What’s the Point?

Preston Harold gives us a mathematical lesson on the concept of a “point.” In this installment we will quote him at length as we prepare to discuss how Jesus understood the concept, which we will explore in the next post. Now, for your pleasure, Preston Harold:

Zero must be seen as the whole, beyond examination, and therefore its measure, unapparent, is expressible only in negative terms, so that zero’s division must correspond to: (-/- = +). But this simple division is equivalent only to taking the diameter of a circle; to define the center point in its being, the product of this division must be divided by itself, so that the whole equation of zero-divided must correspond to: (-/- = +/+ = +). Again, the positive sign (+) is presented as answer, just a s the configuration of the cross appears when one determines the center point of a circle by bisecting its diameter. The center point defined by the cross cannot be seen as a correspondence to negative-one or positive-one; it is neutral in its position and must correspond to one-neutral for one-whole. The point itself cannot be defined, except as it is defined by the cross (+), that is, in the definition of the cross itself.


Nicomachus said that a point is “the beginning of a line, or an interval, but is not itself line or interval.” The point enfolded in the cross is not the beginning of either line, but is an interval in both lines, and is the one point so arranged and sustained by the opposing horizontal and vertical lines or “forces.” One might say that this point is defined in negative, positive, and specific terms, so that it is the only point in actual being.

Until next time, peace.

The Cross as Mathematical Solution


When all of Jesus’ statements are applied mathematically, and when one considers the full import of His presenting the cross (+), the positive sign, as His symbol and all-embracing answer it would appear that His mathematical concepts moved beyond those of His day, and that He attempted to describe the reality of the operation of the energy that mathematics attempts to describe…this study poses His words against the concepts of Nicomachus of Gerasa…both He and Nicomachus use “father and son,” and “teacher and pupil,” to symbolize “greater and the lesser,” or the concept of opposites, unequal; but in Jesus’ concept these opposites meet and are reconciled in the unity of one, or sameness.

Here Preston Harold describes the similarities between the teachings of Jesus and Nicomachus, striking as they are. But whereas Nicomachus writes that “when a point is added to a point, it makes no increase, for when a non-dimensional thing is added to another non-dimensional thing, it will thereby not have dimension…,” Jesus took another point of view.

This is to say, when the cross (+) as symbol and all-embracing answer is applied to the problem of “sum of nothing added to nothing,” it would say that Jesus did not overlook the word added – the symbol (+) introduces the problem of organization, or, as Eddington put it, of “and.” The cross as answer indicates that there cannot be a “non-dimensional thing,” –or, one might say, until a point has dimension or until it is defined, a point is not a point: the cross has dimension and it also defines a point, or gives a point dimension. The cross (+) as answer and symbol calls forth the concept of negative (-) and positive (+) numbers.

Harold now goes onto describe how one becomes itself the unit of measure when seen in contrast with zero. It shifts in its capacity from a mere digit to an active function, from a noun to a verb.


In the view of this study, Jesus realized that the correspondence between one and the whole, zero, and between one and each other ensuing digit, differing only by one, makes of one, measure itself. This is to say, one is not merely a unique digit: it is, rather, a principle, or action involving opposites, “minus-one” and “plus-one,” upon which the whole operates. Thus, Jesus saw that in the definition of one as an operative principle, the definition of the underlying principle upon which one and all operate could be grasped. And as Jesus examined His own mind the “sum of nothing added to nothing,” which must perforce involve the division of “nothing,” or the whole or zero, the positive (+), the cross, arose as the only possible answer to the problem of “naught divided by naught.” This, because the problem itself is posed in terms  that may be seen only as a negative divided by a negative which produces a positive answer. Or, one might say, that if through use of zero-0-an infinite increase in number may be drawn, then unlike the number one, when zero multiplies itself it produces more than itself: it must forever reproduce itself plus.

Until next time, peace.