Adaptive Tension Systems: Towards a Theory of Everything?
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Adaptive Tension Systems: Towards a Theory of Everything?
Heikki Hyötyniemi
Helsinki University of Technology
Control Engineering Laboratory
P.O. Box 5500, FIN-02015 TKK, Finland
Abstract
Assuming that there really exists some general theory of complex systems, one has strong guidelines
for where to search for it. Such theory has to address the distributedness of the underlying actors in
the absence of central control, and it has to explain emergence in terms of self-regulation and some
kind of self-organization of higher-level structures. It is the neocybernetic framework of Adaptive
Tension Systems (also known as “elastic systems”) that is one candidate theory offering such visions,
making it possible to make assumptions about the “Platonian Ideals” of complex interacting systems.
As application examples, this methodology is here employed for analysis of molecular orbitals and
orbiting mass systems.
1 Introduction all of them: They all consist of distributed networks
where local-level interactions of more or less mind-
It is intuitively clear that there is something in com- less actors with only very simple functionalities result
mon beyond different kinds of complex systems — in self-regulation and self-organization that is visi-
is it not? At least in the complexity and chaos the- ble on the global level. The divergence of the mod-
ory communities such belief has been loudly pro- els, in the spirit of the celebrated “butterfly effect”
moted. However, as the promises have never been is just an illusion, as it is conververgence and stabil-
redeemed, this “chaoplexity” research is seen as an ity that that are the key issues in surviving systems.
icon of “ironic science”. The complexity theory can- It seems that the framework of adaptive tension sys-
not be based merely on intuitions. tems based on the neocybernetic theory (also known
But the “theory of everything” should neither be as elastic systems) offers the necessary functionalities
based only on mathematics, as has been claimed by (Hyötyniemi, 2006). It turns out that the emerging
the quantum theorists (Ellis, 1986). Not everything structures can be studied in the framework of prin-
can be expressed in formulas in a credible way — cipal components (Basilevsky, 1994). How to detect
even though system hierarchies are finally reducible the cybernetic nature of a system, then?
to the level of elementary physics, quantum theories Traditionally, the similarities between complex
do not offer the best modeling framefork for, say, systems are searched for in the static (fractal) surface
cognitive systems. However good models for micro- patterns. However, the deep structures based on in-
scopic phenomena can be found, they have little to do teractions and feedbacks are dynamic and they can
with macroscopic systems; they are not the most eco- only be captured by mathematical tools: the actual
nomical way of describing the emergent-level phe- observed patterns are dynamic balances in the data
nomena, thus being no good models at that level. space, and potential patterns are characterized by dy-
What is a good compromize between the extremely namic attractors. The similarities in underlying struc-
heuristic visions and the utterly down-to-earth analy- tures are analogies between mathematical represen-
ses? Mathematics is a necessary language, but intu- tations. Or, being more than formal similarities, such
ition and heuristics should be guiding what kind of analogies should perhaps be called homologies. In-
mathematical constructs are discussed; there are too deed, there exist some mathematical structures that
many directions available, but only a few of the routes can be seen as manifestations of the neocybernetic or-
lead to directions addressing relevance. What, then, dering principle.
are the relevant issues to be emphasized? Nothing very exotic takes place in neocybernetic
The underlying realms beneath complex systems mathematics – no “new science” is needed. Old sci-
are very different. However, something is shared by ence suffices, but the new interpretations spawn acompletely new world. Surprisingly, the resulting known as Huckel’s method, also reducing the anal-
models are analogical with cognitive ones, so that the ysis of energy levels in molecules into essentially an
subjective and objective “everything” can perhaps be eigenvalue problem (Berson, 1999). However, this
united once again. method is still based on combinations of atom or-
In this paper, it is shown how the above view can be bitals, and being based on crude simplifications, it is
exploited in analysis of physical systems, small and regarded as an approximation.
big. As application examples, modeling of molecules It is also quite commonplace that linear additiv-
and modeling of celestial bodies, are discussed. ity of orbitals is assumed on the molecular level —
normally it is atomic orbitals that are added together,
now it is molecular orbitals directly. Indeed, basic
2 Neocybernetics in the small physics is linear; the problems are normally caused
by the huge dimensionality of the problems. This
What if elementary physics were simpler than what all — linearity, eigenvectors — sounds like very
has been believed, what if understanding molecules neocybernetics-looking.
would not take a nuclear physicist? Below, the neo- The challenge here is to combine the neocybernetic
cybernetic analogy in cost criteria is employed. model with current theories and models.
