Janos has taken an interest in quantum computing using Cage as an entre.
All well and good, but there are a few points to be made.

All of western mathematics until the 20th century assumed that statements
in mathematics were "true" or "false".  One found out whether they were
"true" or "false" by "proof" - a series of logical steps carried out by
the rules of mathematics from basic demands called postulates or axioms.
"Axiomic Proof" is the gem of Greek Mathematics.  So wonderful a tool is
it, that it ran away with itself, providing a procrustean standard to
which other forms of human knowledge were poured, regardless of the amount
of pureeing involved.  It is tempting, after all, once the argument can
be reduced to proofs, there is no disagreeing with the result.  Thus
mathematical purity as the ultimate touchstone held most of the history of
western philosophy in thrall.  The other opposition was intuition.  back
and forth one can trace the dominant mode of thinking - with the
mathematical ideal giving way to the intutive one.

This lead Kant to declare that Newton's physics and Euclid's geometry were
true a priori.

In the late part of the 19th century it seemed everything could, by
classification and logic, be reduced to certainty, to geometrical and
aboslute determinancy.  The problem of freewill loomed in philosophy -
how can one have free will in a universe that is determinisitic?

- - -

Then came "the thirty years that shook physics" - certain problems, it was
found, could not be solved by reference to a euclidian space with absolute
time.  It began with a series of discoveries by Rutherford, Dirac and
Einstien about the nature of the atom and particles.  It culminated in two
theories - the theory of general relativity, and the theory of quantum
electro dynamics.

It is this last which, on the surface seems strange.  In it, we cannot
determine all of the information about a particle or system, because
measuring the system alters other variables.  If we know where, we do not
know what momentum, if we know how much momentum, we do not know where.
The quantum state of an unmeasured particle is *all* of the possible
states, and to determine the result, we must taken into account everything
that *might* have happened, even if it did not.

The computers we use are happily classical in the face they present, though
they depend on quantum mechanics for their functioning, every bit of data
is "true" or "false" and every calculation runs to an end which is "true"
or "false" - or which gives an error.

But imagine instead of only true and we have some pieces of information
which have not been measured, and which might be either true or false.
Currently we are learning to make such components, and we have shown that
quantum logic works.  But that is as far from a working machine as Boole
and Neuman taken together are.

Such a bit is called a "qbit" - for quantum bit.  A quantum bit is neither
true nor false - but both at once.  And so long as only calculations are
done which do not demand an answer, it remains so.  However, if the result
is requested, the quantum bit takes on a value.  Some times that value can
only be 1 or 0 - and sometimes it will be a "random" result.  It might
seems strange to say that at one step of the calculation the qbit "must be"
1, and at the next step, so long as it is not measured, it could be either,
but so it is.

- - -

Or rather, it seems nonsensical from one stand point.  But human history
is about finding new ways to conceive of problems, or finding old ways
that have new uses.

Consider, if you will, the opening of Wagner's Tristan und Isolde.  It
is clearly tonal, it implies tonality in every gesture and with every
progression, but it does not have a "key" for quite some time.  So too the
opening of Beethoven's fifth symphony - D Major, or D Minor? Until the
middle note is supplied, both at once.

This process is analogous to the way we percieve quantum effects.  Until
there is a definitive sign one way or the other, there are many sections of
music which could be in many keys, and they remain so, as long as something
is not done that affirms them.  Play the same section of music again, and
it will seem to be in the key that has been established, even though it is
the same section of music.  Take out the cadence, and it seems to drift
again.

In otherwords, music has, for a long time, pondered thee idea of
unreconciled opposites, of moments which exist both here and there at
the same time, which collapse only at some clear sign.

Stirling Newberry
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http://www.mp3.com/ssn

[If you'd like to discuss issues on the history or philosophy of science,
 please do so privately.  Thanks.  -Dave]