Appendix A
Terms of Use and Definitions Defined
The Concept and Label
For the purpose of clarity I have created these definitions for the concepts that have been presented. Most are terms from the Mechanics branch of Physics. When speaking of Dimensions, Time and Space, Matter, Energy, Gravity, and the like, it is important to be clear as to implication of the concept under consideration. Each complex physical definition tends to rely on the simpler ones used to define it. By the rule of logic, if one fact out of a hundred is wrong, then the actual logical conclusion, using all one hundred facts, that is reached is wrong.
The purpose in writing these definitions is to make an effort to have something of tangible means to help define and describe the view of reality that is presented. The following definitions are intended to help one understand the universe around oneself, including that piece of space two feet in front of oneself. In this work, the concept Label will usually be in a larger bold font on the line above the actual definition. A concept is a concept about a concept. The concept of a concept is a concept. The name for an object, or thing, is the Label, that the originator of the concept, or discoverer of said object or maker of said thing, thought was best in describing, in summation, that particular object, thing, or concept. That is at least until the translators got a hold of it.
Since there is more than one Label for an object, concept, or thing, or more than one originator of a concept i.e. in different countries in different times, there tends to be more than one person that comes up with some word for the same concept, thing, or object. There are many descriptive words in the American form of the English language. Certain words have more than one meaning or concept attached to it, and a plethora others that tend refer to the same one concept, object or thing. If you have any real questions, consult the definition of the Label of the concept in question in a dictionary and look for the next closest meaning.
Information from Internet related sources are reprinted here for your convenience. Websites, such as: “HyperPhysics, (http://hyperphysics.phy-astr.gsu.edu/hbase/hph.html)”, were used as a source of information on many Physics related topics. The use of block quotes will frame the information from said source, and other sources, when the topic of definition already has had some previous discussion that is relevant to the concept at hand.
As an example, in the following quote from the HyperPhysics web site, “Physical Units” is the beginning of where Physics starts out, and is an example of ‘concepts and labels’.
Physical Units
Mechanics is the branch of physics in which the basic physical units are developed. The logical sequence is from the description of motion to the causes of motion (forces and torques) and then to the action of forces and torques. The basic mechanical units are those of Mass, Length, and Time. All mechanical quantities can be expressed in terms of these three quantities. The standard units are the Système Internationale or SI units. The primary SI units for mechanics are the kilogram (mass), the meter (length) and the second (time). However, if M, L, and T denote the units for these quantities, in any consistent set of units, then the scheme of mechanical relationships can be sketched out.
In the above quote, “…if M, L, and T denote the units for these quantities, in any consistent set of units, then the scheme of mechanical relationships can be sketched out…” in essence, sums up the main thrust of this part of this paper.
Primary Fundamental Physical Concepts
The Point
The point is a concept in need of a definition. Mathematically speaking, a point marks the beginning and the end of a line, or an intersection of two or more lines. One can define a point to give it meaning and use one or more dimensional concepts to do it.
What does a point look like? What are the properties of a point? A point is the collinear view of a line, which is perceived as a ‘flat’ sphere that has the same perpendicular view from all ‘sides’, within our universe. This ‘flat’ sphere shaped point has no dimension or volume in our ‘reality’, yet it exists to define dimension and form said volume.
Why use a sphere to model the Point? A sphere is the most common shape in the universe. All stars and planets become spheres. A sphere is the simplest of shapes and forms, for it has one center point, one single surface of the same shape as the center point, and one single continuous edge easily seen from any angle, 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 represents the simplest of geometrical concepts from which all other concepts arise. Within each point reside all the properties needed for dimensional constructs.
Extension - as Distance
Distance is one measure of the concept of Extension. Extension is that which exists between two points. One takes two points, anchors the first point, and calls it the Origin, and then one takes the second point and Extends it away from the origin and Distance is what is created in between. Another term that could be used is displacement.
