Michel Petitjean Wrote:
>More than 70 messages were emitted since the beginning of the
>session, discussing about entropy and information, and sometimes
>about symmetry.
>Nevertheless, the relations of these concepts with order and disorder
>has been little evoked.
>There are definitions for information, entropy, and symmetry.
>I am convinced that order (or disorder) merits its own definition,
>and that, once this definition is exhibited, we could work to
>establish relations with other concepts. Existence of order and
>disorder only through intuitive assertions is not satisfactory.
>Does somebody could exhibit physical or mathematical definitions
>of order or disorder, apart from "entropy is disorder" ?
I am impressed that the editor of Entropy would offer such an open
question. Your supposed to assume this is resolved (Boltzmann), yet
complex, or unanswerable in simple terms. I have never believed in a
complex universe. Complexity is something we don't understand properly.
Prior to general relativity, our understanding of the large-scale
structure of the universe (what is now space-time), was I think in a
state of vague comprehension similar to our present comprehension of
order and disorder.
A general theory of order and disorder must bring together all the
elements of order we experience, explaining both the physical patterns
we observe so vividly and also the hidden order related to probability
and potential. What is the order of the early universe? What is the
order of a star? A spiral galaxy? A general theory must reveal how the
simple density order of a star is different from the order of a spiral
galaxy, or the order of a snowflake. All are physical patterns. But what
then is the order of available energy or work? What is the order of
rhythm and music? What is the order of fresh deck of cards or
alphabetization? What is the order of a grocery store? What is the order
of an entropy correlated with symmetry?
A general theory must explain the inconsistencies in the existing model
of understanding, and Dr. Lin is exposing a very signficant
inconsistency. Isn't symmetry an expression of order? The second law
indicates that order is generally decreasing, while disorder is
increasing. The dense past is obviously ordered, yet density, the
roundness of a star for example, is a very general type of order
compared to the intricacy of a snowflake. We can easily recognize the
order of symmetry or anti-symmetry in a checkerboard, yet what of Dr.
Lin's correlation between entropy and symmetry. Lin has exposed
something that can't be denied. In extreme, symmetry is ugly, boring,
lifeless. But does this mean symmetry is not order? Is there also a
correlation between entropy and disorder? There is clearly finely
ordered patterns at colder temperatures, such as a snowflake. Near
absolute zero, cesium atoms line up in columns and rows. A little
further we run into Einstein-Bose condensate, the union of atoms into a
single medium. The atoms are not really destroyed. They are somehow
still inside that medium. When warmed they differentiate. Uniformity,
symmetry, is order, but how does it relate to the order of the young
dense universe? Why is there any order at extreme low temperatures, if
generally disorder is increasing? Could the second law be inaccurate
about disorder increasing?
There is a new element at hand, where the tensions concerning the
meanings of order and disorder peak, which is actually a good thing.
Cosmologically, the expansion of the universe is accelerating, which
disturbingly indicates the course of time is on a crash course with
absolute zero in either finite or infinite time. How do we define
absolute zero in respect to order and disorder? It appears now that
absolute zero is not just a hypothetical or impossible temperature of
matter, it is a potentially real cosmic state in our future, a state of
zero mass, energy, density, temperature, and time. Empty space isn't
suppose to exist, yet if expansion is accelerating, the arrow of time,
our future, is inevitably in direct alignment with zero. But what is a
universe stretched flat? Nothingness? Is it disorder? Isn't empty space
perfect symmetry, the extreme of ugly symmetry!
How does all this fit together?
Lauri Gröhn wrote:
"Why should there be just ONE definition of order? Why not have a
metadefinition of order for defining various 'orders'?"
That indeed is the trick. There is not one general type of order. Nor is
there a general disorder. There are two specific types of order, and
only two. The density of the past and the symmetry of the future are two
different types of order, although the order of the past is not simply
characterized by density. The future, is perfectly characterized by
symmetry, uniformity, balance, neutrality. The past is a little more
complex, but not much.