2.1 Standard theories of molecules
2.2 Cybernetic view of electrons
Atoms are already rather well understood. The con-
temporary theory of atom orbitals can explain their There is no central control among individual elec-
properties to sufficient degree. However, it seems that trons, but the electron systems — atoms, molecules
one needs new approaches to understand the emer- — still seem to be stable and organized. Either there
gent level, or the level of molecules. Molecular or- is some yet unknown mechanism that is capable of
bitals are interesting because the chemical properties maintaining the stability and the structures — or, it is
of compounds are determined by their charge dis- the neocybernetic model that applies. The latter as-
tribution — essentially these orbitals reveal how the sumption is now applied, and the consequences are
molecule is seen by the outside world. studied. It is assumed that “electron shells”, etc., are
The molecules have been a challenge for modern just emergent manifestations of the underlying dy-
physics for a long time, and different kinds of frame- namic balances.
works have been proposed to tackle with them: First, The starting point (set of electrons) and the goal
there are the valence bond theories, where the indi- (cybernetic model) are given, and the steps in be-
vidual atoms with their orbitals are seen as a construc- tween need to be motivated 1. So, assume that the
tion kit for building up the molecules, molecule or- nuclei are fixed (according to the Born-Oppenheimer
bitals being just combinations of atom orbitals; later, approximation), and drop the electrons in the system
different kinds of more ambitious molecule orbital to freely search their places.
theories have been proposed to explain the emergent When studying the elementary particles, traditional
properties of molecules. In both cases it is still the thinking has to be turned upside down: For example,
ideas of atom orbitals that have been extended to the it seems that in that scale the discrete becomes con-
molecules. Unfortunately it seems that very often tinuous, and the continuous becomes discrete. Dis-
some extra tricks are needed: for example, to explain tinct electrons have to be seen as delocalized, contin-
the four identical bonds that carbon can have, pecu- uous charge distributions; however, their interactions
liar “hybridizations” need to be employed; and still have to be seen not as continuous but discrete, being
there are problems, a notorious example being ben- based on stochastic photons being transmitted among
zene (and other aromatic compounds) where the “bot- the interacting charge fields. This view needs to be
tom up” combinations of atom orbitals simply seem functionalized.
to fail. And, unluckily, it is exactly carbon and its First, study the macroscopic scale. Assume that
properties that one has to tackle with when trying to there are two charge fields i and j, variables x i and
explain living systems and their building blocks. xj representing their intensities. Energy that is stored
When thinking of alternative approaches, it is en- in the potential fields can be calculated within a single
couraging that molecules have been studied applying
discretized eigenvalues and eigenvectors, too: for ex- 1 Of course, “knowing” the end points and trying to fill the re-
ample, Erich Hückel proposed an approach that is maining gap, is a risky way to proceed!charge field as implement the emergent neocybernetic structures
xi
(Hyötyniemi, 2006). If the assumptions hold, there
1
Ji,i = c ξ dξ = c x2i , (1) is self-regulation and self-organization among the
0 2 electrons, emerging through local attempts to reach
potential minimum. Not all electrons can go to
where c is a constant, and among overlapping fields
the lowest energy levels, and “electronic diversity”
as xi
emerges automatically. Surprisingly, because of
Ji,j = c xj dξ = c xi xj . (2) their delocalization, “overall presence” and mutual
0
repulsion, the electron fields implement explicit
If the charges of i and j have the same sign, the poten- feedback, following the model of “smart cybernetic
tial is positive, denoting repulsion; otherwise, there is agents” (see (Hyötyniemi, 2006)).
attraction.
The result is that the charge distribution along the
However, the macroscopic phenomena are emer-
molecule (molecular orbital) is given by the principal
gent and become analyzable only through statistical
components of the interaction correlation matrix that
considerations; in microscopic scales, there are no
can be calculated when the organization of the nuclei
charges to be observed, only interactions. For two
is known. Because of the distinct nature of electrons,
fields i and j to intreract, the photons emitted by the
they cannot be located in various energy levels simul-
fields need to meet — denote this probability by p i,j .
taneously and eigenvalues become distinguished.
