The Universe and the Mathematics:
Why They Are So Well Matched
Take 1A - Modified October 13, 2006
John Lawrence Reed, Jr.

Part 1
When I was a boy, I suspected that there was a common thread that ran
through all physical systems, and connected all physical laws. The more
I learned, the closer I came to identify it. A recurring thought of a
short lived image. A focused but momentary insight. A sudden and clear
panoramic view, but again and again, it disintegrated and was gone.
Defining this thread, putting my finger on it precisely, was for a long
time, just outside the range of my consciousness.

The most difficult physics problem for me, at that time, was the
conceptual understanding of atomic structure. A mathematics had been
conceived and refined, by Bohr, Heisenberg, Schrodinger, Born, Dirac,
Feynman, and others, developed expressly for the operational, or
scientific analysis of atomic phenomena. My view of atomic structure
remained unclear for a long time,* with or without the mathematics.
Today the mathematical descriptions of the universe on the blackboard
and in the published papers are abstract and (to me), devoid of any
conceptual connection to physical reality.**

The American physicist, Steven Weinberg, 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
physicist mathematician has an unformed idea as to what many of his or
her, quantitative abstractions represent conceptually. 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." Eugene Wigner wrote this in a 1960 essay
and continued by noting that, the ease by which the mathematics applies
to the universe is, "a... gift which we neither understand nor
deserve."

While I did not concern myself at the time, with our intellectual
qualifications as the beneficiaries of the gift, I did seek to
understand why it was so effective. Wigner's essay was a major
influence on my early thinking, so it was with special interest that I
read the recent words of Lawrence M. Krauss in his 2005 book titled,
"Hiding in the Mirror". Krauss addresses the ideas presented by
Wigner in the 1960*** essay. Krauss writes, "... are our physical
theories unique... do they represent some fundamental underlying
reality about nature... or have we just chosen one of many different,
possibly equally viable mathematical frameworks within which to pose
our questions... in this... case would the physical picture
corresponding to... other mathematical descriptions each be totally
different"?

Krauss colors Wigner's concept in a shade perhaps, more reflective of
his own. My coloring of Wigner's concern is slightly different.
Although Wigner questioned the uniqueness of our physical theories,
Wigner did not question that the mathematics reflects a fundamental
aspect of the universe. Rather, Wigner pointed out the "uncanny"
usefulness of mathematics, and expressed some uncertainty with respect
to our reliance on the significance of the experimentally supported
predictions of mathematics, to serve as a sole and solid basis on which
to verbally formulate our "unique" conceptual physical theories. Wigner
approaches the idea that the selection of a mathematical model
determines the questions that we ask. He suggests that once we select a
mathematical model, both our questions, and the answer to our questions
are preordained. In other words, because the mathematics adapts to the
real world so well, our mathematical model may be easily colored by the
possibly erroneous "a priori" subjective assumptions that we attach
to the quantities that we perceive.

Where Wigner noted the "uncanny" usefulness of mathematics, I noted
that the usefulness remains, regardless of the veracity of our a priori
assumptions. As an example, first consider the Ptolemaic, earth
centered model of the solar system. Ptolemy based his model on a divine
notion for symmetry. Perfect circles and perfect motion. A circle is an
efficient enclosure of area. Equal arc lengths will radially enclose
equal areas. This is an efficient area enclosing symmetrical property
of the circle itself (see Take II). The efficient enclosure of area
falls out of each contrived orbit as a property of the perfect circle
and its perfect motion. In Ptolemies model it is the consistent
efficiency of the orbits that enable the model to be as useful as it
is. The sole quantitative connection to the real universe in this
"still useful" model, is the efficient, least action, time-space
property, attendant to each of the otherwise contrived, circular,
cyclic and epi-cyclic orbits. The Ptolemaic model shows that accurate
mathematical predictions serve us to a limited operational extent, but
provide no absolute basis for an accurate conceptual view. Viewed
through the clear lens of hindsight here, we can see that our
conceptual questions must be framed correctly, prior to applying the
mathematical model beyond its operational context. Must we frame our
conceptual questions any less correctly today?

