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decreasing from front to back is the cost (and ability to pay) for war. Without the
financial capacity to make war, threat goes from left to right smoothly at the back of
the box as tension gradually increases without the onset of armed conflict. When
effective fighting capacity is cheap and/or already well funded, the country well
armed, the increases in threat go from left to right at the front edge of the box and
encounter the cliff of catastrophe and war is declared. Cost of, or ability to wage war
varies from the front to back, and serves as the splitting factor. Considering prison
riots, social tension is the normal factor and alienation (degree of identification with
prison authority) is the splitting factor.” Using factial expressions of dogs sketched
by the Konrad Lorenz, Christopher Zeeman then of Warwick Mathematics Institute
in England, considered countenances reflecting increasing rage as the normal
factor, the amount of fear was the splitting factor. Increasing rage at high fear
increased smoothly at the back of the box; at low fear, increasing rage falls off the
cliff to an animal attack at the front of the box.” He paced as he talked, occasionally
looking up to see if | was following him. He continued,
“A light above the box casts a shadow from the roof to the floor, outlining the
gradually widening fold created by the transition from the smoothly rising back of the
roof to its ‘S-shaped’ front. This triangle on the x-y causal floor is the region in which
the discontinuity in the result surface roof results and is called the bifurcation set. An
increasing amount of the causal ‘normal factor’ is represented from left to right
along the *x’ dimension, the results of which change smoothly at the back of the roof
but encounter a discontinuous jump up or fall down crossing the inaccessible
crevice in the °S’ fold at the front of the roof. Again, the triangular shadow on the
floor made by the fold indicates the parameter region in which discontinuous
changes in the result surface occur. The reason the parameter that determines the
front to back location of the left to right movement of the ‘normal factor’ is called the
‘splitting factor’ becomes obvious. Its value determines whether the results induced
by increasing amounts of ‘normal factor’ will be smoothly changing or generate a
discontinuous jump. The entire visualizable object is called a cusp catastrophe and
it along with higher dimensional parameter region-inspired shapes such as the
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