Newsgroups: bit.listserv.geodesic
Subject: Applied Computational Cosmography (Long Part1)
Date: 14 Nov 1994 14:25:45 -0500

Applied Computational Cosmography
Part I -- First Steps

June 17, 1992
Revised & Expanded November 5, 1992

Richard J. Bono
Brownsville, TX. 78521

Compuserve: 70324,1712
Internet: 70324.1712@compuserve.com
, rjbono@AOL.com

Applied Computational Cosmography
Part I -- First Steps

I.      Introduction

II.     Generalized Computations & Complexity
        A. Problem Solving
        B. Computational Complexity
                -Example: integer scanning
        C. Supercomputer Paradox
        D. Computational Design Science

III.    Computational Synergetic Geometry (CSG)
        A. Caveats
        B. Description of the CSG Paradigm
                -Fast Fourier Transform (FFT) analogy
        C. CSG Components
                -Inputs & energy
                -Processing elements & structures
                -Geometrical framework
                -Transformations & mapping
        D. Efficiency
                -Thermodynamic considerations
                -Loudspeaker analogy
                -Efficiency of the CSG
        E. Dynamic Modeling with the Jitterbug
                -The jitterbug model
                -Complexes of jitterbugs
        F. Neural Networks, Cellular Automata, Lions and Bears (Oh My!)
                -Generalized neural nets
                -Generalized cellular automata

IV.     Implementation Methods
        A. Hardware
                -Processing elements
                -Euler's topology & Gibbs' phase rule
        B. Software
                -Gibbs' phase rule
                -Structure mapping & modeling tools
        C. Input/Output

V.      Applications
        A. The Grand Challenge Problems
                -Climate modeling
                -Quantum physics
                -Crystal Engineering
                -Managing the human genome
                -Non-linear systems
                -Machine vision
                -Cognition
                -The shortest-network problem
        B. Balancing your Checkbook
        C. "Trivial" problems and CSG

VI.     Summary & Conclusion

VII.    References


Applied Computational Cosmography
Part I -- First Steps


The application of synergetics to the theory of computation is
examined.
 The need
 for a new method of computation is discussed in
terms of problem solving
 and
 computational complexity. Preliminary
discussions of a proposed
 Computational
 Synergetic Geometry (CSG) lead
directly to descriptions of CSG model
 components and implementations.
Potential applications of the CSG model
 are
 examined. A list of
preliminary development tasks is outlined.


Introduction

This paper is a preliminary discussion of ideas and methods towards the
implementation of a
 generalized Computational Synergetic Geometry
(CSG). The CSG is a
 completely new and
 previously undisclosed
computational paradigm. As such, the author must
 make clear that the
concepts and ideas presented in this paper are not yet definitive. When
inaccurate, I hope to be at
 least definitively inaccurate.

The application of Computational Synergetic Geometry is based on two
steps. The first step is to
 reorder the problem at hand using
synergetic geometry. It will be shown
 that this immediately
 yields a
simplification of the problem that can be processed with reduced
space-time resource
 requirements on conventional computers. The second
step is to apply
 synergetics to the method
 of computation itself. This
will yield massive performance advantages and
 provides insight into
the nature of the problems we are trying to solve. Implementation of
these
 steps will require a
 fundamental shift in the way we view the
interaction between our
 conceptual models,
 computations and
experimentally demonstrable reality.



Generalized Computations & Complexity


Problem Solving

Computations are designed to solve problems. The present theory of
computation recognizes
 that some problems are solvable and others
simply are not. A problem is
 unsolvable if no
 algorithm can solve it.
An unsolvable problem will not converge to a
 solution even when given
infinite space-time resources. Some solvable problems require extremely
large space-time
 resources. The solvability of such problems becomes
one of economics
 (i.e., "What's knowing
 the answer worth to you?").

One of the objectives of computer science is to identify which
problems,
 because of unsolvablity
 or space-time resource constraints,
should not be attempted.

Most problems involve irrational numbers in their calculations. If we
want
 to compute the
 volume of a sphere with a given radius, R, we use
the following equation:

                                V = (4/3)*R^3


Pi (*) is an irrational number that is approximated by truncating to
fixed
 number of decimal
 places. Pi is introduced in our calculations
because of the linear focus
 of analysis. R.
 Buckminster Fuller
discovered the synergetic geometry based solely on
 radial and
circumferential, rather than linear and cubic accounting. Fuller
explains:


"Physics thought it had found only two kinds of acceleration: linear
and
 angular.
 Accelerations are all angular, however, as we have
already discovered. But

physics has not been able to coordinate its
mathematical models with the
 omnidirectional complexity of the angular
acceleration, so it used only
 the linear,
 three-dimensional, XYZ,
tic-tac-toe grid in measuring and analyzing its
 experiments. Trying to
analyze the angular accelerations exclusively with
 straight
 lines,
90-degree central angles, and no chords involves pi (*) and other
irrational
 constants to correct its computations, deprived as they are
of conceptual
 models."


