29 August 2005 | Draft
Resolving the Challenge of Faith-based Terrorism
Eliciting the dynamic of two-body, three-body and n-body variants
- / -
* Two-body problem
* Three-body problem
* N-Body problem
* "Two-body" terror experience
* "Three-body" terror experience
* "N-body" terror experience
Finite vs Infinite
Terror of the sublime
Varieties of dynamic resolution of faith-based terrorism
* 1. One-body "solutions"
* 2. Two-body "solutions"
* 3. Three-body "solutions"
* 4. Configurative "solutions"
* 5. Emergent behaviour "solutions"
* 6. Embodied "solutions"
* 7. Peripatetic "solution"
The suggestion here is to focus on the the number of elements in a variety
of systems in the light of the long-explored mathematical distinctions between
three-body and N-body
problems. The assumption is made that, as a pattern, the latter constitute a
useful template through which to explore n-body systems of other kinds.
This investigation is made in the context of the framework of general
systems as currently sustained by the International
Society for the Systems Sciences, following the early initiatives of the
Society for General Systems Research. General systems recognizes a degree of
isomorphism between systems of apparently different type.
The purpose of this exploration is to use the ordering of the more tangible
systems to gain greater insight into the challenges of the less tangible systems.
In particular the concern is with perception of threat (especially that associated
with terrorism) arising from views sustained by fundamentally irreconcilable
religions (such as Christianity, Islam, and Judaism). The aim is to suggest
that the set of worldviews may be seen as either a one-body
problem (where there is exposure to only one worldview), or
a two-body problem (where there is exposure to two
worldviews), etc. The two-body case offers a description of the dynamics of
the relation between God and Satan, for example -- or between any two religions
that tend to demonize each other. The three-body case might then offer insights
into a more fruitful dynamic between the Abrahamic religions, for example.
In experiential terms, the terror associated with the other in a two-body case,
might then be understood in terms of the dynamics of a form of "two-body
terror". That between the three Abrahamic religions might be understood
as "three-body terror". It is assumed that the faithful of particular
religions are effectively terrified by the perspective of any alternative.
The merit of such an approach is that it offers guidelines for the avoidance
of inappropriate oversimplification, whatever particular resolutions are considered
applicable under certain constraints. It also points beyond the tendency towards
the search for structural static resolutions to the need to
explore dynamic resolutions -- as possibly being the only ones
offering sustainable relations between the "bodies"
The following table has rows associated with different "systems",
of which the first are those well-recognized by mathematics and physics. The
structure of the table draws attention to the possibility of recognizing isomorphic
conceptual challenges within non-physical systems, whether biological, social,
conceptual, or experiential. Such isomorphism has long been a theme of general
systems research (cf James Grier Miller, Living
(Sun, Moon, Earth; triple stars)
(cf coaction cardioid)
("clash of cultures")
(wave vs particle)
("crisis of crises")
The purpose here is simply to point to the complex formal descriptions of the
dynamic relationships in each case. Note that simpler satisfactory solutions
may be found in each case if particular constraints are allowed. Many mathematicians
have given considerable attention to the solution of the equations of motions
for n gravitationally interacting bodies.
Two-body problem: The two-body problem
is the challenge of determining the movement of two rigid point masses in mutual
orbit about each other [more].
It can be solved analytically. In mechanics, the two-body
problem is a special case of the n-body problem that admits a closed form
solution. This problem was first solved in 1687 by Isaac Newton who showed that
the orbit of one body about another was either an ellipse, a parabola, or a
hyperbola, and that the center of mass of the system moved with constant velocity.
If the common center of mass of the two bodies is considered to be at rest,
each body travels along a conic section which has a focus at the centre of mass
of the system. If the two bodies are bound together, they will both trace out
ellipses. If they are moving apart, they will both follow parabolas or hyperbolas.
In a nice analogy with planetary motion, the quantum two-body problem is exactly
solvable. The most commonly encountered version of the problem, involving an
inverse square law force, is encountered in celestial mechanics and the Bohr
model of the hydrogen atom.
For an illustrative applet, see Joachim Köppen (Orbits
of One Body around Another, 2001)
Three-body problem: This is the problem
of determining the mutual gravitational interaction of three massive bodies
It involves finding the positions and velocities of the three bodies, which
are interacting with each other gravitationally -- at any point in the future
or the past, given their present positions, masses, and velocities. It has been
demonstrated to be impossible to solve in the general case, namely when the
three bodies are in a random configuration. The resulting motion in most cases
turns out to be chaotic, making it impossible to predict precisely what paths
those bodies would follow.
The problem can only be handled in certain special cases. Joseph-Louis
Lagrange showed that there were at least some solutions to the three body
problem if the three bodies move in the same plane and it was assumed that the
mass of one of them was so small as to be negligible. In the solution which
bears his name, the three bodies move in unison, always maintaining the same
positions relative to each other. If we think of a two body system (like the
simplified Earth and Sun system) then the 5 points at which a third small body
may be found are now known as the Lagrange
points (L-5 points). These mark positions where the gravitational pull of
the two large masses precisely equals the centripetal force required to rotate
with them. Three are unstable and two are stable. The unstable points lie along
the line connecting the two large masses. The stable Lagrange points form the
apex of two equilateral triangles that have the large masses at their vertices
As noted by James P. Sethna (The
Restricted Three Body Problem, 1996): "After Newton solved the
problem of the orbit of a single planet around the Sun, the natural next challenge
was to find the solution for two planets orbiting the Sun. Many of the best
minds in mathematics and physics worked on this problem in the 19th century".
