The Universe and the Mathematics:

Why They Are So Well Matched

Take 1A - Modified June 6, 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. However, 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 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. 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. If anyone takes exception to this

so far, I am open to attack.

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: "... 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 we 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 indicates, 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 surface earth 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 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 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. If any disagree with this

conclusion, I am open to attack.

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.

Consider:

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.

Again, if I am in error, please attack.

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

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 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.

johnreed