In today's world of mathematics, numerically defined concepts are invented that somehow defy any possibility of definition. Mathematicians distinguish at times the indistinguishable. Take the case of what are referred to today as dimensionless numbers. Numbers that reflect dimension refer to mass, length, velocity, electric current, time, concepts along these lines. While dimensionless numbers refer to those of trigonometry, the number of degrees in a circle, the numbers relating to exponents of powers; that sort of thing.

We can readily understand what the mathematicians are attempting to do. They are distinguishing between different number series and counts, those that reflect specific aspects of spacetime, and those that do not. The dimensionless numbers refer to constant number series, similar to what the ancients employed in their reckoning systems. Only the ancients reversed the order of counts. To them, the 360c of the day-count calendar was highly significant, and therefore those numbers relating to the 360-degree sectors of a circle were historically significant. The numbers relating to the constant number series 1, 2, 4, 8, 16, etc., were apparently less significant.

Today, as we have explained in other essays, the 1, 2, 4, 8, 16... constant count series is employed in the use of the binary system, given its relationship to the behavior of electric current and switches. What is dimension in one system, and dimensionless in another system, in fact, wind up being one and the same thing. The ancients appear to have employed any number series as either a constant series or an historically significant series. Their understanding seems to be have been more relational in this sense, and less concerned with the definitions.

In other words, even an historically significant number series could be employed as a constant number series, for in terms of computation, it matters not which number lies on a particular side of the equation. That understanding of quantified reality would be called the theory of relativity today. From the perspective of computation, one may employ any number as a constant or as a variable, in relation to specific spacetime events.

As defined, there is really no such thing as a dimensionless number; nor, is there such a thing as a constant number. Yet, these concepts assist us in comprehending the computations that we effect regarding the behavior of matter-energy. The closest thing to a dimensionless number would be a symbolic number, of a completely assigned theoretic meaning, with no relationship to any other spacetime event. Such a number does not exist.

The number of degrees within a circle (i.e., 360c in our system) would appear to represent a neutral, dimensionless number, unrelated to mass, time, length, velocity, or such specifics as electric current. Yet, that number, 360c, relates to the spacetime event known as a circle, and within ancient artwork it would appear that the ancients knew that a circle could contain any number of sectors (260, 360, 364, 378, 584, etc.). They were not limited by thinking that the 360c was a dimensionless, constant number. In fact, one could exchange the 360c count of the number of degrees in a circle for the number of days in a year, or in a multiple cycle of years (i.e., 3600 years of 360 days, etc.).

Every number reflects dimension; in that every number reflects spacetime coordinates, even if those coordinates are those of a circle. For a circle represents a specific relation of spacetime: the number of sectors within that particular space, at a given time and in a given relationship. The translation between dimensionless numbers and numbers with dimension is simply that, a translation in spacetime. Every number is measurement; two by itself makes no sense. In fact, it is impossible for a number to exist without a relationship, without being defined dimensionally, without being relational to all else that exists. Two something, two anything means mass; means space; means time. Dimensionless would signify two nothing, which is a contradiction of terms: for nothing can never be two.

You might conclude that we are having fun with this idea about dimensionless numbers; and we are. But, essentially, nothing that exists is without dimension ---even the so-called dimensionless numbers. To understand mathematics in any other manner leads to the kinds of affirmations that we read all the time about ancient reckoning. Traditional scholars tell us that the ancients erred in using a 360 day-count calendar. Yet, these same scholars do not stop to think about our own employment of a 360-degree circle, which we have defined for all times, and all purposes and reason within out mathematical and geometric systems of today.

We would never dream of teaching our students to think that a circle may consist of 260 degrees, or possibly 378 degrees. That is simply put, a silly idea. Yet, the ancients appear to have comprehended, as any school child today understands, that a circle may be divided into as many sectors as one wishes and is physically able to attain. Yet, all of our so-called dimensionless numbers within trigonometry, relating to the number of degrees in a circle, and the numbers relating to exponents of powers, deny many analytical possibilities. It is difficult for this author to comprehend how we have been able to do so many of the things that we have accomplished in science. We have accomplished them basically because reality, the behavior of matter-energy, continues its path with or without our theoretical definitions.

Nothing that exists is without dimension, and to state this can only confuse the students more than they already are confused with a theoretical math that relies more upon alphabets than upon numbers. All that exists, every spacetime event, every form of matter-energy, reflects dimension. The numbers of trigonometry, the degrees of a circle and angles, reflect fixed proportions within the numbers themselves, within spacetime, within the proportion and boundaries (dimensions) of a the circle. They reflect length, distance.

The numbers relating to exponents of powers reflect specific relationships of the numbers themselves, which we have seen reflect even the behavior of the planets in their apparently circular orbits around the sun. One may simple refer to Kepler's Laws in this respect.

One might find comfort in conceiving of a number, such as 4 miles per hour as being with dimension, and 4n, a particular exponent of another number as being dimensionless. But, both numbers reflect and accomplish the same thing. Four miles per hour is relational to a number per number. By ignoring such a simple fact, we often find the common explanation of powers and exponents of numbers, as the cube representing a number three times itself. A number to the fourth power is defined as multiplying that number times itself four times. Obviously, this verbalization of the exponents is impossible to effect.

For never does one multiply a number times itself any number of times more than once, when one effects the square of a number, as in 2²:

2² equals, or is achieved by multiplying the number two times itself:

That is the only time that we ever multiply a number times itself; at the level of the square. After that, we multiply the number times the product of the square, and the product of the cube, and so on.