More generally, only the planar restricted
three-body problem can be simply treated, although even this case has proved
surprisingly difficult to solve even though the three masses move in a common
The gravitational three-body problem has been called the oldest unsolved problem
in mathematical physics. Unlike the two-body problem, there is no closed analytical
solution. Numerical orbit integrations have to be used to determine the evolution
of a typical three-body system. Most of these are unstable. In astrophysical
systems, they decay either into three separate stars moving away to infinity,
or into a binary star and a single star. There are however some stable configurations.
Recently a new category of stable three-body orbits has been discovered in which
the three stars chase each other in a figure-eight orbit.
Eugene Butikov (Collection
of remarkable three-body motions) has provided a series of applets
which provide some understanding of the "fascinating trajectories of three-body
motions that delight the eye and challenge our intuition".
For an illustrative applet, see Joachim Köppen (Three
Bodies in Gravitation, 1997)
N-body problem: The n-body
problem is the problem of finding, given the initial positions, masses,
and velocities of n bodies, their subsequent motions as determined by classical
mechanics, i.e. Newton's laws of motion and Newton's law of gravity (cf K R
Meyer. Periodic Solutions of the N-Body Problem, 1999) [more]
The many-body problem
in quantum mechanics in quantum mechanics, is posed as the question of solving
for more complex problems than the hydrogen atom, for example, the chemistry
of all realistic molecules
|It would indeed be remarkable if Nature fortified herself
against further advances in knowledge
behind the analytical difficulties
of the many-body problem. (Max Born, 1960)
"Two-body" terror experience: The suggestion
here is that there is a case for the experiential framing of the encounter with
a single source of terror as having dynamic properties analogous to the encounter
- any attractor
- a black hole understood in astrophysical terms
- a gravitational well
In each case the "attractive" properties recall:
- the "fascination" experienced by a prey faced with a terrifying
predator, under certain circumstances
- the experiential "temptation" associated with "falling into
sin", as articulated by certain religions (notably as the encounter with
"demonic" and "satanic" influences)
- the experiential "terror" of the unknown associated with exploring
alternative belief systems, labelled as highly dangerous "unbelief"
-- severely condemned (and even forbidden) by the authorities of one's conventional
People may be effectively petrified by such "encounters", as explored
in Terror: Refocusing the interreligious challenge from "Thinking after Terror",
To avoid such terror, and any associated danger (notably to one's "identity"
or to one's "soul"), it is understandable that the authorities of
a locally dominant belief system consider themselves totally justified in eliminating
any possibility of exposure to such threats by placing emphasis on:
- security from predators of any kind, originally to the point of eliminating
dangerous "wild animals", but notably in their contemporary form
of exploiters, muggers, and terrorists; "gated communities" may
be set up to isolate ("us" from "them", as a source of
- eliminating exposure to any "temptations of the flesh" that may
lead one into "sin"
- eliminating exposure to any "temptations of belief" that may lead
one to give credence to other belief systems and become attracted to their
domain -- or into the ultimately terrifying dangers of non-belief
As a "two-body" problem, there are various "solutions",
in the light of the mathematical model:
- Collision: such may be the attraction, that one is drawn
uncontrollable into the field of influence of the terror source without any
possibility of release -- as with a spacecraft crashing into the Earth
- Orbit: with appropriate skills, one may be drawn into orbit
around the terror source, without necessarily being drawn
into it -- with the following variants:
- uncontrollable orbit: in such a case, one periodically dips too close,
gets burnt and bounces back, with the risk of being ultimately unable
to bounce back ("a moth around a candle flame") -- resulting
in destructive collision
- controllable orbit: in such a case, one is locked into
a stable orbit, unable to get out of it
- orbit offering possibility of escape: here one has the resources and
skills to escape from the gravity well
- orbit enabling a landing: here one has the resources and skills to navigate
through the atmosphere and land in the strange environment
- Deflection: under particular circumstances, or with particular
skills, one may be propelled away from the influence of the terror source
These options describe situations in which the terror source is in effect static,
and imply that one is oneself (as the other body) relatively small in attractive
capacity. The situation may however be different:
- Proactive terror source: in this case the source may deliberately
seek one out (as with muggers, prostitutes, aggressive salespeople, proselytizing
missionaries, or assassins)
- Much smaller terror source: in this case the source may
be akin to a very specific "temptation" (an alcoholic drink, a cigarette,
a chocolate, pornography), known to trigger unwelcome consequences
- Invisible terror source: in this case the terror is undectable or
in some way omnipresent
Both the above descriptions obscure qualities of terror associated with existential
exposure to what may be experienced as the "field effects" of the
terror source -- perhaps when exposed to those who experience the world in radically
different ways from oneself. In this case one has a more or less direct experience
of the geometry of those fields, notably how one may be twisted within them
to experience reality differently. An instructive description of the "traffic
on this geometry", and of how the geometry is "felt", is provided
by mathematician Ron Atkin (Multi-dimensional Man: can man live in three-dimensional
space? 1981) as summarized elsewhere Comprehension:
social organization determined by incommunicability of insights. This
notably points beyond the two-body case.