One point is the origin, the second point, not the origin, is moved away from the origin, this action creates Distance between the two points. You move from the origin to the second point, you are crossing that created distance. The term “magnitude” is also used synonymously with distance. Extension is the Structural Vector.
Extension - as Time
Time is also a measure. When creating a Hypervector of Extension, Time is also involved. Looking at Extension in linear terms, its units are distance-time, where time and distance are in a direct relationship to each other. From a physics point of view, distance is mathematically identified, quantified, and standardized. In the International System of units, MKS, the unit for distance is the “meter” which is the “M” in MKS. From a physics point of view, time is also mathematically identified, quantified, and standardized. In the International System of units, MKS, the unit for time is the "second" which is the "S" in the MKS.
Vector - as Hypervector
A Vector is the snapshot concept of what forms between two points that had been moving relative to each other. A simple vector is a distance or magnitude that has a direction, and always referenced to an Origin point (0,0, ... ). A Hypervector of Extension is a 1D concept object that is a construct. The 1D construct forms edges. A line, considered in mathematical terms, is a 1D formation. The mathematical Line and the physical Hypervector are synonymous terms for the same concept object.
The two points can be referenced by one or more dimensional constraints. As an example a 1D point is referenced by: x. A 2D point is referenced by: x, y. A 3D point is referenced by: x, y, and z. A 3D+1T space-time point is referenced by: x, y, z, t, and a 4D point can be referenced in a linear context by w, x, y, z all the while, the object of contention, the Hypervector, that which is between the two points, which in spite of the number of dimensions used to reference each of the two points, is the object that is formed, that of a Hypervector, is a 1D object, in a multiple dimensioned environment. Operations that use vector calculus are of particular importance in solving the physical concept problems that were suddenly presented to this writer. A vector quantity is a static concept because it is after the fact, as in the past. The Hypervector concept that is used here is one of a dynamic structural physical relationship between the various primary concepts of dimension by extension, change, and a form of dynamic mass that create the past with the present from the future.
Linearity
Linearity, 1/Distance, or per unit of distance, is the inverse of the concept of Distance. This is not the same as the negative “x-axis” of a flat geometrical plane. Measurements over linear distance, of use, of increases or of decreases, all occur by traveling though completely, or applying over completely, one unit of distance or its equivalent. There is no true ‘negative’ distance.
Time-Flow
The concept of Time is what flows from point-moment to point-moment. The Flow of Time is the Dynamic vector. As dynamic, somewhat cognizant and volumetrically stable blobs of matter, we are at the moving point of the tip of a time vector, the other end of which is anchored at ones origin. Time is about change. Each Flow of Time vector becomes a ‘warp thread’ of reality. The Flow of Time vector appears to be collinear to the direction of one’s travel through Space. The normal passage of time is linear. The measure of time is scalar.
From a physics point of view, time is mathematically identified, quantified, and standardized. In the International System of units, MKS, “second” or sec., or “S,” is the unit of measure for time, and the “S” in MKS.
Frequency
Frequency is the concept of repetition and cycles. Frequency is also the scalar inverse of the concept of time flow, 1/t, or per unit of time. 1/t is also defined as: “Apply.” If you apply something, you do it over time. If you apply something regularly, you do it frequently, or at some frequency, such as “once per day”.
Frequency is the number of like events, or number of like objects formed, that transpires, in any given unit of time. The nature of sound includes the concept of frequency. Sound is transmitted in air by alternating non-linear high and low pressures traveling in linear waves. Vibration in matter and the transmission of Light also have the concept of frequency in their very nature as well.
From a physics point of view, frequency is mathematically identified, quantified, and standardized. In the International System of units, MKS, “cycle/sec,” or “Hertz” is the unit of measure for frequency.
Dynamic Mass
Dynamic Mass is the concept of a unit vector with ‘punch’. Dynamic Mass is a tangible abstract concept. Dynamic Mass is what gives, matter and energy, reality. Dynamic Mass is a fundamental property of matter, energy, momentum, inertia, and gravity/thrust/push. Dynamic Mass is not “inertia”. Mass has been given a physical unit of measure, in SI units, which is the amount of matter in a Platinum / Iridium cylinder, of specific volume, with the label of “kilogram”, a scalar number, and is the ‘K’ in MKS.
