Infinity - Point
Infinity
In the ancient Greek world, οAnaximander (610-546 BC), son of Praxiadis from Miletus in Asia Minor and a disciple of Thales of Miletus, dealt with Infinity in strictly scientific terms. Infinity is that which is called “becoming” and has eternal continuity within it.
If we identify the concept of “infinite counting of numbers” with the “infinite creation of the continuity of dividends” we come to the conclusion that the world is created from all eternity, its existence can only be understood in the sphere and not in an extending straight line.
In his time, Anaximander sought, a “Principle of Everything” beyond materiality, and found it in the concept of the Infinite.
Theophrastus informs us that Anaximander arrived at a view “on the Infinite”, that it is a substance unlimited in both shape and size. “Nature is indefinite both in kind and in size”. Anaximander’s Universe is “Immortal”, does not decay, does not die, is creatively inexhaustible and always alive, in its essence has spontaneous motion and “continuity” defines its existence.
Anaximander’s views, which are being thoroughly studied in our time by the great Space Centres of the world, include not only scientific but also philosophical views, worthy of useful studies. In order to capture the concept of the world in its full explanation, Anaximander constructed the first cosmic sphere, which presents a likeness of the Universe, a cosmological map.
Early on his intellect had grasped a general law οgoverning all parts of the cosmic Universe and his studies were adapted to the data of his self-created sphere. The study on the infinite property of the Universe (Megacosmos) and the infinite property of matter (Microcosmos) in our time creates intense debates with opposing views of the scientific community. Einstein, a prisoner of the theory of Relativity, considers the “Universe Infinite” with a corrective congenital view, “but within limits”.
The “Big Bang”, which is the subject of much of the scientific community’s study, suggests a “beginning of time” and a “beginning of creation”. However, the intense philosophical thought of the ancient Greek Hellenists and Attic philosophers states that : “whatever has a beginning has an end” in the time that defines it. And because the concept of end abolishes the Eternity of “becoming” this, as a philosophical view, is contrary to the ultimate purpose for which nature, man, the Universe, God himself exists.
Point
The opposite view of the Infinite consists in the “Point” In space the point is an entity which occupies a position, but has no dimensions in length, width, height. The absence of its measurable elements appears as zero as a limit, but not to infinity. The entity of the point attests to existence. So “it is”.
Euclides was the first in Mathematical Science to use the word “point”, while Aristotle, earlier, called the “point” by the word ” moment “. Euclid in his “Elements” explains in mathematical terms the word “point” as follows : “point is, part of nothing”, that is, the point does not occupy any space. In Euclidean Geometry and in all known geometries the explanation of points remains the same, except for a few exceptions where the concept of points is completely abolished.
Democritus calls the individual in his time as undivided, i.e., indivisible. Regardless of the fact that, today, science has split the atom, the name remains the same. Plato’s views, according to the information given by Laertius, attribute the assertion that : “There are things that are divided into parts, the Partials, and things that are not divided into parts, the Undivided.
In the classification of undivided are defined: The Unit in Arithmetic, the Point in Geometry and the Νote in Music. In the Ancient Greek world, as well as in today’s world, the concept of the “Point” was the subject of many debates with many positions and oppositions. In Croton, Italy, the Pythagoreans attached particular importance to the concept of the “point” which was a special foundation of their geometry and cosmic theories.
In Cartesian Geometry the point is identified with its coordinates, i.e. having a three-dimensional Euclidean space, the point is defined as the ordered triad a, b, c, where all three letters are real numbers defining length, width and height. And if we consider that in multidimensional spaces or in a particular space, its dimensions are defined by its coordinates, which it is possible that the points define the coordinates and are themselves without substance, reduced to “nothing”.
In the theory of Relativity where there is no real distinction between time coordinates, we can choose a new set of coordinates, determined by specific points, where, e.g. the defined new spatial coordinate is a combination of the old first and the old second coordinate. Here too, the points are present. The question that ultimately arises is : while in spacetime coordinates are created by defined points, points have no entity and reason for existence.