Krauss continues: "... because we have made huge strides in our
understanding of the nature of scientific theories... since Wigner
penned his essay... I believe we can safely say that the question he
poses is no longer of any great concern to scientists." During the
course of my life, my wide ranging research has included the study of
every publication in english print, that I have found, that seeks to
present a popularized view of theoretical physics and the attendant
mathematics. In my many years at this endeavor Krauss, to his credit,
is the only author I have read that directly entertains Wigner's
essay. Further, the cutting edge of science is focused on technological
progress. Consequently, the focus of Wigner's concern is not seen as a
subject that qualifies for research grants. Therefore, as near as I can
determine, the question posed by Wigner was never of any great
concern to other scientists. Although Wigner's concern is clearly
restated as a question, and the answer to that question resides within
obtainable bounds, we have been content to leave the question
unanswered, and use the mathematics as though the mathematics is a
crystal ball, enabling us a near mystical means by which we decipher
the universe. I am reminded of the quote, perhaps by Dirac, "... my
equations are smarter than me." (paraphrased).

Wigner's concern, together with many other concerns,***** did represent
a significant problem to me. Even to the extent that my intent to
pursue a professional career in theoretical physics was eventually
derailed.****** Now, much to my surprise, Krauss indicates that the
question has been answered as the result of "huge strides we have made
in our understanding of scientific theories..." Krauss continues:
"We understand precisely how different mathematical theories can lead
to equivalent predictions of physical phenomena because some aspects
of the theory will be mathematically irrelevant at some physical
scales and not at others."

The word "precisely" as used with the scientifically represented,
quoted word stream above, is a loosely chosen, unclear and misleading,
application of the english language. Many physicist mathematicians
today, regard any spoken language as inadequate, even trivial, when
compared to the more rigorous, and more intellectually forgiving
mathematics. The initial difficulty of learning the mathematics,
combined with its operational effectiveness when applied to physical
processes, provide to the physicist mathematician; the academic
humanist; and to educated humanity at large; the 'illusion' that a
"deep" intellectual connection to physical reality exists, that is
revealed through the mathematics, and accessible only to the physicist
mathematician. This mindset provides an unquestioned and unchallenged
world academic platform, that enables the physicist mathematician to
put forward any sort of theoretical fantasy, so long as the fantasy
retains a mathematical consistency with respect to experimental
prediction. To the theoretical physicist mathematician, "any"
notion that is not "outlawed" by the applied mathematics, say quantum
mechanics or general relativity, is viable.

As a clear and representative example of the extent of this view,
consider the following quote from Stephen Hawking, in response to a
question on the conceptual validity of an extra-dimensional universe.
The question: "Do extra dimensions really exist has no meaning. All
one can ask is whether mathematical models with extra dimensions
provide a good description of the universe." And "...one cannot
determine what is real. All one can do is find which mathematical
models describe the universe we live in." Extra dimensions are
obvious "artifacts" of the mathematics. These are theoretically
brought to the real world conceptual table here by Hawking, with a
proclamation that I find uncomfortably similar to: 'Verily, verily, I
say unto you "All we can ask..." and "All we can do..." will be
revealed by our crystal ball.' Hawking, one of the high priests in
the field, speaks for most all theoretical physicist mathematicians.

God like pronouncements on the limitations of our capacity for
knowledge, coupled with the ineffectual (See Brian Greene's PBS,
offering: The Elegant Universe) disclaimers as quoted above, together
with the unbridled faith, humanity at large places in the conceptual
views attendant to the mathematics, are factors that caused me to
engage in, what has turned out to be a life long quest, one purpose of
which was to understand why the crystal ball extends the "decreed"
limits so effectively. I believe that the mathematics is the present
key to understanding the universe. I believe that it is a master key,
capable of opening many locks. The key must be ground so all the locks
open. To accomplish this we must understand the focus and limitations
of the key itself.

