1. MAP 56
The Cusp of Catastrophe: Rene Thom,
Christopher Zeeman and Denis Postle
The word catastrophe comes from Greek tragic drama (seeMap 2) and refers to the
sudden twist of denouement in the plot, as when Oedipus changes from
authoritative investigator to disgraced criminal, from insider to outsider, originator
to originated. Catastrophe theory is the invention of Rene Thom, the French
mathematician; Christopher Zeeman, a professor of mathematics at Warwick
University, has made considerable progress in creating analogues of catastrophic
social events and developing topologies of multi-dimensional surfaces; and Denis
Postle, a British television producer and science writer, has made extensive
applications of the theory to the dynamics of mind and behaviour. Catastrophe
theory can be useful wherever there is a spectrum of interaction between two or
more independent influences, forces or variables which combine to influence some
mood or behaviour in a manner leading to discontinuous jumps, oscillations and
changes, often of a sudden and catastrophic nature.
Take, for example, the combined influence of the superego and the id in Freud's
psychoanalytic theory (see Map 9). The id, we may recall, consists of clamourous
libidinal energies and drives. The superego consists of internalized moral
prohibitions and aspirations derived from parents and authorities of childhood. The
map opposite consists of a three-dimensional graph with a flat lower surface and
folded upper behaviour surface. The lower surface includes the two independent
forces: the superego, which increases in strength from point A to point B and all
across the surface from point C to point D; and the id, which increases in strength
form point A to C and all across the surface from point B to D. These two forces
combine to influence the behaviour surface above, in a manner that depends
entirely upon their relative strengths. In the vicinity of a on the behaviour surface
both forces are so weak that their conflict is minimal. In the vicinities of points c and
b first the superego is so weak, and then the id is so weak that conflict is still minimal
and behaviour smooth. But in the vicinity of point d an immensely powerful
superego is struggling to hold in check a raging id. The map shows the cusp by
which a surface range of behaviour labelled moralism has folded itself above
another range of behaviour labelled lust; degrees of moral fervour are measured by
the increasing distance between the lower and behaviour surfaces, reaching a
maximum at d-D. We can immediately see what will happen if the superego
slackens or the id force increases. Behaviour will shift away from d towards c with a
catastrophic descent from moralism to lust, the Reverend Arthur Dimmesdale of
The Scarlet Letter caught with his trousers down. Hisego helpless to mediate between
a fierce sexuality and a puritanical inhibition. The shape of the cusp has been
projected upon the lower surface in the area within the dotted lines. This is called a
bifurcation set and maps the precise points at which moralism jumps to lust and
back again. The behaviour within the bifurcation set is not available to the
individual caught in this conflict between id and superego. He teeters between
extremes.
Note the extraordinary vindication of Freud's theory which the cusp catastrophe
represents. There is the unconscious folded beneath the conscious mind, the latter
repressing the former which is ever likely to erupt. The danger of a catastrophic
regression, the intellectual defence against impulse, the denial of mounting feelings,
the reaction-formation in which moralism escalates, the desperate inner anxiety of
going 'over the edge', and the ego desperately straddling a growing fissure, a split in
the centre of the personality.
Our 'first' catastrophe is told in the myth of the Fall (see Map 4) and can be
mapped in a style similar to Freudian theory, but using degrees of obedience and
freedom instead. Hence in diagram 1 the lower surface A-D, B-C measures
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Obedience
The map opposite is a cusp
catastrophe and models the effect
of two independent variables,
known as 'control dimensions',
upon a third range of behavioural
outcomes. In this example the cusp
has been used to model a situation
familiar in Freudian theory. On the
lower surface of the graph degrees
in the strength of the patient's
superego are measured from lelt
to right across the surface A-B,
C-O; while the strength of the id
forces are measured on the
surface A-C, B-C to give a
hypothetical coordinate X. Hence
this client has a very strong
superego barely containing an
almost as strong id. The effect of
this is shown on the upper
behaviour surface where a
conscious moralism represses
underlying lust. Should the
superego weaken and the
superego-itt coordinate move
from X to Y, a catastrophiC
descent occurs from moralism to
lust as behaviour jumps
discontinuously across the
bifurcation set. Within this cusp
moderate eroticism is totally
unavailable to the patient who
teeters to and fro between
inhibition and lechery.