Then the effective potential is
When speaking of molecules, the “inputs” u j de-
J = p1,1 J1,1 + p1,2 J1,2 + · · · + pn,n Jn,n . (3) note the more or less fixed positive nuclei, whereas
xi denote the molecular orbitals within the molecule.
The symbols xi and xj have dual interpretation: they It is interesting to note that there are no kinetic
constitute the charge distributions, but simultane- energies involved in the energy criterion, and no ve-
ously they are probability distributions. As the pho- locities or accelerations are involved. As seen from
ton transmission processes are independent, the inter- the system perspective, the charges are just static
action probability p i,j is proportional to the average “clouds”. This means that some theoretical prob-
product of the intensities, or x i xj , so that lems are now avoided: As there are no accelerating
charges, there are no electrodynamic issues to be ex-
pi,j = E {xi xj } . (4)
plained as no energy needs to be emitted, and the sys-
Assume that the charge fields are divided into two tem can be in equilibrium. In contrast, such elec-
classes, the negative ones into “internal” and the pos- trodynamic inconsistencies plagued the traditional
itive into “external” ones. Further, assume that the atom models where it was assumed that the electrons
external fields are collected in the vector u, internal revolved around the nucleus, experiencing constant
ones remaining in x. The sum of energies among the centripetal acceleration, so that radiation of energy
negative charge fields can be presented in matrix form should take place.
as What is the added value when studying the new
1
J = xT E xxT x, (5) view of molecules? Whereas the electrons are delo-
2 calized, the heavier nuclei can be assumed to be better
and, correspondingly for positive charges, localized. The key observation here is that the analy-
sis of the continuous space — modeling of the charge
J = −xT E xuT u. (6) distribution of electrons — changes into an analysis
of a discrete, finite set of variables, or the nuclei. The
For the total energy one has idea of neocybernetic “mirror images” is essentially
J(x, u) = J +J employed here: rather than studying the system it-
(7) self, the electrons, its environment is analyzed. In
= 12 xT E xxT x − xT E xuT u.
this special case it is the environment that happens to
The above criterion J(x, u) is exactly the same be simpler to operate on.
cost criterion that was derived for ordinary Because of the properties of eigenvectors, the dis-
(neo)cybernetic systems (here it is assumed that crete orbitals are mutually orthogonal. Traditionally,
the balance is found immediately, so that x̄ ≡ x). it is assumed that there is just room for a unique elec-
This means that when appropriate interpretations are tron in one orbit (or, indeed, for a pair of electrons
employed, and when the cost criterion is minimized with opposite spins). However, now there can be
over time, the solutions for electron configurations many electrons in the same orbital, and there is noneed to employ external constraints about the struc- the orbitals, that is, for each carbon atom the number
tures, like assumptions of spins,
√ etc. The charge field of valence electrons in the system is increased by the
can be expressed as ψ i = λi φi , where λi is the number vC = 4, for hydrogen v H = 1, and for oxy-
eigenvalue corresponding to the orbital-eigenvector gen vO = 6. What kind of simplifications to (8) are
φi , so that the overall charge becomes ψ iT ψi = λi . motivated?
The “variance” λ i is the emergent measurable total The time-independent discrete Schrödinger equa-
charge in that field. This means that there are some tion that is studied can be seen as a quantized version
conditions for the charge fields to match with the as- of (8)
sumption of existence of distinct charge packets: −V0 φi + V φi = Ei φi , (9)
1. Eigenvalue λ i has to be an integer times the el- where φi are now vectors, 1 ≤ i ≤ n, dimensions
ementary charge, this integer representing the equalling the number n of atoms in the molecule;
number of electrons in that orbital. because of the structure of the expression, these
are the eigenvectors of the matrix V − V 0 corre-
2. The sum of all these integers has to equal the sponding to the eigenvalues E i . In the framework
number of valence electrons, sum of all free of the eigenproblem, now there is a connection to
electrons in the system. the neocybernetic model structure. Comparing to
the discussions in the previous section, there holds
These constraints give tools to determine the balance
Ei = λ2i , the eigenvectors being the same. Rather
configuration among the nuclei.
than analysing the infinite dimensional distribution of
How to quantize the continuous fields, and how to
electrons, study the finite-dimensional distribution of
characterize the effects in the form E{uu T }, and how
nuclei; one only needs to determine the n × n ele-
to determine the parameters? And how is this all re-
ments of the potential matrix V − V 0 to be able to
lated to established quantum theory? In short, how
calculate the orbitals (or the negative charge fields
are the above discussions related to real physical sys-
around the positive nuclei).
tems?
