The most difficult physics problem at that time was the conceptual
understanding of atomic structure. A new mathematics had been conceived, and
refined, by Bohr, Heisenberg, Schrodinger, Born, Dirac, Feynman, and others,
that had been developed expressly for the operational, or scientific analysis
of atomic phenomena. Actually, atomic structure is but a part of the larger
realm of natural phenomena that the new mathematics was eventually applied to.
However, our view of atomic structure remained rife with conundrum and paradox,
with or without, the new mathematics.
Today much of the new mathematician’s description of the world on the
blackboard and in the published papers, is abstract and devoid of any
conceptual connection to physical reality. Steven Weinberg, an accomplished
contemporary physicist, wrote, "... it is always hard to realize that these
numbers and equations we play with at our desks have something to do with the
real world." With the phrase, "...something to do with the real world",
Weinberg reveals that the mathematician has only an unformed idea as to what
his abstractions represent conceptually, and no idea why they apply to the
universe so well. Consider the words of the late Hungarian mathematician and
physicist, Eugene P. Wigner, "... the enormous usefulness of mathematics in the
natural sciences is something bordering on the mysterious ... there is no
rational explanation for it."
It is in the contemplation of the remarkable, and on the face,2 extremely
fortunate connection, between the mathematics and the operation of the stable
systems in the universe, that I found the thread that had so long eluded me. It
turned out that there is, in fact, a rational explanation for it. Galileo may
have been the first to formally assert that, "... the laws of nature are
written in the language of mathematics." Today we may elaborate.
Stability in the field requires economy in cyclic motion.1The invariant aspects
of the stable systems within the physical universe, toward which we necessarily
direct our investigative efforts, function from the principle of least action.
Equivalence and symmetry are intrinsic to the principle of least action.
Mathematics in general, as is evident from Euclid, and when applied through
theoretical physics, feeds on equivalence and symmetry. It is illuminating to
note that what the mathematics represents well, its area of focus, is precisely
the action stable systems must follow to maintain perpetuity in the field. The
rules and laws and generalizations that result from the economic mathematical
abstractions, derive necessarily, from a physical system's potential for
stability, and not from a separate reality, for any of its postulated or
experimentally observed operational quantities. The mathematics fits the stable
universe because mathematics (equations) can easily represent the economic
properties of stable systems.
As a result, all our classical conservation laws speak to the economic orders
of form attendant to stable system action. This is not to say that there are no
causes or underlying reasons for the order we observe in the universe, beyond
the principle of least action. Rather, it is to say that our laws and
principles are derived solely from, and speak solely to, the principle of least
action.
Consider the continuing words from Eugene Wigner, "... it is just this uncanny
usefulness of mathematical concepts that raises the question of the uniqueness
of our physical theories." The extent of the uniqueness of our physical
theories is defined by the properties they retain after ultimate reduction to
their most basic state. In this form they are consistent with, or reduced to,
the static orders of form attendant to an instant or complete cycle of stable
system action, be it as in the inverse square property of an economic sphere,
the circumference line segment ratio to, its radially enclosed area in the
Euclidean circle, or the planet's trajectoral time interval ratio, and its
swept out area of the economic orbital conic. These are all encompassed by the
principle of least action.
The consequence of these observations, is the realization that we can create an
abstract, bare bones, mathematical system that fits experimental measurement
reasonably well, solely by utilizing operational quantities that are
economically compatible, symmetrically consistent, or otherwise without effect,
with respect to the invariant kinematic orders of form attendant to stable
system action. Wigner approaches the idea that one can mathematically define an
experimentally verified conserved quantity, complete with a local numerical
magnitude, and if that quantity operates according to the principle of least
action, without further influence, or effect, it can be proportionally applied
to any other stable system, utilizing its locally derived magnitude, by virtue
of the invariant, economic, time-area, or frequency-wavelength aspects, common
to each stable system. This suggests that with any inaccurate, seminal, a
priori knowledge assisted5 dynamic assumption, one can add too, subtract from,
and in many ways modify the seminal assumption, in order to maintain a fit with
the experimental evidence.
Aside from the kinematic quantities common to stable systems, our operational
quantities are products of our assumptions and expectations, which in turn are
derived from, and limited by, our sense perceptions. The consequence of this,
is that all mathematical models of stable physical systems, are at some point,
conceptual creations of the observers. This suggests that devising an
operationally effective mathematical scheme based on the idea of mass,6 or high
energy particle collision data and principles of symmetry, does not necessarily
raise the operational quantities to the level of a physical reality.
The fact that we can alter the energy of a proton into primarily transient
energy states we collectively call bosons and fermions causes us to conclude
that a proton object is composed of quark objects, whereas, by our argument so
far, this does not even reasonably follow. 7 The quarks have a physical
justification that is dependent on the trails of transitory atomic fragments,
created by high energy collisions in the atmosphere, or in the laboratory. I
introduce the question here. Of what significance is an isolated transitory
(unstable) energy state? Murray Gell-Mann put the theory together from the
host of data9 available, but he never believed that it truly mirrored, real
world quantities. Consider Steven Weinberg’s words again. "... it is always
hard to realize that these numbers and equations we play with at our desks have
something to do with the real world."
