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 provides 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 it would 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, however, there is no ball that Galileo could roll on a smooth, hard, and horizontal
surface, such as a tabletop, a glass highway, or whatever without limits and forever. Perpetual horizontal motion, in fact, is logically impossible in the real world and even in the
mind, as much as infinite regress. For a motion to be infinite, even by mere semblance, it would have to be
circular. 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 finite by its order of cause
and effect. Every straight line has a beginning and an end. Even if people cannot tell where it began or where it will end, like railroad tracks away in the distance, if it does not make a circle, it lacks the curve of perpetuity. Therefore, no straight line is ever infinite, because infinity has no beginning and no end, and any infinite motion would have
to have the infinite resource of a circle, even in the form. Whatever motion would be infinite must be circular, as much as always coming back around, which eliminates the notion of perpetual
The only way to have an infinite roll is if it always is coming back around to the beginning, so one cannot tell the difference in where it began or would end, and forming a perfect circle, so that all points along it are the same, and in the same ratio to the center. Any
rolling marble set loose by Galileo would have to come back around to the beginning forever, as much as the end(s), along its endless circuit, again and again, at all times to
have even a metaphor of the infinite in its limit.
Galileo and Newton would have more problems than could be imagined trying to resource infinite motion with a marble, since it could not continue in any straight
line, within any reasonable amount of time, regardless of friction and impressed forces anyway. It could only go in circles and over a very long time, yet instantaneous withal, at once along all points of its path, since the reflective quality from within infinity is circular: as much as 1,2,3 and A,B,C of forever. And an infinite progression is not possible
by marbles because time and space are finite.
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 any infinite or constant motion, or speculation, regardless of friction and air resistance, since that which is absolutely infinite cannot be excelled.
"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, neither Galileo, Newton or heliocentrism can measure the indivisible by divisions, and every horizontal line is a divided segment.
For Galileo's marble down a ramp or Newton's mountain top musket ball to have an infinite motion, it would have to be everywhere along the course
at once, instantaneous in the entire path, and have infinite velocity and size. Having to be everywhere at once
to have an infinite source, prepared for all things from the top forever, in omnia paratus de summo perpetuo, it would be beyond increase and any manipulation, as an infinite velocity
cannot accelerate, since it already is infinite.
If anything ever is not absolutely infinite yet, it never will be ... even much later, however long it would possibly
take to develope. Infinite motion cannot speed up more, and it must be absolutely instantaneous, whereas no natural or lesser motion can take place instantaneously, and in many cases it may speed up, at least a little, if not a lot. All motions less than the
infinite must have halves, and therefore are never purely instantaneous, and they may accelerate or decelerate, increase or decrease, et cetera. A marble 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 description to reckon perpetual horizontal motion.
problem with heliocentrism is not from friction but geometry and math, which also represent the essential and
categorical difference between the infinite and the finite. It is the inescapable nature of finitude itself that runs to
a wall of exhaustion against infinity. There
is no rarefied and frictionless 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 of one form or another is already in the nature of all substance and being itself.
If Galileo's marble was able to roll
away as far as Saturn, one day, it would only be halfway to the point twice as far away. If it went to the point from Saturn twice as far away, it would only be halfway to the point twice as far away again. If it went to the very most distant visible star, it would only have made it halfway to the point twice as far away from there. Progress in straight lines is of a lesser kind that is always fractional
and can never be infinite. Every straight line and motion along a straight line can be divided into sections from beginning
to end, and therefore is not fairly representative of infinity.
The mathematical elements
of angular and linear velocity 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 the same species of motion in the formal and active terms of measure.
V = w r is different from r = d/t, where circular velocity can represent greater concentration of force. W incorporates pi, an endlessly repeating number, and even at the greatest speeds possible
does not represent extension in space beyond “r”, 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 and turns,
parva theta theta, merely this and nothing more, to a mild form of hypnosis, over many quaint and curious volumes of forgotten lore, by the circular perambulations, 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. A gravitational line of Galilean relativity could go, "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, infinity is not simply a matter of extension in space or innumerability, knocking at
the door. A rapping tapping knocking strangely, tap, tap, tap, at the chamber door, while the nodding weary sleep.
Nameless evermore and the unexpected, would people more than dreaming fairly believe with any standard rule of detachment that there are more stars than 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, and 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
When these two numbers, the terrestrial and astral, would be added together, by any means, blades of grass and stars, how close would they be to infinity?
Infinity at the chamber door? Rapping and tapping, tap, tap, tap. Only
this and nothing more, deep into the darkness peering ...
'Tis the wind and nothing more!
Ah, distinctly to remember, even in December, that the stars are not closer for big numbers to infinity than seeds of earth, and the volume of the surface of the Earth on which they rest, even
in bleak December, so why not just multiply the Earth's flocks and crops by two, and all they would represent in great and small, and forget the stars to say for evermore.