"Parvus error magnum
in finis", small error big in the end, so it goes for a circular principle that things come back around, even when wrong, and it fits in too with heliocentrism of Big G and little g(9.8).
Galileo, for example, first discovered and charted his way into abstract
little "g"(9.8) by rolling metal balls down ramps. The old man conducted hours and hours of painstaking research, rolling balls down inclined planes
to study acceleration and establish that, according to him, objects with different weights accelerate equally under the influence of "gravity". Even
when the fact is that they do not, he would maintain that they do, because the differences in acceleration, as they would be discovered at times, were yet conveniently small, according to his terms in the lab, so small, only so slight, for comparison in view
of the greater differences in weight.
In defense of the principle of uniform
acceleration, due to "the force of gravity", exercised universally over all objects, he said, “So far as I know, no one has yet pointed out that
the distance travelled in equal intervals of time, by a body falling from rest, stand to one another in the same ratio as the odd number beginning with 1."-1 One of these to one of those, et cetera, and what a measure of proportionality that would be for counting all things.
As Sextus Empiricus figured things too, "numero
cuncta assimilantur", all things are assmilated by number; and whatever point or division is at least by one, since everything is in the least at least by one again as much as the others.
As it goes,
tranquil fish of knowledge rest in cool mountain waters, and any theory reduced to the mere statement that if a thing exists, then it does exist, becomes an easy way of proving anything. Easy work if it is, so it must be too is a simple way to reckon, as indeed
attributes may imply one another and so many peculiar properties.
This is a picture, this is a picture, and this is a picture as well, where the golden mean or whatever fraction for a ratio divided
by one is always the golden mean or whatever fraction again, of course. As the golden mean or whatever fraction multiplied by one is what it is for another instance universalis, this is another picture. An ingenious way if stupid perhaps for saying that in natural units of division, the "force of gravitation" amongst things, as a physical construct in nature, may also be
set equal to one, like that, like a picture for constancy in details, as one of these to one of those, when inserted parenthetically into an equation to represent rate by distance of fall.
The universal basis of heliocentric fiction, the wonderful cape of confused gravitation, like incremental divisions by one, is not actually any active force at all, other than what already would be accomplished by something else, or be present by some form of impetus and
development of momentum. SInce division or multiplication by one leaves everything as is, it is not saying very much for the theory of Copernicus or Galileo, since the heavier weights
still fall and roll faster and more heavily. Even if the differences in some cases can be marked down as comparitively slight, or hardly to notice for Galileo's argument, yet the heavier they come, the harder they fall. Tickled with a feather or hit smack dab with a hammer, in the midst of the air betwixt and in between, let the toes and nose of honest response be the guide.
To express his
principle of perpetual horizontal motion, he said, “I mentally conceive of some movable projected on a horizontal plane, all impediments being put aside" ...[and] "that the equable motion on this plane would be perpetual if the plane were of infinite extent".-2 Infinite progression, however, is as faulty as infinite regress, yet the image was a key component of the way he would develop a foundation for gravity,
little g(9.8), and the world of heliocentrism. If it may seem odd that this has anything to do with whether the Sun orbits the Earth, or the Earth orbits the Sun, it still became an important talking point to Galileo, and almost would provide a way to fit the infinite into a place among things that it might othewise not go.
The crafty discussion he made of his experiments with metal balls and ramps was to construct in the mind an image of equivalence so hypnotic that people could be convinced to believe that rest is the same quality as motion, and motion the same quality
as rest. By hypnotic effects and induction, they could at least be led to confuse the two; and these stories of Galileo would later form the seed of Newton's own counter-intuitive and erroneous first and third "laws" of motion.
-Imagine then that a metal ball or marble let go rolls down
one ramp, across a table, and then up a second ramp. To begin the picture of equivalence, imagine that, if the two
ramps are identical, the ball will reach virtually the same height in the second ramp as that from the first where it started. In the same way, if a marble is let go to roll down the inside of a large bowl, it will roll through the bottom and then up the other side virtually level with the starting height.
