The Universe and the Mathematics:
Why They Are So Well Matched
Take 1A - Modified June 6, 2006
John Lawrence Reed, Jr.
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. However, my view of atomic
structure remained unclear for a long time*, with or without the
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 late 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
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 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 "a priori" 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. 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 epicyclic orbits. The Ptolemaic model
suggests that accurate mathematical predictions serve us to an
operational extent, but inherently, provide no absolute basis for an
accurate conceptual view. When viewed through the clear lens of
hindsight, we can see that our conceptual questions must be framed
correctly, prior to selecting the mathematical model. Must we frame our
conceptual questions any less correctly today?
Following my analysis of the Ptolemaic model of the solar system, I
concluded that our limited perceptive ability, combined with the ease
of application of the mathematics to the universe in terms of time and
space, reflects both, a weakness and a strength. We cannot allow the
easily applied mathematics to lead us blindly into conceptual areas
where we have limited perception. 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 our laziness in conceptual thought. 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, rationally comprehensible
understanding of natural phenomena.
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 Take 1D, 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.
Kraus continues with: "... 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. Therefore, as near as I can determine, the question
posed by Wigner was never of any great concern to other scientists.
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. 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 mystical means by which to decipher the
universe. I am reminded of the quote, perhaps by Dirac, "... my
equations are smarter than I am." (paraphrased)
Wigner's concern, together with many other similar concerns****, did
represent a significant problem to me. Even to the extent that it
eventually derailed my intent to pursue a professional career in
physics. Now, Krauss suggests 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
verbal stream above, is typically, a loosely chosen, unclear and
misleading, application of the English language. Many physicist
mathematicians today, regard any spoken language as inadequate, when
compared to the more rigorous, and more intellectually forgiving,
mathematics. 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 anything but 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 suggests, only to the point of recognizing that the symmetry
need not manifest as a perfect circle?
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.
All we apparently lack is a centrist view of our place in the universe.
We are composed of surface earth matter. We are inertial objects. Our
particle physics model rests on the idea that 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 initially 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 examine cosmic particles that passed
through the magnetic field within the cloud chamber. Finding the
particle was regarded as a successful prediction for the mathematical
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 predictive
mathematical model is sound. We say that it predicts experimental
results. One problem that is obvious is that the likelihood of finding,
say, any particular additional particle, is just as probable, 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,
we have no absolute basis on which to conclude that the released packet
maintained a granular state inside the atom.
Even so, during the 20th century the notion for symmetry and our
unquestioned assumption that the particle maintains granularity inside
the atom, served to rescue us from the detritus covered field that
consisted of some 400+ so called, elementary particles*****. Murray
Gell-Mann developed his new age Ptolemaic, symmetrical, mathematical
model, to account for what had become 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,
Murray Gell-Mann put them together in an experimentally consistent,
symmetrical order, that he called "The Eight Fold Way". This model
required the rather 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 accepted. Gell-Mann himself, had to be cajoled into believing it
was real. As contrived as it was and is, it met our stated scientific
requirements. Who can challenge that? Clearly its name is a reference
to eastern mysticism. It appears that our reliance on symmetry while
catering to a shallow requirement for successful prediction, together
with our a priori assumptive baggage, led us right where we deserve to
be. Perhaps Wigner saw further than I had first considered.
In any event, 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
celestial 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
action between the celestial bodies that apparently generate the field.
We can, as inertial objects, use it to predict our navigational
requirements through the field.
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 planet orbits, or, the least action planet orbits are the reason
we can isolate the independent quantity inertial mass, and our tactile
sense of attraction to the earth is caused by something else.
Is this a reasonable "either/or" proposition? Mass causes the least
action planet orbits, or, the least action planet orbits allow us to
isolate the quantity inertial mass? Or, can they both be true?
While I cannot show that inertial mass enters into the earth 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.
The orbits function within the constraints of a least action time-space
based principle. Freefall functions within the same constraint.
Whatever the cause (see johnreed take 1D) of the shared principle, that
principle allows us to isolate inertial mass on the balance scale. 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) with respect to the "tactile sense of attraction"
we feel as resistance and quantify as 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 "unencumbered"
field with respect to mass, required for Newton's first and second
laws, would 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.
Einstein's idea that Newton's first law applies to planet orbits
because the planets follow a curved space-time geodesic, merely extends
our erroneous view of inertial mass by further co-opting the least
action planet orbits, within another new age Ptolemaic, mathematical
model. Here we gained a new and further obfuscating label for the least
action planet orbits: the geodesic.
Krauss concludes with, "Thus seemingly different mathematical
formulations can... be understood to reflect identical underlying
physical pictures." So much for the meaning of the word "precise".
So much for Wigner's question. So much for the conceptual
significance we attach to mathematical predictions based on loosely
defined objects of our perception. And as Eugene Wigner may have noted,
we have yet to acquire the intellectual capacity to properly use our
gifted crystal ball.
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 explanation 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-space, least action******** properties common to stable physical
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 universe, we do not
inadvertently allow our least action dependent, mathematical models, to
include our perceived, overly generalized, locally isolated (surface
planet), a priori assumptions, solely on the basis of a quantified
consistency within specific local (surface planet) cases of kinematic
least action events. And we must circumspectly guard against including
multi-dimensional fantasies made possible by our gift of a crystal
ball, especially in view of the open window that allows for additional
fantasy made possible by Heisenberg's principle, within the
constraints of Planck's constant.
*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 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. **** The particles that are created and
released by the elements are fundamental. Those particles found
regularly in cosmic streams might also be regarded as fundamental.
Those particles that we have bludgeoned into existence are most
certainly, primarily rubble.*****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 mathematically predicted "blackhole". The blackhole eventually
became another major concern in my thinking.******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). *******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.