Krauss continues, "Moreover, we now tend to think in terms of
"symmetries" of nature... reflected in the underlying mathematics."
Krauss is not the first author I have encountered that sets great
importance to the mystical notion for a symmetry in nature. He is
however, the first to place the notion directly at Wigner's door. Nor
is he the only physicist mathematician that considers the mathematics
as an "underlying" and therefore controlling aspect of nature, however
contrived the mathematics may, or may not be. Krauss perhaps offers
that the symmetries in nature are the reason that the mathematics
applies so well to the universe. I can agree with this to the extent of
its conceptual clarity. However, the idea for a symmetry in nature is
not new. The idea was held by the Ancient Greeks some thousands of
years ago. The Greeks believed in a divine, therefore perfect symmetry
for the motion in the heavens. The Greeks conjectured that perfect
circles represented the symmetry. Have we progressed, as Krauss
indicates, only to the point of recognizing that the symmetry need not
manifest as a perfect circle?

Following my analysis of the Ptolemaic model of the solar system, I
considered our limited perceptive ability. I concluded that the ease of
application of the mathematics to the universe, in terms of time and
space, is both a weakness and a strength. We cannot allow the easily
applied mathematics, to lead us into otherwise (outside the operational
limits of the mathematical model) incomprehensible conceptual ideas,
that we validate intellectually, solely on the basis of our limited
perceptive abilities. We cannot include quantities within our
mathematical models that are loosely defined by the words of the
language we think in terms of, and expect the rigor of a mathematical
model to clarify and compensate for, our laziness in conceptual
thought. As evidenced by the Ptolemaic model of the solar system, our
reliance on perceived events to build the conceptual model, requires
that our conceptual foundation for the mathematical model, be error
free. If we carry any erroneous a priori assumptive baggage into the
mathematical model, that mathematical model will eventually be shown to
be a new age Ptolemaic mathematical model (if we are fortunate). We
require circumspect conceptual reasoning**** concurrent with our use of
the mathematics. As a place to begin, we must precisely answer the
comparatively simple, fairly straight forward question: "Why does the
mathematics work so well on the universe?", if we wish to obtain a
non-mystical, non-fantasy based (non-new age Ptolemaic), rationally
comprehensible understanding of natural phenomena. Fortunately, I
will answer this question within the four corners of this post.

Part 2
Through hindsight we can clearly see that Ptolemy based his contrived
mathematical model on a centrist view of our place in the universe, on
experimental observation, and on a divine notion for symmetry. The
Ptolemaic model makes it clear that the notion for symmetry and
experimental observation is not sufficient to serve as a sole guide by
which we base our present day conceptual models. Ptolemy built his
mathematical model to match the observational data. One can thus say
that it predicts events. Recently we built our particle physics model,
according to a notion for symmetry and to match the experimental data.
Note that each model is built on a notion for symmetry and on perceived
data. Today, all we apparently lack is a centrist view of our place in
the universe.

We are surface earth inertial objects. We are composed of surface earth
atoms. Our particle physics model rests on the idea that surface
earth atoms are composed of more fundamental surface earth particles.
The particle notion began with the Ancient Greeks and was applied to
the internal structure of the atom after J.J. Thompson separated the
electron from an atom. We assumed that the electron maintained a
granular state inside the atom, and patterned its structural existence,
inside the atom, after our solar system, following the results obtained
from the decisive gold foil, particle impact and penetration
experiments, carried out by Rutherford and his students. The problems
this model presented, guided our investigation through the 20th
century. Where we required extra mass, we predicted that a neutrally
charged particle existed within the atomic nucleus. Such a particle was
located outside the atomic nucleus, by the use of a cloud chamber to
detect cosmic particles that passed through the magnetic field within
the cloud chamber. Finding the particle was regarded as a successful
prediction for the mathematical model.