Solvable computational problems which require unreasonably large
space-time resources may be
 effectively simplified by converting their
basis to a synergetic
 accounting system. Synergetics
 does not require
the use of pi or any other irrational number to provide
 results.
Simplification of
 problems via synergetics will increase computational
performance on
 conventional machines by
 an order of magnitude while
halving memory requirements.

Computational Complexity
 The theory of computation includes the
determination of computational
 complexity. If any
 process can be
described by an algorithm, the space-time resource
 requirements can be
determined. The determination of complexity involves the analysis of
the
 algorithm used to
 define the computational sequence. A simple
example will illustrate the
 trade-off between time-
 space resources.

In his book, "The Turing Omnibus," A.K. Dewdney describes the analysis
of
 two different
 algorithms used to solve a rather simple problem. n
positive integers are
 stored in an array A.
 The problem is to
determine if any of the integers are identical. Dewdney
 describes the
algorithms STOR and SCAN in pseudo-code as follows:

                SCAN                            STOR

        for i*1 to n-1 do                       for i*1 to
 n do
          for j*i+1 to n do                       if
 B(A(i))*0
            if A(i)=A(j)                            then
 output A(i);
              then output i and j;                  exit
              exit                                else
 B(A(i))*1
            else continue

Analysis of the worst-case time complexity of the SCAN algorithm yields
a
 quadratic time
 function, n2. The storage requirements are clearly n.
STOR has a
 worst-case time complexity of
 n, but requires more storage.
If m bit numbers are used, STOR will need a
 maximum of 2m
 memory
locations.

This example illustrates several ideas. Finding a minimum complexity
algorithm for a given
 problem, even a simple one, is not a trivial
task. Time complexity
 minimization is generally
 more important than
space minimization (there are exceptions, but memory
 is generally
inexpensive when compared to time). The best-case space-time complexity
would be linear (n).

No known polynomial-time algorithms for problems with exponential
complexity have ever
 been found. These problems represent the
worst-case space-time
 complexities (2n or more).
 These types of
problems will never be solved on a sequential computer.


Supercomputer Paradox

The term supercomputer is generally used to describe computing machines
that are optimized
 for processing speed. Many different supercomputer
architectures exist,
 some of which exhibit a
 large degree of
parallelism. The supercomputer has allowed the science and
 engineering
disciplines to find solutions to complex physical problems through a
'brute-force' approach.
 Fuller explains:

"It is a paradox that the computer, in its very ability to process
nonconceptual
 formulae and awkwardly irrational constants, has
momentarily permitted
 the
 extended use of obsolescent mathematical
tools while simultaneously
 frustrating
 man's instinctive drive to
comprehend his direct experiences. The computer
 has
 given man physical
hardware that has altered his environmental
 circumstances
 without his
understanding how he arrived there."

The need to modify the way we approach computation is clear. As stated
earlier, problems must
 first be simplified by conversion to synergetic
geometry. This will
 provide an automatic
 performance boost. The next
step is to make the computations themselves
 operate within a
synergetic framework that is closely matched to the problem. The system
synergy (meaning the
 behavior of whole systems unpredicted by the
behavior of their parts taken
 separately ) should
 supply a performance
boost of several orders of magnitude. Computing
 machines based on the
CSG model would be true supercomputers. The investigator modeling a
part
 of Universe
 benefits not only from improved performance, but also
from improved
 understanding of their
 model.

Computational Design Science
 Each of the items outlined thus far,
describe the emergence of a
 computational design science.
 Design
science maintains that faithful observation of Universe is the
 basis of
successful
 invention. A computational design science is necessarily
comprehensive
 (i.e.,
 multidisciplinary) in nature. The computer
scientist, physicist,
 biologist, and philosopher (to
 name a few) will
all contribute to developing and understanding the models
 of the
physical
 phenomena which they create. The idea behind the CSG model is
not to
 reinvent the computer or
 computation but to instead tap into
the intricate workings of nature's
 transformations. Innovative
artifacts produced with this comprehensive development method have
gradually transformed the
 man's physical environment and are today the
key to humanities' ultimate
 success in Universe.


Computational Synergetic Geometry (CSG)


Caveats

Having established the need to rethink our approach to computations
(both
 the problems we
 want to solve and the computations themselves),
we can now take the first
 tentative steps
 towards exploring the
uncharted. What follows is a description of one
 possible computational
scenario. It may not be the only one. It may not be the best one. It is
hoped that the ideas
 presented here are researched and investigated
further. The final
 implementation of a
 Computational Synergetic
Geometry will not likely resemble what is
 described. Each journey
must, however, start with a first step.


Description of the CSG Paradigm

The idea behind the CSG paradigm is simple: apply synergetics to the
science of computation.
 Information in the CSG paradigm is modeled as
energy. A structure is
 defined as the base-level
 processing element
(quanta). Frameworks are geometrical frames composed of
 optimal
arrangements of structures. Energy (i.e., information) flows through a
framework composed of
 structures. Transformational mapping rules
determine whether energy is
 absorbed by the
 framework or dissipated by
it. Energy is neither created nor destroyed. It
 can be transformed
into
 different states.

