Exerpts combined

[thejohnlreed]

Exerpt on Ptolemy:
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 epi-cyclic orbits.

A circle is an efficient enclosure of area. Equal arc lengths will
radially enclose equal areas of the circle. This is an efficient area
enclosing property of the circle itself. It is consistent with
Kepler's law of areas which law would be redundant in the case of
perfectly circular orbits. With the circle it is the circumference arc
and its radially enclosed area. In the orbit it is the time interval
of the orbit and its radially enclosed area. The law of areas is a
function involving time and space. It is a least action function. So
Ptolemy constructed several imaginary mathematical circles[*] upon
circles to match the time space function of the real orbits. The least
action aspect of the mathematics in describing the least action
aspects of stable universe systems, assured his success. Imagine it
otherwise.

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 clearer lens of
hindsight, here, 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?

Exerpt on Newton:
In any event, our problem did not begin with J.J. Thompson. Some 2000
years after the Ancient Greeks, Tycho Brahe's careful observations on
the behavior of celestial bodies and Kepler's subsequent careful
analysis of those observations, revealed that the symmetry was in time
and space. The predictable solar and 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 consistent universe. This was heralded as Newton's great
synthesis [*] and is so considered even today.

Isaac Newton defined centripetal force in terms of his second law to
act at a distance by setting his first law planet surface object on an
imaginary circular path of motion at a constant orbital speed. Newton
allowed his moving (planet surface like object) to impact the internal
side of the circle circumference at equidistant points to inscribe a
regular polygon. He dropped a radius to the center of the circle 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".

Taking the length of each triangle base to the limit (approaching
zero) the force vector [ma, mv/t, or dp/dt] at the vertex (B) is by
definition directed along the radius toward the center of the circle
as [mv^2/r][*]. Again, as with Ptolemy we have a perfect circle and
perfect motion where the law of areas falls out as an artifact of the
circle itself.

Newton generalized the equal areas in equal times artifact of the
perfect circle uniform motion 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"

Newton extended the property of his planet surface like orbiting
object to all celestial bodies.

"Every body that by a radius drawn to the center of another body.. and
describes about that center areas proportional to the times, is urged
by a force.."

Newton then tied the force directly to the force he felt and called
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."

In short the force acted on any orbiting object as though that object
is identical to Newton's first law planet surface object where the
force [ma] would then be proportional to the areas and times of
celestial bodies.

Exerpt on the balance scale:
Mass [m] is a magnitude of comparative resistance taken, in the
simplest case, at location on a balance scale using units of weight
[mg] where [g] divides out of the balance operation continually.

At any location that we place a balance scale (as long as the balance
scale is operational at that location), the function of [g] will be
immaterial to the balance scale action. Wherever we place the balance
scale the magnitude of [g] as a factor of the product weight [mg],
will be the same on each pan regardless of the mass magnitudes placed
on the pans[*].

The quantity [m] is derived and conserved. The quantity [g] is a
consequence of location. Therefore the balance scale compares the
resistance of atoms (matter) independent of location using objective
units that are consistent with our subjective definition of force
[mg].

We think we have proved that a universal force [mg] that we call
gravity exists as a property of inanimate matter. We believe it exists
because we feel our weight. We believe it acts on us because we feel
our weight. We define it in units of what we feel, our weight; as the
product of mass and acceleration [mg]. We postulate that inertial
mass [ma] and what we call gravitational mass [mg] are equivalent with
respect to the celestial universe because they are equivalent with
respect to what we measure, define and feel as our weight [mg] and
what we measure, define and feel as force [ma].

[F=ma]
[F=mg]

Since what we feel as Force [ma] may also be quantitatively defined as
[mg] where mass is derived and conserved and [g] is an independent
property of location, we think that the entire universe can be
explained in terms of what we feel. We think that we have "proved"
that what we feel and call "gravity" [mg], is the cause of the
celestial universe motion. So that the changing magnitudes for [g]
external to the balance scale are a consequence of what we feel [mg]
rather than what we feel [mg] being a consequence of our location in
space. If you dwell on it long enough yourself, you'll break out in
laughter.

Developing a mathematical logic through the subjective lens provided
by our senses allows us to define the least action consistent [*]
universe after our own least action consistent image, using the least
action consistent mathematics. Our weight as [mg] and a force that we
feel as [ma]. Both [g] and [a] represent acceleration. What does [m]
represent? Mass? What does mass represent? An amount of matter?

Since [g] is a consequence of location, when we define an object in
units of weight [mg], the quantity the balance scale is comparing is
the quantity mass [m], whereas the quantity we are comparing is the
quantity weight [mg] which changes with location. That's pretty simple
isn't it? If it hasn't caused a seed of revelation in your thinking
you might wonder why I bother to point it out.

When Galileo showed that all objects fall at the same rate when
dropped at the same time from the same height {*} we were all amazed.
We have remained amazed for the last 400 years. So amazed that we
have engaged in extensive research to verify that all objects really
do fall at the same rate, independent of their mass [m], when dropped
at the same time at the same place from the same height (discounting
air resistance).

We are amazed because our primary but subjective functional use for
the balance scale was and is to compare weight [mg]. Consequently we
think that the balance scale compares weight [mg]. Where the action of
the balance scale on balance equalizes the resistance of two non-
uniform (or uniform) pans of atoms, where the quantity [g] divides out
of the equation. Therefore the measure of the comparative resistance
is in mass [m] units.

This is not to say that we cannot use the balance scale for a large
variety of purposes. Here I have simply pointed out that what we call
gravitational acceleration [g] is a consequence of location. Therefore
all objects MUST fall at the rate of [g] at a particular location. If
that does not provide a Eureka moment for you then indeed the fish are
the last to recognize water. Now that we know all objects have to fall
at [g] we can figure out why. You may recognize that heretofore the
question "why" has been frowned upon by the physicist mathematician.

This is because we have incorporated a functioning calculational
system that has been raised to a level higher than the rational use of
words (sometimes called thinking), based on "what" we call
gravitational force [mg]. Recall that Ptolemy based his functional
mathematics on an earth entered universe. We base our present
mathematics on a force that we feel. As a result our conceptual
thinking is dumbed down and made a slave to the overly simplifying
practically functional least action consistent mathematics. The notion
of gravity will work for us practically at any location we can occupy
in the universe. However, the notion of gravity and its attendant new
age Ptolmaic mathematics in a theoretical application constricts us
and leads us into a false abyss. It is a bear to clarify.

Exerpt on the Conclusion:
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
least action consistent behavior of 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.

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