With the Ptolemaic model we had some fairly solid observational
evidence to support it. Today we predict a particle and on finding it
somewhere outside the model, we conclude that our mathematical model is
predictively sound. We say that it predicts experimental results. One
problem is that the likelihood of finding (sooner or later) say, any
particular additional particle, is possible, with or without the
mathematical model that requires its existence. Another more subtle
problem is this: When an atom releases a packet of energy, either
spontaneously, or as the result of experimental modifications, or as
the result of severe natural causes, we have no absolute basis on which
to conclude that the released or absorbed packet maintains a granular
state inside the atom. The fact that we can view the atom in terms of
"particles in equilibrium", and conduct successful experimental
operations with this as a guide, does not mean that the "particles" of
energy that exist outside the atom, retain that form within the atom.
The fact that high energy particles pass through crystals, must be
studied in the context of how low energy particles pass through those
crystals, etc. In fact, the particle-wave duality of these packets of
energy demand such studies.

During the 20th century the notion for symmetry; experimental data; and
our unquestioned assumption that the particle maintains granularity
inside the atom; served to rescue us from the detritus covered field
that eventually consisted of some 400+ so called, elementary
particles.******* Murray Gell-Mann developed his new age Ptolemaic,
symmetrical, mathematical model, to account for what became a sea of
flotsam and jetsom as a result of the high energy experimental research
into particle physics. By picking and choosing from an array of
already created particles, Gell-Mann put them together in a symmetrical
order, that he called "The Eight Fold Way". This model required some
new, rather bizarre properties, as well as the uncomfortable idea for a
fractional charge. In desperation perhaps, and with some desire to
maintain credibility in the field, and to secure the continuation of
research grants, the model was affirmed. Gell-Mann himself, had to be
cajoled into accepting it as real. As contrived as it is, it meets our
stated scientific requirements. Who can challenge that? Clearly its
name is a reference to eastern mysticism. Our reliance on symmetry,
while catering to a shallow requirement for successful prediction,
together with the inclusion of our erroneous a priori assumptive
baggage, led us right where we deserve to be. Perhaps Wigner saw
further than I had first considered.

Part 3********
In any case, our problem did not begin with J.J. Thompson. Some 2000
years after the Ancient Greeks, Tycho Brahe's careful observations and
Kepler's subsequent careful analysis of those observations, revealed
that the symmetry was in time and space. The predictable solar
time-space symmetry was subsequently co-opted by Isaac Newton, and used
as the carrier for our tactile sense of attraction to the earth,
quantified in terms of our locally isolated (surface planet) "inertial
mass", and declared as the controlling cause of the order we observe
in the celestial, least action universe. This was heralded as
Newton's great synthesis********* and is so considered even today.

We cannot overly generalize sensory quantities that operate solely
within least action parameters, beyond the specific frame within which
they directly apply. Where we quantify a force we feel, in terms of our
inertial mass, as isolated on the planet surface, and applicable to
surface planet inertial mass objects, within the planet field, we
cannot generalize that notion of force, to serve as the cause of the
time controlled action between the celestial bodies that apparently
generate the field. We can, as inertial objects, use it to predict our
operational and navigational requirements through the field.

Consider the Newtonian frame:
Isaac Newton defined centripetal force in terms of his second and third
law, to act at a distance, by setting his first law object on an
imaginary circular path of motion, at a constant orbital speed. Again
we find a perfect circle and perfect motion. Newton allowed the moving
object to impact the internal side of the circle circumference at
equidistant points to inscribe a polygon. He dropped a radius to the
center of the polygon from each vertex (B) of the polygon to describe
any number of equal area triangles. "...but when the body is
arrived at B, suppose that a centripetal force acts at once with a
great impulse..."(Principia)

Taking the triangle base length to the limit approaching zero, the base
length and the arc, of the velocity driven and time consuming
trajectory of the moving object, can be represented as arbitrarily
close in length as desired. The velocity vector as centripetal
acceleration (v/t), or (dv/dt) at the vertex (B) is by definition
consistent with the curvature of the circle, and is ultimately directed
along the radius toward the center of the circle as centripetal force
(mv^2/r). Note that Newton used a perfect circle and perfect motion to
derive centripetal force from instantaneous acceleration where the only
change in velocity is direction. Here the equal areas in equal times
again falls out as a mathematical artifact of the efficient area
enclosing circle itself. This efficient property of the circle is
reflected in the real elliptical orbits as Kepler's law of areas,
where velocity includes both magnitude and direction such that the
efficient area enclosing property of the circle is maintained. Newton
generalized the equal areas in equal times property of the perfect
circular path to any curved path directed radially around a point.
"Every body that moves in any curve line... described by a radius
drawn to a point... and describes about that point areas proportional
to the times is urged by a centripetal force... to that point."
(Principia) Newton extends the mass generated property to include two
bodies in elliptical orbit. "Every body, that by a radius drawn to
the center of another body... and describes areas about that center
proportional to the times, is urged by a force..." (Principia)
Newton then ties the mathematical idea for a centripetal force to
gravity. "For if a body by means of its gravity revolves in a circle
concentric to the earth, this gravity is the centripetal force of that
body."(Principia)

