### Uncertainty in Science, and Society



There have been many derivations of the Heisenberg uncertainty
principle[1][2],... And many interpretations of that relation
applied to non-electric signals [3][10].

The Fourier derivation is one of them[8]. The signal processing
or Fourier approach starts off with the idea that the uncertainty
in the time of a signal (t) and the frequency of the signal (w)
are related as:

A)     \delta t \delta w >= 1/2

from which the Heisenberg relation is obtained as:

B)     \delta t \delta hw >= h/2

or

C)     \delta t \delta E >= h/2

The relation A) is interpreted as:

You cannot simulataneously know the time of a signal and its
frequency with infinite precision on both variables.

A more exact interpretation is that you need time to measure
the frequency and the amount of time you need is determined by
the Nyquist limit. The time you must expend in determining the
frequency is at a lower limit when you have a priori knowledge
of the frequency you are measuring, but when you don't have
such knowledge, the time can be considerably longer. This
non-deterministic expenditure of time leads to a corresponding
uncertainty in the temporal position of the signal.

A more intuitive interpretation is to say that the knowledge
of the temporal position (the time) of the signal is
"complementary"[5] to the measurement of frequency _before_
you measure that time. If you measure the time first,
then you know exactly where the signal is on the time line,
but the frequency is indeterminate at that exact point in
time because you can't measure frequency at a point in time,
only over an interval of time (unless you already knew the
frequency[4])

The simplest interpretation is to say that the measurement
of the temporal position of the signal (its time) just isn't
conceptually compatible with the measurement of frequency.
More specifically, the definitions of these two quantities
in an a priori non-deterministic measurement are anti-correlated[2].
There is no such thing as an "instantaneous frequency measurement"
of some unkown signal. The is no such thing as "the frequency
of an infinitely small sample of a signal". We can say these
concepts are become "meaningless" when we know the
exact value of the complementary variable.

A more general interpretation is the concept of
"the center of mass" of rigid rod becomes meaningless when as
the rod extends towards infinite length. This is why you can't
determine where the center of the universe is.
It's anywhere you like, it's completely uncertain where it is,
the center is arbitrary, it's position is relative. These all
mean the same thing and this interpretation is consistent with
the idea that you gain more time in relativity theory at the
expense of space contraction[7].

Heisenberg's uncertainty is a special application of a more
general uncertainty theory that says: some pairs of concepts
are complementary and you can't have perfect instantiations
of both at the same time.

If you are driving a car, you cannot measure your exact position
and velocity at a specific point. "Velocity" has no meaning for
specific points in space it is only defined over some interval
of space. So you make up an uncertainty relation:

D)          \delta x \delta v >= k

where k is some undetermined factor[6], this relation gets
the same interpretation as Heisenberg's:

E)          \delta x \delta mv >= mk

where m is mass, or more quantum mechanically in terms of
de Broglie's relation:

F)          \delta x \delta p >= h/2

where p is momentum.

But the basic interpretion is simplistic and has less to do
with "particles" and "waves"[9], than with the philosophy of
"measurements" at all scales from micro to macro-cosmic.
That's why there is a whole separate field called
"measurement theory", but really these ideas have been considered
for well over 4000 years now by philosophers and theologians
investigating the meaning of distinguishments (measurements) and
non-distinguishments (observations and metaphors) and dualisms
(correlated complementary concepts) and valuations
(what is exactly is "money" ?).

Norbert Wiener[10] writes on the generalized uncertainty principle:

"It is theoretically not possible to develop the
statistics of the semantic and behaviour languages
to such a level taht we may get a fair measure of
the amount of information that they contain. Indeed
we can show by general observations that phonetic
language reaches the receiving apparatus with less
over-all information than was originally sent, or
at any rate with not more than the transmission system
leading to the ear can convey; and that both the semantic
and behaviour language contain less information still.
This fact again is a corollary of the second law of
thermodynamics, and is necessarily true if at each stage
we regard the information transmitted as the maximum
information that could be transmitted with an appropriately
coded receiving system."

This is a connection between information theory and
linguistics, which has been developed more recently
with more rigor.

Wiener noted the political-cultural-social impact of
such ideas but other notable scientists in the areas
of measurement theory, communications theory, and
information theory, and linguistics also write of the
impact of ideas on measurement (which we do at many
levels in society from measuring quanta to "measuring"
whether or not we like Picasso.)