Before the publication of The Physics Preview, the "... something to do with
the real world" aspect of the mathematics, had not been clearly articulated. As
a result we assumed a too literal interpretation, for the operational
quantities within our theoretical constructs, and the mathematicians and
physicists were taught, and accepted the physical reality of the theories they
learned. What this meant for the rest of humanity was: absent a clear
understanding of the connection between the mathematics and the stable systems
in the universe, and as long as the physicist had something that worked as a
mathematical model for a physical system’s action, humanity was stuck with
the operational quantities used within that model. Quantities that are the
conceptual nomenclature for the new mathematical constructs that define the
action in stable systems. These operate within an idealized operational
representation of stable physical systems, as perceived aspects of those
systems, and are subsequently conceptually applied to the real universe,
describing it solely in terms of the stripped down rarefied model.
We are given these quantities as real objects, and we are told that they are
fundamental aspects of the universe. The most recent additions are the logical
result of an unquestioned, never verified, one hundred year old seminal
assumption. Colored quarks have no real existence in the universe, yet, today
the academic humanist must reason from a theoretical reality, composed of
colored quarks, joined together with gluons, within a time dilating, curved
space universe. Why? Because mathematics has something to do with the real
world.
"This fool wishes to reverse the entire science of astronomy;"...Luther on
Copernicus, 1539
john...@dr.com
http://www.geocities.com/thejohnreed
>This
>guy Shaefer,argued that good calculations may be more reliable than
>experiments.(much like you said)
I think that good calculations allow us to predict events beyond our
theoretical understanding. To say that a correct mathematical calculation is
synonymous with conceptual understanding however, is completely bogus.
One can take an abstract mathematical system that is complete fantasy and
predict very accurately and not have a clue to the workings of the universe.
The mathematicians have ripped off the rest of acadamia by trying to, and
succeeding in, supplanting the real universe with their fantasy schematics.
Witness the serious study of time travel. Witness a universe that doesn't exist
that we see every nite by virtue of little visibility objects called photons.
Experiment is the final arbiter that one must fall back on in a re-evaluation
of our current paradigm. When one questions the mathematical ideas of black
holes, worm holes, curved space etc., one discovers that they all rest on
assumptive expansions from base theoretical errors.
So, in my world view, only the experimental hard data counts. All the roosters
who think that they make the sun rise every morning see the evidence proving
their mathematical atrocities at every hubble view...
Ptolemy has been pardoned... replaced by very accurate and functional schemes.
But when one looks for a black hole in the sky, one finds something that proves
the rooster right.
my regards Herb,
johnreed
You Dirtbag,
Witness the number of times in history a mathematician has made a scientific
breakthrough only to have science get the credit. Notice the similarity of
the formula for the area of a circle and Einstein's marvel. Witness that we
have NO BELL prize for mathematics. Mathematics remains the ho-hum and oh
so boring field of drudgery for drudgery's sake. I will have you know that
had anyone or any texbook bothered to mention that Copernicus, Galileo, and
Newton were at heart mathematicians, I would have been much prouder of my
math skills at a much younger age. Space is in reality a volume ... that
can only be defined absolutely in 3 dimensions. However, with study, the
4th dimension, anticipation, can be extrapolated and even predicted. And
the science of prediction is what engineers bet on daily.
Mrs. L
Mrs. L,
I disagree. Though, mathematics is a very neat, useful and stimulating
subject, I believe much of Newton's mathematical developments were done to
support his quest for the understanding of how nature works. I'm not as
certain about Galileo. You may be right about Copernicus. Don't get me
wrong, I love mathematics and marvel at it's totally self consistent and
near perfection. Much like philosophy, however, abstract thought and mental
exercises can only carry you so far before one is forced to apply it to
experience.
Mrs. Livingston wrote:
Well, wasn't it also mathematicians at hart who had earth flat neatly calculated
and airplanes impossible and lots of other no nos?
We all er. There is no point in name calling if we think the other fellow is
wrong, because the probability is that we are both wrong.
Regards, Slavek.
Hahahaha , let EL here this. This throws his math ability out the window....
.He aways brags about his math ability. So what, people win the Nobel Prize in
Physics for PHYSICS not math.
>> the formula for the area of a circle and Einstein's marvel. Witness that
>we
>> have NO BELL prize for mathematics. Mathematics remains the ho-hum and oh
>> so boring field of drudgery for drudgery's
Well pure math. really is boring to me and is hard to understand. Applied
math., is much more interestng. When you can apply math to something REAL, in
the real world, it makes more sense, and one can understand it better.
sake. I will have you know that
>> had anyone or any texbook bothered to mention that Copernicus, Galileo, and
>> Newton were at heart mathematicians, I would have been much prouder of my
>> math skills at a much younger age. Space is in reality a volume ... that
>> can only be defined absolutely in 3 dimensions. However, with study, the
>> 4th dimension, anticipation, can be extrapolated and even predicted. And
>> the science of prediction is what engineers bet on daily.
