics) as a model of physical 'reality'; it is no more an interpretation
of a formalism than Newtonian mechanics is an interpretation of the
formalism "F = MA" (and a bunch of other formalisms dressed up as
differential equations). Newtonian mechanics is about--is an
interpretation of the observed behavior of--apples and moons and billiard
balls and things like that.
Not as a matter of physics, but as a matter of cultural history,
Newtonian physics represented a triumph for those--who did not include
Newton, who was into alchemy and things like that--who believed that the
rational mind could 'see'--i.e., anschauen or intuit--the ultimate reality
of the world by abstracting from the world all thought of, or reference to,
anything subjective, anything merely human.
The triumph of this view was, of course, a defeat for anyone who was
interested in human thought, culture, or desires. Erstwhile humanists
tried to turn themselves into scientists and excluded everything subjective
from their ontologies, lisped in numbers, and brought forth monsters, as
neo-classical economics did with its rational--but uninterpreted--
formalisms who go about maximizing transitory desires by slithering along
indifference curves. Those humanists who remained true to their cause were
told that their interests were positively meaningless, and meaningless at
least in part because the poor humanists could not abstract their
subjectivity from the part of the world that they were attempting to
describe.
With this history, it is understandable that humanists tended to
snigger when they heard rumors out of Copenhagen that the physicists were
discovering that their own observations were changing the outcome of their
experiments.
But, as I understand it, the problem with quantum mechanics is much
more serious than that. It was not just that physicists found that they
were trying to do the equivalent of plotting both the position and velocity
of an invisible baseball by throwing invisible pingpong balls at the
baseball and observing how the pingpong balls bounced. The physicists'
difficulty was that they could only predict the probability of where the
baseball, or one of the pingpong balls, would turn up and--and this is the
rough part--that that probability distribution described the behavior of a
wave, not of a ball or some other type of particle. I can't recall the
details of the double slit experiments, but it was quite clear--and had
been clear to Newton--that light behaves like some sort of wave rather than
like a particle. But when something actually interacts with light, then
the light equally clearly appears to be made up of photons, i.e.,
particles.
Equations (formalisms) were written which could predict what one would
observe in any given experiment involving photons or other subatomic
particles, but the physicists could not come up with any noncontradictory
interpretation of what light (or anything else that exists in the subatomic
world) was. The variables in some of those equations could only be
interpreted as particles, while the variables in other equations could only
be interpreted as waves. But the two sets of equations described the same
reality, and, I believe, that it was discovered that they could be
rewritten so that they could not be interpreted at all. But whatever form
the equations took, they worked fine, in the sense that they precisely
predicted the probability that during an experiment an observer would
observe a particle at a given time and place, provided always that that
time and place were both large enough to admit of an observation.
As I understand it, the Copenhagen interpretation can be stated in two
complementary ways: i) there is just the observations and there is no
underlying reality other than those observations and the uninterpreted
equations predicting what will be observed or ii) for one type of
experiment the underlying reality can be considered to be waves while for a
complementary experiment the underlying reality can only be considered to
be particles. So one can take one's choice: no reality or multiple
inconsistent (but complementary) realities.
With this interpretation the whole idea of some sort of Platonic
reality, idealistic or materialistic, was cast aside. One ended up with
true statements that did not refer to anything or with 'things' about which
one could not make a noncontradictory statement.
This interpretation is not, however, part of quantum mechanics. There
are other interpretations that one can choose. One of them is to posit
hidden variables, some reality at a level deeper than the wave/particles.
The only trouble with this interpretation is that there is experimental
evidence, so I understand, that any such hidden variables would have to be
so well hidden that no experiment in quantum mechanics could reveal them.
Another possibility--one that makes me most uncomfortable--is that
everything that could happen with some probability does in fact happen,
each in a different universe. No one has suggested anyway of testing this
interpretation either. And then there are those who argue that it is only
an observation by a human being that can actually bring a quantum particle
into existence and postulate the strong anthropic principle that we are
here because the universe is--against all probability--the perfect place
for critters like us and that the universe exists as it does--in esse, not
just in posse--only because we are here to observe it; another untestable
interpretation.
Physicists working with quantum mechanics do not need to worry about
these interpretations. A computer chip can be designed in accordance with
the principles of quantum mechanics and it will work, no matter how the
designer interprets--or fails to interpret--the underlying quantum
mechanisms (if there are any underlying quantum mechanisms).
Something may someday replace quantum mechanics that is not confronted
with these problems, but that something will not be quantum mechanics. It
will supply answers to different questions, and the problems of
interpreting quantum mechanics will be forgotten, along with quantum
mechanics. Perhaps this new and as yet undreamed of theory will admit more
easily of interpretation and allow the physicists to delude themselves once
again that they have been able to view reality in the raw. I would not,
however, hold my breath awaiting that day on which old Plato will be, for a
while, vindicated.
It seems to me that the importance of all this--to the extent that I
have not gotten it all muddled up--to humanists, is that our last best hope
of actually seeing reality, nature, what-have-you, as-it-is has blown up
like bubble gum in the physicists' faces.
Some may find it nervous making, but I should think that most humanists
would be delighted that our advance guard has returned from Plato's cave
and reported that the shadows are there, all right, but that there is
nothing projecting them. It may not be true that things are what they
seem, but it seems to be true that there is nothing else that they can be.
Am I an anti-intellectual for hoping--and assuming--that reality is
dead? The world has not been changed after all by the development of
quantum mechanics. There is still plenty to think about; especially if one
is not a physicist.
I await the correction of my misconceptions.
Peter D. Junger--CWRU Law School--Cleveland, OH--bitnet: JUNGER@CWRU