The framework may also undergo transformations. The framework adapts to
the changing states
 of energy. Thus, the system optimally balances
syntropic/entropic energy
 states. The framework
 transformations allow
recycling of the initial energy conditions
 eliminating the need for
intermediate results. This optimally reduces computational complexity.

An analogy based on conventional computation is the Fast Fourier
Transform
 (FFT). The FFT
 transforms time-domain data to the
frequency-domain. The FFT operates on
 data that is
 discretely and
evenly spaced in time . In the FFT, n input time-domain
 data points
are
 transformed into n Fourier coefficients that define the complex
frequency
 domain of the input
 signal at n discrete frequencies.

The FFT can loosely illustrate some useful similarities to the CSG
paradigm. Time-domain data
 inputs (input energy states) are converted
to frequency-domain data
 outputs (output energy
 states). The
conversion occurs after intermediate results are calculated
(energy/framework
 transformations). The CSG differs from the FFT in
that it allows the
 initial energy conditions to
 change state, allows
recycling of initial energy, and is inherently
 dynamic.



CSG Components


Inputs & Energy

It has become increasingly common to describe physical phenomena in
terms
 of their
 information processing properties. Information, like
energy cannot be
 created or destroyed. The
 information leaving the
system cannot be greater than the information
 entering the system. In
CSG space, information behaves as energy does in Universe. Information
(hereafter referred to
 as energy) can change states (i.e., can be
syntropic/entropic,
 associative/radiative). Radiative
 energy may not
be initially "useful". It may require association with
 other,
possibly neighboring
 energies to provide utility.


Processing Elements & Structures

Processing elements are modeled as structures. A structure is the
base-level processing element
 or quanta element. The ideal model of the
quanta element incorporates the
 fundamental unit of
 synergetic
geometry. Each quanta element is self-contained and change's
 state
depending on the
 requirements of the whole system.


Geometrical Framework

Geometrical frameworks of structures may be built. Frameworks consist
of
 optimally arranged
 and dynamically adaptive environment of
structures. An example will
 illustrate how this can be
 used. A
simulation of the "unzipping" of the DNA molecule may be modeled
 by
arranging the
 processing elements in a tetrahelix array. The properties
of the specific
 DNA molecule being
 investigated are then transformed
and mapped onto the array. As processing
 begins the array
 adapts to
the changing format of the molecule.

The configuration of the geometrical framework is such that it follows
the
 requirements of
 minimum energy. The requirements of minimum energy
conditions are in turn
 a function of the
 interplay between the
physical forces being modeled and spatial
 constraints. The fact that
space has shape must be accounted for in the CSG model. The concept
that
 space has shape is
 examined by Arthur Loeb in his book Space
Structures:

"Space is not a passive vacuum, but has properties that impose powerful
constraints on any structure that inhabits it. These constraints are
independent of
 specific interactive forces, hence geometrical in
nature."


Transformations & Mapping

Once the geometrical framework of structures is established, behavior
"rules" are mapped onto
 the structure. All structures in Universe have
access to a total of twelve
 degrees of freedom.
 The applied mapping
may constrain or release any, all or none of the
 degrees of freedom
available to the system. This may occur dynamically during the
processing
 cycle and is
 dependent on changes in the system
synergy/entropy. This method allows
 input of known, partial
 energy
states initially and leads to transformations of the entire system
based on the mapping
 rules.


Efficiency

Efficiency in a physical system is defined as the ratio of energy used
to
 energy available to a
 system. No known system in Universe can have
an efficiency greater than
 100% due to the
 conservation of energy
(Universe is finite but non-unitarily conceptual).
 In physical
systems,
 low efficiencies imply wasted energy. The CSG model of
computation must
 take efficiency into
 account. Unlike physical
systems, the energy "wasted" in systems with low
 efficiency can still
do
 useful "work." This is because energy is not really wasted, it is
transformed. The energies "lost"
 in a CSG system are transformed into
other, possibly unexpected (therefore
 synergetic) energies.

A simple example based on a physical device is the loudspeaker. A
moving-coil loudspeaker is
 essentially nothing more than an
electrical-mechanical-acoustical energy
 transformer. This
 device has
notoriously low efficiencies usually about 1%. This means that
 for
every 100 watts of
 electrical energy input to the device only 1 watt is
converted into useful
 acoustical energy.
 Ninety-nine percent of the
input energy is transformed into heat. Heat is
 considered undesirable
from a design standpoint and it must be dissipated to prevent damage to
the device.


The efficiency of a CSG model will be based on the following factors:

        1.) How well matched the problem is to the initial geometrical
            framework of structures.
        2.) How much energy must be used during the transformations
            (transformations are not
 free!).
        3.) The state (i.e., constrained or not) of the twelve available
            degrees of freedom.

It may be that an initial framework of structures used to model a
problem
 may be fairly
 inefficient. Successive transformations of the
system during processing
 should lead to a nearly
 100% efficiency.


