1/4/98

Spatial Dimensionality by James Clifford Cranwell

Abstract:
Spatial Dimensionality is a completely new way to understand the way dimensionality actually works. It is based solely on irrefutable logic. And although it is easily understandable by anyone, it requires an open mind and a completely new way of thinking. If we look back in history, there was a point in time when everyone thought the Earth was the center of the universe and the Sun revolved around it. Even the educated people of the day wouldn't have had any doubt to the validity of this concept, based on the fact that you can actually see the Sun rise and set (supposedly orbit) around the Earth on any given day. Extremely accurate measurements of the Suns supposed orbit could have been taken. Leading the whole scientific community to believe they have proved something to ten or twelve decimal places...not only falsely confirming the theory, but also giving a fundamentally incorrect foundation for others to build upon.
Even though you have precisely measured something,
you may be absolutely wrong
Therefore, even though everyone thinks something works in a certain way and can actually see it with their own two eyes, there is still an allowance for something happening in a completely different manner, and there is always an easier explanation or more than one way to explain something. There can even be a completely new math based on particle lengths, it doesn't mean everything else is incorrect... it just means this can also be correct and deserves consideration.

Spatial Dimensionality

Contrary to popular belief... nothing is even remotely solid. At the sub atomic level it is well known the nucleus radius to electron orbital ratio is one hundred thousandth. That makes the volumetric or spatial difference one quadrillionth. 
   (4/3)Pi 1^3                  1 
  ----------------  =  ---------------------  =  one quadrillionth
 (4/3)Pi 100,000^3     1,000,000,000,000,000
This ratio is approximately the same size as a spherical dot above the letter " i " (the proton) on the fifty-yard line in a football stadium (the orbital) everything else is empty space. So if we think of or visualize a huge sphere the size of a stadium (a small moon for instance) in reality the amount of actual continuous mass (just nuclei) is equivalent to the solid dot above the " i " (made of only protons) cut up into one quadrillion times 1,000 billion billion pieces and evenly dispersed (that's one quadrillion "i" dots to fill the sphere (ignoring sphere packing) then 1,000 billion billion atomic radii to fill the "i" dot). That's why the moon is only there when someone is looking at it...if we couldn't see vibrations of electron energy, the moon would be completely unnoticed.

Differential geometrics

When we differentiate, we get the instantaneous change in whatever equation or shape we consider. It's easy to visualize because the starting equation or figure, for instance a 3-dimensional cube ( y = x 3 ), gets lowered down a degree in power or dimension. i.e. ( y' = 3x 2 ) this can be equated to three planar 2-dimensional sides of the cube or the instantaneous change needed to increase the length, width and height (volume) of the cube, so, this means to instantaneously increase volume, tack on area to half the outside surface. Taking this one step further we arrive at ( y'' = 6x ) this is simply six 1-dimensional lines or the instantaneous change needed to increase the length and width (area) of the three planes, every plane needs two lines (length and width) to increase its area, three planes times two lines equals six lines total. Now it gets even easier...six points ( y''' = 6 ) are the instantaneous change needed to increase six lines in length (notice the six points are zero-dimensional). Now we arrive at ( y (4 ) = 0 ) this is the instantaneous change needed to bring the six points in or out of existence. 
                  x4 
  (integral y) = ---     y =x3    y'=3x2    y''=6x     y'''=6     y(4)=0  
                  4     
                         cube     planes    lines     points     null  
                (4-D)    (3-D)    (2-D)     (1-D)     (Zero-D)
A big problem occurs when we try to integrate something cubic ( x 3 ) into the fourth dimension...in this case ( integral y ), we have an exact mathematical representation of it ( x 4 /4 ) and if x = 1 we know this is equal to 1/4's worth of fourth dimensional volume (tesserarea?) but, what shape is it? Is it a snapshot in time? Is it an hypercube? Is it a mysterious visitor from the fourth dimension?