"Three-body" terror experience: In this
case, there are two sources of terror external to oneself -- and one's own reactions
may make oneself become a source of terror. Managing this experience is much
more complex. The dynamic is illustrated by:
- Sun-Moon-Earth: In many traditional cultures, various terrifying situations
are associated with some relative movements of Sun and Moon: terrors of the
night, the possibility that the Sun might not rise, eclipses, the Moon being
"eaten", winter, etc
- "Eternal triangle": Many have been exposed to the terrors of triangular
relationships and the complex associated dynamics: temptation, discovery,
exposure, betrayal, etc (NB folk tales might describe the relation between
Sun and Moon in such anthropomorphic terms)
It is possible that the dynamics of the exposure of an individual of one faith
(eg Christianity) to those of two other unfamiliar faiths (eg Islam and Judaism)
might be experienced as terrifying in similar ways. In this sense Jerusalem
might be understood as a focus of terror.
"N-body" terror experience: In this case,
the situation appears even less orderly -- and is typically experienced as chaotic.
Managing this experience is even more complex. The dynamic is illustrated by:
- Prey with multiple predators: The best recognized example is the isolated
prey attacked by a pack of wolves, or by a gang of enemies -- as in the case
of some urban street violence situations. Terror emerges anew from every side
-- and unpredictably.
- Martial art expertise: The best recognized example of the response to such
a situation is offered by media dramatizations of the response of a master
of kung-fu (or some equivalent discipline) to such multiple attacks.
- Paranoia: For the hyper-nervous, any group of people may be experienced
as threatening in the above sense, possibly to a degree unimaginable to those
without that sensitivity
- Amusement arcade: A "terror tunnel" ride in an amusement arcade
may be deliberately designed to provide a sequence of terrifying experiences
(emerging unpredictably from the dark)
There are interesting assumptions that tend to be embedded in the challenge
of addressing a two-body, three-body or n-body problematique. These are associated
with understandings of what is:
- a "body": what kinds of "entity" lend themselves to
description as "bodies", and what kinds do not? For example, for
Jude James: "The inhuman alignment of the body in a state of porosity
sited within the catachrestic space of its own emergence as interface in the
'now,' is the mechanism for the necessary alignment on the material plane,
both to access and to maintain the state of becoming of the porous body within
the 'now' in performativity" [more]
- a "solution": what kinds of solution emerge from buying into faith
in a predictive logic, and what kinds do not; is a solution a comprehensible
- a "dynamic": why is a dynamic "unsatisfactory" unless
it is explicable within a particular kind of logic?
- uncertainty and unpredictability: why is uncertainty essentially terrifying?
It might be asked whether the inability to provide satisfactory three-body
solutions, except under particular constraints, is due to the manner in which
"body" and "solution" have been locked into a particular
logic. This gives special meanings to "body" and "solution"
-- despite their abstract representation in mathematics -- that may not be as
general as circumstances require. Aspects of the challenge have been highlighted
in the incompleteness theorems of Kurt Gödel (see below). The inability
is therefore a consequence of a logic imposed upon what is perceived and conceived
-- a logic that is inadequate to more general cases that may be characteristic
of much experience. Any conception is memetically constrained. A current challenge
relating to the issue of terrorism is whether al-Qaida is a "body"
and how eliminating "terrorism" and "extremism" are to be
understood as "solutions".
Interesting examples of other kinds of "solution" to the n-body problem
are, for example:
behaviour, whether of birds or fish, as studied by the complexity sciences
(cf "boids" as
a computer simulation of flocking behavior)
- atomic structure, as exemplified by the periodic table of the variety of
elements; the periodic table may be understood as a set of solutions to n-body
In such cases it might be said that the "solution" is effectively
"embodied" by the dynamics of the phenomenon. In computing terms,
such a solution might be understood as an "analogue" solution in contrast
with a "digital" solution.
Under a system of faith-based governance, whether religious or scientific,
these issues become especially significant:
- the "body" of a faith or a church may be especially important,
as with Christianity, particularly when emphasis is placed on faith in that
- any preoccupation with the "body", and the material world of mundanities,
may be a particular challenge to a faith
- the "body" of scientific knowledge may be especially important
to the world of science, especially the nature of the faith in that body
- subtle distinctions may be made between any notion of "body" and
that of a "community" of believers in any faith-based system, whether
religious or scientific:
- considerable significance is attached to the "scientific community"
- in the case of practioners of a religion, emphasis is placed on the
"Christian community", the Islamic Umma or the Buddhist
- an interesting distinction is made between the "international community"
and the "bodies" variously understood to be associated with
it or expressions of it (eg UN, OECD, etc). However the Bush-appointed
UN representative, John Bolton, is famously quoted as saying: "There
is no such thing as the United Nations. There is only the international
community, which can only be led by the only remaining superpower, which
is the United Sates."
