Space: The Final Frontier

The concept presented in our last installment, five “intervals” needed to completely secure or “house” one of them, and three “intervals” moving against two “intervals” as two “intervals” react against three “intervals” to accomplish this, is presented in Jesus’ equation of One. He says:

…five in one house divided, three against two, and two against three.

Preston Harold says:

To insure that these words be recognized as a mathematical formula, Jesus gives an explicit division of the household. He states it as: father against son, mother versus daughter, mother-in-law versus daughter-in-law. Only if the mother plays a dual role—that is, mother is also mother-in-law – can these six “factors” be reduced to five forces, the number of forces “at issue” in one’s household as given in the equation. And only if every family were four in number with one son married, and one daughter unmarried, could the words apply to life. Jesus spoke symbolically or poetically, but He spoke as a mathematician…

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Jesus states the field formula so explicitly that His words bespeak a still “finer division” underlying the matrix. That is, he describes the forces at issue as: father versus son, and son versus father; mother versus daughter, and daughter versus mother; mother-in-law versus daughter-in-law, and daughter-in-law versus mother-in-law. His words give rise to twelve signs, eight negative, four positive, thereby “elaborating” the ratio of negative to positive force, presenting the concept that a still finer division of forces underlies the “field” – a force that involves “doubly stated double negatives” giving rise to a negative effect which is of positive value in life, an effect that sustains the division of the manifestly positive factors and/or measurable dimensions of one thing.

Harold goes on to explain how both negative and positive polarities are necessary for the manifestation of life:

This negative effect that is of value in life, but can be expressed by “nothing positive,” may be described only as Lao-tzu describes Tao:

We put thirty spokes together and call it a wheel;

But it is on the space where there is nothing that the utility of the wheel depends…

Therefore just as we take advantage of what is, we should recognize the utility of what is not.

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This, Tao—Holy Ghost, zero, nothing explicable—has endless descriptions which yet cannot describe the nature of it:

There is something formless yet complete

That existed before heaven and earth.

How still! How empty!

Dependent on nothing, unchanging,

All pervading, unfailing.

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Is it not space? Only by paradoxical exclamation points can the fullness of it in the universe be implied, so that “Tao never does; Yet through it all things are done.” Space may be seen as pre-existent unity and multiplicity at once, as continuous creation of positive value by means of the eternal presence of “nothing manifest” in which one and all have their being.

Until next time, peace.

The ONE Point

If Jesus realized that a point may be seen as a “beginning” or as an “interval,” but not as a defined whole, line or interval, then the question became: how many “beginnings” or “intervals,” which may be symbolized as (o), are necessary to define a point or to give it “actual being”? – that is, not to define the operative positive force itself, which may be said to correspond to the vertical line bisecting the horizontal diameter of a circle, but to define one point in the circle that the cross enfolds? Or, the equation may be put, simply: how many “intervals” (o) are required to draw the configuration of the positive sign (+), which appears as answer to the problem of the product of zero divided, and also defines a point?

Five “intervals,” (o), are the fewest that will satisfy this situation:

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The number five, itself a spherical number, completely “houses” the one point defined. If five is the “measure” of one, defined, one cannot measure the same in every direction: in the figure above, both the vertical and the horizontal line “count” three intervals, but if they are “taken apart” one line will “inventory” more intervals than the other.

…The two smallest segments of a line that can exhibit one degree of difference and move to completely secure and reinforce one “corpuscle of light” must measure three intervals (o) in one segment, two “intervals” (o) in the other. As the three-interval segment moves perpendicular to the two-interval segment, the two-interval segment may divide and close against the three-interval segment as it passes through, thus securing and reinforcing its center point. This action may be symbolized:

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Both segments perfectly share and equally sustain the one-interval that becomes a “corpuscle of light.”

Until next time, peace.

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.

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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

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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.

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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.

Jesus’ Mathematical Influences

Preston Harold speculates on other means by which Jesus may have acquired his mathematical knowledge.

But one does not have to look altogether to the unconscious for Jesus’ source of mathematical knowledge. Within His reach was Alexandria, the center of mathematical studies and of Neo-Pythagorianism. Here, Nicomachus of Gerasa, one of the “golden chain” of philosopher-mathematicians, is presumed to have studied, for Gerasa was a city in Palestine, primarily Greek – it is near to the place where Jesus cast demons called “Legion” into the swine – and it is probable that Nicomachus did not receive all of his education there… Nicomachus is thought to have flourished between the middle of the first and second centuries, but it is possible that he was a contemporary of Jesus, and he could have brought Alexandrian mathematics to Palestine, placing his knowledge within easy reach…

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Many of Jesus’ statements regarding one reflect Nicomachus’ thinking, which, in turn, rests upon the mathematical knowledge of his day. Nicomachus had much to say of one, which he saw as unity. Jesus’ mathematics came to rest in His concept of one, which appears to have arisen from His grasp of the operation of signed numbers and the concept of zero.