The cube isn't solid

Remember, nothing is even remotely solid, so you will rack your brain trying to visualize the integration of a solid or in this case an actual misconception. Any 1-dimensional object is a line. Any 2-dimensional object is a plane, but that's a slice of a supposed cube, and can't be thought of as for instance a sheet of paper because, if we integrate enough of them into a stack, we have a solid cube of paper and by now we know nothing is solid. The cube can't be solid. So that form of thinking is simply wrong (note: The one dimensional line would also have to be in segments, and although we can actually integrate lines into a plane...the lines in this case are never arranged parallel so they won't form a continuous plane). The cube isn't solid but since it is there, it must be made of something. If we call the basic unit of whatever the cube is comprised of a particle. The particle must be capable of conveying information, for instance electro-magnetic vibrations. And since there are different frequencies and/or strengths of vibrations with multiple simultaneous combinations, a zero-dimensional single point particle would be incapable of achieving this. It can spin or move but there is no chance of Simultaneity. The next possible alternative is the 1-dimensional line or string (any intrinsic universal characteristic will always be the simplest and at the same time most efficient option). The string seems to be the shape of choice in this case. On a musical instrument, a violin for instance, the string can convey a multitude of vibrations, tones and harmonics. This means there can be a lot of simultaneous information transmitted along a one-dimensional string. There is no need to attempt theoretical construction of a particle made of 2-dimensional planes because...if we integrate enough of them into a stack...

Particle Integration
...So, the basic building blocks of particle construction must be line segments or strings. We could actually have 2-D planes but, they would have to be made of strings and therefore be mostly space. Their arrangement makes all the difference... The way this actually works is by using axial directions as dimension. The basic unit of the x 3 variety is the X-Y-Z axes shaped particle, this is three strings joined at their centers. If in this example y = x 3 and x = 1, then the three axis will be 1/3 in length (X, Y and Z are 1/3 long) with a total length of one. All widths are infinitesimal. When we differentiate x 3 we get 3x 2 , this is 3 plus sign or XY axes shaped particles with a total length of 3, that makes 6 axis with 1/2 length... this is also the exact amount of length needed to add one quadratic XY particle to every axis of the original differentiated particle giving the XYZ an instantaneous change. ...Working this in reverse we see that as we integrate something into a higher power it changes the shape by adding an axis and it shrinks in size giving it a greater density. So the mysterious fourth Dimensional object may still look exactly like a supposed 3-dimensional cube but it will be of much greater density and its basic (atomic) structure will be of tetrahedral axes shaped particles, 1/4 total length f (1) = x 4/4 = 1/4 with 1/16 length axis (one fourth of 1/4 total ), it gets small very rapidly. More particles are needed to fill any volume because of the shorter lengths and tighter pack, ergo higher density. Now it is easy to see... in a field of 2-D ( XY ) particles we can only traverse horizontally and vertically. When we bump this up one dimension into 3-D we also have the toward and away axis, alas we still can't move on a diagonal, for that is reserved for the higher dimensions.

Spatial dimensions
An Abbott Flatlander living on a two dimensional plane would actually be living on an infinity of dimensions if he can turn or move through every angle or vector direction on the supposed plane. Remember...there can't be an actual continuous plane. An actual working two dimensional model of space would be an infinite array of 2-D axes shaped particles arranged in a plane with the negative or expansive force vibrating through their continuum (matrix). In this 2-D model light is coerced into traveling in straight lines in only two directions (This model can also warp or flex, forcing the curvature of light). If you took enough 2-D particles and curved and connected them into a spherical surface shape, it would be misinterpreted as 3-D. Nothing is actually 3-D and/or solid. Now that we know the basic workings of particles at the quantum level and we know vibrations occur in every possible direction, a 3-dimensional particle will not sufficiently transmit vibrations along a diagonal, 3-D doesn't work. The particle capable of angular conveyance must be of higher dimension, have the most efficient shape to pack space with the least amount of material and have the smallest angle of symmetrical invariance. It turns out to be a particle with 10-dimensions or ten axes, any more axes and they won't connect or pack. This can be visualized as ten axes joined at their centers with every individual axis terminating on the vertices of a Dodecahedron or the set of twenty points...... 

    ( +-x/y, +-xy,   0)  where y = (Ö5+1)/2 = 1.6180339887498948482...     
    ( +-xy,   0, +-x/y)        x = G /(20Ö3) 
    (   0, +-x/y, +-xy)        G = 1 /(10Ö26-1)c
    ( +-x,   +-x,  +-x)
This allows for vibrational conveyance in every possible direction, is stackable hyperbolically and will pack space "face centered cubic" this corresponds to a lattice (arrangement, not size) which the center of every sphere or particle is the set of all points (x,y,z) where x, y, and z are integers adding up to an even number. This axial concept allows for an actual visual of higher dimensions. Now it is easy to see how any length, for instance g = 1/(10Ö26-1)c, divided up correctly can be a direct representation of a particle(s).