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New Mechanics: The Foundation

As that of the controversy between External and Internal Relations Theories: External works with the "material point" -and/or-the-Supreme-Monad of Newton-and-Leibniz. Internal Theory is supposed to deal with Topological "accumulation points"; where the "material point"-and/or-the-Supreme-Monad has the singular nature of the One. In contrast, Topological "accumulation points" are always plural; where the being the "material point"-and/or-the-Supreme-Monad is the limiting case for Topological "accumulation points" (June 2004).

If Newton's three laws are sufficient only for the world of solids, should be there a law that is appropriate for objects?


It can be easily concluded that if it is evident that among existing objects there are some that are something in motion and something at rest and if we have accepted that it is impossible to be and not to be simultaneously, and we have shown by means of this that it is the firmest of all principles and if "every body continues in its state of rest, or of uniform motion in a right [i.e., straight] line, unless it is compelled to change that state by forces impressed upon it" (Newton) that there is the world of solids that are at rest and the world of objects that are in motion.

Therefore, I suggest that the world of solids forms Ether, and the Force of interaction between objects is the Measure of Ether in my interpretation of Kepler's law of interaction between objects:


where tr and tr' are trigonometrical functions: sec, sin, cosec and cos ;

where 0 is the condition of rest;

where d l and d m are the increments of the matters 1 and spaces of objects; they are called 'appearances' 2 : if d m and d l do not exist then (l/(m + d m))*tr( d l/ d t) and

(m/(l + d l))*tr( d l/ d t) is equal to null -- these objects are solids;

where F is the continuously modifying Measure of Ether or, what is the same, the force of interaction between objects;

where there is the Law of Preservation of substance:

m1 + m2 + 2dm + dM + M' = Mon,

l1 + l2 + 2d1 + dL + L' = Lon,

where m1 is one interacting object's matter and l1 is its space -- the object's orispher ;

where m2 is another interacting object's matter and l2 is its space -- the object's orispher ;


where Mon and Lon are the abstract matter and space of the Supreme Orispher ;

where M' and L' are the sum of abstrac t matters and spaces of all smallest apeirons at rest, which constitute Ether: actually, they are the constant ' G ' that is the variable constant ' G '. The presence of this variable constant ' G ' proves the substantiality 3 of Ether if there is the Whole -- the appearance of the constant variable ' G ' in Newton's interpretation of Kepler's law of gravity 4 explains why Newton's version of Kepler's law and Newton's three laws should (!) coexist in the traditional physics.

As for me, the idea of the Whole means that there is a finite number of the smallest parts of this universe -- of apeirons -- and that there is the Supreme Orispher that contains itself the Whole world. This term -- oorispher -- used to be applied by Lobachevskii in his geometry and I use Poincare's model of it 5 : if there are the given geodesic path a and a point A not on a , there is no geodesic line (or, what is the same, path) through A , which lies in the plane 6 containing both a and A , and which does not/does intersect, I can deduce that an orispher is a sphere with a constantly changing radius, where this radius strives to become infinitely big; where "big" does not mean a size in comparison with some arbitrarily chosen measure of space, but a measure of quantity of apeirons , which are united in this set of them, in comparison with their entire quantity. Put another way, if a radius of a object's orispher becomes infinitely big this object becomes a solid within this orispher and paths of all smaller objects that may compose the given object intersect in the endlessly remote point C (see the appendix Geometry ) before the objects that composed the given One begin to exist outside the given One's orispher after the given One ceased to be the One 7 . It means that the geometry for which all oobjects' paths intersect transforms to the geometry for which all paths do not intersect.

My next speculation that logically emanates from all the preceded assumptions is that if for the end should not be just any last object, but the best One, sharing the basic concept of Idealism and believing that everything aims to become unchangeable, eternal, and to find its end in truth, I can conclude that objects strive to complete themselves and to rest. For example, objects with magnetic properties strive to restore their lack of matter and rest; objects with electrical properties attempt to fix their shortage of space and rest -- objects endeavor to be (!) solids.

Another reason I started use the idea of the Whole is that I suppose that it may be inferred that the Force of interaction between all objects depends on defects in all objects and the entire series of changes is comprehended in this: the loss of motion and consequent integration, eventually followed by gain of motion and consequent disintegration -- all objects sooner or later will compose solids and these solids are the only Limit for apeirons in motion.

The understanding of the Pythagorean concept of apeirons -- what is unlimited has no telos (end) and is a-telos , which means both 'endless' and 'incomplete' plays a veryy important part in my mechanics:

a) 'objects' means qualitative measures-descriptions of sets of apeirons in motion;

b) a 'solid' means that a former object do not have any detectable nature and that it is an apeiron at rest;

where keeping-the-same is on the side of solids, change on the side of plurality of objects.

Indeed, Newton's three laws of physics do not take into account that objects have spaces and matters and that all changes in the conditions of objects should be found only as modifications of their spaces and matters 8 . Turning the world of contemporary science upside down, I state that there is no space between objects but the spaces of objects -- objects always exist within one's orispher . It means that objects can be detected if and only if they change. I implly that in the simple case of two similarly oriented Cartesian reference frames, moving along their common (x,x') axis, the transformation equations cannot be put any more in the form:


x'=x- v t y'=y z'=z t'=t;

where x,y,z and x',y',z' are the space coordinates of a given object, and v is the speed of one system relative to the other because it is evident from the geometry of Lobachevskii that an orispher is a space of objects -- uniform motion in a right [i.e., straight] line is an abstraction and insofar as the measure of space should be quanntitative and topology provides the means for the quantitative analysis:

-- it appears that for any matter of the given object there is only one the object's space; which the universal pair of matterr and space exists only for the condition of the object's rest such that:

where m1 and m2 are the constant meanings of matters of any two different solids,

where l1 and l2 are the constant meanings of space of any two different solids;


where P is the constant Density of solids and it is called 'the constant Density' of solids: the experiments with solids are usually called 'nuclear explosions' -- any mass-matter-content has only one strictly determined space-form-shape and vice versa; where objects with an equal condiition within the given object's orispher are called 'shells' of this orispher . The shell is a space such that any path which joins any two objects with the same condition is wholly within this space; there are several shells within any orispher corresponding to the conditions of its objects if there is more than one smallest apeiron within the given;

-- the Density of objects such that:


is called the "continuously modifying Density of objects";

If the continuously modifying Density of solids is constant:


the continuously modifying Density of solids is called "the Density of "things-in- themselves"" 9 ; solids with this Density are in the condition of uniform motion in a right [i.e., straight] line -- they are to be (!) dead.

