[Redbook5:293][19880815:1628]{Cusps}[15th
August 1988]
.1628
I
have written* for information on Thom’s Catastrophe Theory** –
something I heard of many years ago, but only by name, and meant to
follow up (and should have), but work etc., I guess, intervened. All
I know of it now is that in Thom’s theory catastrophes are a kind
of (presumably, mathematical) fundamental form incarnate (presumably
in nature); and that it has something to do with cusps. *** A Cusp
turns out to mean, ‘technically, the intersection of two
curves’.**** In mathematics,# however, it seems that ‘A simple
cusp is a point on a curve where the curve crosses itself, and where
the two branches of the curve share a common tangent, the branches
being on opposite sides of the tangent. For example, y2
= x3.
The
curve above has a simple cusp at the origin, where the x-axis is the
common tangent.’#*
*(to
E[ncylopedia]
B[ritannica]
[who
operated a question-answering service for buyers of their
Encyclopaedias])
**[See
end of footnotes, below]
***(It
became popular in Europe in Gothic
architecture – frequently decorated with leaves, heads etc.) (cf
[[Redbook5:145][19880609:2400
[sic]]{Art, Architecture and Politics}[9th
June 1988],]
145
eg
[The ms sketch is very much smaller but cannot be further reduced here]
(Architecture)
****E[ncylopedia]
B[ritannica]
III,810.
In
S[horter] O[xford] D[ictionary] it is also ‘apex’, ‘peak’.
#(I
have given maths a rest recently (although I ‘wanted’ to go on)
in order to spend time on Booklet [sic]
&c)
#*(Collins
Gem Basic Facts Mathematics)
**[
‘Originated
by the French mathematician Rene Thom in the 1960s, catastrophe
theory is a special branch of dynamical systems theory. It studies
and classifies phenomena characterized by sudden shifts in behaviour
arising from small changes in circumstances. Catastrophes are
bifurcations between different equilibria, or fixed point attractors.
Due to their restricted nature, catastrophes can be classified based
on how many control parameters are being simultaneously varied. For
example, if there are two controls, then one finds the most common
type, called a "cusp" catastrophe. If, however, there are
move than five controls, there is no classification. Catastrophe
theory has been applied to a number of different phenomena, such as
the stability of ships at sea and their capsizing, bridge collapse,
and, with some less convincing success, the fight-or-flight behavior
of animals and prison riots.
The diagram above is taken from the Web & is not in the ms.
]
[continues]
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