Galileo devised his ramp experiments not only to have a math-equationed rule, to go with his false law of falling bodies -- in abstract uniform
free fall acceleration due to gravity -- it was also to support the notion of infinite horizontal motion. This notion
would provide the basis for Newton's first "law" of motion, that "every body perseveres in its state of rest, or of uniform motion in a right line, unless it is compelled to change that state by forces impressed thereon."-1
axiom matches Galileo's abstraction, where he rolls a metal ball down a sufficiently steep ramp into a smooth horizontal plane, and then the ball continues to roll, on and on, and on, forever ... as would it were were it not for friction. In "Two New Sciences" Galileo had written, "imagine any particle
projected along a horizontal plane without friction ... now it is evident that this particle will move along this same
plane with a motion which is uniform and perpetual, provided the plane has no limits."
By nature not only friction, however, there is no ball that Galileo could roll without limits and forever, on a glassy smooth horizontal surface, such as a tabletop, glass highway, or whatever. Since at least some tension is in everything, as without tension there would not be anything, not friction either, which is only a kind of tension
itself, Galileo is working in round squares and other nonexistent objects when he talks about "gravity".
Wherever gravitation ceases, it also fails to exist; yet it is said to be universal, even in relation to objects of limited size, which do persist in contrast to the theoretical limitlessness of gravitation
among them. Since universal gravitation would make any situation an intolerable crowding, it must be something different that makes the Moon orbit the Earth.
For the sake of "gravity" no one can refer to simple heaviness or substance, and perpetual horizontal motion in the sense of a straight
line is a ruse. Yet true, as "this sentence is not true", Galileo or NASA may say there is no problem from gravitation of heliocentrism among sets or stars in the cosmos, since anything may follow as well from another impossibility. In fact, logically it is as impossible as much as infinite regress.
This is plain not only in theory but in fact. In the real world and even in the mind, for a motion to be infinite, even by mere semblance, it would have to be circular in the magnitude of an uncausable sphere.
Naturam expellas furca, tamen usque recurret: one can expell nature with a pitchfork, but she always comes back. "For the divine Logos that most men call fortune runs a circular course."-2
Any motion in a straight line, a "right line" as Newton calls it, is obvoiusly finite by the order of cause and effect. Since every straight line has a beginning
and an end, even if people sometimes cannot tell where it began or where it will end, like railroad tracks
away in the distance, where it does not make a circle it lacks the curve of perpetuity. As no straight line
is ever infinite, because infinity has no beginning and no end, any infinite motion would have to have an infinite resource even in the form. Therefore, whatever motion would be infinite must be circular, as much as always coming back around is eternal, which eliminates the notion of perpetual horizontal motion in straight lines.
Since the only way to have an infinite roll is always to be coming back around to
the beginning, to form a perfect circle at once, where all points along it are as the same, in the same ratio to the center, in such a case, one cannot tell the difference in where
it began or would end. Any rolling marble set loose by Galileo would have to come back around to the beginning forever, along its endless circuit, again and again, at all times, as
much as all the ends, to have even a metaphor of the infinite in the limit.
Galileo and Newton, trying to resource infinite motion as perpetual
with a marble, would have more problems in magnitude than could be imagined. Since to be so great, it would not continue in any straight line within any reasonable length of time, regardless of friction and impressed forces anyway, it could only go in circles, and over a very
long time, yet also not more than an instant indivisible that would be impossible to capture in time. For the order of magnitude there is instantaneous withal, as at once along all points of the greatest path.
Since the reflective quality from within infinity is circular and indivisible, as much as 1,2,3 and A,B,C of forever, an infinite progression is not possible
by marbles or particles such as atoms anyway, because time and space are finite themselves. Relativity's theory of the cosmos as motion, or motion as the cosmos, however far,
or its version of infinite regress or progress in things, cannot go on and on and on without resolution, since even the bottomless pit too is only another bad situation in cause and effect.
"In demonstrable matters a reduction must be made to principles the intellect knows per se, so too in investingating what anything is", like gravity, "otherwise there would be an infinite regress and
all science and knowledge of things would perish".(166) Infinite regress does not explain multiplicity, size, or nature, as whatever importance there is in motion or any number like 365 is not justified by only one more.
Galileo rolling metal balls down ramps and Newton shooting rifle bullets from the top of
the Himalayas, "De Principia", are obviously not credible sources of infinite or constant motion. Since that which is absolutely
infinite cannot be excelled, the speculation fails regardless of any preferred description of friction or air resistance.
Like never before, "any perfection that can exist in numerically different things is more perfect if it exist in several than if it exist merely in one. Therefore, what is absolutely infinite cannot be found in several numerically
different things."-3 In other words, as would have been noticeable from the start, neither Galileo, Newton or heliocentrism can measure the indivisible by divisions, of course, and every horizontal line is another divided segment.