Bohm [11] writes on the impact of quantum theory with
societies notions of individuality vs. mutuality:

"We treat other people as objects, and eventually you must
treat yourself as and object, saying, "I must fit in here,
and I must do this and be that and become better," or whatever.
But "society" is not an objective reality- period. It is
really created by all the people through their consciousness.
It has become "objective" features which you can point to
once people have created it, particularly because there are
so many taking part- it is statistical.
The same thing happens in physics. If you try to measure one atom
exactly you can't do it- it participates. But if you take a
statistical array of atoms, you can get an average that is
objective. It comes out the same no matter who does it, or when.
The average comes out but the individual atom does not.
And in society you can also get average behaviours, which are
often predictable. But they are not very significant, compared to
the thing that really moves us and makes society come into being.
Individually and collectively - together - we have a consciousness
which creates society, and sustains it with thought, intellect,
feeling, and so on." [italics his]

Authors in linguistics, information theory and
communcations theory that explored similar ideas connecting
their works to politics, culture and society are:
Saussure(diachronic and synchronic "Fourier analysis" of linguistics),
Chomsky (computable grammars),
Wiener(Cybernetics),
Foucault(linguistic quanta),
Huxley(double-speak),
Bohm (quantum Theory),
McLuhan ("The Media is the Message"),
Sapir-Whorf (Linguistic Relativity theory),
Quine (Translation Indetermincacy theory), ...
just to name a very few.

Uncertainty is a facit of life no less that certainty. In china,
the words "danger" and "opportunity" are intimately synonymous
reflecting the idea that we derive movement or change from uncertainty
and risk.

It is an inescapable idea that each action is uncertain to some
extent and so potentially dangerous such that we will not in the
present know what effects our actions have on the future. Each
action generates both expected and unexpected results to various
degrees depending on where we are in time. For instance, if I
burn a tree "now" for heat, that is "good" if I am very cold,
but it is only "good" now. Later in time, I may consider it "bad" if
I'm then starving and need to eat fruit from the tree. Such
measurements as "good" and "bad" are temporal. "Ethics" fluctuates
in time like a wave; but morality doesn't (This is similar to
the Einstein-Bohr debate where Einstein in a sense argues that there is
an underlying reality or morality, over which we superpose the
uncertain and fluctuating ethical reality of Bohr).

We may say abortion is "bad" when times are good, and "good"
when times are "bad". Abortions in an overpopulated world may
become the more desirable of two evils(see Aristotle).
The same idea concerns nuclear power, if we can't afford _not_  to
use nuclear power, we use it despite the fact that we know it is
a dirty and dangerous source of energy. What determines whether
we will survive such transgressions of "morality" is to what extent
we percieve our position in a much larger context of spatial-temporal
history. It is essential to optimize such a strategy of "ethical reversals"
which would otherwise lead to quickly exhausting our thermodynamically
limited options.

------------------------------------------------------------------------------
[1] A Least Squares Analysis of the Uncertainty Principle,
John Forkosch, Am. J. Phys, 39/4
[2] Fuzzy Thinking, Bart Kosko (geometrically in terms of
Cauchy-Schwartz inequality), pg 114-115
[3] Word & Object, Willard van Orman Quine (translation indeterminacy),
pg 172 for a connection to Einstein's relativity theory.
[4] QM doesn't consider that this knowledge is present a priori,
otherwise there would be no reason to do a simultaneous measurement.
[5] or "non-commutative" since if you reverse the order of the measurements
you can get an exact measure of the complementary variable, you just
can't get an exact measure of both.
[6] I think probably one can derive the Special Relativistic
relations in the sense of E), [2] and [7].
[7] Special relativity, A. P. French, pg 104 "Another interpretation
of the Time-dilation Experiment"
[8] Signal Processing in C, Reid and Passin
[9] wave-particle duality expresses the _conceptual_ uncertainty
even further, but when you question whether a Dirac blip on
your oscilloscope is a particle or, a wave which is zero
everywhere except at one point, you run into a conflict of
concepts; can you always tell which is the "carrier" and
which is the "signal" ? Some artists and philosophers take
this to extreme and paint the white canvas all white, or
others like Foucault and Magritte paint paradoxical
linguistic-visual "quantum" dualisms like:

Ceci n'est pas une pipe ?

(Foucault's book is subtitled: "an Art Quantum")
An Art Quantum

"Quantum" is synonyous with dualism.

Quantum physicists still make a racket out of hyping and hawking
"duality" no less than many religions. But they also do alot of
nice things with that funding, so nobody really minds. They just
put it out of their minds.

It's alot like IPOs in the stock market, you don't bad-mouth a new company
because its not delivering a profit _today_. You hype it up to get funding
for it, because you "believe" in it. You believe in its future profits.

That's like particles and waves. The waves (wavefunctions) are your
beliefs (probabilities) of the future of the particle but the quantum
as a tangible particle, only exists when it is measured in the present,
just like when you sell (measure) a stock. Its value goes from
being speculative, or subject to wave-like fluctuations due to many
possible opinions (like the "Many-Worlds" interpretation of QM) of the
stock's value, into a tangible, exact and localized value, like a particle.

The really tricky part is that: even this tangible "cash" that you sell
the stock for, is speculative itself. Foreign exchange rates, fluctuations
of inflation,... so cash is particle-like but really it is a "quantum" or
wave-particle.
[10] The Human Use of Human Beings-Cybernetics and Society, Norbert Wiener,pg 81
[11] On Dialogue, David Bohm, page 88
[12] Course in General Linguistics, Saussure


Home