Euclidean Pi and its rivals (AppMenk)
Although since Einstein all physicists know about the curvature of space and even of time, the unique status of their cherished number Pi has in no way been challenged although it is a typical Euclidean flat ‘un-curved’ number or a theoretical (transcendental) factor, which may fail to do its job properly in real curved space. In my natural number geometry I deal with 3 different values for Pi derived from one rational number: 800/81 or 9.87654321. The elaboration of this simple natural number logic and geometry is undertaken because of the believe that mathematics is the key to the ‘workings of reality’ (Wirkungen der Wirklichkeit).
Einstein did mention a different value for Pi in curved space and said it would be smaller, because with higher velocities a circle circumference would shorten on an equal remaining diameter. I beg to differ regarding this constant diameter because with high velocity rotations there occurs a vortex and when we imagine the vortex we see it before us in our washing basins when the water is sucked out by gravity and vacuum and gets regulated by the vortex geometry, so that for instance air (substance!) can get in. Space also curves similarly as a vortex on the small scales so the centre point of the vortex does not at all lie in the plane of the upper circles of its boundary. We see in the mechanics of the vortex the contraction of a circle movement. And this contraction is expressed with a bigger value for Pi, because the radius contracts with constant circumference.
This theory of space and natural number geometry is the basis of an ontology and regards curvature of space as a local state of the all-pervading aether-deepfield. I hold the view that there is contraction and expansion of space and that the curvature of space around a star is a contraction of space, forming a higher density which density eventually condensates into the liquid/gaseous body of the star. The gravity lensing of stars is a typical example of space contraction where the geodesics come closer together around the body and its inertial field surrounds it as a shell. We see here how the fabric of space is moulded by the star-mass and its gravity field, its ‘lee-field’ in my parlance. In this view stars are the inner border points of space
The closer to the surface of the body, the denser space and its pixalls, so an object is heavier because its density of pixalls is greater, where the pixalls form the mass of the body, on top of the mountain you are lighter than in the valley. Gravitational acceleration is accumulation of space-pixalls in the body. The specific density of space would be generated by cosmic field-pressure, which results from all energy sources in space taken as a whole (variation on Mach principle). The acceleration from gravity is two-fold. Because of the general field-pressure (G?), the general pressure gets higher near a body, because the counterpressure is more and more blocked by the body, this creates the lee-field of the body, the so-called gravity field, which is directed towards the blocking object.
The so-called ‘attraction’ is actually ‘lack of counterpressure’ and the acceleration derives from the object ‘gaining weight’ because of the higher density of pixalls it acquires while falling, and this higher density in the body generates more pressure from the general field, kind of feed-back, which causes the acceleration.
On the moon this lower density of pixalls made the bodies much lighter, it may also have contributed to the ‘distortion’ of the space-perception of the astronauts, which mainly must have been caused by the greater curvature of space on the moon surface, which made things seem smaller and closer than they were. (see Appendix Menkaure etc.)
The existence of gravity waves is no surprise for those who hold on to the time-honoured “aether”-view where the idea of a medium filling space is fundamental, the ‘there is something rather than nothing’-idea, (not Leibniz’ relational ‘non-existing’ space) and if we know one thing about a medium it is that it transports waves. The kind of waves it transports and to what degree depends on the specific qualities of the medium (permitivity) and the source. Waves cannot exist without a source and a medium because they are no ‘things in themselves’, they exist thanks to the medium or media that allow and transport energy. So the much hailed proof of gravity waves is also the proof of space as a medium and then we are back at the “aether”-view.
Lorentz maintained that space has a kind of qualities and substantiality which he called ‘ether’ (1906), Einstein in 1920 in Leiden, agreed with him.
