everything you've learned in school as "obvious"
becomes less and less obvious as you begin to study the universe
for example, there are no solids. there's not even a suggestion
of a solid. there are no absolute continuums
no surfaces. no straight lines
buckminster fuller
.
the more abstract the truth you want to teach
the more you will have to win over
the senses in its favor
nietzsche
. .
some los angeles
housewives attend
pole dancing classes
note it is never the other
way around: aint no stripper
paying a housewife to learn how
to drop the kids off at soccer practice
.
this analogy illustrates the mathematical idea
of antisymmetric relation: an arrow a-->b
implies that there is no arrow a<--b
.
causality is an antisymmetric relation:
if a causes b, b cannot cause a
if event a occurred before b
then b must follow a
.
a symmetric relation is one
such that a-->b implies
existence of a<--b
same as a--b
.
an edge
is not arc
2-way street
instead
of 1
.
correlations are symmetric relations
if a and b are correlated, then
automatically so are
b and a
.
. .
the concept
of dependence permeates
the earth and its inhabitants in
a most profound manner. examples of
interdependent meteorological phenomena
in nature and medical, social and political
aspects of our existence, not to mention
the economic structures, are too
numerous to be cited
individually
moreover
the dependence
is obviously not deterministic
but of a stochastic nature
however
it seems that none
of the departments of statistics
engineering, economics and mathematics
in the academic institutions throughout the world
offer courses dealing with dependence concepts and measures
d mari & s kotz / correlation and dependence, 2001