3n, or the cube of a two is not 2 x 2 x 2. Obviously, we may write this procedure in this shorthand manner, but a very significant element is missing. And, yet, much of the writing within mathematics, and even within the treatment of the ancient reckoning systems is offered in this shorthand manner. Ancient, historically significant day-counts are constantly offered as being, for example, 2 x 2 x 2 x 2 x 2 = 32; or, as 7 x 9 x 13 = 819. In fact, most scholars even deny the possibility that the ancients employed the procedure of multiplication. It would appear that they simply utilized the method of doubling and halving the numbers; or, trebling numbers and dividing by three.

The selected examples above are actually:

2 x 2 = 4 x 2 = 8 x 2 = 16 x 2 = 32

7 x 9 = 63 x 13 = 819

And, even the previous registrations are a shorthand form of the procedure. Yet, in spite of this, many insist on saying that powers treat the procedure where a number is multiplied by itself x number of times. Even the symbolic form of 2 x 2 x 2 x 2 x 2 appears to be saying the same thing, but we know different; yet, we do not say what we know.

Therefore, the dimensionless number 2n is actually a two dimensional (2 x 2) number that produces a third dimension (4). The dimensionless number 3n is a four dimensional number (2 x 2 = 4 x 2) that produces a fifth dimension (16). The dimensionless number 4n is a sixth dimensional number (2 x 2 = 4 x 2 = 8 x 2) that produces a seventh dimension (16). And, so on for the remaining infinitely so exponents. But, we must caution, that all of this remains within the symbolic confines of our contemporary definitions; we are not treating these examples as we would from the perspective of the ancient math and geometry. We are merely reviewing the terms of contemporary language in math.

The ancients appear to have interchanged any number with any other number, while constantly knowing how to relate one number within itself and in relation to all else. So, one may have a number series (as one dimension), and then a symbolic exponent (another series), along with a constant series (still another dimension), etc. All numbers are interchangeable within that system, and it matters not which one reflects specific aspects of spacetime, because we know that they all reflect spacetime; that is the first thing we must consciously know how to relate. All numbers are relational and multi-dimensional. Word-concepts begin to limit the wealth of perception of the numbers themselves.

The baseline of the Great Pyramid has been cited as having been originally set at 756 feet (although there are differences of opinion on this point). In the square of this particular number, one might consider the exponent (2n) as being a dimensionless number in relation to a number with dimension (756feet).

756² = 571536

The 2n cipher is dimensionless in that it does not represent a mathematical procedure, other than a symbolic one within contemporary mathematics, meaning that its symbolism represents actually a shorthand form for writing:

756 x 756

Now, as soon as we move to the cube of this expression, the shorthand form is deceiving:

756³ = 432081216

One may imagine: 756 x 756 x 756 even though, we know that this is not true in the sense that it is impossible to actually carry out a computation in this manner, since we cannot ignore the fact that an important step in the computation (571536 x 756) has been hidden from view by the notation of exponents. So, in this sense, one could concede that a dimensionless number does not actually exist, but then we seem to be facing a circular argument (no pun intended).

The ancient may have conceived of an alternative path of computation:

Such a computational procedure may be telling us the significance of number series, such as 756, 567, 576, 657, and related numbers within the series, such as 7056. For it is tempting to think of the ancients as having employed a system of computation based upon the simplest principles possible.

Especially, when we consider the fact that 3168c and 153c are historically significant numbers themselves, and we see that they relate with ease to computations of powers of three.

There are two historically significant counts within this computation: 27c and the number series 5076c. Through simple addition one may arrive at the cube of 756c. The difference between the 576c and the 5076c is represented by the maya long count itself:

The difference between the 756c and the 7056c kemi counts is represented by the kemi 63c:

The ancients may have been speaking in a mathematical language whose simplicity of structure we have yet to comprehend. Both the ancient kemi and the maya employed the 360c calendar. We have observed in other essays how the 666c lies between the kemi 756c and the maya 576c, with a difference of 90c in either case.

576 + 90 = 666 = 756 - 90

The symbolism may have reflected the ease of computations. Thirty six may be read as "three sixes" in a sense. Both systems seem to have employed the concept of the sacred nine. And, the maya had a time period that was 1872c fractal, when halved is 936c.

The difference between 9 and 36 is represented by the number 27c, another ancient kemi count (9 + 27 = 36); whereby 27 mediates nine and thirty-six. Within the ancient system of reckoning, one obtains the view that the variables are constant, and the constants are variable. Every event reflects dimension; nothing lies outside of the dimension of spacetime. At one moment a particular number may lie on one side of the equation, and at another moment it may lie on the opposite side of the equation. In fact, the very concept of "equation" comes into question; the very idea of what is relational must be reviewed all over again.

One may comprehend that the historically significant number, 360c, is specifically determined, albeit erroneously chosen, number. Yet, one may view this number as representing a variable one minute and as a constant the next. The situational context and analytical moment determine and define the particular concept to be employed for any given event. On a circle of the Great Cycle, which has often been cited as representing 25920 years of the Earth's revolution around the Sun, pi would be symbolically in correspondence to the number 2268c (as we have analyzed previously). The number 2268c has been identified as an historically significant number/fractal coming out of the ancient Nineveh culture.

For such an occurrence of numbers to appear in this relationship, one must necessarily invoke the concept of happenstance; there is no way that this coincidence of mathematical terms could have been consciously chosen by the ancients. And, yet, this author suspects that the ancients knew much more than traditional scholars are willing to concede.

The dimension of the ancient numbers reaches far beyond the confines of contemporary procedures. Relating numbers like 576, 5076 or 756 and 7056 might appear to be farfetched in today's mathematics, but we are treating a system of analysis whose basis we have yet to fully recognize, much less comprehend.

Any distinction between numbers with dimension and dimensionless numbers, within the ancient reckoning method, appears to disappear rapidly with the computations.

It matters not which computation we choose, the historically significant numbers and their fractals appear on either side of the equation.