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
the ever-rolling great beyond, as Newton's 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 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 set to roll forever
on a limitless glassy smooth horizontal surface, such as an unlimited tabletop, glass highway, or whatever it could be that would obtain. Since at least some tension is in everything,
as without tension there would not be anything to remain, not a spark of frictionless friction either, which is only another kind of tension itself, Galileo would rather be working in round squares and other nonexistent objects when he talks about "gravity".
Wherever gravitation ceases, of
course, 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, which is supposedly so much about them and among them. Since universal
gravitation would make any situation an intolerable crowding, too much of whatever it is and overcome any place, it must be something different that makes the Moon orbit the Earth.
For the sake of "gravity" it seems no one can refer to simple heaviness or substance in a way of final clarity,
and perpetual horizontal motion in the sense of a straight line is a funny ruse. Yet true to formula, as "this sentence is not true", Galileo or NASA may say there is no problem from gravitation of heliocentrism set loose among sets or stars in the cosmos,
since anything may follow as well as another from impossibility. In fact, logically it is as impossible as much as infinite regress, and 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.
As Aristotle wisely observed, the first principle of eternal motion has always been the circle, round and round, as much as the cave or the cloud. Naturam expellas furca, tamen usque recurret: one can expell nature with a pitchfork,
but she always comes back, as strong or stronger than before. "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
the distinct difference of an infinite resource per se, a circular difference also as something all the way around even in the form.
"In no case is it possible for an infinite force to reside in a finite magnitude", or for the finite to be infinite, therefore, whatever motion would be infinite
must be exceptionally of another sphere beyond, rotatory rotationis exceptionalis in excelsis as Tullius Quintus called it, as much as always coming back around from any point like before is eternal, which eliminates the notion of perpetual horizontal motion
in straight lines.
Since again it is rather again the nature of circular motion that implies the eternal,
the only way to have an infinite roll is always to be coming back around, to the beginning to form that exceptional
perfect circle at once, where all points along it are as the same, in the same ratio to the center, in such a case of total rarity, where one can never tell the difference in where it began or would end. Any rolling marble set loose by Galileo would
have to be coming back around to the beginning forever, having for one as all the same places for starting point and goal along its endless circuit, at all times again and again,
as much as all the round ends, to have even a metaphor of the infinite in the limit.
Since neither could traverse an infinite series, as impossibilities like that do not happen, Galileo and Newton trying to resource an infinity zone of motion as perpetual, to justify heliocentrism in theory with a marble, would have more problems in
magnitude than could be imagined. 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 qualified of demonstration for all that
than an instant indivisible that would be impossible to capture in natural time. For the order of magnitude there is absolutely instantaneous withal, even only at first reference, a present infinite exceeding all bounds at once along all points of the greatest
Seeing it as it is at least by analogy, that the reflective quality from within infinity is something
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 total motion, or total 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 is not a competent agency to explain multiplicity, size, magnitude,
or nature, as whatever importance there is in motion or any number like 365, for the example of a year, is not justified by only one more. In as much as every number is unique, at least as well expressed as one, sometimes the dime's worth of difference is
all anybody needs to know.
Even if there are many instances of difference, quantity as substance has no contrary,
and an endless chain is impossible, as links in a chain and numbers themselves are not justified by infinite regress. Then neither is heliocentrism, and Galileo rolling metal balls down ramps or Newton shooting rifle bullets from the top of the Himalayas, "De Principia", are obviously not credible sources of infinite or constant motion either. Since that which is absolutely infinite cannot be excelled, the speculation fails regardless of any preferred description of friction, tension, containment,
or air resistance.
Like never before, everclear and never to love again, never never never, 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, that which is absolutely infinite, or beyond all compare, cannot be found in several numerically different things.-3 In other words, as would have been noticeable from the start, neither Galileo
nor Newton nor heliocentrism can measure the indivisible by divisions, of course, and every horizontal line is another divided segment in the issue. Since the greatest cannot be excelled, the shadow of the immeasurable is immeasurable and immeasurable
also in relation to anything else.
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 so refined 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 is a lot to ask. For infinite
resourcing, that thing prepared for all events from the top forever, in omnia paratus de summo perpetuo, like first principles, it would be beyond any manipulation or addition by
science, as an infinite velocity cannot accelerate, since it already is infinite and of no increase.