What about the 7 dimensions I showed in regard to space-time?
>>
>> Mrs. L
>
>Well, wasn't it also mathematicians at hart who had earth flat neatly
>calculated
>and airplanes impossible and lots of other no nos?
Nope that was atheists. It took theists to correct this.
>
>We all er. There is no point in name calling if we think the other fellow is
>wrong, because the probability is that we are both wrong.
>
>Regards, Slavek.
>
You are a Slave K.
(Smart Home Page)
http://members.nbci.com/Smart314159/index.html
==> 3D EFFECTS & Sound <==
<Topics>
The New Atomic Testament ( The Smart Atomic Model )
The Unified Helix Spiral Field Theory
....and more.
S. Enterprize Company wrote:
> What about the 7 dimensions I showed in regard to space-time?
Specifically:
Delusion, illusion, arrogance, stupidity (infinite), unjustified persistence,
ignorance and cockiness.
> >> Mrs. L
> >
> >Well, wasn't it also mathematicians at hart who had earth flat neatly
> >calculated
> >and airplanes impossible and lots of other no nos?
>
> Nope that was atheists. It took theists to correct this.
So, Ptolemy was an atheist according to this 4321 grasshopper.
> >We all er. There is no point in name calling if we think the other fellow is
> >wrong, because the probability is that we are both wrong.
> >
> >Regards, Slavek.
Have a nice summer and watch out for starlings, Slavek.
You Dirtbag,
Witness the number of times in history a mathematician has made a scientific
breakthrough only to have science get the credit. Notice the similarity of
the formula for the area of a circle and Einstein's marvel. Witness that we
have NO BELL prize for mathematics.
[EL]
That is a keeper. :)
"NO BELL" prize. :)
><snip ... not worth repeating ... >
>
>You Dirtbag,
>
It would help tremendously if I knew what was not worth repeating, to warrant
such a summary execution.
Perhaps "atrocities" was the clinching word. And those really fall on the laps
of the physicists.
>Witness the number of times in history a mathematician has made a scientific
>breakthrough only to have science get the credit.
This is somewhat confusing as well. It seems to state that mathematics is not a
branch of science. But forget that, there are injustices everywhere. A tour of
the internet will provide you a picture of this in most every academic and
scientific field. We all have stories to tell that relate to our own little
worlds.
As you know, development in the mathematics is far ahead of real world uses for
much of it. By the time a need for an archived structure occurs, the pioneer in
mathematics that put it together is often, long since dead.
But a line exists between mathematics and other sciences that can be crossed
by a mathematician, that could enable Nobel recognition in the designated
field, even though no degree in that field is owned.
>Notice the similarity of
>the formula for the area of a circle and Einstein's marvel.
Einstein's marvel will one day be Eintein's marble. This will occur after the
new age Ptolmaic math is viewed for what it is.
>Witness that we
>have NO BELL prize for mathematics.
What's there to give a prize for? Solving Fermat's last theorem? Mathematics
must apply to more than mathematics for anyone but a mathematician to guage its
significance. I think it might rest on gunpowder and guilt and atonement to the
world.
Mathematics remains the ho-hum and oh
>so boring field of drudgery for drudgery's sake.
You describe arithmetic here, or at least my interest in it as a kid. But
algebra kind of caught my attention and geometry inspired me. Trig thrilled me
and calculus electrified me. Anything but drudgery.
I will have you know that
>had anyone or any texbook bothered to mention that Copernicus, Galileo, and
>Newton were at heart mathematicians,
I don't think anyone would disagree that the quest of these persons, if success
was to occur, required that they become proficient to some degree in the math.
I think that Newton fits your description best and Galileo perhaps a distant
second, but Copernicus first had an idea and never developed his math skills
even to the level of Ptolemy's skills, which were quite good. But Maxwell is
the guy that would fit it best.
I would have been much prouder of my
>math skills at a much younger age.
Pride is good for the young. It facilitates motivation and encourages
development. I think that integrity supplants pride as we get older. Then, wth
pride one risks resting on old laurels.
No matter how hard we seem to try to live a good life, we do many things
inadvertently that cause us regret. An argument, a harsh word, a slight, that
years later we recall, when it is too, too late to rectify. Those who live a
long life can retain their integrity, but pride takes on the role of an
inconsequential.
Space is in reality a volume ... that
>can only be defined absolutely in 3 dimensions. However, with study, the
>4th dimension, anticipation, can be extrapolated and even predicted. And
>the science of prediction is what engineers bet on daily.
No argument here. Ptolemy even used a much more elementary math to match the
universe action to the requirements of the church. He did this with intent and
it was rather bizarre and complex.
One can say that the church required Ptolemy to operate with a gross built in
conceptual error. With a powerful tool like mathematics, just how many
conceptual errors can we allow the mathematics to accomodate?>