It is possible that the "body-centered" approach needs to be complemented
by one which emphasizes the significance of the dynamic that enables perception
of the "body", which effectively constructs it. In the contrast between
particle and wave theories of light, for example, it is the waveform which calls
for greater attention. Any understanding of "community" may perhaps
be more significantly described in terms of interweaving waveforms -- as is
notably the case with atoms or molecules.
In this sense a distinction can be made between a faith-based system as a singular
"body" (a "massive particle") and a faith as a set of interweaving
The terrifying relationship between incommensutable faith-based systems, whether
disciplines (C P Snow's "two
cultures": sciences, humanities), or religions (Huntington's "clash
of civilizations": Christianity and Islam, notably), may be better
understood as the relationship of sets of waveforms -- perhaps implied by "movements
of opinion". The emphasis is then on the "dynamic" rather than
on the "body" -- an emphasis carried to a higher degree by current
usage of "community". The respective "bodies" are effectively
dynamically gated conceptual communities (cf Dynamically
Gated Conceptual Communities: emergent patterns of isolation within knowledge
The excessive focus on the distinct "body" in any of these faith-based
cases ensures that the experience of other "bodies" is associated
with a form of terror -- terror at any dynamic that is not associated with the
description of the "body" with which one is familiar, or with which
one identifies. Using an astrophysical metaphor, terror is created by exposure
to external gravitational effects. At the same time, there is the irony that
all faith-based systems claim to seek ways of transcending the "body":
- In the case of religion, it is the rejection of the flesh and its temptations
-- in the search for union with the Divine.
- In the case of science, it is the effort to transcend crude data in the
search for explanatory theories -- in the search for an ultimate Theory
As the prime source of terror at this time, the intractable relationship between
the Abrahamic religions (Christianity, Islam, Judaism) is insoluble as a three-body
problem, despite references in the Qu'ran to The
People of the Book, viewed in Islam both as an articulation of tolerance
(Qur'an 29:46) ) and as an expression of an adversarial relationship
(Qur'an 5:51) with Christanity and Judaism. As a three-body problem,
particular cases might be usefully explored. What has not yet been explored
is the nature of the dynamics of their existing relationship. In effect that
relationship is a form of "solution" -- whether we like it or not.
It is terrifying because each "body" has a heavy conceptual investment
in a stasis (or internal dynamic) that is brought into question by the exposure
to other forms of stasis (with their own internal dyanmics) -- with which it
is then obliged to engage in a terrifying dance. Hence perhaps the folktales
about appeasing the terrifying Beast by entrainment -- entrancing it through
music and, by implication, dance (cf Attitude
Entrainment: Communicating thrival skills and insights, 2004). Hence,
also the prohibition against music and dance by fundamentalists in various religious
Finite vs Infinite
The definitional challenges of the previous section can be related to two well-known
challenges in mathematics and to understandings of mathematical theology:
- finite vs infinite: the core difficulty of the search for "solutions"
to n-body problems is their definition within a finite system. This is to
be contrasted with efforts to give expression to understandings of infinity,
most notably as explored by Georg
Cantor. There are phenomena -- especially love, grace, and possibly terror
-- that do not lend themselves to description within finite systems. As a
mathematician and minister, Sarah Voss
(What Number Is God?, 1995; Zero: Reflections about Nothing,
1998), has responded to increasing recognition of mathematical metaphors which
she terms mathaphors: "Ideas drawn from mathematics can greatly extend
our spiritual worldviews" (Mathematical
Voss then notes regarding Cantor, a deeply religious mathematician, that:
"In the Cantorian world there also exists an entity that is infinitely
many yet simultaneously infinitely sparse; the infinite both is and is not
infinite; incompleteness is intrinsic to the structure of the system. What
happens if something like Cantorian set theory applies to an area other than
mathematics? Could it describe a theological or spiritual truth as well? When
confronted by the variety of religious traditions in the world, people tend
to ask, "Whose faith is right?" The religious exclusivist says, "Mine is."
The inclusivist says that lots of religions appear to be right, but that they
are all included in one "real" way to salvation or liberation. The pluralist
says, "You can have yours and I'll have mine, and that's just fine." A Cantorian
perspective offers another option: The part may have the power of the whole.
When we use Cantorian set theory as a metaphor for thinking about contemporary
religious pluralism, we find a wonderful precedent for accepting what might
appear to be unacceptable contradictions between religions. In other words,
many different religious traditions may independently be "equivalent" to the
one whole truth."
the work of Kurt Gödel
is especially significant for drawing attention to the fundamental incoherence
of any conventional mathematical explanation, namely for any formal theory
in which basic arithmetical facts are provable, it is possible to construct
an arithmetical statement which, if the theory is consistent, is true but
not provable or refutable in the theory. Gödel showed is that in most
cases, such as in number theory or real analysis, it is not possible to discover
the complete list of axioms. Each time a statement is added as an axiom, there
will always be another statement out of reach. This leads to recognition of
This argument therefore suggests that there is a need to "turn the problematique
round" -- precisely by giving form to a dancing relationship. Perhaps current
attempts might be contrasted with this approach as efforts to "fit a square
peg into a round hole" -- or at "squaring the circle".