For Galileo's marble down a ramp or Newton's musket ball from the mountain top to have an infinite as perpetual motion, thus to be everywhere along the course at once, as instantaneous as simultaneous in the entire path, it must in some
way too have infinite velocity and size. How could they manage such a thing? Having to be everywhere at once, for infinite resourcing, prepared for all things from the top forever, in omnia paratus de summo perpetuo, like first principles, it would be beyond increase and any manipulation by science, as an infinite velocity cannot accelerate, since it already is infinite.
If anything is not infinite already, it is not likely that it will be, even much later. If potentially is not actually, not yet, however long it would possibly take for
things to develop, actualities may not be so absolute as "gravity". However, infinite motion cannot speed up more, and it must be absolutely instantaneous as simultaneous, whereas no natural or lesser motion can take place as instantaneously as simultaneously.
In many cases, the slower or the faster may speed up, at least a little in cause and effect, if not a lot.
All motions less than the infinite must have halves, and therefore are
never purely instantaneous, as they may accelerate or decelerate, increase or decrease, et cetera. Simultaneity may be fun, but a marble mixed in cause and effect cannot start at some finite point with infinite velocity, and neither can it accelerate into
infinity, so Galileo, Newton, and heliocentrism have an impossible situation beyond all description to reckon perpetual horizontal motion.
The problem with heliocentrism, therefore, is not merely from friction but also geometry
and math. There the essential categorical difference between the infinite and the finite is represented over and over. Again and again, it is the inescapable nature of finitude itself
to run to a wall of exhaustion against infinity. There is no rarefied frictionless environment of a vacuum anywhere to escape this, as much
as there is no absolutely empty vacuum anyway, because no two points in space can be separated by nothing.
Mathematical density in an atmosphere of one form or another is already in the nature of all substance and being itself.
If Galileo's marble rolled away as far as Saturn, it would be only halfway to the point
twice as far away. If it went to the point from Saturn twice as far, it would be only halfway to the point twice as far away again. If it went to the very most distant visible star, it would be only halfway to the point twice as much. As progress
in straight lines is of a lesser kind, that is always fractional, it can never be infinite. As a multitude is not without limit, every straight line and motion along a straight line can
be divided into many sections from beginning to end, and, therefore, is not fairly representative of infinity.
The mathematical elements of angular and linear velocity in total are not so much the same either. If baseball pitchers did not wind up, obviously
they could not generate the same speed, and linear and circular velocities, as they go across their range, represent different functions, and are not exaclty the same species
of motion in the formal and active terms of the measure.
V = w r is different from r =
d/t, where circular velocity can represent greater concentration of force and density. W incorporates pi, an endlessly repeating number, and even at the greatest speeds possible does not represent extension in space beyond the uniform curvature established
by the radius. Wr could be of some practical equivalence or co-variance to d/t but not as much formally as coincidentally or by accident. The circular motion implies greater potential for concentration of force, because of the greater potential available in
it from repetition, so wr is almost like dt, after multiplying d/t by t^2.
If it were now to go back from day to night, to once upon a midnight dreary, v = wr, by circles then turns, parva parva, theta theta, merely this and nothing more, to a mild form of hypnosis,
over many quaint and curious volumes of forgotten lore, the hypnotic and astral effect that contemplation of infinity, as a circular function, may have upon the mind can be demonstrated by the common way in which many people prefer to associate the infinite
with outer space, rather than the earth, by the circular perambulations. A gravitational line of Galilean relativity could go in reverse, therefore, "how can all the stars and seven traditional planets, and moons of Jupiter and Saturn, be in motion, yet not
the earth, when they would approach the galactic infinite, theta theta, and the earth does not"?
But is that really fair to the heavens or the earth, to say that the numbers
as numbers are bigger that way than the other way, when the property of infinity is considered clearly? After all, to all the finest recollection, infinity is not simply a matter of extension in space or innumerability, as things come knocking at the door.
A rapping tapping knocking, comes strangely at times, tap, tap, tap, at the chamber door, while the nodding weary sleep.
Nameless as evermore and the darkness unexpected, would
people more than dreaming fairly believe with any standard rule of detachment that there are more stars than weeds or blades of grass? Any seeds of earth that have settled are settled
as much as the earth. Whether grass or oak, acorns or mimosa trees, how many little particles and things around the earth, that are settled as the earth itself, are there anyway? Is there not more to number of things (past, present, and future) that are quiet
on the Earth than there are stars?
When these two numbers would be added together by any means, the terrestrial and the astral, in blades of grass, weeds, and stars, how close would
they be to infinity?
Infinity at the chamber door? Rapping and tapping, tap, tap, tap. Only a ghost, if this appearing, an apparition and nothing more, deep into the darkness peering ...
'Tis the wind and nothing more!
Ah, agriculture, the wealth of barns and crops, and distinctly to remember, even in December, that the stars are not closer
to infinity for big numbers than the seeds of earth (and the volume of the surface of the Earth in its characteristic sphere on which they rest, even in bleak December) so why not just multiply the
Earth's flocks and flora by two, and all they would represent in great and small, and forget the stars to say for evermore, for evermore.