The Dimensions of Space and Time |
"Space" is defined as: a boundless three-dimensional extent in which objects and events occur and have relative position and direction.
These 3 Dimensions are mathematically portrayed as three orthogonal lines called the x, y, and z-axis. Defining space this way, creates “volume” in space, viewed as a cube, called "Cubic" and portrayed as the Cartesian coordinate system in algebra.
This theory relies on the fact that “space” really has one abstraction called "length" and units called meters (m). And the “volume” of space is really the one abstraction of “length” in three orthogonal orientations given the different names of length, width, and depth depicting the direction.
Thus, a “dimension” must be understood not to necessarily be a different abstraction, but also to include an extension of the same abstraction in a direction that is otherwise impossible to define.
Accordingly, Daniel Webster defines "time" as: a non spatial continuum that is measured in terms of events which succeed one another from past through present to future. Considered the 4th dimension, time definitely exists in physical phenomena measured in units of universal “change” called seconds (s).
As "length" is the basic abstraction of “space”, “change” is the basic abstraction of "time" - defining the 4th dimension as only the first dimension of time called “change”. The abstraction known as “change” is proven to propagate in directions that are otherwise impossible to define giving rise to 3 dimensions of time.
An accurate definition of time must depict personal experience and be applicable to the laws of science and reason. A perspective of time based on the sphere appears to be the only reasonable concept that depicts the reality of this universe, knowing that its anti-axiom, space is based on the cube.
Time is viewed as the Polar coordinate system or Trigonometry, representing 3-Dimensional spherical “instances”. The views of space and time are related by the sine function of time and the Cartesian geometry of the sphere (Spherical Trignometry). A general concept in calculus proves that these functions are differentiated by the multiplilcative inverse (1/x), focused by the exponential function (ex) and calculated by a factorial power series: xn/n!.
A single dimension of change can define velocity (change in position), but NOT acceleration (change in velocity – or (change in change) in position). Assigning dimensions of “change” to “time” is as natural and valid as assigning dimensions of “length” to “space”. In fact 2-D and 3-D time are already assigned to various phenomenas.
Acceleration already defines 2-D Time and the Electric Field, Flux, Current, Force, Resistance and Potential as well as a general definition of power already defines 3-D time – howbeit lacking a concise “meaning” to associate 3-D time to an abstraction of change. The question arises: what does s3 convey as far as motion is concerned or for that matter what does s2 convey? Physics already promotes the squaring and cubing of time, without defining it. Is it the area under the space-time curve?
The three dimensions of time are called linear (duration), variance, and repetition (frequency) depicting orthogonal ways in which change is noticed. In each dimension of space, the length has left, right, and center and in each dimension of time, the change has past, present, and future.
3-D time can be seen in any “event” such as going to the store, but the strict reliance on time in computer programming provides analogies with precise dimensional analysis while using well-defined temporal terminology non-existent in most domains. Change is also “solidified” in processor “instructions”.
An analysis of Parallel processing used by vector processors to simultaneously execute various “vectorized” instructions accurately depicts the dimensions of time in Run-Time or big “O” notation.
The Linear time is the time it takes an algorithm to run. The sequence of instructions (changes) forms a "duration" using one dimension of change with components of past, present, and future.
The Variance is the distribution of instructions over multiple processor elements (vectorization). The more variance, the faster the run-time or the quicker time is perceived (time flies when your having fun - activity). Distributing instructions (change) over several processors (or divide and conquer algorithms) involve the simultaneous execution (change) of each element - illustrating the 2nd dimension of time.
The Frequency is the "loops" in the algorithm - either performing the distribution or repetition in a single processor. The run-time is most affected by the "loops". As an algorithm's "duration" can be proven to be a function of the "distribution", its "distribution" can be proven to be a function of "loops".
"Distributing" is assigning instruction(s) to each processor - provably equivalent to "looping" through each processor. Furthermore, any loop in a single processor can be proven to be equivalent to looping through each processor.
Even an irrational number has an algrorithm to computed the successive digits. The loops in this algorithm is in fact the frequency of irrationality!
The acceleration is the derivative of the velocity. Accurately portraying time, frequency is postulated to be the derivative of (or change in) the acceleration called "jerk". Circular motion is assumed to have a “continuous” frequency or "change in acceleration" definable by a cubic equation – mathematically verifiable (time normalization).
Acceleration's current definition “circles” velocity's motion or change in position (seconds) forming change in change raising seconds to the second power (s2). And harmonic frequency is theorized to “sphere” this change forming change in change in change raising seconds to the third power (s3).
"Squaring" the length is multiplying the length by the width defining area. "Circling" the change is multiplying the change by the variance defining "activity". Thus, Area is related to width as activity is related to variance. The more things vary, implying a second dimension, the more a 2-D activity is perceived in it.
Likewise, "Depth" is viewed as the 3rd dimension of space, and "frequency" or “harmony” as the 3rd dimension of time. "Volume" is considered ALL 3 dimensions of space and the “Field” is considered ALL 3 dimensions of time.
As length, width, and depth defines an object; the duration, variance, and frequency defines an event. And as 3-D space unites to form the "volume" of space, 3-D time unites to form the "volume" of time –which unifies the field by defining its unit with an equation that solely relates mass to light!
It is impossible to unify anything without forming a “Unit”! The theorized unit (s3) will be proven to define mass, the ONLY unit based on an artifact, via light - effectively removing the artifact without theorizing a mass generating God particle. However, in order to accurately explain the UFT, the serial concept of time must be normalized.
Next - The Normalization of Time
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© 2001 By Daryl E. Waite (dewaite1@hotmail.com) (All Rights Reserved worldwide)