Dynamic Modeling with The Jitterbug

Dynamic models of physical phenomena require a dynamic transformational
basis. One such
 basis for a large class of phenomena may be based on
Fuller's "jitterbug"
 model. Fuller's jitterbug
 model consists of a
cuboctahedron (i.e., Vector Equilibrium or VE) with
 flexible
connections at
 the vertices. The structure formed is not stable and
consists of eight
 faces with triangular
 outlines and six faces with
square outlines. This structure's lack of
 stability enables motion.

The jitterbug describes a series of dynamic transformations of the VE
in
 which all its vertices
 move towards the systems center at the same
rate (Note: the reader is
 encouraged to
 experiment with an actual
model of the jitterbug at this point. See A
 Fuller Explanation by
Edmonson for more details). The jitterbug goes from a vector
equilibrium
 to a stable octahedron
 passing an unstable isocahedron
along the way. Another possible
 transformation is the formation
 of a
quadrivalent tetrahedron.

The importance of the jitterbug model is in the nature of its dynamics.
The transformations in
 shape and size occur without a change in the
quantity of material. This
 illustrates how physical
 changes in phase
occur. When phase changes occur the quantity of a
 material stays the
same but
 that materials properties change radically. The contraction
of the model
 operates around four
 independent axes thus making the
transformations four-dimensional in
 nature.

Complexes of many interconnected jitterbugs exhibit similar properties.
Adjacent VE create
 octahedral cavities. Both types of polyhedra are
required to fill space.
 Though extremely difficult
 to visualize, the
transformation of a jitterbug complex converts the VE to
 octahedrons
while the
 octahedron convert into VE. Edmonson explains the
significance:

"...the unique symmetry of the VE combines with this newfound jitterbug
property to produce a model of omnisymmetrical motion, a radiating wave
of
 activity. Just as the IVM [Isotropic Vector Matrix] is a static
conceptual
 framework---describing the symmetry of space---this model
illustrates the
 concept
 of dynamic, 'eternally pulsating' energy
events in space. It causes the
 IVM to
 come to life."

This dynamic model allows direct visualization of energy-wave phenomena
and may help
 elucidate quantum gravitational theories such as the
Loop-String/Ashtekar
 theory . The jitterbug
 model provides a good
starting point for investigating the
 transformational properties of the
CSG
 paradigm.

Neural Nets, Cellular Automata, Lions and Bears (Oh My!)
 The CSG model
appears to be similar to two well-known computational
 paradigms: the
neural
 network, and cellular automata. CSG is similar to, but entirely
unlike any
 of these paradigms. To
 explain this seemingly contradictory
statement, we must examine each
 paradigm in general
 terms.


Generalized Neural Networks

Modern neural network paradigms were originally developed as models of
biological nervous
 systems. The intent was to gain insight into
learning and cognition. It
 soon became apparent
 that the models
developed showed promise in allowing machines to achieve
 human-like
performance in fields such as speech and image recognition. All
neural
 net models attempt to
 achieve high computational performance by
way of a dense interconnection
 of very simple, non-
 linear
computational elements. Richard Lippmann explains:

"Neural net models are specified by the net topology, node
characteristics, and training or learning rules. These rules specify
 an
initial set of weights and indicate how these weights should be
 adapted
during use to improve performance."

At first glance, the neural net appears to be a direct analogue to the
CSG. A series of processing
 elements (structures) is massively
interconnected in a specific topology
 (framework). The
interconnections are supplied weights that are dependent on the
learning
 rules (mappings). Once
 the system is trained, information
(energy) is applied to the inputs and
 propagated through the
 systems
(transformations) and read as the result. The differences are
significant. The neural
 network topology is fixed and planar (i.e.,
two-dimensional) whereas the
 CSG is dynamic and
 four-dimensional in
terms of dynamic axes & degrees of freedom. The
 mappings used in the
CSG system are not training rules but are instructions on how the
system
 should react in certain
 situations. It affects not only the
energy being processed but also the
 topology of the framework.


Generalized Cellular Automata

Cellular automata are discrete space-time models that have sufficient
local rule capacity to
 conceivably model Universe . They were invented
in the late 1940's by John
 von Neumann
 who was attempting to construct
a self-reproducing machine . Cellular
 automata are
 characterized by
dividing space into small, discrete units called cells.
 Each cell takes
on a
 binary value of 0 or 1. The cellular automation takes on an
initial value
 at some time, t. Rules
 local to a specific cell
determine the cell value at some later time
 (i.e., t+1). Time in the
cellular
 automation also takes on discrete values. When compared to
the CSG model,
 cellular
 automata suffer from problems similar to those
of the neural network;
 mainly the lack of four-
 dimensional dynamics
and modeling capabilities.

Each of these paradigms have one thing in common with the CSG model.
They
 are all classed as
 emergent computations. Each model exhibits
synergy. The behavior of the
 whole system is
 greater than the sum of
its components. Unexpected global behaviors
 emerge from many local
interactions. The essential difference between each of these paradigms
is
 that the CSG model
 is inherently dynamic and four-dimensional. In
addition, a training phase
 (as in a neural network)
 or local rules (as
in cellular automata) will not be required. Instead,
 the problem is
directly
 mapped to the framework of structures. Transformation rules
govern how the
 energy within the
 system will flow and change state.
The transformation rules govern the
 behavior of the whole
 system and
not just the local cells.