To determine the matrix of potential energies
among the nuclei, the challenge is to determine the
2.3 Neocybernetic orbitals terms corresponding to the first term in (8). The diag-
onal entries of V − V0 are easy: Because the “lo-
It is the time-independent Schr ödinger equation that
cal potential” is assumedly not essentially affected
offers a solid basis for all quantum-level analyses
by the other nuclei, the atoms can be thought to be
(Brehm and Mullin, 1989). It can be assumed to al-
driven completely apart, so that the non-diagonal en-
ways hold, and it applies also to molecules (h is the
tries vanish; the diagonal entries then represent free
Planck’s constant, and m e is the mass of an electron):
separate atoms, so that the electron count must equal
h2 d2 the number of available valence electrons, that is, the
− ψ(x) + V (x)ψ(x) = Eψ(x). (8) i’th diagonal entry is proportional to v i2 , where vi
8π 2 me dx2
presents the number of valence electrons in that atom.
Here, V (x) is the potential energy, and E is the For non-diagonal entries, the sensitivity to changes to
energy eigenvalue corresponding to the eigenfunc- distant nuclei becomes small, so that the term with
tion ψ(x) characterizing the orbital. As ψ(x) is the second derivative practically vanishes, and the
continuous, Schrödinger equation defines an infinite- corresponding entry in the potential energy matrix is
dimensional problem, and as x is the spatial coordi- according to basic electrostatics approximately pro-
nate, in higher dimensions this becomes a partial dif- portional to vi vj /|rij |, without normalization. Here,
ferential equation. Normally this expression is far too |rij | stands for the distance between the nuclei i and
complex to be solved explicitly, and different kinds of j.
simplifications are needed. Traditional methods are When the preliminary potential matrix has been
based on reductionistically studying the complex sys- constructed, elements of the matrix V − V 0 have to
tem one part at a time, resulting in approaches based be justified so that the eigenvalues of the matrix be-
on the atom orbitals. come squares of integers, and the sum of those inte-
Now, start from the top: As studied in the previ- gers equals the total number of valence electrons.
ous section, assume that it is simply a non-controlled So, given the physical outlook of the molecule in
play among identical electrons that is taking place in equilibrium, one simply carries out principal compo-
a molecule. It is all “free” electrons that are on the nent analysis for the “interaction matrix” V −V 0 , find-
outermost shell that are available for contributing in ing the set of “discrete orbitals”, or orbital vectors2.5
2 ~7 2 ~4 2 ~4
1.5 1.5 1.5
1 1 1
0.5 0.5 0.5
0 0 0
-0.5 -0.5 -0.5
-1 -1 -1
-1.5 -1.5 -1.5
-2 -2 -2
-2.5
-3 -2 -1 0 1 2 3 -3 -2 -1 0 1 2 3 -3 -2 -1 0 1 2 3
2 ~3 2 ~3 2 ~3
1.5 1.5 1.5
1 1 1
0.5 0.5 0.5
0 0 0
-0.5 -0.5 -0.5
-1 -1 -1
-1.5 -1.5 -1.5
-2 -2 -2
-3 -2 -1 0 1 2 3 -3 -2 -1 0 1 2 3 -3 -2 -1 0 1 2 3
~1 ~1 ~1
2.5 2.5
2 2 2
1.5 1.5 1.5
1 1 1
0.5 0.5 0.5
0 0 0
-0.5 -0.5 -0.5
-1 -1 -1
-1.5 -1.5 -1.5
-2 -2 -2
-2.5 -2.5
-3 -2 -1 0 1 2 3 -3 -2 -1 0 1 2 3 -3 -2 -1 0 1 2 3
2 ~1 2.5
2
~1 2.5
2
~1
1.5 1.5 1.5
1 1 1
0.5 0.5 0.5
0 0 0
-0.5 -0.5 -0.5
-1 -1 -1
-1.5 -1.5 -1.5
-2 -2 -2
-2.5 -2.5
-3 -2 -1 0 1 2 3 -3 -2 -1 0 1 2 3 -3 -2 -1 0 1 2 3
Figure 1: “Cybernetic orbitals” ψi in the benzene molecule (see text). The larger dots denote carbon nuclei and the smaller
ones hydrogen nuclei, distances shown in Ångströms (1 Å = 10−10 m). The orbitals, shown as circles around the nuclei, have
been scaled by the corresponding λi to visualize their relevances. The circle colours (red or blue) illustrate the correlation
structures of electron occurrences among the nuclei (the colors are to be compared only within a single orbital at a time). There
is a fascinating similarity with benzene orbitals as proposed in literature (for example, see Morrison and Boyd (1987))
ψi and the corresponding eigenvalues E i and elec- molecules. The “bonding energy” is the drop in to-
tron counts λi . The elements of the vectors ψ i reveal tal energy, or the difference between the energies in
around which nuclei the orbital mostly resides; the the molecule as compared to the free atoms; possible
overlap probability p ij is spatial rather than tempo- values of this energy are discretized, now it (without
ral. scaling) is 1·72 +2·42 +3·32 +6·12 −(6·42 +6·12 ) =
For illustration, study the benzene molecule: ben- 12.