2. LEVEL 8/MAP 56
Lower surface
...
1
I
I
I
I
"
_--x
/
/
/
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3. MAP 56/LEVEL 8
increasing degrees of freedom. Mankind could remain free within the law of God (or
the ecology of the Garden) by remaining close to point c on the behaviour surface,
but no sooner did Adam's freedom involve disobedience to the ecology of the
Garden, than the move towards d precipated his Fall,the very shape of which move
is serpentine. Adam's deployment of a tree of conscious purpose upset the network
of cybernetic restraints (see Maps 48, 50, 55).
The cusp also represents a kind of crucifix between the 'known self and the
'unknown self' in Harry William's psychotheology (see Map 5) as the individual
suffers crucifying tensions between mind and body or faith and doubt. If the
integrity of personality is literally 'buried within the cusp', then crucifixion between
the extremes and a 'descent into hell' where the buried values lie, is a necessary
prelude to 'resurrection' where the prisoner arises from his tomb and the Fall is
redeemed.
The S shape of the cusp also bears a remarkable resemblance to Carl lung's
concept of The Way, the winding path from thinking to sensation to intuition to
feeling by which those in analysis find their way from the conscious surface to the
unconscious depth (see Map 10). There they discover archetypes, self-portraits of
the instincts, with axeswhich criss-cross in a manner extraordinarily similar to those
of multi-dimensional catastrophe models, where three, four, six or more variables
create fold-within-fold. And who looking at the persona (mask) on the behaviour
surface can doubt that its shadow lurks behind, a dark brother hiding in the cusp?
And beyond the shadow lies the soul-image, for which the persona yearns because
it has shut itself away from its 'lost opposite'. Straighten out the folds in the
behaviour surface and we see that soul-image is indeed at the other end (see
diagram 2).
There is a theme to the catastrophic events running through this book. The
subject attempts to maximize one dimension or value of behaviour but discovers
that there is always another end. The way to become more certain, for example, is
to entertain doubt, not to evade every issuethat threatens you with uncertainty or
to think 'positively' or practise positivism. Professor Parkins in Map 13 tried to
maximize certainty, detachment, fact, and empiricism, but instead was haunted by
their opposites, doubt, horrid intimacy, anomaly and fantasy. There arose from the
bed in cusps and folds 'an intensely horrible face of crumpled linen'. The creature
appeared dead yet alive, random yet ordered, intimate yet alien. Now such
contradictions terrify precisely because the centre of integrity of behaviour has
disappeared into the fold or cusp. Under normal circumstances life becomes death,
order becomes random, the alien becomes intimate and so on, but where
'becomes' falls within the bifurcation set and the opposites lie outside it, these
oppositions are juxtaposed in sinister contradiction.
The doomed attempt to maximize but one dimension was implicated in R. D.
Laing's theory about the onset of schizophrenia (in Map 14). As a child, Julie was,
according to her parents, 'sweet, obedient and clean', by which they meant that
she was exactly and only as they defined her, a being-in-itself, of refined 'goodness'.
In an attempt to live in this unlivable situation, Julie developed a schizoid
personality organization which split her experience into a false self upon the
behaviour surface and a true self hidden within the fold. Behind the 'sweet,
obedient and clean' surfaces which her parents commanded, her 'true self was
'angry, rebellious and dirty'. No sooner did .she reveal this hideously discrepant
aspect, than her parents had her certified insane, 'Better mad than bad.' In diagram
3, we see the schizoid personality originating at the point of the cusp and gradually
widening as the two selves part company. This increasing discontinuity of
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4:1
dominate
boss Ie
exploit
reject
.