The universe of time, the cosmic evolution of the universe is literally
a process of transformation from the extreme of one type of order to the
extreme of a whole other type of order. There are two types of order in
nature, not simply order and disorder. Generalizing order has been our
mistake. We exist in an intermediary phase within the transition between
the two orders, so everything we see is a product of the two orders
combined together. We can only see the two orders in pure form at the
beginning of time and at the end of time, although we cannot think
simply in terms of the point of the big bang being the extreme of the
first type of order, because there is more to the order of the past
behind the scenes of the big bang. Hence we don't see the order of the
past clearly. And we don't recognize that time ends at zero yet, so we
don't see that order clearly either.
The two types of order are extremely simple. We actually know them both
very well. We do after all exist in a world structured exclusively by
them. The first type of order is best referred to as grouping order.
Grouping order is the order we are accustomed to recognizing. At the
grocery store, all the products are organized into groups. Books in the
library are organized into groups. Your home is likely organized
utilizing grouping order. The socks are together in the drawer. The
dishes are in the cupboard. There is also the grouping of matter into
stars, and planets, where there is further grouping of particles into
elements. Stars are further grouped into galaxies. Galaxies are grouped
into clusters and superclusters. But a spiral galaxy we see nature
utilizing both grouping and symmetry.
The prototype example of grouping order is the process of setting up the
game of checkers or chess. That process involves taking all the game
pieces of one color (black) and placing them on one side of the board,
then all the pieces of another color (white) are placed on the opposite
side of the board. Grouping order is characterized by dividing things
apart. Oppositely, symmetry order, is characterized by combining things
together. In one direction things become individual and pronounced. In
the other direction things become balanced and uniform.
The checkerboard upon which chess or checkers is played is an ideal
example or prototype of symmetry order. The squares are not divided
apart into separate groups, they are mixed together evenly. Notice the
opposition. You can either separate things into groups, or mix them
together evenly. And mixing things evenly is not disorder. A
checkerboard pattern exhibits obvious order, until we blend the color of
each square perfectly even. This is because each two squares are like
the divided apart checkers. Each individual colored square represents a
measure of grouping order. Each is a group of colored points. The
strange thing is that if we push the order of the checkerboard pattern
toward greater balance and uniformity, the appearance of order
disappears. The colored squares, like mixing two colors of paint, become
one color (like many particles becoming a unified condensate). In fact
the order visible in a checkerboard pattern is pronounced only because
each square is still a case of grouping order. In greater extreme, the
order of a checkerboard becomes smooth and even, plain boring and ugly.
We are not accustomed to recognizing a uniform pattern as order. When
things balance out, when gases escape confinement and spread throughout
the room we say disorder has increased. The available energy has decreased.
Yes, entropy has increased, but disorder has not increased, because the
fact is, there is no such thing as a general disorder. All there is are
two types of order which are opposites, and so the order of one type is
the disorder of the other type. The disorder of grouping order is
symmetry order. The disorder of symmetry order is grouping order. The
entire assortment of imaginable patterns available to the passage of
time are created only by mixing together grouping and symmetry.
To explain this, imagine setting up checkers, except the goal of the
game is to move the pieces from opposite sides one at a time until the
game piece colors match up with the checkerboard colors. We are moving
the game pieces from grouping order to symmetry order, and in between
the two opposing directions of order we find ourselves in what appears
at first to be disordered states. There are many unique patterns.
However, notice that in moving any piece in any direction, you either
increase grouping order or increase symmetry order. You can only move
away from like colored pieces to improve the overall symmetry order of
the pattern or toward like colored pieces to create greater grouping
order. In the same way, the universe can only expand or contract. We can
either divide things apart or blend them together. Systems don't move
from order to disorder. They move from grouping to symmetry. We are just
not accustomed to recognizing the plain, boring, ugly, order of extreme
uniformity, balance, and symmetry as order. Dr. Lin has come the closest
to uncovering this model that I am aware of.