To put an image of equivalence of motion in the mind, the metal ball and the marble are seen as coming close to the same height when they finish as when they started. However, the truth is that the marble and metal ball do not really finish at the same height as that from which they started.
Never mind the little part, even if not only friction, since Galileo had a more crucial observation. Use another
receiving ramp that is less steep and longer than the first second one. Once again, the image of equivalence, that
the ball let go ends up at virtually the equivalent height from where it started, plays in the mind, though this time it had to roll farther to get there. Do the experiment again with another receiving ramp more level and longer than the second third one, tilted up only slightly, and the ball will
eventually reach its starting height, said Galileo, but it will have to roll and roll more to get there on the other side. The lower the angle of the receiving ramp the longer the ball
will roll to reach the same height from where it started, where for the sake of equivalence it should be imagined that the ball invariably will roll that far.
that the receiving ramp was perfectly flat, not tilted at all. Then, said Galileo, in that case the metal ball and the marble would roll on and on, horizontally forever, if not for friction. But the flatest ramp that is the last image in the series is really a form of mildly hypnotic suggestion
in infinite progression. It is a thought experiment, not a real one, to introduce a new law of nature: that any object moving horizontally will continue moving horizontally forever, at the same speed, unless something happens to interfere, like "friction". Newton's first law of motion is a generalization of the principle. However, it is not scientific or logical, since infinte progression is as faulty as infinite regression.
It only is a thought experiment that presents a subtle and mildly hypnotic form of suggestion.
Ignore experience and the gift of common sense,
therefore, and what can actually be seen of the inclined planes and marbles. Rather listen to Galileo intone about infinity, and more important than the limiting details there in the ramps,
that actually can be verified, there is a greater and idealized "truth", an abstract and mathematical world of the
mind, where marbles and metal balls can roll on and on in horizontal planes forever. To the mind under the
influence of Galileo, things may be reversed, nature confused, and there could be a plane beyond measure, in "absolute space", where, contrary to Aristotle, purely natural and horizontal
motion is perpetual.
Constant horizontal motion, even outside
the curve of a circle, to say or imply straight along, on and on at one level, was important to Galileo and the development of heliocentrism for a few reasons:
a) it provided a theoretical basis for gravity, even as a lateral force in perpetuity; and gravity needed to be a constant and powerful lateral force also, to imagine that the Earth could be orbiting the Sun.
b) it provided a theoretical basis for relativity and heliocentric "invariance"(undetectable "unaccelerated" motion) and equivalence in various relatively "inertial" frames of reference, et cetera.
c) it contradicted Aristotle's common sense logic
and scientific observation that things loosed across the Earth tend also to come to rest on the Earth, as the Earth is always at rest before them: and
that like goes to like, simile gaudet simili, as likeness will increase, and "that like is known as well as perceived by like".-3
Aristotle would have noticed that the rolling metal balls
and marbles did not really finish, even on the first roll, exactly as high as where they had started, and that they all also exhausted themselves
over little time and came to a state of typical and completely authentic rest. Galileo would
howl at Aristotle's stupidity and troglodyte naivete, then invoke Lenin and the central bank of the communist party of Italy, and say that he was missing the point of his revolutionary new science, as that
by gravity "distance is proportional to times squared."
In some cases maybe, but everything like that is proportional to multiplying or
dividing by 1, as well as it goes with one of these to one of those, among hower many things, on and on. In virtue of the situation, Aristotle would have to respond that distance is equivalent to rate by time, of course. However, the rate of acceleration
is not affected by "gravitation", as described by Galileo, as much as bricks are not feathers, and gravity and acceleration are not equivalent: but always concede to divide or multiply by one, to figure
the constant force of Galileo's "gravity" in natural units, in lab experiments of limited contrivance, to be safe.