The role attributed to divinity in this context has been neatly expressed by
Gregory Bateson (They Threw
God Out of the Garden, CoEvolutionary Quarterly, Winter 1982)
... Original Sin was the discovery of planned purpose; and that, following
this discovery, Adam and Eve expelled God from the Garden.... The general
notion was that God symbolized the systemic and cybernetic nature of the environment
which inevitably took vengeance on man's short-sightedness. It occurs to me
now that this little parable can be considered to be a serious truth -- especially
if we turn it upside down.
I suggest that one of the things that man has done through the ages to correct
for his short-sighted purposiveness is to imagine personified entities with
various sorts of super natural power, i.e., gods. These entities, being fictitious
persons, are more or less endowed with cybernetic and circuit characteristics.
In a word, I suggest that the supernatural entities of religion are, in some
sort, cybernetic models built into the larger cybernetic system in order to
correct for noncybernetic computation in a part of that system. I do not believe
anybody has said this, but I do not think that this view of religion contradicts
what has been said by others -- the religious, the mystical, and the scientific.
Terror of the sublime
It is readily assumed that any relationship with divinity is free of any degree
of terror. The fear associated with any encounter with God is however widely
recognized -- God may indeed be terrifying (Is
God a Terrorist: Definitional game-playing by the Coalition of the Willing?).
Fear of God has been acknowledged
down the ages [more
noted by by Charles H. Hinnant (Schiller
and the political sublime: two perspectives, Spring, 2002):
Francois Lyotard (Postscript to Terror and the Sublime) declared
that "as for a politics of the sublime, there is no such thing. It could
only be terror. But there is an aesthetics of the sublime in politics."
- Edmund Burke (A
Philosophical Enquiry into the Origin of Our Ideas of the Sublime and the
Beautiful, 1757) showed no hesitation in arguing not only that the sublime
is governed above all by the emotion of terror but also that terror becomes
sublime only "when it does not press too close."
- Friedrich von
Schiller likewise emphasized that "the sublime object must, of course,
be frightening, but it may not recite actual fear." (On the Sublime:
Toward the Further Development of Some Kantian Ideas)
More relevant to the theme of this exploration is the probability that any
rapprochement with a divinity, other than that central to one's faith, may be
experienced as even more terrifying. The relationship between faiths is therefore
necessarily associated with a degree of terror -- a terror of otherness -- seldom
acknowledged in interfaith dialogue (cf D Tracy, Dialogue with the Other:
the inter-religious dialogue, 1990). Each faith may therefore be understood
as offering a window on a different kind of terror of which it is effectively
the guardian. This contrasts with the belief of co-religionists that their own
religion is in no way associated with terror.
The terror of the divine, as a form of the "other", is readily transformed
into terror of any "other", as noted by Reverend Tom Goldsmith (American
Funk, November 1995):
Now there is so much terror of the other: the person of color, the immigrant,
the homosexual, that we seek communities which preserve the narrow focus of
| I believe that the 21st century will probably
be a century of exploring the mechanism of "becoming." It is indeed rather
sad that even if you can imagine that cosmology, or the origin of life are
associated to successions of bifurcation, we know very little about the
mechanism of bifurcations. We may safely assume that everything in our universe
is evolving in the same direction of time: rocks evolve in the same direction,
stars, galaxies, supergalaxies, all objects evolve in the same direction.
We age all together. We can only conclude that our universe seems to be
ruled by a semigroup with broken time symmetry. It is an open world in which
the direction of time plays a central role.
Ilya Prigogine (The
Arrow of Time)
Varieties of dynamic resolution of faith-based terrorism
In the light of the above, there are possibly seven distinct approaches to
resolution of the faith-based dynamics that engender, or are experienced as,
terrorism. Meaningful solutions may indeed be understood as different forms
of structured dialogue (cf Anthony Blake, N-Logue:
an introduction) and may be explored in the light of intractable conflict
(cf Guy Burgess and Heidi Burgess, The
Beyond Intractability Knowledge Base Project, Conflict Research Consortium).
The focus here is however on the nature and dynamics of the terror which informs
interfaith dynamics -- consideration of which tends to be avoided in efforts
to frame the situation positively and in a spirit of mutual tolerance.
1. One-body "solutions": Any such solution
involves some form of special identification with the divine or the transcendent.
This is the ultimate aspiration of any faith-based agenda -- whether understood
in mystical terms as the union with God or as a Theory of Everything.
The key issue is the reconciliation with the terror associated with that identification
and its experience -- knowing the "will of God". The solutionbs might
then take the following forms:
- becoming that terror and acting as an expression of its, as many absolute
tyrants have done (including religious leaders)
- identifying with the positive attributes of the divine to the exclusion
of the negative and problematic -- as is typical of saintly mystics
- transcending the paradoxical value polarity between terror and the sublime,
thereby creating an ambiguous impression to others, perhaps typical of gnostic
These "solutions" tend to evoke questions about what is not absorbed
into the ultimate synthesis. The answers may be expressed unsatisfactorily in
"weak" explanations of "Acts of God" or of the "collateral
damage" associated with technocratic understandings of the Theory of Everything.