The concept of “Dynamic Mass” used here is not a scalar quantity, nor a static-past quantity, instead it is considered to be the Causative Vector. Dynamic Mass is an ‘at Cause’ unit vector that forms physical, structure producing, relationships between the various primary concepts of dimension by extension and time, that evolves as a dimensional property of the point. Dynamic Mass is that property of a point that gives solidness to matter. Dynamic Mass is what gives, and takes, the effort behind the action of change. Dynamic Mass is the ‘Woof’ Thread of reality. Dynamic Mass is what causes stuff to be.
When it comes to the structure of everything, it is the direction and application of “mass” that is different in each concept. Mass, distance and time are each expressed in the concepts known as ‘matter’ and ‘energy’. Albert Einstein is known for his concept of Energy, E, as E = mc2, in that equation Einstein has said that mass and energy are equivalent through the application of a specialized squared velocity term, “c2,” with ‘c’ being the speed of light in a vacuum. Multiplying (velocity x velocity) is equal to (distance x distance) / (time x time) = d2/t2. Dynamic Mass is a dynamic unit vector responsible for the construction of ‘Space-Time’ (see Append. C). Dynamic Mass can become Energy, E, by multiplying mass * (velocity x velocity) as E = m x d2/t2.
Matter can also be described in similar terms. Matter has mass, has volume, exists for some time, is capable of rotation on three different axis, generally is composed of neutral and charged particles and is a function of Hypersurface geometry. So, using this information one can define Matter, M, as M = md3t, or mass x distance x distance x distance x time. Here, Space-Time, is defined as d3t, and when multiplied by Dynamic Mass, becomes matter.
Specific-ness
Specific-ness is Inverse Dynamic Mass. Inverse Dynamic Mass is the concept of 1/Dynamic Mass. Inverse Dynamic Mass is a vector, just like Dynamic Mass, its direction, in our frame of reference, is opposite to that of Dynamic Mass. Inverse Dynamic Mass is a 1D unit vector like Dynamic Mass. Together, the two opposite vectors form another dimensional axis with can be parallel or perpendicular to any of . In various relationships with distance and time, it gives information of ‘specific’ nature in per unit of mass, such an example would be Specific Volume = m3/kg.
Rotation
Rotation is the concept of a change of a point of view or direction. To look “back” is to see where you have come from, i.e. the origin. In order to look back, you need to “rotate” to change your point of view, or direction, to look “back” in the “opposite direction” from which you came. We can now rotate to change our point of view, which is the direction that we are currently using to see one of the six main directions available to us relative to our original orientation or point of view. In the MKS standards, a unit of rotation, or a change of direction about an axis is the Radian.
In terms of a geographical nature, the compass with its North, South, East, and West has long played a role in changing one’s direction to one degree or another. When we were children, we learned about rotation in our exercise and play. The three actions that describe rotation about an axis of the human body are: twirling, summersaults, and cartwheels.
“Up”, “Forward”, “Left”, “Back”, “Right”, and “Down” are all different directions to which one can rotate. Forward is the reverse, or opposite, of Back. Left is the opposite of Right. Up is the opposite of Down. Left, right, up, down, all are perpendicular to forward as well as to back, which is the opposite of forward, and a second person sitting next to you, looking in the same forward direction as you are, has a collinear or “parallel” view, and when applied to the viewing of a line, gives the end view of said line, which becomes the point view.