Of course Lauri, all this applies to music or sound very easily. Any
note is grouping order. An even rhythm of notes is symmetry order. One
steady tone is like one color of paint, it is symmetry order except for
the tone itself, which is grouping order, as it is above silence.
Silence is extreme symmetry order. White noise is symmetry order. Two
quick beats is greater grouping order. The crescendo is a strong mix of
both grouping and symmetry, with all the instrument noises together, the
opposition to silence, being grouping, but each instrument playing at
the same time is also a measure of symmetry. Now it should be easy to
see that a drum has less symmetry by nature than a violin.
The nature of grouping order is division, separation, distinction,
individuality, density, pronunciation, opposition, and conflict.
Symmetry order involves balance, integration, combination, uniformity,
homogeneity, singularity, formlessness, symmetry, and unity. The two
orders reflect two basic natures in the Universe, and also two
directions of increase that are opposite to one another. We can easily
find these two orders as conflicting influences in nature, in society,
in psychology, in politics. Republicans versus the democrats.
Conservative verus Liberal. This polarization is different from positive
versus negative, white or black, which is within grouping order itself.
This conflict is past versus future.
Fundamentally the self, anything definitive and pronounced, is grouping
order. The self relative to the many, one group relative to the whole,
is a fundamental theme in literature and movies. Clubs, states,
countries, race, class, interests, are all ways that we group together.
Sometimes those groups clash with eachother. Sometimes they clash with
the whole. Anything indefinite, uniformity, neutrality, zero, empty
space, is symmetry order. Symmetry order is not the cancellation of
sides, it is the combination of parts into a whole. Everything in the
frig thrown in a pot and cooked for ten hours becomes a uniform whole.
The universe isn't getting smaller, it is getting larger, becoming
whole. The funny things is, in understanding order properly, one
realizes that if anything is disorder, it is the imbalances of grouping
order, the past. Symmetry is actually the truest order. So the universe
is actually becoming more ordered, becoming one.
The spiral structure of a galaxy exhibits obvious symmetry, but the
grouping of stars into that galaxy as opposed to an even distribution
throughout space is obviously grouping order. To understand how the big
bang represents the extreme of grouping order we have to consider the
process of setting up the checkerboard, and recognize that the universe
is characterized by positively and negatively charged particles. The
point of the big bang is not simply all matter collapsed into a dense
point. It is all the positives separated from all negatives. It is
positively charged matter, the protons, separated from all the
negatively charged matter, the mirror anti-protons. In essence what I am
saying is that the point of the big bang is merely half of the whole.
And so there is a mirror universe, identical to our own, except it
begins from a negatively charged big bang. In reference to our universe,
it is made of anti-matter. The entire process of time involves the
matter from one side invading the other, in particle form as the
electron point particles that cannot be spatially extended in our
positive space, and also uniformly which is what is causing each
universe to expand larger. The process is like opposite sides of a chess
game invading each other, until only the uniformity and balance of the
checkerboard is left behind, on the surface.
Applying the transformation of grouping order into symmetry order to
cosmology in general is involved but the result is no less complex than
applying relativity to the structure of space-time. What before seemed
incomprehensible turns into a very descriptive model of understanding.
Things like, why is there so much matter and no anti-matter, or why is
the proton so large compared to the tiny electron point particle,
suddenly make sense. Why does time begin with a bang and always travel
toward zero? Because zero is the cosmic balance point, the point of
perfect symmetry. Omega zero is the balanced whole, the timeless
infinite Universe.
That is an explanation of two orders fast and furious. I will be
publishing a book this summer. For further reading you are welcome to
visit my websites:
http://macrocosmicsymmetry.com
http://everythingforever.com
Devin Harris
Received on Sat May 22 00:53:52 2004
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