Galileo (1564–1642) 
Galileo Versus Newton
Ralph Marinelli^{ a};
James D. Stewart^{ b};
Michael Duffy^{ c}
a. Rudolf Steiner Research Center, Royal Oak, MI b. Rudolf Steiner Archive & e.Lib, Fremont, MI c. Emerson College, UK

Newton (1642–1727) 
In
researching the works of Galileo, it was discovered that
Galileo^{ 1} had precluded the
establishment of the theory of universal gravitation and
that his work went unheeded. He did so with a
mathematical analysis and an experimental demonstration
that clearly reaffirmed the irreducible qualitative
difference between curvilinear and linear motion, thereby
precluding the validity of considering linearity as being
the fundamental building block of curvilinearity –
a necessary premise of the theory of universal
gravitation. We had previously discovered that universal
gravitation was a theory that never became a fact under
the tutelage of Rudolf
Steiner^{ 2, 3, 4}, etc. and were thereby read)
to detect what others had missed. A minimum case is
presented; an elaboration will follow.
In
order to demonstrate that solar system dynamics are machine
dynamics, Newton^{ 5} and
Borelli^{ 6} theorized that the
curvilinear (conic section) motions of the solar system
were reducible to centric linear motions. This was
supposedly justified by their assumption that when a curve
becomes infinitely small it becomes a line. This idea was
readily acceptable because theoretical scientists of their
times had begun to believe that natural motion was straight
line motion in contradiction to the ideas held by King
Solomon and all great thinkers up to and including Galileo
who considered that natural, creative motion is
curvilinear. Newton went so far as to define the circle as
being a polygon with an infinite number of infinitely small
sides.
Having
theorized geometry and kinematics so that an arc equals a
line Newton extended his theorizing into the realm of
dynamics and deduced that since an orbiting object is at
all times moving in a straight line, linear inertia is
operative in curvilinear motion. As a consequence, the
orbiting object is tending to fly off on a tangent to the
orbit, thus Newton attributed centrifugal motion to the
tendency of orbiting objects to fly off on a tangent. He
attributed it to a cause that was within the orbiting
system. He went on theorizing and deduced that since the
moon, for example, does not depart from its orbit, despite
its tendency to do so, it must be restrained from doing so
by a centripetal opposing balancing force that results in
the moon's orbit. This is the force he called universal
gravitation. He theorized further that the moon held in its
orbit continues to tend to move out on its tangents and
thereby provides the momentum to propel itself along in its
orbit. Thus, Newton theorized the perpetually propelled
solar system dynamics as being machine dynamics. Newton
confirmed his theories by observing that the stone in a
whirling sling, when released to flight, moves out of its
orbit on a tangent to the orbit. Thus, the theory has stood
for 300 years.
However, we have determined through various experiments
both machine and manually operated that an orbiting object
does not “fly off on a tangent;” it is pulled
out radially. The most convenient observation of the
phenomenon is the pitched baseball. The pitcher's arm and
the orbiting ball in his hand constitutes the dynamic
equivalent of the stone and sling. The pitcher executes a
semicircular orbit with outstretched arm and hand and
releases the ball when it intercepts his line of sight to
the target. The ball is seen to be pulled out radially to
its target. If the ball were acted upon by linear inertia
it would move away from its orbit on a tangent at right
angles to the line of sight from pitcher to batter and
baseball would have been impossible.
A
mechanically driven system used to demonstrate that
orbiting objects move out radially was a modified record
turn table that was provided with a continuously variable
speed acdc motor from a sewing machine. A ⅛ inch hole to
serve as an indent to hold a ⅝ inch glass marble at a
radius of rotation of 4 inches was drilled in the table and
a pouch was fashioned to catch the marble as it moves
radially outward. The turn table speed is gradually
increased and stabilized at the increasing speeds until the
critical speed is reached and the marble is pulled out
radially. An improvised, but quite adequate experiment can
be conducted by placing a 25cent coin in the middle of the
heel of the dominant hand, fully extend the arm and rotate
it palm upward in the horizontal plane at constant speed.
It will be very obvious that the coin is pulled out
radially. Many variations of these experiments are possible
and were performed.