zene is the prototype of aromatic compounds, con-
sisting of six carbon atoms and six hydrogen atoms in The presented approach is general and robust: For
a carbon-ring. Altogether there are 30 valence elec- example, the unsaturated double and triple bonds as
trons (6 times 4 for carbon, and 6 times 1 for hydro- well as aromatic structures are automatically taken
gen). The results of applying the neocybernetic ap- care of as the emerging orbitals only depend on the
proach are shown in Fig. 1. It seems that the three first balance distances between nuclei: If the nuclei re-
orbitals have essentially the same outlook as orbitals main nearer to each other than what is normally the
proposed in literature — for example, see (Morrison case, there also must exist more electrons around
and Boyd, 1987) — but now there are altogether 7 them. Spin considerations are not needed now, as
electrons on the lowest energy level! All orbitals ex- there is no need for external structures (orbitals of
tend over the whole molecule; the hydrogen orbitals “two-only capacity”) to keep the system stable and
are also delocalized, and such delocalization applies organized. However, no exhaustive testing has been
to all molecules, not only benzene. Note that the or- carried out for evaluating the fit with reality. In any
bitals having the same energy levels are not unique, case, the objective here is only to illustrate the new
but any orthogonal linear combinations of them can horizons there can be available when employing non-
be selected; such behavior is typical to symmetric centralized model structures.3 Neocybernetics in the large vealing how physical constants are bound together. In
practice, such invariances are equations — when the
Above, analyses were applied in the microscale — other variables in the formula are fixed, the last one is
but it turns out that there are minor actors when look- uniquely determined, so that its freedom is lost.
ing at larger systems, too. Here, the neocybernetic In the neocybernetic spirit, this all can be seen in
approaches are applied in cosmic dimensions. After another perspective again. There is a duality of in-
all, the galaxes as well as solar systems seem to be terpretations: whereas traditionally one searches for
self-organized stable structures. The domain field is invariants, now search for covariants. The idea is
very different as compared to the previous one, and, to apply the elasticity analogy: the same phenomena
similarly, the approaches need to be different. One can be represented, just the point of view changes.
thing that remains is that, again, one needs to ex- Emmy Noether first observed that all symmetries in
tensively employ intuitions and analogies. However, nature correspond to conservation laws; is it so that
rather than exploiting the analogy in forms, as above, all conservation laws can further be written as an elas-
analogy in functions is applied this time. tic pairs of variables?
3.1 From constraints to freedoms 3.2 Another view at classical physics2
As explained in (Hyötyniemi, 2006), neocybernetic When exploiting the above idea of employing degrees
models can be interpreted as seeing variation as in- of freedom in a new area, one first has to select an ap-
formation. They try to search for the directions propriate set of variables — such that they together
in the data space where there is maximum visible carry emergy in that domain. When speaking of me-
(co)variation; as seen from above, this means that chanical systems in a central force field, it turns out
such systems orientate towards freedoms in the data that one can select momentum to represent the inter-
space. As exploitation means exhaustion, feedbacks nal state of the mass point system, and force can be
that are constituted by neocybernetic systems “suck seen as external input:
out” this variation from the environment. Along the
axes of freedom, forces cause deformations: the sys- c
x = p = mv and u=F = , (10)
tem yields as a reaction to environmental tensions, to r2
bounce back after the outside pressure is relieved —
where m is the mass of the mass point, v is its ve-
exactly this phenomenon is seen as elasticity in the
locity, r is its distance from the mass center, and c
system. When the system adapts, freedoms become
is some constant. The central force is assumed to be
better controlled, meaning that the system becomes
relative to inverse of the squared distance; this holds
stiffer, or less elastic.
for gravitational fields, for example.