Spin
Spin is the concept of continuous rotation about one, or more, of the spatial axes. Spin is the continuous rotation of vectors about their origin point. Spin can take place around the middle point of a vector or about one of the ends of a vector. Rotation can occur on or around any of the three perpendicular axes of any 3D object moving through time. A half rotation, or spin of ½ is the constant Pi, 3.14159… that is also equal to ½ of a circle of Radians, or 180 degrees. A spin of one would be equal to 2Pi, or 6.28318, or 360 degrees, which is equal to one cycle, a unit of Frequency. Spin is fundamental to the structure of matter. Structural unit vectors are continuously rotating forming “dynamic virtual surfaces” that are maintained.
Dimension
Dimension, in the physical world of reality, is one complex concept. Distance, in looking forwards and backwards, only gives a dimension of just one. One has just the one line with its two directions of forward and backward and the magnitude of the line that is created between the two ends of the one line, or vector. If one has right and left as well as backwards and forwards, with forward and backward being perpendicular to left and right, one has two dimensions which can define a surface. One dimension, as viewed from the perpendicular of the direction of the dimension, can be seen as a line, or edge, or as a point from an end view. A surface as viewed from a perpendicular angle is flat, while it’s end view is a line or edge. Three lines, each perpendicular to the other, form three dimensions.
We live in a universe that has dimension and more than just one. Space has three dimensions that give us our volumetric proportions of length, width, and depth. Time is tied at the hip to space and is the fourth dimension. There is more than just the four. Each set of dimensional relationships, formed at each intersectional point in the fabric of space-time, change on a continuous basis according to the frames of reference between the observer and the observed. Dynamically created 4D Hypersurfaces, on 6D Hyper-structures, form, what we are, and the environment, in which we exist.
Hypersurface
Hypersurface is the concept of a 4D Geometrical Surface formed by a 6D object. There are several Hypersurface types. Each represents a configuration of a ‘dynamic vector point’, as viewed in a 6D environment. What we view as a quantum point of matter is really a Hypersurface that is dynamically produced by rotating structural unit vectors, and it is the shape of the geometry, which is determined by the scalar length, and ratio, between unit vectors and the direction that the unit vectors are pointing, (i.e. +1 or –1, or 0) that gives the Hypersurface its form and function.
In string theory, the extra dimensions are small and wrapped up into tiny little strings. Here, they’re just the opposite. The extra dimension is huge, just like the other three; it is just rotated ninety degrees out of view from the other three. What we gain with just one extra dimension of extension is one more degree of freedom in rotation. Having one more degree of freedom, with one extra dimension of extension, allows us to imagine our 6D object with its 5D surface from more than just the end view. It should be understood that the mechanical branch of physics gives us two ways to view any given situation involving ‘motion’ (e.g. another example of duality or polarity ;)) and thus two forms of units, the familiar linear dimensional point of view and the rotational point of view.
Linear, straight line, orientation, is easier for most people to understand. It is easy to progress from 1D to 2D to 3D and so on. In terms of rotation it is relatively easy to rotate about any of the three linear axes with which we are familiar. We know we can make lines and objects with edges that are straight. We can travel in straight lines if need be. In the rotational motion arena, wheels, motors, gears, bend, shear, frequency, etc. are familiar concepts that involve rotational motion. Mathematics has evolved several different coordinate systems. The most familiar linear coordinate systems are the 2D Quadratic (x, y) and the 3D Cubic (x, y, z). The familiar rotational coordinate systems are 2D Polar (r, <), 3D Cylindrical (r, <, h) and 3D spherical (r, <, <). These 3D coordinate systems are integrated 2D surface elements wrapped tightly around a 3D object in a 3D+t (4D) environment. The third dimensional element for any volume is given by integrating ‘dr’. Various String Theories use multi-dimensional concepts and inevitably get caught up explaining it from a linear point of view. Depending on which ‘S’-Theory you examine, one finds anywhere from 9 to 11 dimensions being used to explain how things got started, and how we got ‘here’ from ‘there’. These 9D to 11D include the other concepts of time and mass. Einstein already sort of gave us eight dimensions using extension and time in his Cosmological Constant.
