Tuesday, October 7, 2008

Six Dimensional Geometrical Objects:

On the scale of the very small, one has QED. On the macro scale there is us, at the mesoscale there is everything that is on the surface of this planet. On the cosmological scale, one has stars, star systems, galaxies, globular clusters of galaxies, and even larger structures. Then there is GR. It takes a lot of the very small to create a small portion of the very large. It takes a star to create slightly bigger chunks of the very small. What is in common: A spherical coordinate system.
The universe is made up of photons, protons, electrons, and neutrinos plus space, time, and gravity. The neutrons are composed of an electron and a proton, and they convert between neutron to an electron and a proton, can then recombine to reform a neutron. Each conversion process is assisted by the interaction of a neutrino, so the neutron is not unique, however it appears that the neutrino acts as the ‘catalyst particle’ within the nucleons of a nucleus. Neutrinos are possibly, wholly responsible for the reaction.

Spherical Geometry, it seems, is the common link. Here, Time is considered to be a dimension and a vector. We live in a universe that has more than just four dimensions. Space has three dimensions that give us our volumetric portions of length, width, and depth. Vectors of unique unit type, and their inverse, opposites go to form each linear dimension, yet everything that we have been taught is in terms of linearity, instead of terms of spherical rotation.

A Dynamic Hypersurface, is based on spherical coordinates, and is viewed as a linearly mobile, rotating, point sized structural object composed of one or more Relationship unit-vectors, in a 4 degrees of freedom of rotation (4DFR) Multi-vectored Space-Time-Mass environment. Each Hypersurface type represents a configuration of a 4D Point Structure, and as viewed in the diagram, from our environmental view they all tend to look the same:

In string theory, the extra dimensions are small and wrapped up into tiny little strings or M-Branes and P-Branes. Here, they’re just the same as the other dimensions. The extra dimension of extension is just ninety degrees away from everything we know and see. What we gain with just one extra degree of freedom in rotation is one more dimension of extension. Having one more degree of freedom, allows us to imagine a view of our 4D environment collapsed to a curved surface on a 6D Hyper-object from more than just the parallel or end view. Four degrees of freedom apply to Dynamic Hypervectors of Extension, Time-Flow and Dynamic Mass.

This is our 3D+t view of any of these seven 6D structures, no matter where we looked, or what direction we were looking, and should one come across one of these, try to remember it, however, typically one won’t even see the above views as the individual Dynamic Hypersurfaces are too small to see, unless somehow they are combined to form a macro-sized structure viewable to the naked eye. Each structure has the same two D-R unit-vectors; each is a 2DF Hypervector rotating in one plane perpendicular to the other. Our view of any of the structures, rotated 90 degrees left, right, up, or down typically would look the same. Because of the circular nature of the structures, trying to visualize the structures, in linear 2D or 3D, or 4D, or 5D just by math has not been the best approach mainly because of the lack of any real experience to base the math. It is like giving Mr. 3D a choice of another axis’ to rotate about but all he can see is an infinite number of directions to turn (a full circle of them) to but can’t fathom how to physically turn about any one of them. However, maybe he can rotate himself and a section of his ‘Plane of Reference’ through the higher dimensional gelatin to gain a better perspective of his gelatin.

These are the 5D and 6D side views of the 6D rotational geometrical structures that form everything from the smallest of structures to the largest of structures. The curved ‘fabric’ spacetime Einstein had imagined exists in six dimensions as curved spacetime, with each dynamic surface element (dx, dy) being ‘flat’, just like any 2D surface in our 3D1T world, as our current correct observation tells us that spacetime is ‘flat’ in 4D. Both cases are true. The Dynamic Hypersurface (see cross-sections above) is exactly a ‘surface’…over a six dimensional object that supports a flattened 3D1T (4D) ‘volumetric’ structure within the Hypersurface. This condition is exactly similar to that of Mr. 3D in his 2D1T world. Yet, these same structures are in evidence in our world, we just can’t see them from a side view like they are shown above because we are linear 3D1T and they are 6D. Surface of a sphere is calculated from 4πr^2, and by integration to get the volume of the sphere, 4/3πr^3, by further integration we can achieve a formula of calculation for a Hypersurface as 1/3πr^4.

The Point (4DFR)

A Point is a concept in need of a definition. What are the properties of a point? For some, a point is the beginning, for others it is the end. A Point is the concept of how the universe began, as an origin, i.e. the concept of the Origin of the Universe and it’s beginning as a Point.