It is doubtful Galileo would appreciate Aristotle for common sense
criticism or paleolithic wisecracks in the avant garde laboratory. Ptolemaic "Syntaxis Mathematica" conservatives would have to go. There was trouble and time to develop a proper liberal and progressive background for little g(9.8), and one day perhaps dogs would be able to fly to the Moon too, like Kepler or Lady Gaga. If spaghetti could fly like bat wings that far, like 252,000 or 253,000 miles away. Where one can land on the Moon at apogee, he should be able to land on it at perigee, of course, and vice versa.
But before flying to the Moon in dreams, or like Kepler with demons, which was an old-fashioned way, he would need to consolidate new breakthrough insights about the cosmos, including
a feeling that time, not space or energy, is the essential variable that governs the world. Putting time first would open a better abstract plane for
interpretations of gravity, and putting time first would be the best way to sustain his experiments with motion. So when Galileo was working in the
lab with inclined planes and rolling metal balls, it was not an ordinary level of geometry or terrestial affairs. "As above, so below" astrologers, mystics, and occultists have said, and when he was taking
notes, Galileo would be fiddling with the cosmos and metaphysics as much as the infinite.
In the beginning, the set-up was bare-bones:
a wooden ramp with a thin groove down the middle, a bag of metal balls and marbles, and a series of movable catgut strings. The strings lay toward the
bottom of the ramp, within the groove, all pulled tight at a right angle to the downward roll of the balls across the surface of the ramp. When a ball
crossed a string, it would make an audible click.
After kicking Aristotle and Ptolemy out of the lab, Galileo could hear a ball cross
each string in turn ... because of "gravity"! It was little "g" at work, like one of the little people nobody can see. Painstakingly, as a fool would
be wise, he would roll the balls again and again down the ramp, trying to position the strings so that the travel time between each pair was
equivalent. To support his theories, the strings and incline needed to be arranged so that the time interval it took a ball to descend, rolling from section to section, was as equal as equivalent among the clicks in between.
He had five strings, A,B,C,D, and E, positioned at different lengths of separation along the surface of
the ramp, where he finally fixed it so well that a ball let go from the top would move to string A in the same time that it would move to string
B ... and so on to C, D, and E at the bottom. Out of this comparison he was able to build a math table and equation that would form the basis of little
g(9.8), and his smashing theory of uniform gravity in free fall acceleration, to explain why the Earth orbits the Sun.
distance between strings in little increments yielded results in two columns and five rows where:
Time(in seconds) Distance(in inches)
Start to A 1
A to B 1 3
to C 1 5
C to D 1
D to E
In Galileo's opinion, a game of marbles like this, according to elevation of limited contrivance in a lab, could be expressed as a function of time and the force of gravity alone. Since there were five divisions in the ramp for a total of 25 inches, (1 + 3 + 5 + 7 + 9), and the pivotal roll was five seconds, he could say that a
ball rolling down one of these ramps at gravity's command traveled precisely t^2 inches, as t is time.
In terms of the ramp, "in 1 second, a ball rolled 1^2 inches, in 2 seconds 2^2 inches, in 5 seconds 5^2 inches and so on."-4 What
was equivocally equivalently important in the exercise was that the math table, the law, and its equation did not say anything further about radius
or weight, or anything of the what how in the elemental conditions employed, or how the situation related accurately in specifics to the law of universal proportion and which way the Moon goes.
Time(in seconds) Distance(in inches)
Start to A 1
Start to B 2 4
Start to C 3 9
Start to D 4 16
Start to E 5 25
Therefore, Galileo thought that itwould be fine to extrapolate from such business that all objects around the Earth, regardless of their specific weight
and actual heavy density, fall at exactly the same rate. So according to Galileo, roll a cannonball and a BB down a ramp side-by-side, and they would descend rolling alongside each other at uniform rates of acceleration ... "ad infinitum" too, due to gravity. So on and so on, alwaysthemore nevertheless, yet force in motion and rate of acceleration are not separable terms, since they always go together, since
more force will mean more acceleration. All other things being equal, down the same or similar ramps, a bowling ball with greater radius and weight will pass a BB, if there is enough time and space given for the difference in force to develop.