2. Two-body "solutions": Such solutions
are related to the well-recognized challenge of dealing with "otherness"
and terror of the "other", especially the collective or corporate
other . Alterity, namely the otherness of the "other" is recognized
in philosophical and theological thinking. "Fear of the other" and
the challenge of otherness are frequently cited in relation to:
- faith-based conflict [more],
in contrast to communion [more
more], and the otherness
of the divine [more]
- ethnic conflict (cf Rina Lazar, Knowing
hatred, International Journal of Psychoanalysis, 2003)
- cultural relations (cf Chhanda Gupta and D.P. Chattopadhyaya, Cultural
Otherness and Beyond, 1998)
- politics of colonialism and post-colonialism [more],
and political otherness [more]
- interpersonal relationships
The question is whether the mathematical approach to framing the stable solutions
to the relation between two bodies offer unexplored insights into the challenge
of the other.
3. Three-body "solutions": These could
result from careful exploration of the conditions for viable restricted solutions
of the three-body problem. They are necessarily dynamic rather than static,
namely they are dependent on the different bodies -- in the light of analogues
to the gravitational effects between them.
Eugene Butikov (Collection
of remarkable three-body motions) provides applets to illustrate what
are effectively some of the special case "solutions" to the three-body
problem (from which insights might be derived for the relations between any
set of three interacting belief sysrtems):
Many other examples of orbital motions can be found in an extensive package
of educational software developed by Eugene Butikov (Planets
and Satellites) and distributed by the American
Institute of Physics. The software enables students to explore the application
of classical dynamics to stars, planets, natural and artificial satellites,
and manned and automatic space vehicles.
It is possible that such visualizations could trigger insights regarding new
kinds of relationships between the Abrahamic religions, for example.
It is ironic that much may also be learnt about such solutions from the experience
of fairground amusement
rides. These include a wide variety of devices found in funfairs and amusement
parks designed to appeal to various senses of riders -- and notably to "terrify"
them (cf 25
Years of Orbiting, Fairground Mercury, 2001; Christine Hahn,
Fairground Machines, 1979; The
Philip Bradley fairground collection, 2005). It is interesting that
interactive software has now been developed to encourage children to conduct
research into the design of ride layouts [more].
There is continuing interest in the imaginative design and development of new
rides and the experience they offer (cf Edward M. Pribonic, Twisting
and Turning: simulating the stresses of a thrill ride tests the real-world soundness
of a cinematic illusion, 1999). Specific attention is given to these
through computer modelling for safety engineering [more].
Online tutorials exist to enable mathematicians to display the forces experienced
in various fairground rides [more].
In these cases the "terror" is transmuted into the kinds of terror
experienced through the dynamics and gravitational effects of fairground machines.
This raises the question of the nature of the interface between "thrill"
and "terror" -- and how this relates to "risk" (An
Assessment of Risks at Fairground Rides: A report produced for the Health
and Safety Executive, 1990).
4. Configurative "solutions": Here there
are various models:
Here the "terror" is transmuted into that which might be associated
with (possibly high-density) three-dimensional traffic with a degree of centro-symmetric
ordering, in contrast to the terror which may be experienced in high-density
traffic in an urban grid-type system of roadways and junctions.
A suggestive pointer with respect to configuration is provided by the language
of a patent that effectively addresses the issue of compositions of fundamentally
irreconcilable materials, including "matter" and "anti-matter"
(Composition of matter
having defined energy states (EP443836: Software Patent, 1991)
A composition of matter C, prepared by combining a composition of matter
A with composition of matter B, at precisely defined energies, and wherein
said energies of A and B are defined by the solutions to relativistic two-particle
wave equations utilizing the transverse photon exchange interaction. Compositions
of matter A and B each have intrinsic spin quantum number equal to 1/2. Composition
C has utility in numerous energy, communication and defense applications.
5. Emergent behaviour "solutions": In the
light of the emergent behaviour that can be associated with the n-body situations
of much-studied flocking behaviour, there is a case for exploring the minimum
set of rules required of bodies to engender emergent order in the dynamics between
As noted above, flocking
behaviour has been the subject of extensive study in the artificial life
focus of complexity studies -- initiated by the work of Craig Reynolds with
his Boids simulation (Flocks,
Herds, and Schools: A Distributed Behavioral Model, 1987; Boids:
Background and Update + dynamic visualization, 2001). This simulation
of the relative movement of simple agents is based on the following basic rules
governing their individual movement:
- Separation: steer to avoid crowding neighbours (local flockmates)
- Alignment: steer towards the average direction of neighbours (local flockmates)
- Cohesion: steer towards average position of neighbours (local flockmates)
With these three simple rules, the flock moves in an extremely realistic way,
creating complex motion and interaction that would be extremely hard to create
otherwise. The emergent behaviour is like that of a flock of birds, a school
of fish, or a swarm of insects. More complex rules can be added, such as obstacle
avoidance and goal seeking. Recent studies and links may be found in a paper
by Lee Spector, Jon Klein, Chris Perry and Mark Feinstein (Emergence
of Collective Behavior in Evolving Populations of Flying Agents, Proceedings
of the Genetic and Evolutionary Computation Conference, GECCO-2003).