Concisely then, all the clear, cognizable concepts, were creatively conceived, concentrated, completely compressed, and confined to a coalesced object. All concepts were conceived and clearly created though an act of cohesive, coherent, concentric, cognizing by a considerable comprehensive consciousness, with but a compunction, did conceptualize and compact all concepts into one coalesced concurrent condensed Point of Origin.

'In The Beginning’, the first Point is the universe, and is the Origin of all Points. When the Big Bang went “BOOM,” The One Point became many. It was a geometrical exponential expansion: 1, 3, 27, 19683, 7625597484987, etc. The Big Bang, “The Origin of All Points” having occurred, we can now start to define more complex concepts now that we have more that one point with which to work.

Mathematically speaking, a point marks the beginning and the end of a line, or an intersection of two or more lines. A Point also has the same mathematical definition and includes the collinear dimensional view of a line (looking parallel along the line, i.e. an end view); otherwise, it is perceived as a ‘flat’ sphere that has the same perpendicular view, as viewed from all ‘sides’, within our universe. This sphere shaped Point has no dimension or volume in and of itself relative to our “4D Space-time”, yet it is there to define dimension. A sphere is the simplest of shapes and forms, for it has one point of origin, one single contiguous surface of the same shape as the center origin point, and one single continuous edge easily seen from all angles, which is also the same shape as the center point from which it is formed.


The point of The Point is that the concept of The Point, as a sphere is:
  • The sphere is the simplest of all geometrical concepts from which all other concepts arise.
  • Within each Sphere reside all the properties needed for higher dimensional constructs.
  • The universe naturally uses a spherical coordinate system.

Dynamic Point Laws
    • Each Point can act as an origin.
    • Each Point can act separately.
    • Each Point can act in concert with any other Point.
    • Each Point is tied to all other Points.
    • Each Point adds or transfers its properties to the next and in turn receives a property set from said next Point.
    • All Points can act together.
    • One Point can affect all the other Points.
    • All of the other Points can affect just one Point.

What we see as a point in our 4D environment is really a ‘cross-section’ of something that has more than four dimensions. To imagine as an example, we can talk about ‘Mr. 3D’. Mr. 3D has 2D in terms of extension, and 1D of time so that he knows motion. He knows about left and right and up and down, but not about forward or backward. He can’t see ‘In’ or ‘Out’. He can move around objects in his 3D environment, but all he sees is a dot, a line, or a line of dots or moving lines and dots. Concepts like ‘square’ and ‘circle’ are abstract and tough to visualize or prove. The only way he can determine a shape is to move around it. He can only rotate left or right about an axis that is normal to his plane of ‘reality’. He can move in any direction save for the direction of the axis of rotation that is ‘normal’ to his plane of existence. He cannot rotate ‘in’ and ‘out’ of his plane, only within it. Now we can introduce various objects into his plane of existence. Our objects are 4D in our ‘Hyperplane of Existence’. When we move our 4D objects to intersect his plane, he can only see their cross-section edge. If we were to put our finger through his plane, he would see only solid lines that were impassable, after awhile he might find that he could go around but just not through. As we move our finger into his plane he would notice that the line he sees is changing length. He is able to determine distance, angle, color, and his 2D position relative to the position of our finger. Mr. 3D has limited view and knowledge of anything beyond his 3D (2D plane, 1D time) environment.

When thinking about objects, that appear to be singularity orientated, such as particles and Blackholes, the cross-sections that we see in our environment are actually 5D Hypersurfaces imposed on a '6D Hyperspace' structure / environment. Dimensions noted here, are always perpendicular to each other. All four 'linear' dimensions of Extension are perpendicular to each other. We can only see in 3D. The fourth is 'just around the corner,' out of view. A Point in 4D, is a line in 5D, is a curved surface on a 6D object. Time-Flow and Dynamic Mass are Hypervectors similar to that of Extension.

Points are the basis of everything. It is the properties that we can ascribe to any one Point that creates differences from any other Point and since we have laid out the concept groundwork of the Point, it is now easier to see that Dynamic Hypervectors are formed between any two Points. One Point acts as the Origin Point the other acts as the Dynamic Point. Hypersurfaces have designated scalar truth table values such as [±1, 0] which yields the structure for ‘Infinite Hyperplanes’. Dynamic Path Hypersurface Elements are formed by rotational (α, ß, (R1,Θ), (R2, φ)) Dynamic Hypervectors, with four degrees of freedom of rotation. The first degree is about the longitudinal direction of a unit-vector, ‘R’, and yields the ‘plus or minus’ Polarity value of the scalar, while the second, third, and fourth degrees of freedom is the rotation of a Dynamic Point at the end of the dynamic longitudinal section, (r = Pd – Po) acting as the head of the arrow, about an Origin Point. It should be noted that π equals one degree of freedom of rotation. In the One Equation, the first half of the equation uses 0 to 2π, this equals 2DFR, while the second half of the equation uses -π/2 to π/2, the range of which is equal to π, 1DFR, together they yield a 3DFR.