“Zusammenfassend können wir sagen: Nach der allgemeinen Relativitätstheorie ist der Raum mit physikalischen Qualitäten ausgestattet; es existiert also in diesem Sinne ein Äther. Gemäß der allgemeinen Relativitätstheorie ist ein Raum ohne Äther undenkbar; denn in einem solchen gäbe es nicht nur keine Lichtfortpflanzung, sondern auch keine Existenzmöglichkeit von Maßstäben und Uhren, also auch keine räumlich-zeitlichen Entfernungen im Sinne der Physik. Dieser Äther darf aber nicht mit der für ponderable Medien charakteristischen Eigenschaft ausgestattet gedacht werden, aus durch die Zeit verfolgbaren Teilen zu bestehen; der Bewegungsbegriff darf auf ihn nicht angewendet werden.” (Einstein Leiden 1920)
It is rather incredible that space is still treated as a void by most (Relativity) scientists, while Einstein himself has declared that the general theory of relativity is unthinkable without an ether, although he was unhappy with the concept’s connotations. In many ways this approach here often agrees with Einstein’s analysis of space, especially when he says things like : matter is a state of space, space as oscillating field of singularities.
In my specific approach of the ether electro-magnetism is a ‘state of space’, which emerges when triggered, this is the reason why light does not get tired, it is carried by the ‘deep-field of infinite energy’ (‘luminiferous/lightcarrying aether’), so a ray of light is an intrinsic state and excitement of the motionless (as a whole) but vibrating deep-field of space particles (pixalls)(strings??).
The ‘photon’ does not exist, in this view, it is the sparking of the zero-dimension of pure light through the centres of the space-pixalls, the elementary fields with a zero-dimension black hole at their centre. It is the vortex curvature of the black hole that obscures the pure light at its centre. Since the pure light is in every pixall, everything is made of pure light. The Yin-Yang symbol is a perfect expression where the white segment is the pure light and the black spot the black hole of the black space segment in which the white spot is the spark of pure light.
This approach also solves wave-particle duality, the detected photon is just the spark of a local space-pixall partaking in the light-wave. Matter has no eigen-substance (self-substance) and neither has the photon.
Here we get to the heart of what I call the zero-dimension, this is the borderpoint of space. So space is borderless on the outside but bounded inside in every point of space. If we see every point in space as borderpoint we can imagine what the zero-dimension is by means of the horn-torus (donut), which has one centre point which is the boundary of the whole torus surface in just one point, the 2-D representation of the surface of this unique torus is a square. The whole dynamic of space at the smallest levels is spherical incoming wave pressure with toroidal outgoing radiation; this is the absolute rudimentary level where the basic geometry of space is supposed to play out in resonances and it is simplified geometrically by reducing the horn-torus to a square and the sphere to a circle. This is the basis of the natural number geometry I propose.
…… physicists are still trying to work out the bizarre implications of a minimum length. In superstring theory, a mathematical relationship called T-duality suggests that one can shrink a circle only so far. As the radius contracts, the circle gets smaller and smaller and then bottoms out, suddenly acting as though it is getting bigger and bigger.
“This behavior implies that there is a minimum ‘true size’ to the circle,” Dr. Giddings said. Many believe this will turn out to be roughly comparable to the Planck scale.
We see here the interesting shrinking of the circle which cannot but end in a ‘horn-torus’, the basis of my space-pixall geometry and even more surprising is that there is this tipping point when it suddenly grows bigger and bigger. This is a possible inversion of my idea that at the smallest levels there is a spherical contraction and toroidal expansion. It is though heartening to see how close my model gets to string-theory at the most elementary level. Like strings my model is purely logical, but based on geometry.
My approach is a rather different worldview and cosmology, at times ‘out of the box’ and ‘original’, but mostly based on the same accepted scientific data. The point is that the conventional interpretation is left behind here and a radical new approach is its replacement, or rather a latter day Pythagorean approach which advocates the view that most fundamental interactions are based on resonances and that, since resonances are natural number phenomena, the natural numbers are quintessential for understanding the ‘workings of the world’ or ”Wirklichkeit”.