Implementation Methods

Implementation of the CSG model to computation will require a
fundamental
 shift in the way we
 view the interaction between hardware
and software. The differences
 between the two will
 become less
apparent. This is because, in the CSG model, hardware and
 software
fully
 complement each other. The hardware consists of conventional
components
 with flexible
 interconnection schemes that must obey
Euler's topology formula. The
 software consists of
 descriptions of
the transformation rules and mappings that are operative
 in the model
and must
 obey Gibbs' phase rule. Hardware and software elements must
work like a
 lock and key. The
 design methodology for both hardware and
software must address both issues
 at the same time.


Hardware

The basic processing elements used in a CSG implementation will all
share
 some common
 features. The processor will essentially be
independent of the framework
 topology used. This
 will allow different
processor types to be configured and integrated into
 a single CSG
framework. The key to the CSG hardware implementation is not in the
CPU,
 but in the
 communications links and in making them dynamically
reconfigurable.
 Dynamic reconfiguration
 is essential for allowing
energy flow to follow the path of least
 resistance (i.e., from high
potential to the 'ground' state). The only other requirement, from a
hardware standpoint, is that
 the system memory must be distributed.

Of off-the-shelf processing elements, the INMOS Transputer is the
leading
 candidate for
 exploring CSG implementations. The Transputer
family of processors are
 ideally suited to
 forming large,
reconfigurable networks of processing elements. Each
 Transputer is a
RISC based
 CPU with on chip communication links and memory. The
Transputer
 represents an ideal
 starting point for investigating the
CSG model. Ultimately, a special
 purpose processing element
incorporating features specific to a CSG implementation must be
developed.

The framework of processing elements used in the CSG model would be
based
 on two well-
 known principles: Euler's topology and Gibbs'
phase rule. Euler's
 topology deals with the
 superficial aspects of the
framework. It defines the number of processing
 quanta required as well
as their interconnection topology. Gibbs' phase rule defines the
degrees
 of energetic freedom
 available and how much energy needs to be
added (or subtracted) locally to
 bring about other
 states. The two
principles demonstrate complementarity. Euler's topology
 deals with
energy as
 radiation while Gibbs' phase rule deals with energy as
matter. The
 hardware topology is
 dependent on Euler's topology while
the transformations and mapping rules
 are dependent on
 Gibbs' phase
rule.


Software

Programs written for a CSG model will differ substantially from
conventional programs.
 Conventional programs outline in exact detail
the sequence of operations
 that are to occur. A
 misplaced instruction
may cause the whole system to "crash". CSG software
 will instead
consist
 of a set of descriptions that outline the way the system can
transform.
 Initial energy will be
 directly mapped to the structural
framework. A CSG model will be able to
 change state given
 that enough
energy exists and that the system has sufficient unconstrained
degrees-of-freedom.

Gibbs' phase rule determines the number of degrees of energetic freedom
that are available to the
 system based on the initial energy conditions
and the given framework
 topology as described by
 Euler's formula.
Gibbs' phase rule will also be used to determine how and
 under what
circumstances the system can change state. The state changes are the
key
 to CSG modeling. The
 system is essentially given instructions on
how it can change state and
 then allowed to let the
 initial energy
flow, transform, and change state as required.


Input/Output

The CSG will handle the bulk of input/output tasks graphically using
conventional scientific
 visualization techniques. Object-oriented,
graphical building blocks can
 be used to define
 frameworks,
structures, transformations and initial conditions. Real-time
 display
of
 computational progress and results will also be used. A method of
"compiling" framework
 definitions will be required. This compiler would
take into account the
 topological, and spatial
 constraints to form an
appropriate structural framework.

Several tools will need to be developed to facilitate I/O. A tool will
be
 needed to help map the
 initial energy state to the structural
framework. This tool should
 optimize the initial placement of
 energy
in the system given the constraints defined by Gibbs' rule. Another
tool that will help
 setup the structural framework will be required.
This tool will allow
 complex structures to be
 built and mapped using
the quanta elements. This tool will also define the
 frequency of
modular
 subdivision required and then configure a suitable framework of
quanta
 elements using Euler's
 formula.


Applications

Thus far, this paper has defined the need for a better method of
computation, outlined CSG
 functional groups and introduced some CSG
implementation issues. The
 following section deals
 with the question:
"Yeah, so what can I do with it?".

Today's supercomputers are essentially solving problems with large
amounts of computational
 complexities that make them difficult to solve
easily. The problems,
 however, are generally
 simple. Manipulation of
matrices is an example. It is not difficult to add
 two matrices
together.
 What is hard is waiting for the result when each element of
an extremely
 large array must be
 added together...one-by-one.
Supercomputers solve these problems by
 brute-force. Massively
 parallel
machines provide a fairly elegant solution by performing the
 operation
in one step. What
 is lacking from these solutions is an integrated
whole. This is what sets
 the CSG model apart
 from these methods. By
changing the way we view the problem and then
 mapping it onto a
complementary computational framework, we focus on the nature of the
problem instead of
 numerical computational techniques.


