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 smooth, hard, and horizontal surface or whatever, such as a tabletop or a glass highway. Perpetual horizontal motion, in the sense of a straight line, in fact, is
logically impossible as much as infinite regress. In the real world and even in the mind, for a motion to be infinite, even by the 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 obvoiusly finite by the order of cause and effect. Since 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, 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 to be always coming back around to the beginning, to form a perfect circle at once, where all points along it are 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, as much as all the ends, along its endless circuit, again and again, at all times, to have even a metaphor of the infinite in the limit.
Galileo and Newton would have more
problems than could be imagined trying to resource infinite motion with a marble. Since to be so great, 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 for the order of magnitude instantaneous withal, at once along all points of its 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.
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 friction and air resistance.
"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, 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 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 by science, as an infinite velocity cannot accelerate, since it already is infinite.
If anything is not absolutely infinite yet, it never will be ... even much later, however long it would possibly take to develop. 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, as 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 all description to reckon perpetual horizontal
The problem with heliocentrism is not from friction but geometry and math. There the essential and 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 and 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 and atmosphere of one form or another are already in the nature of all substance and being itself.
If Galileo's marble rolled away as far as Saturn, 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 be only halfway to
the point twice as far away. 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 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 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"?
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, knocking at the door. A rapping tapping knocking, comes strangely at times, tap, tap, tap, at the chamber door, while the nodding weary sleep.
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 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 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, and nothing more, deep into the darkness peering ...
'Tis the wind and nothing more!
Ah, agriculture, 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 crops by two, and all they
would represent in great and small, and forget the stars to say for evermore, for evermore.