The ‘first’ degree half of the above equation yields a circular perimeter created by a 2DF Dynamic Point (2πr). The rotating D-R unit-vector will form in situ an ‘Infinite Hyperplane’ (πr^2), 2D1T. Any two Infinite Hyperplanes, acting in concert together, will always be perpendicular to each other, thus Infinite Hyperplanes exist in all directions, thanks in part to Heisenberg’s Principle. An Infinite Hyperplane is one of seven different Hypersurfaces. The ‘second’ degree half of the above equation describes a Dynamic Hypersurface Path Element, with limitations, that goes through ‘zero’, in a rotational plane that is perpendicular to the rotational plane of the ‘first’ degree half of the equation, (2D1T), that due to the rotation of the first plane, (2D1T), forms two of the 6D ‘linear’ dimensions. The 6D ‘linear’ dimensions are really 4D1T1M ‘not so linear’ dimensions.

The One Equation (4DFR)

The One Equation, with just 3 of the degrees of freedom of rotation described, given a Linear 6D frame of reference, will generate multiple Dynamic Hypersurface geometries. Just two Dynamic Relationship Vectors, comprised of one or more unit-vectors, head to tail, creating a third Dynamic Hypervector, with scalar values that constantly change, each DRV rotating in a plane perpendicular to the others, can create seven different Dynamic Hyperspace structures from three Points all by changing the scalar values of each D-R unit-vector that is between each Point. The scalar value of the Dynamic Hypervector is always in flux, subject to the strictures of Heisenberg's Principle of Uncertainty. One scalar can be 1/10th scale of the other. Each DRV  is comprised of Extension, Dynamic Mass, or Change vectors, as derived from the Primary, Secondary, and Tertiary concepts as laid out in Appendixes A, B, and C. It is briefly noted here that the value of Pi, 3.14159..., in radians, is equivalent to any 1DFR. Typically with 3D, one also has 3DFR.

In this writing, the 1DFR is considered to be the longintudinal rotation motion of the Dynamic Hypervector, in relationship to its direction and motion of Extension.  The direction of the angular momentum is perpendicular to the linear extension of the DH.  The scalar value of the DH is in constant Change, and is induced by Dynamic Mass. The DPHE that is dynamically formed, and follows the strictures of the One Equation. As each DVR changes scalar 'length,' so to does the shape and scale of the Dynamic Path Hypersurface Element. The 'P' can represent the dynamic 'Point', as well as the dynamic 'Path' it can follow during a Rotation. The Path Element is perpendicular to the Dynamic Hypervector that forms the Path Element. The DPHE is what we experience. Each DPHE can comprise any physical relationship that can form between 'distance', 'time', and 'mass'. It will be shown that DPHE's can form at any scale, thus from the scale of the 'quantum' to the scale of the 'cosmic', everything comes from the same geometry, and the One Equation.

The linear vector concepts of distance, time, and mass, employ the first degree of freedom of rotation during formation. Each random Point spins about an arbitrary longitudinal axis. When the spin axis any 2 Points are aligned, such that the 'spin' axis of each of the 2 Points is collinear to the spin axis of the other with their angular momentum also in the same direction between them, much like an arrow in flight with feathers that cause the shaft to spin about its long axis. This process causes the 'linear' vectors to form dynamically and the 'spin' provides for the concept of ‘Polarity’.

Dynamic Hypersurface Path Elements form in situ as the DRV's rotate about their ‘origin Points’. The Dynamic Hypersurfaces are well defined in six ‘linear’ dimensions as opposed to five. Each Dynamic Hypersurface Path Element represents, at a maximum, 4 linear, 4 temporal, and 4 specific dimensional constraints and at a minimum 1 linear, or 1 temporal, or 1 specific constraint.
To properly develop the concept of Dynamic Hypersurfaces, that form structures in a Dynamic Hyper-massive-spacetime, we will start with the most primary of concepts, the Point.