*Post by Randall Nettman*In a ridiculous pointless article

On Wed, 26 Nov 2003 08:43:34 GMT, Czar

Drooling Simpleton I

When your economic growth is fueled >primarily

by mortgage refinancing, you're not exactly

building something likely to last.

The lack of knowledge of basic national >income

accounting in the above statement is

breathtaking. For starters, mortgage >refinancing

does not affect any newly produced goods or

services. Therefore it has no direct impact on

GDP. - Tony

SEE!

____

In 1900 the great Prussian mathematician Hilber put forth 23 math

problems for the

20th century, No's 6, 8 and 16 remain unsolved, though the pretty 22 yr

old swe. girl has partially solved No. 16...whoever can successully

solve No. 6 below, I will believe:

http://www.aftenposten.no/english/world/article.jhtml?articleID=3D678371

6. Mathematical treatment of the axioms of physics

The investigations on the foundations of geometry suggest the problem:

To treat in the same manner, by means of axioms, those physical sciences

in which mathematics plays an important part; in the first rank are the

theory of probabilities and mechanics.

As to the axioms of the theory of probabilities,14

it seems to me desirable that their logical investigation should be

accompanied by a rigorous and satisfactory development of the method of

mean values in mathematical physics, and in particular in the kinetic

theory of gases.

Important investigations by physicists on the

foundations of mechanics are at hand; I refer to the writings of Mach,15

Hertz,16 Boltzmann17 and Volkmann. 18 It is therefore very desirable

that the discussion of the foundations of mechanics be taken up by

mathematicians also. Thus Boltzmann's work on the principles of

mechanics suggests the problem of developing mathematically the limiting

processes, there merely indicated, which lead from the atomistic view to

the laws of motion of continua. Conversely one might try to derive the

laws of the motion of rigid bodies by a limiting process from a system

of axioms depending upon the idea of continuously varying conditions of

a material filling all space continuously, these conditions being

defined by parameters. For the question as to the equivalence of

different systems of axioms is always of great theoretical interest.

If geometry is to serve as a model for the treatment

of physical axioms, we shall try first by a small number of axioms to

include as large a class as possible of physical phenomena, and then by

adjoining new axioms to arrive gradually at the more special theories.

At the same time Lie's a principle of subdivision can perhaps be derived

from profound theory of infinite transformation groups. The

mathematician will have also to take account not only of those theories

coming near to reality, but also, as in geometry, of all logically

possible theories. He must be always alert to obtain a complete survey

of all conclusions derivable from the system of axioms assumed.

Further, the mathematician has the duty to test

exactly in each instance whether the new axioms are compatible with the

previous ones. The physicist, as his theories develop, often finds

himself forced by the results of his experiments to make new hypotheses,

while he depends, with respect to the compatibility of the new

hypotheses with the old axioms, solely upon these experiments or upon a

certain physical intuition, a practice which in the rigorously logical

building up of a theory is not admissible. The desired proof of the

compatibility of all assumptions seems to me also of importance, because

the effort to obtain such proof always forces us most effectually to an

exact formulation of the axioms.

So far we have considered only questions concerning the foundations of

the mathematical sciences. Indeed, the study of the foundations of a

science is always particularly attractive, and the testing of these

foundations will always be among the foremost problems of the

investigator. Weierstrass once said, "The final object always to be kept

in mind is to arrive at a correct understanding of the foundations of

the science. ... But to make any progress in the sciences the study of

particular problems is, of course, indispensable." In fact, a thorough

understanding of its special theories is necessary to the successful

treatment of the foundations of the science. Only that architect is in

the position to lay a sure foundation for a structure who knows its

purpose thoroughly and in detail. So we turn now to the special problems

of the separate branches of mathematics and consider first arithmetic

and algebra.

Easto

I live in the hell of WebTV