I think that Pythagoras would have spent some time studying the systematic regularities I have found in natural numbers in geometry and in number-logic, but I am afraid that today’s mathematicians won’t spend their time on the work of an outsider with no credentials. It is true, I have no credentials in math or physics, but as a philosopher I base my knowledge mainly on principles, logical reasoning and a peculiar private mathematics, which never stops teaching me and connects spheres of life which seem completely foreign to each other on the face of it, but go back to the same geometry time and again.
In the natural number logic that I introduce there are several numbers for Pi, to accommodate different number-associations (curvatures). One of these, which is a square root 2 number, is 2.22222…V2 (20V2/9) called: Qute, the root of a rational number, 9.8765432098…… = 800/81, a new universal Pi-squared for the torus formula. The other two roots of this number 9.87654321 are 22/7 and 28/8.91 (= (4 x 7/11) x (10/9)^2). **
To give an immediate example of the Qute number’s operation and what it reveals as a substitute for Pi (how ‘cute’ it is), we turn to Kepler’s coefficient for dense-packing: Pi / V18 = 0,740481… which was just recently (2017) canonized as a now proven mathematical truth. When you substitute Qute for Pi, the two square roots cancel each other and you are left with 20/9 over 3 which makes 20/27 = 0.7407407…. and here we immediately have a handsome picture, a cube of 3 in 27 unit-cubes holds approximately 20 unit-volumes in balls. I hope this makes a difference for the reader, note the minimal numerical difference of only 0,00025…..
This way many formulas with Pi and V2 can be translated into natural number ratios, which give unexpected ‘global’ insights in relationships that normally are obscured by Pi’s incompatibility.
Rational numbers have periods, which periodicity is a sign of a cycle or a wave. These periods are also related to primes (via repunits).
Via the repunits one can prove that with every power of 10 more numbers, only 1 to 6 new primes are added, so it gets less and less. Nobody thinks that suddenly there will appear a close cluster of more than 7 primes in successive powers of 10 numbers.
The flexible value for Pi is, I think, one of the great achievements of this natural number-logic. The deeper idea being that Nature calculates in natural and rational numbers expressed in flexible geometries, where points are not connected by rigid lines but by waves and where geometric forms vibrate and morph into one another at all levels.
The most prominent characteristic of the calculus is that all is expressed in the numbers 1-14, which includes the first 6 primes, it is all utterly basic and complementary .
**[[there is the V3 version of Pi in either 18/9.9xV3= 3.149…(concave-Pi) and 1,813 xV3= 3.1402… (1813= 49×37, smaller than Pi!)(convex-Pi). For V5 we have 13.91/9.9 xV5 is 3.141788…(very close!), then there are V7 as 1.187 xV7=3.1405…, which is virtually the same as one V3-Pi as 3.1404… both convex-Pi and lastly the V11-Pi here is: 9.38/9.9xV11= 3.1424… (9,4/9,9V11= 3.1491, like V3-Pi) which is again a concave Pi. It must be said here that the roots of 5, 7 and 11 hardly ever play a role, but these conversions show how numbers can be moulded into natural number ratios and made fit for the system]]
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Der erste Denker, der den reinen monistischen “Substanz-Begriff” in die Wissenschaft einführte und seine fundamentale Bedeutung erkannte, war der große Philosoph Baruch Spinoza; sein Hauptwerk erschien kurz nach seinem frühzeitigen Tode, 1677, gerade hundert Jahre bevor Lavoisier vermittelst des chemischen Hauptinstruments, der Waage, die Konstanz der Materie experimentell bewies. In seiner großartigen pantheistischen Weltanschauung fällt der Begriff der Welt (Universum, Kosmos) zusammen mit dem allumfassenden