The question is whether such "basic rules" can be understood in terms
of the most basic value elements of a "global ethic" governing the
relation between religions (or between any belief systems) [more
| more]. It is possible
that efforts towards such a global ethic have been effectively "over-designed",
to a degree that has alienated many religions -- in practice if not in principle.
Very simple "dynamic" rules might be less offensively constraining
and might avoid calling into question "static" principles of particular
religions. It is interesting that "flock" is a common descriptive
metaphor in various religions, notably the Abrahamic -- although none stresses
the dynamics of a flock, preferring to focus on the role of the shepherd.
The rules engendering flocking behaviour might then be interpreted in faith-based
- Separation: ensuring "space" for other neighbouring belief
systems, rather than seeking deliberately to occupy their space
- Alignment: adjusting the direction of development in terms of the average
direction of development of neighbouring belief systems
- Cohesion: ensuring movement towards the average position of neighbouring
Does the boid visualization provide
insights into interfaith systems of relationships -- or into interdisciplinary
systems of relationships? Bram van Heuvelen (Emergence
and Consciousness: Explorations into the Philosophy of Mind via the Philosophy
of Computation, 2000) successfully explores the relevance of such boid-like
emergent behaviour for consciousness.
It is important to note that the emphasis is on "neighbouring". The
rules govern local behaviour not the emergent global behaviour of
all bodies. Aspects of this argument have been explored elsewhere (Human
Values as Strange Attractors: Coevolution of classes of governance principles,
Gated Conceptual Communities: emergent patterns of isolation within knowledge
In these cases the "terror" is transmuted into the kinds of thrills
analogous to those associated with the risks and skills of piloting and navigation
in aerobatics [more].
More problematic however are the negative interpretations of the metaphor --
with the emphasis on "herding" a flock, notably by the suitable positioning
of threats. Conspiracy theorists would readily expect the suitable planting
of "terrorist" bombs as a 21st century simplification of the challenges
of global governance (cf Promoting
a Singular Global Threat -- Terrorism: Strategy of choice for world governance,
Boid-like behaviour has proven to be of considerable interest to the US military
(cf Nancy J Wesenstein et al. Cognitive
Readiness in Network-Centric Operations, Parameters, Spring 2005).
A particular interest relates to swarm scenarios (Joshua J. Corner and Gary
B. Lamont, Parallel
Simulation of UAV Swarm Scenarios, 2004). The focus is on the ability
to achieve a form of n-body control over automata that perform surveillance,
defensive or attacking functions -- all of which may be experienced as terrifying
to those exposed to them. The nature of such scenarios has been extensively
and imaginatively explored in media representations of vast "dark hordes"
controlled by unseen "dark forces". Ironically it is boid-type simulations
that ensure the visual realism of such effects.
The military and imaginative activation of n-body terror could usefully justify
an adage such as the following: "If you are unconcerned with the n-body
problem, be aware that some terrifying n-body solutions have you specifically
in mind"! The "more complex rules" added to govern boid-like
behaviour can be readily modified from defensive "obstacle avoidance and
goal seeking" into an attack mode of which the citizen is the focus.
6. Embodied "solutions": The "flocking"
approach to ensure emergent order suffers from a major disadvantage in that
it is based on a set of external rules -- even though these may constitute
a consensual ethic.
A somewhat different approach is to ask how such rules can be internalized
and to look for models of how this is accomplished. Individual belief systems
might refer to this process as education, inculcation or indoctrination -- with
respect to their own belief system. It is far less evident how such education
is achieved with respect to behaviour of individuals or groups in distinct faith
"vehicles" on different pathways, however interwoven. The desperate
attempts by the UN, through UNESCO, to promote a "culture
of peace" are an indication of how the challenge is currently framed.
Perhaps the most obvious model is then that of drama (cf Aesthetics
of Governance in the Year 2490, 1990; Participative
Democracy vs. Participative Drama: lessons on social transformation for international
organizations from Gorbachev, 1991). Traditionally the relations between
the gods have been described in dramatic terms, whatever values were exemplified
by that process -- whether creative or destructive. Understandings of the movement
of bodies in the solar system have traditionally been conflated with the dramatic
relationships among the gods. Pantheons of gods might then be analyzed as n-body
problems (or solutions).
In this dramatic sense the perceptible relations between the Abrahamic religions,
and the bloody violence and terror that they engender, are "solutions"
to a many body problem. Just as fundamental particles may collide with the release
of destructive energy, or molecules may encounter each other with analogous
outcomes, the terrifyingly destructive drama between religions is indeed a "solution"
-- however apparently primitive.
What is missing from this dramatic perspective is the description of it as
drama. Dramatization of particular stories, about Israelis and Palestinians
for example, may be produced -- evoking great controversy. But the dramatic
interpretation of the sweep of historical relations between the Abrahamic religions
is not attempted -- so as to evoke recognition of how dramatically impoverished
it is and to identify ways in which the dramatic expression could "move
on", to embody a richer aesthetic, rather than being stuck in uncreative
"sitcom" cycles of violence.