The Grand Challenge Problems

Grand challenge problems deal with modeling aspects of our environment
that have a significant
 impact on humanities' quality of life. The
computational requirements for
 grand challenge
 problems are daunting.
Solving these problems and learning their
 underlying processes is a
key
 task along humanities critical path to success.

Climate modeling

The earth's climate is dynamic. One hundred million years ago tropical
plants thrived at high
 latitudes. Eighteen thousand years ago ice
sheets covered most of the
 northern hemisphere.
 Future climatic
changes will be driven not only by natural fluctuations
 but by human
activities as
 well. Gauging the effects of pollution, ozone depletion,
volcanic
 activity, and nuclear war
 (World War III is over, but the
weapons still exist) will become
 increasingly important, as will
developing methods to alter the current course.

Current climate models vary according to the length of time being
simulated, as well as their
 spatial resolution. Even the most complex
general-circulation models are
 sharply limited by
 the spatial detail
resolution. Today, no computer is fast enough to
 calculate climatic
variables
 everywhere on the earth's surface and in the atmosphere
within a
 reasonable time span
 (remember complexity?). The CSG model
applied to climate modeling will
 help to reduce the
 computational time
required as well as increase the spatial resolution
 available to the
model.
 This will lead to very accurate climate models.


Quantum Physics

No field stands to benefit more from Computational Synergetic Geometry
than quantum
 physics. Quantum physics uses computers of unparalleled
complexity to
 investigate its theories.
 These computers are commonly
known as particle accelerators. Large
 particle accelerators are
 very
expensive to build and operate. The need for accurate modeling and
simulation tools
 becomes clear. Fortunately, synergetics provides the
ideal modeling tool
 for investigations into
 quantum electrodynamics,
the electroweak theory and quantum
 chromodynamics. Synergetic
 modeling
coupled with the CSG model should provide unprecedented insight
 into
the nature of
 the atomic and sub-atomic domains. Quantum mechanical
modeling using the
 CSG system, will
 allow researchers to focus on
experiments that provide the most insight
 into the nature of the
quantum mechanical world.


Crystal Engineering

The forces that assemble molecules into natural crystals can be
utilized
 to produce a variety of
 important materials. The properties
of a crystalline material depend
 greatly on the arrangement
 of the
molecules in the crystal. Little is known about the factors which
control the assembly of
 such crystals Scientists are trying to learn
what types of molecules and
 what types of conditions
 will produce
crystals with unusual and useful properties.

Molecules assemble in dense packing arrangements which minimize space
and
 balance
 attractive-repulsive forces. This closest-packed
arrangement minimizes the
 total energy of all the
 forces among all the
molecules. Prediction of the lowest energy
 configuration is not
possible
 today. The CSG model with its inherent ability to model
spatial
 constraints and to deal with
 energy minimization would be the
ideal method of predicting molecular
 crystal structures and
properties.


Managing the Human Genome

Researchers are currently compiling the genetic code sequences that
make
 human beings what
 they are. The human genome is the totality of
genetic information
 contained in human
 chromosomes. Analysis of the
human genome will provide clues into human
 origins and
 insight into
the complex functioning of the body. Once codified the
 problem will be
accessing,
 assimilating and cross correlating the tremendous amount of
data
 generated. Access,
 interpretation, query, integration,
visualization, test and study are all
 functions required in a
 genome
database manager. The CSG model will allow for "intelligent" access
 to
this data by
 seeking and classifying patterns within the data set. This
method can be
 extended to any large
 data set given that an appropriate
mapping schema is provided.


Non-linear Systems

Synergetics shows us that Universe in inherently non-linear. Nature
depends on circumferential
 and radial accounting rather than linear and
cubic accounting.
 Mathematical "correction factors"
 have been devised
to compensate between what our linear models tells us
 and demonstrable
physical reality. These correction factors have led directly to the
development of non-linear
 systems analysis. Our currently non-linear
mathematical models show high
 orders of
 unpredictability which we term
chaos. Chaos appears across several fields
 such as medicine
(prediction of heart attacks), weather forecasting (hurricane
prediction),
 celestial mechanics (the
 n-body problem) and control
systems analysis. By modeling non-linear
 phenomena using the
 CSG
method, we will see the inherent order and symmetry which is currently
masked by our
 outdated mathematical models.


Machine Vision

Machine vision is the energy-processing task of understanding a scene
from
 its projected
 images. An image is composed of a 2-dimensional
array of feature values.
 The task of a
 machine vision system is to
understand the scene depicted by the image.
 Vision is easy for
 humans,
although the mechanisms involved in human understanding of a scene
 are
unknown. A
 key problem for machine vision implementations is that
understanding an
 image requires a priori
 knowledge of the task domain.
Today's image understanding systems are
 often unable to see
 objects
that cannot be matched to a stored representation. The CSG system
 with
its inherent
 ability to deal with topological detail and with its
ability to map scene
 characteristics into its
 structural framework
should be able to understand general scenes.