~IP
.
ey submit
weaken
cling
depend
0"
BIFURCATION SET
MAP REFERENCES
Bifurcation, see also
schismogenesis, 47-51, 57-60;
Catastrophe, see also Fall,
tragedy, 2,4,24,35,54,57-60;
Contradiction, 14, 40, 49-50;
53-5; Maximization, see linear
thought, 4-5,14-16,22,28-9,34,
43.

4. LEVEL 8/MAP 56
-----,I~
I~
18
I::J
I
I
I
I
I
CATASTROPHE
I
ever-increasing catastrophes
I
+
behaviour causes a psychotic break, as Julie oscillates uncontrollably between true
and false selves, utterly obedient then shrieking recriminations.
These catastrophe surfaces also make good sense of Henry Stack Sullivan's
reciprocal self-systems in Map 34. In their pathological forms the dynamisms lose
their centre and only the outer extremes remain, leading to psychotic, neurotic and
criminal behaviours. For example, one person becomes stuck in the dominating
and exploitative mode pushing the other into the reciprocal extremity of
submission and weakness. The extremity of one excites the extremity of the other
and they oscillate, with the middle range of behaviours falling into the cusp or
bifurcation set (see diagram 4).
How do we begin to repair catastrophes? Clues come from Level 4 on creativity.
Koestler, in Map 27, defines creativity as the discovery of connectedness or
bisociation between a conscious surface and a submerged surface. Creative ideas
bubble up through the cusp during moments when the mind is resting enabling the
creator to 'think on two planes'. In divergent thinking (see Map 28) or lateral
thinking (see Map 29) the mind jumps from level to level turning tables on
exploiters. A major prophylactic against catastrophe is to question the proposition
that the two or more values, or forces, influencing behaviour are necessarily
independent of one another. Both the tradition of Anglo-Saxon empiricism and the
Marxist-Hegelean doctrine of contradictions see conflict between independent
forces where this might not be so. The act of creation discovers connections.
Similarly Martin Buber in Map 35 redefined such ideas as distance and relationship,
abstract and concrete, in terms of an indivisible I-Thou connectedness which also
relates categories. Note that the point where the cusp begins on the behaviour
surface is very like Buber's narrow ridge, with a precipice that soon yawns if this
divide is not negotiated.
The sigmoid curve, introduced by Jonas Salk in Map 46, is the gentle curve by
which genetic evolution takes corrective action just as the cusp begins to fold. Salk
is saying that unless we develop the evolutionary values of 'both ... and', nature's
dialectical pattern, an evolutionary catastrophe will enfold us trapping us between
ego and being values (see diagram 5).
Catastrophe theory gives perhaps its most dramatic support to Gregory
Bateson's concept of schismogenesis, 'the growing split in the structure of ideas',
precipitated by mutual interaction and clearly evidenced by the widening
bifucation set. We can now appreciate the path of the alcoholic in Map 48 who
cycles from alcoholic pride to falling off the wagon, to sobering up, to pride and
falling again (seediagram 6). Finally we see that fascism caught in such self-exciting
contradictions as Freedom-Fate, Domination-Submission,
Loyalty-Rebellion,
Violence-Love, fulfills Yeat's prophecy, 'turning and turning in its widening gyre the
falcon cannot hear the falconer ... things come apart the centre cannot hold ... '
As the cycle widens the catastrophic jumps from freedom to fate, violence to love,
gather in frenzy and intensity and half of Europe is sucked into the vortex (see
diagram 7).
One thing is certain we cannot entertain lightly the theories of contradiction
propounded by Hegel and Marx (seeMaps 52, 53); we could be talking of the end of
the world. The Greeks knew better (seeMaps 2, 57, 58): they enacted on stage, at a
meta-level above reality, the process by which value absolutes buckle beneath
peripeteia into their antithesis. Such scenes shocked the entire civic culture into
looking, suffering and learning to survive (see Maps 2, 57, 58).
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