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 Newtonian "gravity" would pretend. However, as sticky as things may be, paint, tape, and glue, infinite
motion cannot speed up more, and it must be absolutely instantaneous, at least as simultaneous as all the sundry so-it-goes, whereas no natural or lesser motion can take place as instantaneously as all that, not so extensively and simultaneously perfect. In
many cases, the slower or the faster may speed up, of course, at least a little in cause and effect as needed.
If not a lot to keep up with in a small world, all motions less than the infinite must have halves besides, something in between, and therefore are never purely instantaneous, as they may accelerate or decelerate, increase or decrease, et cetera. Simultaneity may
be fun, an imagined escape from cause and effect, but a fancy 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, as can be seen, is not merely from friction or things but also geometry and math. In all problems and propositions the essential difference
between the finite and the infinite is represented over and over in what we perceive. Like summaries and categories, again and again all the way around, the inescapable nature of finitude
itself runs 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.
Any two points are the first to consitute tension or relief of whatever half or duality in any side or aspect of things. Whatever of all the ado so much about nothing, "what people mean by the vacuum is the air", which by its special elasticity and tension
is able to convey all temperature and sound however soever it goes.
Anyway the wind from the pipe blows, whatever the color of analysis, it is indispensable that that there be
something in between -- since if there were not always a side, even so many sides in atomic theory, for example, to fill so many crazy books, there were would not be any division for comparison. To reckon in virtue of comparison is basic to understanding,
where again mathematical density in an atmosphere of one form or another is already in the nature of all substance and of being qua 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. To know the ever-rolling circumstance beyond, to discover the
extra super in the differences of things, puzzled in the investigation of likeness and so forth amongst so many, so it goes, that as progress in straight lines is of a lesser kind, that
is always fractional, it can never be infinite. As an extensive 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 exactly 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, not 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 in the conversion 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.
From the units up, if there were a great escape to fly away from false affection, as discovered around a point so much, perhaps like world communist conspiracy,
or the Zaimph de Tanit, to escape the surface is to escape the center and to escape the area as well. From the littlest circles at center to everything outside in extremities of circumference, as far as may be discovered, le bon départ is at right angles
to every tangent. The lovingkind nature of bees, for example, and the ultimate aim in honeycomb, in all the quarters of straight lines, would make another round edge plus ultra and further beyond in outer space, if bees were driven by fire to the higher and
highest degrees. An infinite body of crosses can be seen embracing all the heavens. In the aspects of demonstration to it, there will be many crosses and angles to pass and bear along the way, of course, and always other spheres.
In yonder round belonging, when the going away is from the center, the exit to it goes at so many right angles to existence, even from the depths and stones of Hell.
To make another boundary out there, another magnitude in geometry, to the ghost in the machine, as many as also as far as things may go, to a point something celestial lingers, in fact, around the same divisions and cuts and turns of hoary history.
To a beekeeper a pattern of the infinite may appear in the way things reappear as before and then again, in the cornered allotments and blocks of space, the 1/2 here, the 1/3 there, the quater then the fifth,
et cetera, and more cuts this way or that, turned this way or that, tuned like any other circle of fifths, and one meaning for them all in the figure to obtain in the ultimate dues and rights ... of social units and demons and fish tanks. Keith Richards
too not only Socrates experienced a demon they say perhaps an insect. Wax caps not only honey and the frame. Yes, the social units too, and then the fish with the eyes all circular going round are like another syllogism all put together. A grand syllogism
peut-etre of triangulation, and trains in greatest magnitudes comes forth, and the proofs and demonstrations are spheres. Sometimes needles in the figures and lines of thoughts, and then in Federal Reserve Bank catabasis it comes along, sometimes the Judeo-Masonic
hustle, and sometimes Marxist dialectics, the devil's jokes and ways of the world that come and go about things and round and round.
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, buzzing 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 of aether and the stars. 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 the dusty 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, when the property of infinity is considered clearly? After all, to all the finest recollection, infinity
is not simply a matter of extension or innumberability, as things of space 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 pitch 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 grapes and seeds that have settled are settled as much as the earth. Whether grass, corn, 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? Spirit rapping tapping, tap, tap, tap. 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, the ever-rolling mists and finest dew, and distinctly to remember even in December that the stars are not closer to infinity for big numbers than the seeds of earth. Not more than the surface of the volume of space that may be contained this way or that, the principle itself here or there, wide and far, as one the same thing to separate them all, and so many as so much, in so many characteristics,
sometimes joys of forgetful fruitfulness on which they super-severally may rest, even in bleak December. So why not just multiply the Earth's flocks and flora by two, and all that they would represent in great and small, and forget the stars to
say for evermore, for evermore.