Cognition

Cognitive science deals with psychological research into the nature of
human thinking. The
 theories that are developed are machine models of
human thinking.
 Cognitive science attempts
 to quantify the comparisons
of human mind with machine to benefit the
 understanding of human
cognition. The CSG model applied to cognitive science should provide
valuable insights into
 the nature of human thinking.


The Shortest-Network Problem

The optimum layout of a telephone network topology or a electronic
circuit
 layout depends on
 solving what is known as the
shortest-network problem. The computational
 complexity of
 solving for
the shortest total route of even a 100 point network becomes
 extremely
large in both
 space and time resources. Once again, the CSG model with
its inherent
 ability to deal with
 topological detail and it flexible
mapping schema should provide solutions
 to this problem with
drastically reduced computational resources.


Balancing Your Checkbook

"Will a CSG be able to balance my checkbook?"
 It should, given that
the appropriate mapping and transformational rules
 exist. The question
arises from an examination of the 'trivial' problem and the CSG. A
trivial
 problem is one that
 essentially a 'no-brainer'. It is still
important for the CSG model to
 handle such problems to prove
 its
generality and ability to model all physical principles. Some of the
same transformation
 rules applied to quantum physics could be applied
to balancing your
 checkbook. It should be
 noted that other
computational paradigms cannot be reliably used on
 trivial problems (I
would
 not use a neural network to balance my checkbook).


Summary & Conclusion

This paper has examined preliminary ideas towards developing a
generalized
 computational
 synergetic geometry. The CSG model has
been shown to be composed of two
 parts. The first
 involves reordering
the problem using synergetic geometry. The second part
 involves
applying
 synergetics to the method of computation itself. Several
implementation
 concepts have been
 introduced along with potential
applications.

The purpose of this paper is to lay the foundation for further research
and development. The
 following section will outline some of the
preliminary tasks required for
 development.

Documentation of results and exchange of ideas
 The view of the CSG
model is bound to evolve over time due to synergy. It
 is of paramount
importance to document the development and evolution of the CSG model.
The
 key task in this
 area is to define the items in part IV of
Fuller's Comprehensively
 Anticipatory Design Science's
 Universal
Requirements for Realizing Omnihumanity Advantaging Local
 Environment
Controls,
 Which are Omniconsiderate of Both Cosmic Evolution Potentials
and
 Terrestrial Ecology
 Integrities.

Applying synergetics to modeling physical problems
 Initial candidate
problems for synergetic coordination need to be
 identified. The models
for
 these problems must be conceptualized using synergetics. The
underlying
 structures of these
 problems must be identified. Modeling
techniques as well as a descriptive
 language tools must
 be developed.


Development of CSG components

The concepts of the quanta elements and structural frameworks must be
investigated further.
 Development tools for describing the framework
topologies and for applying
 Euler's formula and
 Gibbs' phase rule must
be developed. Initial experimentation using logic
 elements or
microprocessor arrays must be implemented. Further evaluation of the
INMOS
 Transputer and
 the OCCAM programming language is required.

There remain many unanswered questions regarding synergetics and the
theory of computation.
 It is hoped that the ideas presented in this
paper will bear fruit after
 further research and
 development.
Synergetics applied to other fields of study have already
 resulted in
notable
 discoveries (e.g. Carbon-60; the Buckminsterfullerene). The
potential for
 additional discoveries
 is limited only by the initiative
of the individual.


======================

References

Nystrom, J.F. (Jim) Computational Cosmography, First-draft, April 1992.

Gurari, Eitan M. An Introduction to The Theory of Computation, Computer
Science Press, 1987.

Fuller, R. Buckminster, Synergetics: Explorations in the Geometry of
Thinking, Macmillan ,
1975.

Dewdney, A.K. The Turing Omnibus, Computer Science Press, 1989.

Edmonson, Amy C., A Fuller Explanation. The Synergetic Geometry of R.
Buckminster Fuller,
Birkhauser Boston, 1987.

Ramirez, Robert W. The FFT Fundamentals and Concepts, Prentice Hall,
1985.

Forrest, Stephanie. "Emergent Computation: Self-Organizing, Collective,
and Cooperative
Phenomena in Natural and Artificial Computing Networks." In Emergent
Computation. Ed.
Stephanie Forrest. A Bradford Book-The MIT Press, 1991.

Loeb, Arthur L., Space Structures: Their Harmony and Counterpoint,
Addison-Wesley Advanced
Book Program, 1976.

"Gravity Quantized?" Science and the Citizen. Scientific American,
September 1992, pp. 18-20.

Rumelhart, David E., McClelland James L., et. al., Parallel Distributed
Processing:
Explorations in the Microstructure of Cognition, Volume 1: Foundations,
The MIT Press, 1988.

Lippmann, Richard P., "An Introduction to Computing with Neural Nets."
IEEE ASSP
Magazine, April 1987, pp. 4-22.