The challenge here is that such freedoms-oriented
How about the assumed covariation of the selected
modeling is less natural for human thinking than
variables? — For a mass point orbiting a mass cen-
modeling that is based on constraints.
ter, assuming that one only studies the angular move-
Indeed, all of our more complex mental models
ments, angular momentum can be defined as (Alonso
are based on natural language, and human languages
and Finn, 1980)
are tools to define couplings among concepts, or, re-
L = mv r. (11)
ally, constraints that eliminate variability in the chaos
around us. As Ludwig Wittgenstein put it, “world is If there is no external torque, this quantity L remains
the totality of states of affairs”, or the observed reality constant, or invariant, no matter how v and r vary.
is the sum of facts binding variables together. What is Applying the invariance of angular momentum, it is
more acute, is Wittgenstein’s observation that all con- evident that there is a coupling between the selected
sistent logical reasoning consists only of tautologies. variables x and u, so that
Similarly in all mathematical domains: axioms deter- √ √
mine the closure of trivialities, and it takes mathemat- x/ u = p/ F = constant. (12)
ical intuition to reach outside the boundaries, finding
the freedoms where the “life” is. In a way, one is to The variables are also covariants even though the
find the truths that cannot be deduced from the ax- manifested elasticity relationship is now nonlinear.
ioms — in the Gödelian sense! Now, following the steel plate analogy (Hyötyniemi,
When the natural languages set the standard of how 2 The derivations here (as in the previous case, too) are some-
to see the world, also natural laws are seen as con- what sloppy, guided by the strong intuition, hoping that applying
straints: one searches for invariances, or formulas re- some more advanced analysis the loopholes can be somehow fixed2006), there is internal energy and external energy individual accelerations of particles along their tra-
that should be determined within the elasticity frame- jectories.
work. From (10) one can solve for the stored internal There is no real long-term evolution, or “memory”
and external energies, respectively: in the system if there is just one mass point orbit-
v ing the mass center. But in a system of various mass
1
Wint = mν dν = mv 2 points the situation changes, and E{xu} can be max-
0 2 imized. For example, in an early star / planet system,
1 v2 1
= mr2 2 = Iω 2 (13) collisions make the system lose energy, as do the tidal
∞ 2 r 2 effects – average 1/r 2 and v go down, meaning that
c c
Wext = − 2
dρ = , the rotating bodies gradually get farther from the cen-
ρ ρ r
ter, and their velocity drops. On the Earth, this can be
seen in the lunar orbiting taking place ever slower.
where I is the inertia momentum of the rotating point-
On the other hand, less circular orbits are more vul-
wise body, and ω = v/r is its angular velocity. It
nerable to collisions, average orbits becoming more
is clear that these expressions stand for cumulated
spherical. As seen in observation data, variables seem
kinetic energy and potential energy, respectively, so
to become more constant – and the system becomes
that Wint = Wkin and Wext = Wpot . Thus, one
“stiffer”. Thus, cosmic systems truly “learn” towards
can see that the difference between internal and ex-
being more and more cybernetic-looking.
ternal energies in this system transforms into a differ-
ence between kinetic and potential energies — neo- Various mass points can be put in the same model,
cybernetic minimization of the deformation energy so that mi vi are the state variables and F i (in any di-
thus changes into the Lagrangian functional that is rection!) are the forces acting on them, 1 ≤ i ≤ n.
known to govern the dynamics of a mechanical sys- When the principal component structure of this cy-
tem. Surpisingly, the Lagrangian that was found ap- bernetic many-point system is studied, it turns out
plies not only to circular orbits but also to more gen- that the model is more or less redundant: not all
eral non-cyclic motions; the circular orbit represents directions in the n dimensional data space of the n
the (hypothetic) final balance. mass points carry the same amount of information,
The Lagrangian mechanics has exploited the La- many particles in the system behaving essentially in
grangians for a long time — is there some added the same way. Assume that the multi-body kinetic
value available here? Applying the neocybernetic in- energy term 12 ω T Iω with the angular velocity vector
tuition, one can see that global behavior is an emer- ω and (originally diagonal) inertia matrix I, is com-
gent phenomenon resulting directly from local low- pressed so that the dimension is dropped from n by
level actions that one does not (and needs not) know. ignoring the directions with least variation. This es-
What is perhaps more interesting is that in the neocy- sentially means that one is no more speaking of mere
bernetic framework there is possibility to say some- mass points but some kind of conglomerates with
thing about the adaptation, or evolution of the system. more complicated internal inertial structure. One has
On the local scale, minimization of the average de- “emergent inertia” – galaxies, etc., can be seen as vir-
formation energy means maximization 3 of tually rigid bodies.