It is
our experience that one who is enslaved to the concept that
orbiting objects fly out tangentially will not be able to
extricate himself without conducting at least one of the
above or equivalent experiments. We have confirmed the
experiment used in college courses in which an orbiting
object is released to flight via an electromagnetic
coupling and is seen to fly off on a tangent or near
tangent. The reason that this is so is that the orbit is
deformed into linearity by the lengthening of the radius as
the tether momentarily elongates during the disengagement
process allowing linear inertia to be expressed.
It is
obvious that Galileo was very impatient with the concept of
universal gravitation. His response to it was totally at
odds with the entire community of theoretical scientists.
He said that those who would make the arc into a line,
especially mathematicians do not err, they lie because they
know the truth that the arc is a line when the radius is of
infinite length.^{1} Thus
Galileo, the father of modern science and a professor of
mathematics was ignored by the scientific community when he
reminded them of the simple fact that curvature of an arc
is proportional to the radius and not to the length of the
arc. That he did so to no avail, indicates that in
accepting theories, we must not abandon reason.
In
addition to his demolition of the concept of – the
arc is a line – by mathematical analysis, Galileo
conducted an experiment that demonstrated that curvilinear
dynamics were not translatable to linear dynamics. He
allowed two bodies to fall (roll) through the same distance
simultaneously; one through an arc of a circle and the
other through the much shorter chord of the arc. He found
that the object that traveled the arc was the first to
reach the common terminal of arc and chord. Thus, an object
falling in an arc is pulled down with a greater force than
one falling in a line. This force which Galileo detected
but did not identify is the force of levity. We repeated
Galileo's experiment and reproduced his result.
Let us
explain Galileo's experiment in which curvilinear and
linear dynamics were compared. Levity is a force with a
source outside the earth. Since it approaches the earth
from every direction, it must have a source in the cosmic,
spherical periphery at least as far as the sphere outlined
by the orbit of the moon. Like gravity it permeates all
matter. It pulls radially outward on every rotating object
from the earth as planet to the molecules and submolecular
particles in living cells and inanimate matter. It is
passive to linearly moving objects. Thus, in Galileo's
experiment it is passive to the object falling in the chord
but pulls radially outward on the object traveling in the
arc. Thus, the object moving in the arc is being pulled
vertically downward by the vertical component of the
radially directed force of levity. This force adds to the
force of gravity and accounts for the increased
acceleration of the object traveling in the curvilinear
path.
When
it was found that linear inertia is inoperative in
curvilinear motion and that centrifugal motion was radially
directed, it was obvious that we had discovered a new force
– a centrifugal force acting from outside the
orbiting system. This force was described by Rudolf Steiner
but as is his style of teaching, he left its actual
discovery to others. He stated that humankind is obliged to
live amidst error and lies and truth and that we gain our
individual freedom by working to understand and extricate
the truth from the errors and lies. This he called the
special moral battle of the 20th century and beyond.
“Ye shall know the Truth and the Truth shall set Ye
Free.” Of course, such a battle must be fought with
the battle cry of “Love Your Enemies.” We close
with an aphorism from Rudolf Steiner to whom this work is
dedicated: “One must be able to confront the idea in
living experience or else fall into bondage to
it.”
Ralph
Marinelli
Rudolf
Steiner Research Center
2825 Vinsetta
Royal Oak, MI 48071
References:
 Galileo, 1637, Two
New Sciences, pages 95,251252 translated from
Italian to English by Henry Crew and Alfonso De Salvio,
1914, Dover Publications, NY
 Rudolf Steiner, 1919,
First Scientific Lecture Course:
Light Course, Anthroposophic Press Hudson,
NY
 Rudolf Steiner, 1920,
Second Scientific Lecture Course:
Warmth Course, Anthroposophic Press, Hudson,
NY
 Rudolf Steiner, 1921,
Third Scientific Lecture Course:
Astronomy, Anthroposophic Press, Hudson,
NY
 Isaac Newton, 1687,
Principia, revised by author 1713 and 1726.
Translated from Latin to English by Andrew Motte, 1848,
Prometheus Books, Amherst, NY, 1995
 S. Mason, 1979, A
History of the Sciences, Collier Books, New York,
NY.
Revised and reprinted, with permission from the author, from
Frontier Perspectives, Volume 7, Number 1, Fall/Winter, 1998
(The Center for Frontier Sciences at Temple University)