Note that during the time of Newton the primary quantitative property
of bodies included mass, volume, and density. The periodic table was
yet to come and only the most primitive form for the idea of an atom
existed. "...we conclude the least particles of all bodies... to
be... endowed with... inertia." (Principia).

Absent the quantitative idea for an atom, and its unique density with
respect to the element it represents, the only basis that Newton had
for "gravity" was his feel of attraction to the earth quantified in
terms of mass. Note that mass as an emergent local property falls out
of the freefall phenomenon and that phenomenon is a logical extension
of the least action found in Kepler's law of areas. Since mass falls
out of least action behavior locally, it will surely apply to least
action behavior universally. Where we generally apply mass to the
entire universe after our own inertial image, insures that our notion
of physical force applies to us, as inertial objects, it gives us no
absolute basis to conclude that the controlling attraction between
stars and planets is proportionally based on the local measure of mass.
While the weight of atoms in the case of pure elements will be
proportional, one to one, with the weight in terms of mass, in the case
of mixed matter, say surface earth dirt, the proportionality between
the number of atoms and their mass will only be "nearly". Today we
can see that this attraction can be on the atom itself, and not on its
mass (See Take 1D). "... we are to look upon propositions inferred by
general deduction... as very near true...until such time as other
phenomena occur by which they may either be made more accurate, or
liable to exception." (Principia

The idea for gravity is an a priori condition for Newton. Just like it
still is for most of humanity. A fundamental aspect of nature that is
now quantifiable in terms of what we as inertial objects measure as
weight. Our feel of gravitational force has always been an a priori
condition as the basis for our worldview. It gave us an obvious
location for Hell; an easy argument for a flat world; and proved that
the earth was the center of the universe. Today it provides us the
blackhole, curved space, and the Big Bang. So it was that gravity acted
on Newton's first law object in terms of his second and third law
force (ma), (mv/t), and (dp/dt) as (mv^2/r), even at a distance,
accompanying a vectorial, mathematical adaptation to the circle
itself,********** in accord with the centered source of attraction
Newton felt to the earth, and generalized to the entire universe using
Kepler's law of areas.. "...because the equable description of
areas indicates that a center is respected by that force... by which it
is drawn back... and retained in its orbit; why may we not be
allowed... to use the equable description of areas as an indication of
a center about which all motion is performed in free space?"
(Principia)

My analysis of centripetal force as put forward by Isaac Newton
revealed that the law of areas falls out of Newton's perfect circle
and perfect motion as an efficient property, or artifact of the circle
itself. Newton used this property of the real orbits to generalize his
idea of a mass generated centripetal force to the entire universe.
Newton's centripetal force is defined within the parameters of a
perfect circle and perfect motion. A circle is efficient. Newton
connects this efficient property of the perfect circle in perfect
motion to its analog in elliptical orbits. He used the law of areas as
his carrier for a mass derived force. Kepler's laws have since been
regarded as mere empirical facts, that are a consequence of Newton's
laws. It is not the law of areas that is fundamental here. Rather, it
is the principle the law of areas obeys. That principle does not depend
on mass. That principle results in time controlled efficiency. We see
it with Ptolemy's model and we see it now as the carrier for
Newton's notion of gravitational force. When Newton asked "...why
may we not..." generalize the law of areas to the entire universe, as
a carrier for his defined force, it almost seems as though his
subconscious brain suspects something is wrong. Doing so will carry his
idea of centripetal force with it. Making it clear to me that the least
action, time controlled property of stable systems are used as the
carrier for Newton's idea for a mass generated force.