7. Peripatetic "solution": Another "solution",
with a long tradition, may perhaps be derived from that associated with the
peripatetic school of philosophy
founded by Aristotle. The peripatetic axiom, later formulated by Aquinas, was
that "Nothing is in the intellect that was not first in the senses." (Latin:
"Nihil est in intellectu quod non prius in sensu"). The name derives
from the process of walking whilst philosophizing -- or perhaps in order to
philosophize effectively. "Walking the talk" and "Talking the
walk" are interesting variants. The classicial context for doing so, the
rectangular covered walkways of the Lyceum
(peripatoi), may suggest a "rectangular" constraint on the
Iimportance has long been attached to the spiritual insights associated with
labyrinths, especially with how
these are traditionally triggered through walking them (cf Lauren Artress, Walking
a Sacred Path: Rediscovering the Labyrinth As a Spiritual Tool, 1991; Patricia
Telesco, Labyrinth Walking: Patterns of Power, 2001) [more
| more]. It is therefore worth
considering how this process might be the basis for a form of "solution"
-- notably to the three-body problem constituted by the Abrahamic religions.
The great proportion of labyrinths which are walked in this way are centro-symmetrical.
As such they may be considered as offering insight into the one-body problem
of engaging with the higher dimensionality of the spiritual insight of a single
body of faith -- if only in one's own identity. The frequent need to change
direction -- possibly understood as an "initiation" -- in order to
move towards the centre is a significant trigger to reflection on what is not
obvious, however simple it may be claimed to be.
Of more interest to the three-body challenge is the possible existence of labyrinths
with an interwoven three-fold symmetry. An early, and relatively unique example,
is given below. It was notably used by the foundation Mankind 2000 in its catalytic
role in promoting the emergence of international futures research and what became
the online Encyclopedia of World
Problems and Human Potential.
Pre-historic representation of a pattern
of relationships i
ndicative of a potential relation between
(Christianity, Islam, Judaism)
at the Passage Tomb at Newgrange,
In a sense the "gravitational" effects, which are challenging to
sustainability of relationships in the dynamic models described earlier, are
effectively "insulated" here by the structure of the pathways between
the kernels of each of the "bodies". As attractors, the potentially
terrifying core insights of each are not directly "exposed" to those
of the others. The terrifying monster is locked within the labyrinth -- at each
centre? As a labyrinth, these insights can only be sequentially explored by
a particular pattern of walking. The need for such a damping effect recalls
the need for graphite rods for neutron damping in a nuclear reactor to control
the level of reaction and ensure stability.
The emphasis in this solution goes beyond that of embodiment as described above.
It is best associated with the work of Francisco
Varela and others (cf The Embodied Mind, 1991; Laying Down a Path
in Walking: essays on enactive cognition, 1987) and the understandings of
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Gary E Bolton and Axel Ockenfels. Self-centered fairness in games with more
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J. Allan Cheyne and Donato Tarulli. Dialogue, Difference, and the "Third
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Gregory of Nyssa. On "Not Three Gods" [text]
Charles H. Hinnant. Schiller and the political sublime: two perspectives. Criticism,
Spring, 2002 [text]
Kenneth Humphreys. Christianity's "civil war": the struggle for power
P Hut. The Three-Body Problem in Stellar Dynamics, 1984, in The Big Bang and
Georges Lemaitre International Symposium G. Lemaitre, ed. A. Berger (Dordrecht:
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Steven Johnson. Two ways to emerge, and how to tell the difference between
them. Extreme Democracy [text]
- Psycho-social Significance of the Mandelbrot Set: a sustainable boundary
between chaos and order, 2005 [text]
- Thinking in Terror: Refocusing the interreligious challenge from "Thinking
after Terror", 2005 [text]
- Varieties of Terrorism: extended to the experience of the terrorized, 2004
- Towards a logico-mathematical formalization of "sin": Fundamental memetic
organization of faith-based governance strategies, 2004 [text]
- Hyperspace Clues to the Psychology of the Pattern that Connects in the light
of 81 Tao Te Ching isights, 2003 [text]
- Future Challenge of Faith-based Governance, 2003 [text]
- And When the Bombing Stops? Territorial conflict as a challenge to mathematicians,
- Patterns of N-foldness; comparison of integrated multi-set concept schemes
as forms of presentation, 1984 [text]
- Distinguishing Levels of Declarations of Principles, 1980 [text]
- Representation, Comprehension and Communication of Sets: the Role of Number,
George Lakoff and Rafael E. Nunez. Where Mathematics Comes From: How the
embodied mind brings mathematics into being. Basic Books, 1992
M Matsushima and T Ikegami. Evolution of strategies in the three-person iterated
prisoner's dilemma game. J Theor Biol. 1998, Nov 7, 195, 1, pp. 53-67. [abstract]
Brian Paul. Looking for GOD in all the wrong places... like KOLOB [text]
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Stewart Shapiro. Thinking about Mathematics: the philosophy of mathematics.
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