Rietman, Edward, Exploring the Geometry of Nature: Computer Modeling of
Chaos, Fractals,
Cellular Automata and Neural Networks, Windcrest, 1988.

Schneider, Stephen H., "Climate Modeling.", Scientific American, May 1987,
pp. 72-80.

Fagan, Paul J., Ward, Michael D., "Building Molecular Crystals",Scientific
American, July 1992,
pp. 48-54.

Erickson, Deborah, "Hacking The Genome", Scientific American, April 1992,
pp. 128-137.

Cohen, Paul R. and Feigenbaum, Edward A., eds. The Handbook of Artificial
Intelligence
Volume III, Addison-Wesley Publishing Company, Inc., 1982.

Bern, Marshall W., Graham, Ronald L., "The Shortest-Network Problem",
Scientific American,
January 1989, pp. 84-89.

Fuller, R. Buckminster, Critical Path, St. Martin's Press, 1981.


About the Author

Richard J. (Rick) Bono is currently Electrical Systems Engineer for
Teccor
 Electronics Corporation in
 Brownsville, Texas. He received a
BSEE from Texas A&M University in 1984
 concentrating on
 computer
architecture and semiconductor devices. He is recognized as an
Engineer-in-Training
 by the Texas Society of Professional Engineers and
is actively seeking
 licensing as a
 Professional Engineer. He has
served as a member of the Advisory Committee
 for Electronic
 Technology
at Texas State Technical College since 1990. He has recently
 been
selected to
 appear in the first edition of Who's Who in Science and
Engineering.
 Rick's other professional
 affiliations include the
Institute of Electrical and Electronics Engineers
 (IEEE), the IEEE
Signal
 Processing Society, IEEE Magnetics Society, and the Audio
Engineering
 Society (AES). His current interests
 include synergetic
geometry , parallel computing, non-linear dynamics,
 celestial
mechanics, and digital image
 processing. Rick is married, has one
daughter , and is actively defining
 his personal philosophy.


Nystrom, J.F. (Jim) Computational Cosmography, First-draft, April
1992.

Gurari, Eitan M. An Introduction to The Theory of Computation, Computer
Science Press, 1987.

 Fuller, R. Buckminster, Synergetics: Explorations in the Geometry of
Thinking, Macmillan , 1975.

 Nystrom, Ibid.

 Dewdney, A.K. The Turing Omnibus, Computer Science Press, 1989.

 Ibid.

 Ibid.

 Fuller, pp.27, Ibid.

 Fuller, pp. 3, Ibid.

 Edmonson, Amy C., A Fuller Explanation. The Synergetic Geometry of R.
Buckminster Fuller, Birkhauser Boston,
 1987.

 Ramirez, Robert W. The FFT Fundamentals and Concepts, Prentice Hall,
1985.

 Forrest, Stephanie. "Emergent Computation: Self-Organizing,
Collective,
 and Cooperative Phenomena in Natural
 and Artificial
Computing Networks." In Emergent Computation. Ed. Stephanie
 Forrest. A
Bradford Book-The MIT
 Press, 1991.

 Fuller. Ibid.

 Loeb, Arthur L., Space Structures: Their Harmony and Counterpoint,
Addison-Wesley Advanced Book Program,
 1976.

 Fuller. Ibid.

 Edmonson, Ibid.

 Edmonson, Ibid.

 Edmonson, Ibid.

 "Gravity Quantized?" Science and the Citizen. Scientific American,
September 1992, pp. 18-20.

 Rumelhart, David E., McClelland James L., et. al., Parallel
Distributed Processing: Explorations in the
 Microstructure of
Cognition, Volume 1: Foundations, The MIT Press, 1988.

 Lippmann, Richard P., "An Introduction to Computing with Neural Nets."
IEEE ASSP Magazine, April 1987,
 pp. 4-22.

 Lippmann, Ibid.

 Rietman, Edward, Exploring the Geometry of Nature: Computer Modeling
of
 Chaos, Fractals, Cellular Automata
 and Neural Networks, Windcrest,
1988.

 Dewdney, Ibid.

 Rietman, Ibid.

 Forrest, Ibid.

 Fuller, pp. 685, Ibid.

 Schneider, Stephen H., "Climate Modeling.", Scientific American, May
1987, pp. 72-80.

 Fagan, Paul J., Ward, Michael D., "Building Molecular
Crystals",Scientific American, July 1992, pp. 48-54.

 Erickson, Deborah, "Hacking The Genome", Scientific American, April
1992,
 pp. 128-137.

 Cohen, Paul R. and Feigenbaum, Edward A., eds. The Handbook of
Artificial
 Intelligence Volume III, Addison-
 Wesley Publishing
Company, Inc., 1982.

 Cohen, Ibid.

 Bern, Marshall W., Graham, Ronald L., "The Shortest-Network Problem",
Scientific American, January 1989, pp.
 84-89.

 Nystrom, Ibid.

 Fuller, R. Buckminster, Critical Path, St. Martin's Press, 1981.