What Physicists Think About?

The following is the remarkable beginning to a new seminal paper reported in the "physics daily" e-letter.  The whole paper can be found on this archive site.  Because it goes far beyond the normal kind of thing you find in physics papers I thought some of you who are intensely concerned with balance, harmony, resonance and other musical relationships (not to mention truth and beauty) might find it of interest.

Regards,

Amos

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8 levels of harmony and 8 concepts of Complex Systems

D.B. Saakian
Abstract

A set of general physical principles is proposed as the structural ba-
sis for the theory of complex systems. First the concept of harmony is
analyzed and its dierent aspects are uncovered. Then the concept of
re ection is dened and illustrated by suggestive examples. Later we
propose the principle of (random) projection of symmetrically expanded
prereality as the main description method of complex systems.

To understand complex phenomena [1] we suggest to detalize the concepts
of harmony and re ection [2].

1. Harmony.

Considering Random Energy Model (REM)[3] in physics , swan neck as a
symbol of beauty and concept of harmonic person I have found 8 levels of har-
mony. First 6 levels are general, the latter ones are specific for alive systems.
 

1. Symmetry, global or local.

Local symmetry could be considered as information processing property.

2. Variation principle.

3. Parametric resonance or Nishimori temperature [4] eect.

If there is a hierarchy in a system and it is possible to dene the essence for each
of its levels (a word, a number or a sign), there is a harmony, if they coincide.
For the case of reflection one can define a harmonic reflection when the essence
of reflected reality coincides with the essence of reflection.

4 Multi-logical reading of a system.

Every deep truth has several faces and any interesting physical system allows
different ways of solution-REM, Hydrogen atom, 2d Ising model....
 

5. Edge of chaos or existence of almost opposite pure qualities in the same

system.

Such situation was essential for evolution [5],[6], d=1 barrier in strings also be-
longs to this case [7],[2].

6. Modalities.

R.S.Ingarden,A. Kossakowski,M. Ohya introduced [8] modalities as "possible
non- categorical attitudes to reality". From this point of view space, potential
energy, classical entropy, classical information, quantum entropy and informa-
tion are steps of the hierarchical staircase. I add to this list the number of
replicas . Perhaps there are some harmonic situations here: "golden section",
two replicas as multicritical point in generalization of [9]...
One can distinguish dierent modalities by the level of complexity, so it will
be reasonable to expect, the more is complex the system, the higher it
should climb on the modality staircase.

7.Principle of purity.

It is connected with the points 2. and 5., but it is something more. The sur-
vival of system (vital energy!) is connected with the degree in which system
1•can reveal almost opposite pure properties. This property is crucial for human,
without it any serious harmony is impossible. It will be interesting to dene
it on quantitative level for other complex systems. Here it could be connected
with conservation or circulation of some free energy among the hierarchy levels
and while losing this property system becomes dissipate.

8.Principle of minimal reflections.

This principle explicitly works in ethics (nobody likes words "not","but" and
likes modesty) and economics (too much stocks create crush).

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The rest is at http://arXiv.org/abs/cond-mat/0102510.  Enjoy!!

Amos