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