The definition of Inertia emanates from the preceded equations:

In = P'- P

where In is called the "continuously modifying Meaning of Inertia";


-- solids can be imagined as empty sets of apeirons at rest; where any set of apeirons in motion which is not emmpty strives to liquidate its defect and become an empty set which does not have any defect;

-- any closed set has a cardinal number card A 10 equal to the cardinality oof the empty set: the apeiron at rest is an isolated system that makes no exchange with its surrounding.

Accordingly, the death of objects -- a pseudo cut in the infinitum of changes of apeirons -- could be conceived as a Dedekind cut in these oobjects motion; where any given open set of apeirons is dead -- it is (!) a solid that exists out of time measurements -- if the given association of apeirons stopped satisfying the requirement of apeirons to overcome constantly the Limit or, in other words, if the given association of many ceases existing as a set of many and, therefore, loses all its qualities; where relation always presupposes quality and quality relation.

So, the reason for apeirons in motion to be united in a set of them is that if all objects are open sets of apeirons these open sets of apeirons are closer to the condition of the rest than that which any apeiron from these open sets had before association in the open sets of the given objects; where I assume that making a cut in the infinitum of changes of apeirons does not mean making a cut in the infinitum of their existence but means their being in the simple present time of the verb to be of solids.

Certainly, if the 'Theory of Relativity' offers the absolute uniform -- the speed of light -- it means that the answer to the questions -- Does light have a matter at rest and why does not it have it? -- is that light does not have a matter at rest because light in the condition of rest is a solid! And this is the general conclusion to which I am driven with regard to the coexistence of solids and objects: Newton was wrong when he postulated that every body can continue to be in its state of rest because the loss of motion and consequent integration eventually followed by gain of motion and consequent disintegration. It is reasonable to expect that a solid as the One is opposed to the plurality of objects and that the process of converting of the singularity of a solid to the plurality of objects is that mysterious prime move -- the death of the One (the notion of the prime movement may not be required and, de facto, the common logic loses its foundation).

For instance, the famous optical interference experiment of Michelson and Morley in Cleveland in 1887 was devised to measure the motion of the earth through the ether medium by means of an extremely sensitive comparison of the velocity of light traveling in two mutually perpendicular directions. The experiment, when completed in 1887, was supposed to give a most convincing null result and proved to be the culmination of the long nineteenth century search for the ether.

However, Michelson and Morley did not know what they should look for and the null result of this experiment is the major evidence in favor of the existence of the Ether: any modification of solids that compose Ether into objects can be found -- an empty set suddenly becomes a set that has an actually existing power in the sense of Cantor. What is more, there is no a solid that may influence the path of the motion of objects without becoming an object -- the 'ether medium' does not exist in time, and any attempt to find the drift of the Ether will end with the questions: how can the immovable move? how can light have a matter at rest?

Frankly, do I have all the grounds to assume that solids do not interact but act? Is it correct that Newton's mechanics of the three laws is the mechanics of the verb ' to be ' and, accordingly, the new mechanics is the mechanics of the verb ' to become' ?; where I think that it is easy to see from Plato that according to Pythagor "the verb 'to be' must be totally abolished -- though indeed we have been led by habit and ignorance into using it by ourselves more than once, even in what we have been just saying. That is wrong, these wise men tell us, nor should we allow the use of such words as 'something', "of something", or "mine", "this" or "that", or any other name that make objects stand still. We ought, rather, to speak according to nature and refer to objects as "becoming", "being produced", "passing away", "changing"; for if you speak in such a way as to make objects stand still, you will easily be refuted." 11 .

Answering this need to consider objects' changes sub specie aeternitatis I determine that d t is an interval of time less than an interval of time between two extremums (where an extremum is a moment of time, when a given object is dead) in my interpretation of Kepler's law of interaction between objects. Naturally, on the assumption that any cause is consequence and that any consequence is cause and that the continuous interaction of objects is both cause and consequence (within the time of the infinite changes of objects) I feel myself able to suggest that if we use the deductive method of reasoning we should examine objects in the past continuous but not in the simple past and past perfect tenses: if Newton's three laws work in perfect (!) times -- they consider limited (!) quantity of final (!) causes and consequences in finite (!) intervals of time <D t for solids (!)-- they stay out of consideration of continuous (!) tenses 12 and the ethicall question "Why?" for this imperfect (!) world of objects answering the questions "What?, Where? and When?" exclusively.

In other words, I suppose that objects strive to include other objects from their neighborhood 13 within their orisphers according to the rule of Pragmatic Esthetic -- objects aim to unite with everything that can make them better and to become the best One. Therefore, the universe of objeccts is spiritual -- all objects are conscious: they are intelligent; they are purposeful.

Namely, I have a strong belief that if a stone has the same endeavor to become the best as human beings have, there is no substantial difference between a homo sapience and a stone -- mind is the manifestation of apeirons' limitlessness that force them to complete themselves.


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