Infinity and Infinitesimals - Part I
"One is the Onliest Number" I am going to devote considerable discussion to the topic of this essay because the understanding of the true nature of quantity, or numbers, in terms of Reality is essential to changing the basis of one's personal paradigm from separation to Oneness.
In conventional mathematics, an infinitesimal is defined as a number that is greater than zero, but whose value is too small to be measured.
Such a concept seems as refractory to understanding as the concept that Infinity is a value so large that it cannot be measured.
Both Infinity and infinitesimals have the quality of being unmeasurable, so for purposes of space/time Experience, the infinitesimal and Infinity have been disregarded in favor of the fixed, tangible measurement.
However, measurements in general are of very limited value without a reference measurement.
For example, to know what a "meter" is, you must have a reference meter that you can use in order to verify that, in fact, you have measured a true meter.
Otherwise, a meter might be different for everyone who measures it.
The surprise is that, even with a reference meter, no two meters are measured to precisely the same length because accuracy is dependent both upon the limit of resolution of the measuring device and upon the one doing the measuring.
So, is there a reference that we can use no matter what the measurement in question is? Truth is that the only reference we have that never changes is Infinity, but Infinity cannot be measured.
Infinity is the Reference because Infinity is the fundamental essence of Reality.
Remembering that whole dimensions are of infinite measure, all other "references" are shown as arbitrary fractions of dimension, or dimensionals, along whatever whole dimension the measurement is made.
Recognizing the need for a reference, scientists have sought reliable standards to be used as reference measurements.
The ideal, or most reliable, standard would be a finite measurement that is absolute, or that never changes.
Because no such measurement exists, scientists have settled for standards that rarely change rather than one that never changes.
However, choosing any measurement greater than zero, yet less than Infinity is, in truth, an arbitrary choice.
Infinity, while Absolute, is not a measurable quantity, so it cannot be recognized as a standard in the realm of finite measurements.
But Infinity is the only true, or absolute, Reference, so what does this mean in terms of finite standards and measurements? What this means is that any measurable quantity, when compared to Infinity, is so small that a true (absolute) measure cannot be assigned to it, only a symbolic or relative one.
Furthermore, any measure which, by definition, is a limit, cannot have any meaning unless compared to another limit.
Thus, the true meaning of measurements is relative, not absolute, and this understanding opens the door to a new conception of numbers.
This also means that all finite measurements meet the definition of infinitesimal when compared to the true Reference, Infinity.
Thus, the quality of the infinitesimal, rather than being of mere esoteric interest to mathematicians, is of vital importance in understanding Reality.
(continued in Part II)
In conventional mathematics, an infinitesimal is defined as a number that is greater than zero, but whose value is too small to be measured.
Such a concept seems as refractory to understanding as the concept that Infinity is a value so large that it cannot be measured.
Both Infinity and infinitesimals have the quality of being unmeasurable, so for purposes of space/time Experience, the infinitesimal and Infinity have been disregarded in favor of the fixed, tangible measurement.
However, measurements in general are of very limited value without a reference measurement.
For example, to know what a "meter" is, you must have a reference meter that you can use in order to verify that, in fact, you have measured a true meter.
Otherwise, a meter might be different for everyone who measures it.
The surprise is that, even with a reference meter, no two meters are measured to precisely the same length because accuracy is dependent both upon the limit of resolution of the measuring device and upon the one doing the measuring.
So, is there a reference that we can use no matter what the measurement in question is? Truth is that the only reference we have that never changes is Infinity, but Infinity cannot be measured.
Infinity is the Reference because Infinity is the fundamental essence of Reality.
Remembering that whole dimensions are of infinite measure, all other "references" are shown as arbitrary fractions of dimension, or dimensionals, along whatever whole dimension the measurement is made.
Recognizing the need for a reference, scientists have sought reliable standards to be used as reference measurements.
The ideal, or most reliable, standard would be a finite measurement that is absolute, or that never changes.
Because no such measurement exists, scientists have settled for standards that rarely change rather than one that never changes.
However, choosing any measurement greater than zero, yet less than Infinity is, in truth, an arbitrary choice.
Infinity, while Absolute, is not a measurable quantity, so it cannot be recognized as a standard in the realm of finite measurements.
But Infinity is the only true, or absolute, Reference, so what does this mean in terms of finite standards and measurements? What this means is that any measurable quantity, when compared to Infinity, is so small that a true (absolute) measure cannot be assigned to it, only a symbolic or relative one.
Furthermore, any measure which, by definition, is a limit, cannot have any meaning unless compared to another limit.
Thus, the true meaning of measurements is relative, not absolute, and this understanding opens the door to a new conception of numbers.
This also means that all finite measurements meet the definition of infinitesimal when compared to the true Reference, Infinity.
Thus, the quality of the infinitesimal, rather than being of mere esoteric interest to mathematicians, is of vital importance in understanding Reality.
(continued in Part II)