Although Newton defined the least action orbits in terms of inertial
mass, we can perform no experiment that differentiates between the atom
and the mass of the atom, such that we can absolutely conclude that the
earth attractor acts on mass and not on the atom itself. In fact, the
freefall, orbit velocity, and escape velocity, experimental data tell
us that inertial mass "does not" enter into the earth attractor
mathematics. "We are certainly not to relinquish the evidence of
experiments for the sake of dreams and vain fictions of our own
devising." (Principia) However, these results have continued to
center on the incorrectly interpreted freefall data and today, provide
the quantitative basis for Einstein's conjectured equivalence
principle.

Part 4
Either our tactile sense of attraction to the earth (gravity), isolated
quantitatively in terms of our 'inertial mass', is the cause of the
least action, time controlled, planet orbits, as defined by Isaac
Newton; or the least action planet orbits are the reason we can isolate
the independent and emergent quantity "inertial mass" on the
balance scale; and our tactile sense of attraction to the earth
(gravity) is caused by the earth attractor action on our constituent
atoms, holding us to the earth's surface. In other words, mass causes
the least action planet orbits; or the least action planet orbits allow
us to isolate the quantity inertial mass on the balance scale? Is this
a reasonable "either/or" proposition? Or can they both be true, as
defined by Isaac Newton********** and postulated by Alvin Einstein?

Except perhaps for the attitude of the axis of rotation of the planets
(where the orientation of Uranus is of special note) and the spatial
eccentricity attendant to the orbits that may result from the inertial
mass of the planet in opposition to the super-electromagnetic star core
initiated or controlled orbit (see Take V.I), I cannot show that
inertial mass enters into the time controlled planet attractor or
celestial attraction mathematics. I can show, to an experimental
accuracy of twelve decimal places that inertial mass 'does not'
enter into the earth attractor mathematics during freefall, orbit
velocity and escape velocity experiments.************ I can also show
that the least action planet orbits are the reason we can isolate the
quantity, inertial mass, on the balance scale. For: The orbits function
within the constraints of a least action (least time), controlled
principle. Freefall functions within the same constraint (equal areas
in equal times). Whatever the cause (see Take 1D) of the shared
principle, that principle allows us to isolate inertial mass on the
balance scale. For: if all objects did not fall at the same rate, when
dropped at the same time from the same height, we would be unable to
separate the earth attractor surface, accelerative action (g) from the
mass of the inertial object (m) on the balance scale, with respect to
the "tactile sense of attraction" we feel as resistance and quantify
generally as gravitational force (gravitational force = weight = mg).
In other words, if all objects did not fall at the same rate when
dropped at the same time from the same height, we would have no
emergent quantity called inertial mass to investigate. In such a case,
the idealized notion for an "unencumbered" field with respect to mass,
required for Newton's first and second laws, could not exist.
Consequently, I say that inertial mass is emergent in a field that does
not act on the property of matter we feel as resistance and quantify in
terms of our inertial mass, as weight. Therefore, and as experiment
indicates, the earth attractor acts on our atoms and not on the mass of
our atoms.

Einstein's idea that Newton's first law applies to planet orbits
because the planets follow a curved space-time geodesic, merely extends
Newton's definition of an inertial mass (ma) generated view of
planetary motion by further co-opting the least action planet orbits,
within an extended new age Ptolemaic, mathematical model. While
maintaining our centrist view for a mass generated notion for gravity,
Einstein backed into a more accurate, essentially electromagnetic
mathematical frame. Here we gained a new and further obfuscating label
for the least action planet orbits: the geodesic. This is not to say
that the new age Ptolemaic mathematical models are without value. On
the contrary. As Krauss concludes: "Thus seemingly different
mathematical formulations can... be understood to reflect identical
underlying physical pictures." Here, the phrase, "Thus seemingly
different..." when replaced by the phrase, "New age Ptolemaic..."
states the case more precisely.