But not to Galileo, even if bowling tournaments are not won with BB's, where he would say that for any given ramp the same gravitational law of equivalence between all objects would always prevail; and the distance a ball traveled would be proportional only to the time squared and the "force of gravity". All that counted in the design was the height above the ground
from where the ball would be released. With the right ball and the right ramp, Galileo could say that due to gravity alone a weight always
falls as it rolls, a distance proprotional to seconds of time squared, as a function of universal gravitation.
Of course, in time,
space, and energy there is always some proportion, but natural proportionality of things, and Galileo's best contrived ramp, do not prove that there is an interstitial "force of gravity" innate to matter that causes motion. Rather nature itself, which inheres primarily and by itself, and not accidentally, is the principle cause of motion. Form in actuality is as nature is, and the manipulated interpretation
of things for the sake of heliocentrism was outcome engineered. Put a gnarly rock on the ramp, for example, and it will not follow the rule, not for how it is, and a little heavy too. It would not fit the structure of gravitation hidden in the trick.
If setting the ramp on fire would be another example, with charcoal lighter or lighter fluid, a rock
with a funny roll or stuck on the ramp would act like another anti-gravity device, because it lacks a smooth and uniform surface for rolling like a metal ball. As much as it does not roll away, it would tend to nullify the set-up force-field equation
for gravity in the game.
Aside from dropping rocks, cannon balls, melons, and garbage from the Leaning Tower of Pisa, this was how
the distance formula for free fall acceleration and little g(9.8) was developed. Roll marbles but drop rocks, of course, and from this it is said that all objects with greater density and weight than air supposedly fall according to one precise rule of uniform acceleration, written in English units as d = 16t^2, where d stands for distance and t stands for time (and d = 1/2gt^2, where g is 9.8 meters equivalent).
Due to the putative interstitial force of gravity, it is said that acceleration of
an object in free fall is independent of weight, falling as falling, and that in one second, any rock falls a distance of 16 x 1 feet. In two seconds,
a distanceof 16 x 4 feet, or 64 feet, in three seconds, 16 x 9 feet, or 144 feet, et cetera by the seconds squared.
to ramp and marble, the universal table for any abstraction of rock or cannon ball goes:
Start to A 1
Start to B 2 64
to C 3 144
Start to D
Start to E 5
Start to A 1 16
A to B 1 48
B to C 1 80
C to D 1 112
to E 1 144
However, even without interference from feathers, cat toys, or peanut butter as atmospheric friction, or vice versa, according to Galileo's formula, the rate of acceleration is not really so uniform, not more than proportional.
In his own math, falling is not constant other than to fall and accelerate exponentially. The rate of increase in the real world is not independent of density and weight, however, and it does not go on and on ad infinitum.
Every freely falling weight eventually reaches a maximum acceleration in an environment, and none accelerate infinitely, even in a so called vacuum.
Even with Newton's
calculus, a finite weight cannot accelerate infinitely, nor by gravity alone, as absolute infinity can never be fathomed by parts nor by the segments of any curve or pattern of exponents. The putative interstitial "force of gravity" is
not accelerating any weights anyway, since gravity is not even a lateral or vertical force. In every case, there is impetus, momentum, and accommodation of events to cause motion and acceleration.
Anvils of styrofoam, foot-long matches, ping pong balls and ramps all covered in velcro, and other anti-gravity devices, demonstrate that what is really at work in these disingenuous experiments of Galileo are motions
and forces that are all predicated variously in quale quid ... not in undetectable occult action-at-a-distance like "gravitation".
What makes a bb and cannon ball
roll side by side down a ramp for a little while is in the limited details of coincidence. Funny concurrence too, yet motion and force overall become a matter of the factors involved, like radius and weight, as well as density and material circumstance,
and the quality of smoothness of the ball and the surface used for free rolling movement, etc. Something marginal not gravitational is at play among many things, to affect and constitute the results; and specific weight clearly does, in fact, contribute
to the development of force and acceleration in free falling objects.
For instance, not because of Galileo's gravity, people do not play volley ball with volley balls
made of lead or plutonium, but because they are too heavy for sporting material and do not bounce.