Speaking of my message from Mon, 08 Jan 2007, "Re: Was the conversion
of John C Wright numinous?", Julia Thompson said
... a multi-dimensional vector space with "snap" ...
Elaboration later when I have more brain.
I am looking forward to that. Meanwhile, a different topic ...
another mathematical issue ...
Alan Page Fiske, an anthropologist, wrote in `Structures of Social
Life: The Four Elementary Forms of Human Relations' that the four
elementary forms are the bases of groups of equals, of armies and
corporations, of law-bringers, and of competitive (not monopolistic or
oligopolistic) businessmen.
These can be expressed mathematically:
- who is in or out of a group, such as a particular Christian,
Moslem, or Hindu sect -- an equivalence relation is needed and
creates a categorical or nominal scale;
- an army or bureaucracy -- a linear ordering is required and
creates an ordinal scale;
- an interval scale is based on an ordered Abelian group. The
example Fiske gave was of a pre-industrial, agricultural culture
in which he spent several years. In farming. every man would line
up on a field and would stab his hoe down at the same time, again
and again. In American life, everyone votes equally and at the
same time (except not quite).
- a ratio scale is based on an Archimedean ordered field and is seen
in areas which involve comparing apples and oranges. These
otherwise different fruits are compared by abstracting certain
characteristics from them and then comparing them with a third
quantity, such as money.
(The notions have little or nothing to do with numinous experiences --
except that an author who has a numinous experience and who doesn't
cross cultures may prefer an interval scale to a ratio scale.)
The same four mathematical operations make up the basic four needed
for arithmetic. Is it a natural number? Is it bigger or smaller than
another number. What is the result when you add two numbers together?
What is the result when you add another operation, multiplication, to
your rules?
In the 1940s, Luis Guttman said that people perceive using these four
mechanisms. He said that other forms are conflated into those four.
As I say in my (very short) book, `Choice and Constraint',
http://www.rattlesnake.com/notions/Choice-and-Constraint.html
Much progress in science comes from changing the type of scale
used in a measurement. For many centuries, people said `it is
cold outside', in which cold is a category distinct from hot.
Then people said `it is colder today than yesterday'. This is an
ordinal scale. After the invention of the thermometer, it because
possible to say `it is 10 Fahrenheit degrees colder today than
yesterday', making use of an interval scale. [But because a
Fahrenheit or Celsius scale has an arbitrary zero, you cannot say
that one temperature is twice that of another.] Finally, after
Kelvin and Boltzmann brought us understanding, an engineer could
say `the thermal energy content of this piece of iron is 0.6% less
than it was yesterday', making use of a ratio scale.
--
Robert J. Chassell GnuPG Key ID: 004B4AC8
[EMAIL PROTECTED] [EMAIL PROTECTED]
http://www.rattlesnake.com http://www.teak.cc
_______________________________________________
http://www.mccmedia.com/mailman/listinfo/brin-l