Begriff Gott; sie ist gleichzeitig der reinste und vernünftigste Monismus, und der geklärteste und abstrakteste Monotheismus. Diese Universal-Substanz oder dieses “göttliche Weltwesen” zeigt uns zwei verschiedene Seiten seines wahren Wesens, zwei fundamentale Attribute; die Materie (der unendliche ausgedehnte Substanz-Stoff) und der Geist (die allumfassende denkende Substanz-Energie). Alle Wandlungen, die später der Substanz-Begriff gemacht hat, kommen bei konsequenter Analyse auf diesen höchsten Grundbegriff von Spinoza zurück, den ich mit Goethe für einen der erhabensten, tiefsten und wahrsten Gedanken aller Zeiten halte. Alle einzelnen Objekte der Welt, die unserer Erkenntniß zugänglich sind, alle individuellen Formen des Daseins, sind nur besondere vergängliche Formen der Substanz, Accidenzen oder Moden. Diese Modi sind körperliche Dinge, materielle Körper, wenn wir sie unter dem Attribut der Ausdehnung (der “Raumerfüllung”) betrachten, dagegen Kräfte oder Ideen, wenn wir sie unter dem Attribut des Denkens (der “Energie”) betrachten. Auf diese Grundvorstellung von Spinoza kommt auch unser gereinigter Monismus nach 200 Jahren zurück; auch für uns sind Materie (der raumerfüllende Stoff) und Energie (die bewegende Kraft) nur zwei untrennbare Attribute der einen Substanz. (Ernst Haeckel, Weltraetsel)
Pyknose
Vogt nimmt als die gemeinsame Urkraft des Weltalls, als die universelle Prodynamis, nicht die Schwingung oder Vibration der bewegten Massentheilchen im leeren Raume an, sondern die individuelle Verdichtung oder Densation einer einheitlichen Substanz, welche den ganzen unendlichen Weltraum kontinuirlich, d. h. lückenlos und ununterbrochen, erfüllt; die einzige derselben innewohnende mechanische Wirkungsform (Agens) besteht darin, daß durch das Verdichtungs- oder Kontraktions-Bestreben unendlich kleine Verdichtungs-Centren entstehen, die zwar ihren Dichtegrad und damit ihr Volumen ändern können, aber an und für sich beständig sind. Diese individuellen kleinsten Theilchen der universalen Substanz, die Verdichtungs-Centren, die man Pyknatome nennen könnte, entsprechen im allgemeinen den Uratomen oder letzten diskreten Massentheilchen des kinetischen Substanz-Begriffes; sie unterscheiden sich aber sehr wesentlich dadurch, daß sie Empfindung und Streben (oder Willensbewegung einfachster Art) besitzen, also im gewissen Sinne beseelt sind – ein Anklang an des alten Empedokles Lehre vom “Lieben und Hassen der Elemente”. Auch schweben diese “beseelten Atome” nicht im leeren Raume, sondern in der kontinuirlichen, äußerst dünnen Zwischensubstanz, welche den nicht verdichteten Theil der Ursubstanz darstellt. Durch gewisse “Konstellationen”, Störungszentren oder Deformirungs-Systeme”, treten große Massen von Verdichtungscentren rasch in gewaltiger Ausdehnung zusammen und erlangen ein Uebergewicht über die umlagernden Massen. Dadurch scheidet oder differenzirt sich die Substanz, die im ursprünglichen Ruhezustand überall die gleiche mittlere Dichte besitzt, in zwei Hauptbestandteile: die Störungs-Centren, welche die mittlere Dichte durch Pyknose positiv überschreiten, bilden die wägbaren Massen der Weltkörper (die sogenannte “ponderable Materie”); die dünnere Zwischensubstanz dagegen, welche zwischen ihnen den Raum erfüllt und die mittlere Dichte negativ überschreitet, bildet den Aether (die “imponderable Materie”). Die Folge dieser Scheidung zwischen Masse und Aether ist ein ununterbrochener Kampf dieser beiden antagonistischen Substanz-Theile; und dieser Kampf ist die Ursache aller physikalischen Processe Die positive Masse, der Träger des Lustgefühls, strebt immer mehr, den begonnenen Verdichtungs-Proceß zu vollenden, und sammelt die höchsten Werthe potentieller Energie; der negative Aether umgekehrt sträubt sich in gleichem Maße gegen jede weitere Steigerung seiner Spannung und des damit verknüpften Unlustgefühls; er sammelt die höchsten Werthe aktueller Energie. (Haeckel, id.)