essay:determinism and non-determinism
Wed, 3 Mar 1999 00:34:18 +0100 (MET)

Waves in their most abstract ideal sense are continuous and infinite.

Particles in their most abstract sense are discrete and finite.

We only conceptually view these abstract extremes and never
actually measure them. An infinite continuous wave requires
an infinite amount of time to measure. A discrete and finite
particle requires infinite resolution to measure it and verify
that it is truly and indeed, a finite and discrete particle.

The former measurement is one of infinite iteration, while the
later is one of infinite recursion. In this manner are interpreters
and compilers in -their- most abstract sense, are linked to
physical time and physical space respectively.

Not being able to measure either abstract ideal waves and particles,
forbids us from using these terms as absolute classifiers in

If we cannot measure these things precisely in a Boolean sense,
that is, if we can never measure these things absolutely, then
we are always measuring something fuzzily. But we often for the
sake of convenience will classify a measurement as having measured
a particle or a wave, or sometimes, a wave-particle; something
who's classification as strictly wave or stricly particle eludes

We call two classifications which morph into each other "complementary"
or "dual" because neither is resolved without the expense of the the
other. Like a see-saw, as one rises, the other falls. But in the
middle of this see-saw, there is an invariant. The fulcrum point
represents a conserved variable because it does not rise or fall as the
see-saw pivots.

As we observe something which we classify more and more strongly as
a "wave", we observe it less and less strongly as a particle.
Our conserved varible in this case is Planck's constant.

As we observe space more and more precisely, we must pin down that
space and prevent it from changing, we therefore must loose dynamism
in space, as it becomes more an more static under closer and closer
observation. In this manner, resolution of space is at the expense
of time. We discard "time" when we view something statically.

The constant in this case is the speed of light in a vacuum "c". Because
moving into a spatially perfectly static picture, requires an infinite wave
to resolve that space with infinite precision. This infinite wave is
"timeless" because it is "time-invariant". This wave which we must use
to observe an infinitely resolved space must not have any discontinuities
in it. From theorems in information and fuzzy theory, this wave therefore
cannot carry any new information. It is completely deterministic and
therefore travels at infinite velocity (it's state is known a priori to
any measurement).

But when we measure space physically, we cannot infinitely resolve it
in this manner. We are always trading off space for time, and time for
space. It is in this case where we obtain the physical constant "c"
which mediates our best efforts to resolve space and time as separate

All dual complementary concepts are also treatable in this manner.

Macroscopic and microscopic observations are dual complements. When
we classify waves as waves, we do so macroscopically. When we
classify particles as particles we do so microscopically. The more
we call something a "wave", the less we are concerned with it's particulate
underpinnings because all strictly wave properties are properties of
many particles and these properties have no meaning for individual
particles. Similarly all strictly particle properties are properties
of particles and have no meaning which apply to abstract ideal waves.

The problem here is that of the degree of classification. If we
cannot measure absolutely we cannot classify absolutely.

When we say that a particle is a "particle", we can at best say
it is "mostly a particle". When we say a wave is a "wave", we
can at best only say it is "mostly a wave". The "mostly" aspect
implies that a particle is not completely a particle but is something
else as well. What that something else is, is determined by the
complement of the classification.

If we say something is "mostly a particle" then we mean the rest of
it is a "wave". Similarly when we say something is "mostly a wave"
we mean the rest of it is a particle; or more exactly, the rest of
it has particle-like properties.

In the same manner, when we say that a unicorn is "mostly a horse"
we mean the rest of it, is "not a horse".

Anything that is not a particle, is a wave. Anything that is not
a wave is a particle. Anything that is not physics is philosophy.
Anything that is not philosophy is physics.

But as mentioned above, we do not have the luxury of absolutely
classifying things (physical events or perceptions). We more often
than not are measuring alittle of something and its complement
"simulatneously". This "simultaneously" is not a finite fixed quantity
of time, nor is it an infinitely small amount of time.

The amount of this time, it's duration, determines how much we see of
one classification as opposed to its complement. If the duration is
large, then we see more of waves than particles, and we see more
of macro than microscopic effects. If the duration is small, then we
see more of particles because we can distinguish them better within
a small interval of time than a longer interval.

"Culture" and "Society" are dual complements[1].

"Wisdom" and "chaos" are dual complements.

When we seek knowledge of the most general nature, we seek "wisdom".
But being of a "general nature" means that such knowledge is applicable
over a broad range of topics and time. We say ideally, that "wisdom"
is applicable to everything, but more practically speaking, wisdom may be
applicable to a fixed range of topics an over a fixed range of time
as well.

If we say "wisdom" is applicable only for a fixed collection of topics,
it has a "spatial" duration whereas if we say "wisdom" is applicable only
for a fixed period of time, it has a "temporal" duration.

An ideal "wisdom" which has applicability over all topics has an infinite
spatial duration or "context". It therefore cannot have a finite temporal
context because space and time are dual. It is completely deterministic or
equivalently, timeless. This timelessness also makes this "wisdom" static
and hence there is nothing in it that one can call chaotic in the temporal
sense of "randomness". The dual natures of space and time and that of wisdom
and chaos respectively, require that if the contextual duration of something
is infinite, then so too is the contextual duration of it complement.

An ideal chaos, is one in which there is no temporal predictability[2].
In such a case, there can be no wisdom, or rather, any "wisdom" is
fragmented infinitely into infinitely small particles of "space". This
fragmentation of wisdom is "spatial" in the sense that it is dual to
the temporal "randomness". We say then that "temporal chaos" (randomness
of events) is a "spatially non-correlative" (noisy pattern of spatial states).

These are ideal cases which we have indicated earlier are not physically
measureable. We therefore cannot physically compress information into
an ideal wisdom nor encrypt data into an wholely undecipherable chaos.

Physically speaking, there is no perfect wisdom (certainty) nor perfect
randomness (uncertainty).

We only physically measure conservative mixtures of these dual complements.

Clearly we can measure more of one concept than the other of a
dual complementary pair of concepts. This allows us to call some
things "waves" and be reasonably acknowledged by others that we have
made such a classification "correctly". When we say something is a
"particle", it may be a generally acceptable statement even if it can
never be proven beyond doubt.

Something that seems to lie inextricably between one classification and its
dual complementary classification is called an "anomaly" or "paradox" or
"enigma" or "mutt" or "optical illusion", "platypus",... etc.

The "Quantum" from quantum physics is such a "mutt" of "particle" and "wave",
but we can only call something a "quantum" when we have trouble deciding
whether to classify the something as a "particle" or as a "wave".

When for the sake of pragmatism, we make a choice and classify a "quantum" as
a "wave", this choice forces us into a particular set of formalisms which are
complementary to the formalisms we would have been constrained by if we had
chosen to classify the quantum as a "particle".

For instance, we might use the impulse response (Green's) functions
(wave theory) at the expense of Feynman's purely particle mechanics (QED)
based on our choice in classifying a quantum as a "wave".

More often though, we mix formalisms just as we mix classifications and
hybrid formalisms of dual complementary formalisms result. Whereas we
call mutt classifcations "quantum" we might well call these mutt
(hybrid) formalisms by some name to represent them more clearly from
their more pure-bred underlying formalisms. We might just call them what
they are: "hybrids algorithms", or "dual functionals" but in keeping with
our grand old tradition of obfuscation, at least today, I would like to
call them "leviathans" because I think this word best explains what is
happening in the overall picture: that we are seeing the
"system within systems" and realising that this is in itself
a paradoxical situation.

[1] "Finite and Infinite Games", James P. Carse
[2] "The Limits of Mathematics", Gregory J. Chaitin


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