On the other hand, the inertia of 3-dimensional
mv
objects can be seen as an emergent phenomenon.
E {xu} = E {pF } = c E . (14)
r2 For example, the velocities of sub-atomic particles in
electric fields are so high that when looking at ev-
What does this mean? The system evolution really
eryday objects, one only can see the emergent global
tries to maximize the product of the covariant vari-
behaviors that follow the laws of classical physics. In
ables: evidently, a mass point tries to align its move-
the cosmic scale, however, the adaptation towards the
ment in the force direction — on average, applying
gravitational asymptotic structures still continues.
force means acceleration in that direction. Newton’s
second law (there holds F = mv̇ for for aligned
vectors) could be reformulated in a sloppy way as 3.3 Further intuitions
momentum tries to increase if there is force acting,
abstracting away exact representations characterizing Elasticity seems to be rather powerful idea also in ba-
3 Counterintuitively, local emergy maximization in adaptation
sic physics: beyond the observations, in super string
results in global system “laziness”, or deformation energy min-
theories, the elementary particles are seen as vibrat-
imization, similarly as local pursuit towards variation results in ing strings. Perhaps elasticity analogy applies there,
global system “equalization” and variation minimization too?But regardless of the form of the final theories, that determines the wave propagation, the emerging
it seems that thinking of the universe as an elastic behavior representing the statistically most relevant
self-balanced shell reacting to external pressures, this alternative. Similarly, the only realized universe is
“shell” being distributed in matter particles, offers a where the optimality of energy transfer is reached.
useful framework for studying matter. The Heisen-
bergian thinking is to be extended, as it is all interac-
tions (not only measurements) that affect the system, 4 Conclusion:
the effective variables being reflections of the emer- Neocybernetics everywhere
gent balance among the system and the environment.
Measurable variables are “interaction channels”, each To conclude the neocybernetic lessons: everything is
interaction mechanism introducing a string of its own. information; visible matter/energy is just conglomer-
The natural constants are not predetermined, but they ations of information, or attractors of dynamic pro-
are the visible manifestation of stiffness, balance ra- cesses governed by entropy pursuit.
tios between reaction and action. The modern the- Neocybernetic models pop up in very different
ories employ some 11 dimensions where there are cases, not only in those domains that were discussed
some “collapsed dimensions” among them; it is easy above. Many systems can be characterized in terms
to think of these vanishing degrees of freedom as be- of optimization, models being derived applying cal-
ing tightly coupled to others through the cybernetic culus of variations, the explicit formulas (constraints)
feedback controls. The constants of physics should being the emergent outcomes of underlying tensions.
not be seen as predetermined quantities: there are When all behaviors are finally implemented by unco-
propositions that the natural constants are gradually ordinated low-level actors, it seems evident that such
changing as the universe gets older. One of such models could be studied also from the neocybernetic
propositions is by Paul Dirac, who claims that cos- point of view.
mology should be based on some dimensionless ra- The clasical “theories of everything” study a rather
tios of constants. narrow view of everything. It can be claimed that
If the cybernetic thinking universally applies, one a theory that does not address cognitive phenomena
can exploit the understanding concerning such sys- cannot truly be called a theory for everything. The
tems: Perhaps universe as a cybernetic whole is opti- subjective world needs to be addressed as well as the
mizing some criterion? objective one, the theory needs to couple epistemol-
It has been estimated that to have a stable, non- ogy with ontology. In this sense, being applicable also
trivial and long-living universe that can maintain life, to cognitive systems, it can be claimed that neocyber-
the natural constants have to be tuned with 1/10 55 netics is a very potential candidate for such a “general
accuracy. Such astonishing coincidence has to be ex- reality theory”.
plained somehow, and different families of theories
have been proposed. First, there are the anthropic the- References
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