Post by Randall NettmanIn 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