So much for the meaning of the word "precise" when used by the
physicist mathematician outside the rigor of her or his discipline. So
much for God like pronouncements on our capacity for knowledge. So much
for the conceptual significance we attach to mathematical predictions
based on loosely defined objects of our perception. So much for Eugene
Wigner's question, and as he noted in 1960, we have yet to acquire the
intellectual framework that is necessary to properly use our gifted
crystal ball.

Part 5
Fortunately, many, many years ago, during one of my unrelenting
contemplative sessions on the mathematics and the operation of the
stable systems in the universe, I found and retained, the "precise"
rational intellectual framework for it. In one illuminating insight
that accompanied, what I remember as a spring like release of torqued
tension on my brain, I had the answer to the dilemma articulated by
Eugene Wigner, and I had the object of my long sought for "common
thread" that runs through all our physical laws. 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. It is illuminating to note
that the action stable systems must follow to maintain perpetuity in
the field, is precisely an action that mathematics represents well. The
mathematics fits the stable universe because the mathematics easily
represents************* the efficient, time controlled, least
action************** properties common to stable physical systems.

Least action lends itself readily to mathematical analysis. As a
consequence, and as Eugene Wigner alluded to, great care must be taken
to insure that in the study of our least action, time controlled
universe, we do not inadvertently allow our least action dependent,
mathematical models, to include the overly generalized a priori
assumptions, that we attach to the locally isolated (surface planet)
quantities that we measure, solely on the basis of the quantified
consistency within specific local (surface planet) cases of least
action events. And we must circumspectly guard against the
indiscriminate inclusion of the essentially mathematical artifacts of
the mathematical models, in our conceptual world view. This includes
the obvious extra-dimensional fantasies, made acceptable by the blind
faith we attach to the near mystical powers we expect from our gifted
crystal ball, and the additional fantasies made possible by the open
window provided by Heisenberg's uncertainty principle, within the
constraints of Planck's constant.

Endnotes
* Eleven years passed before the results I obtained from my study of
atomic structure, forced me to turn my focus toward gravity. A topic
that until then, represented a solid, unassailable pillar, in my
worldview. The wave nature of particles is a clue to the structure of
the atom. I have briefly applied this clue in Take 6.

** Except as noted herein.

***Actually the Krauss books are informative and entertaining. The
subject complexity is daunting. My kudos to the author. However, Eugene
Wigner's 1960 essay is seldom seriously entertained by anyone but me. I
graduated from high school in 1961. Consequently, Wigner's essay was
a major and continued influence on my subsequent thinking.

**** In Take 1D, "Mass: The Emergent Quantity", I put forward a viable,
rationally consistent, conceptual alternative, to our theory for a mass
derived gravitational force. Through the "present-sight", more finely
ground conceptual lens, provided by Take1D, we can, with some
unexpected amplification, again see the importance of succinctly
defining the quantities we use within our mathematical model, prior to
using the accurate time-space predictions provided by the mathematical
model, to point toward an investigative direction, and prior to
describing the universe in conceptual terms. In Take 1D, I define, and
so limit, the extent to which our perception applies within the
mathematical model, and a clarity falls out of the conceptual model.
Compare this to the many mathematical models today that exploit our
limited perception, in order to provide the foundational basis for the
veracity of the mathematical model, while abandoning any requirement
for conceptual contiguity.

*****As one example, consider Einstein's postulate that all inertial
observers measure the same speed of light, regardless the velocity of
the observer and the light source. Note that light comes in one speed.
It has no acceleration one way or another. It has many frequencies and
many corresponding wavelengths. The discrepancy of velocity with
respect to the observer and source is accounted for by the difference
in frequency and wavelength measured by each observer. Therefore, if we
require the Fitzgerald-Lorentz modification, originally proposed in
response to the missing (and not necessary) "aether" left undiscovered
by Michelson and Morley, it "may" have something to do with a time of
arrival, but it has nothing to do with the measure of lightspeed. As
another example: Take 6 together with Take 1D provides an alternative
view that eliminates the gravitationally predicted "blackhole". The
blackhole eventually became another major concern in my thinking.