Each degree of rotation available allows for one more degree of freedom. With rotation about each of the normal 3D axes, for any given scalar ‘r’, we have three planes of rotation, with each plane of rotation perpendicular to the other. Each plane of rotation becomes an infinite 2D surface element. The fourth degree plane of rotation freedom provides for 12 dimensions (12D) using ‘four dimensions by extension’, ‘four dimensions of Time Flow’, and ‘four dimensions by Dynamic Mass’. Linear is a concept that mankind has developed. The Universe uses a rotational coordinate system.
Given that, from two different perpendicular views of a rotationally formed cylindrical structure, or even a spherical object that looks the same from all views in 3D, other than an end view, the two views are the same in shape, size, and detail, could be considered the same view, then a 6D environment or structural object might be mistaken as a 5D. Depending on the point and vector relationships that create the Hypersurfaces, many wide ranging concepts can be described. From one equation, two unit vectors, formed head to tail, that rotate in planes perpendicular to one another, forming a third “dynamic vector”, one can create seven different Hypersurfaces from a point all by changing the scalar values of each unit vector. Each Hypersurface is a composite of two or more unit dimensional vectors.
Below is a single math equation that gives the geometry for 7 different Hypersurfaces and the one point at 0,0. Each of the seven of the Hypersurfaces has its mathematical inverse. R1 can be a composite vector such as ‘velocity’ which is composed of unit vectors of distance and time in an indirect relationship, d/t, and R2 can be a different composite unit vector of an indirect relationship between mass and time, m/t, by multiplying the two relationships, one can get a relationship such as (mass x distance)/(time x time), i.e. “force” :
Photons have been shown, via repeatable experiments, to have all the classic characteristics of the particle, wave, and field. It is a matter of perspective between the target experimental device and the photon. How the photon is viewed by the ‘surface of contact’ in the experimental device determines how the photon data is interpreted. In the list of concepts, particle, wave, and field, each concept is dimensionally higher in geometric form as one proceeds to the right of the list from the left most in the list. The rotating heliostat, the spectrum-spreading prism, and the photoelectric diode and transistor are examples of surfaces of determination of photonic data. The photon itself is something else altogether.
Polarity
Polarity is the concept of complimentary opposites. General physics uses the concept of ‘spin’ to develop the concept of 'polarity'. It talks about ‘fermions’ and ‘boson’ statistics. One-half integer and integer spin respectively. It gets more complicated and less easy to understand. Given the geometrical perspective of the Hypersurface equation, one can easily see from of the seven or so available 6-dimensional shapes how polarity might come about. In terms of direction, we found that left and right, up and down, front and back were opposite of each other. Some other terms one might see are: Plus and Minus, Positive and Negative, and Heads and Tails, Male and Female. When one looks into a mirror, one sees their opposite. Every vector or line consists of at a minimum of two points that are separated by some distance. Each end is the opposite polarity of the other. Magnets, like the earth, have two opposite poles, a north and a south. The North Pole of a magnet is considered to be the Positive pole as is its South Pole the Negative.
When it comes to our view of a Hypersurface, there is only one side and one 'pole' which is the end view of the axis of rotation. The axis of rotation is always perpendicular to the Hypersurface in view. Depending on the geometry, the Dynamic Hypersurface that is formed, is viewed only as ‘outside’, or only as ‘inside’. Any 'surface', including a Hypersurface, is geometrically still a 2D dimensional element and not a plate with two sides. One might think that polarity might not apply to the Hypersurface, however they would be incorrect. Polarity is of primary importance. The ends of a vector could trade places. Thus, what was a positive pointing vector is now negative pointing vector and what was outside is now inside and visa versa. Invariably, in our universe, any and all surface that is present conforms tightly the volumetric shape that forms it. Thus, surface, a 2D concept, flows over a 3D volume of some shape. In examining any kind of matter that one can name, removing any surface material only reveals more outside surface below it. It is the projected geometry shape of certain Hyper-Objects that gives rise to polarity. There are also neutral geometry Hypersurface objects that do not give rise to polarity.
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