****** As I continued my education, the physical descriptions of
reality that were presented as science left me incredulous. I set out
to make sense out of the nonsense.

******* The particles that are created and released by the elements are
fundamental. Those particles found regularly in cosmic and solar
streams might also be regarded as fundamental. Those particles that we
have bludgeoned into existence are most certainly, primarily rubble.

******** Most of my posts start first from my notes, either mental or
written. When I expand on the post I research the original data and use
it as a source for augmentation. Part 3 of this post is compiled
without benefit of that research and therefore, in my view is but
loosely outlined. It appears that it may be some time before I will
have the place or the time for that research. Since, at my age, death
can come at any time, I will post this today, as is. Incidentally, this
consideration prompts all my posts.

********* My respect for Isaac Newton is as boundless as is my
conception of the universe. We must note that Newton justified the
veracity of his "system of mathematical points" by writing that "since
it is true for all the matter we can measure, it is true for all matter
whatsoever." (paraphrased).

********** To assist the non-mathematically trained reader consider: A
circle can be viewed as a polygon with a near infinite number of near
infinitely short sides. This idea can be represented using the
mathematics because we can rigorously describe the side lengths as near
to infinitesimally short as we wish. Then at each end of each side we
can drop a radius to the circle (polygon) center. This will result in a
near infinite number of near infinitely narrow triangles ranged around
the center of the circle and nearly filling its entire area. This is
similar to the thought process the Ancient Greeks used to derive the
formula for the area of a circle. The area of a square or rectangle is
length times width. It follows that the area of a triangle is half the
area of the square or rectangle. So we have (1/2)x(L)x(W). Which in
triangle nomenclature is (1/2) the altitude times the base. The circle
is nearly filled with the triangles ranged around its center and the
total length of the summed base is nearly the circumference of the
circle (2pir) and the altitude is the radius of the circle. So,
(1/2)x(2pir)x(r) equals (pir^2) the formula for the circle's area.
The "nearly" aspect of the area of a circle is reflected in the
accuracy of (pi) which increases, apparently without limit. The
Greek's circle is defined in terms of length and area. Newton's
centripetal force circle is defined in terms of a moving inertial
object through time surrounding area. Rather than summing the near
infinitely narrow near infinite number of ranged triangle bases to
approach the circumference of the circle, Newton takes one of the
infinitely narrow triangle bases to the infinitesimal limit. As its
base length approaches zero it becomes indistinguishable from the
length and direction of the infinitesimal arc. The radius of the circle
then takes on the direction of the acceleration.

*********** It turns out that Isaac Newton defined gravitational force
such that, general relativity develops on this alternative. Due to
space limitations that I believe should be considered when posting on a
topic, and the fact that the length of this post has far exceeded that
limit, I will expand on general relativity in my next post. I will
entertain quantum mechanics when I expand on Take 6.

************ Isaac Newton's interpretation of the freefall
phenomenon; Albert Einstein's interpretation of the freefall data;
and my interpretation of that data; lead to entirely different
conclusions. I say that inertial mass does not figure into the earth
attractor mathematics, therefore the earth attractor does not act on
inertial mass. Einstein postulated that because the measured, so called
gravitational mass, and the measured inertial mass are quantitatively
the same, they are in fact, the same. I will expand on this in my next
post.

************* One example of many in the math: When we differentiate
the function that describes the area of a Euclidean circle (pir^2), we
get the function that describes its circumference length (2pir). In
other words, we get a least action (efficient) "boundary condition" for
a given closed area function factored by "pi".This is the simplest
example, but it holds true for the function that describes the volume
of a 3D sphere and every other least action (efficient) closed area or
volume function factored by "pi", that I have investigated.

************** A simple example of an efficient or least action (when
taken over time) function, in terms of a static form, is a Euclidean
circle. The circumference is the shortest line length to contain the
greatest area.

If the reader wishes to review the Takes referenced herein, type
"johnreed take" at the Google.group screen and click the search button.
Then click on the sort by date option in the mid-upper right of your
screen to avoid my earlier even more primitive attempts to succinctly
articulate these ideas.
johnreed