Zero, that non-number number that is both nothing and everything.  At the end of his introduction to his book, “Zero: The Biography of a Dangerous Idea,” Charles Seife writes, “The clashes over zero were the battles that shook the foundations of philosophy, of science, of mathematics, and of religion. Underneath every revolution lay a zero – and an infinity… Yet through all its history, despite the rejection and the exile, zero has always defeated those who opposed it. Humanity could never force zero to fit its philosophies. Instead, zero shaped humanity’s view of the universe – and of God.”

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Preston Harold writes:

About the time Euclid was stating his axioms (300 B.C.) an unknown scribe jabbed into a wet clay tablet a point to make the space that zero would come to occupy about a thousand years later when Hindus brought to the court of the Caliph of Baghdad the digit 0, still used today. To the mathematician, zero – 0 – is indeed a perfect pearl for the possibilities opened through this symbol are limitless. Did the digit 0 take shape in Jesus’ mind – or was it another gift of the Magi? In speaking of the “eye” of the needle, Jesus called to mind this configuration: 0, and related it to “naught,” for the “eye” of the needle is the  “nothing” of it that makes it operable; and in this enigmatic statement, He brought God, the absent or “minus” one into correspondence with man, the present or “positive” one, and brought both one’s into correspondence with this “hole,” or whole of “nothing” that takes on a “circular” shape, through which God, “minus” one, draws man, “positive” one, into infinity. Through this correspondence, any one-thing is vested with zero’s enigmatic, unmeasurable properties. But Jesus appears to have realized that although one and zero are corresponding unities, they are not the same in action and reaction.

It is this difference between one and zero that we will look at in our next installment. Until then, peace.

Jesus the Mathematician?

We now begin to look at Jesus’ ministry in quite a unique, “unorthodox” way; as that of a mathematician. Rest assured, when one considers how often Jesus used the number “one” as a part of his teachings, one must wonder at his mathematical knowledge.

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Jesus has never been considered a mathematician. He made but few statements dealing with number. Yet, He made many statements about one, the number that is the basis of arithmetic through which all branches of mathematics become possible. If He described one’s inner structure and the principle upon which one, as measure, operates, He was a mathematical genius. How could this come from the man of Nazareth?

How indeed? At this point I am reminded of the 12 year-old Jesus amazing those present in the Jerusalem temple with his questions, answers, and understanding. From where does his wisdom come?

The realization could have arisen from His unconscious, as has been the case with other great mathematicians. Jung felt that a fruitful field for further investigation was the study of man’s basic “mathematical axiomata – which Pauli calls ‘primary mathematical intuitions,’ and among which he especially mentions the ideas of an infinite series of numbers in arithmetic, or of a continuum in geometry, etc.” Dr. von Franz writes that “William James once pointed out ‘the idea of an unconscious could itself be compared to the ‘field’ concept in physics.’” She says:

“In other words, our conscious representations are sometimes ordered (or arranged in a pattern) before they have become conscious to us. The 18th century German mathematician Karl Friedrich Gauss gives an example of an experience of such an unconscious order of ideas: he says that he found a certain rule in the theory of numbers, “not by painstaking research, but by the Grace of God, so to speak. The riddle solved itself as lightning strikes, and I myself could not tell or show the connection between what I knew before, what I last used to experiment with, and what produced the final success.”

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Keeping in mind that for Harold, the Father dwells in the unconscious, and that Jesus “can only do what he sees his Father doing, because whatever the Father does the Son does also,” and “My Father is working until this hour, and I am also working,” and one can clearly see that Jesus is receiving his mathematical revelations from his unconscious, or Father. But is this the only explanation for his mathematical genius? We will look at other possibilities in our next installment. Until then, peace.

Striving Towards the ONE

To see how the three and four might be transcended we begin by looking at Erwin Schrodinger’s observations of cell division.

In his work, What is Life?, Schrodinger is not concerned with investigating the ancient dilemma of three and four, but he describes cell divisions, and in his descriptions one sees that the “triadic” family structure, mother-father-child, is involved with a “tetradic” pattern – as Schrodinger discusses the hereditary “code-script” that rests in the chromosomes, he says:

…this whole four-dimensional pattern is known to be determined by the structure of that one cell, the fertilized egg.

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He points out that physical laws “rest on atomic statistics” and their “precision is based on the large number of atoms intervening,” whereas the living organism is under the control of “incredibly small groups of atoms, much too small to display exact statistical laws,” but they play a dominant role, control observable large-scale features, determine important characteristics of its functioning, and “in all this very sharp and very strict biological laws are displayed.” These laws insure that each one is always an event in himself, unto himself.

Here we can see that the three and the four both exist within the one and work together towards becoming one.

Old folk-wisdom has also acknowledged the predicament of the three and the four…

The strangest thing about the dilemma of three and four is that some time ago those on the side of three, embracing Euclidian geometry which says that the whole is equal to the sum of its parts, were contradicted in the nursery:

Humpty Dumpty sat on the wall,

Humpty Dumpty had a great fall.

All the King’s horses and all the King’s men

Couldn’t put Humpty together again.

This bit of wisdom is restated by Kluckhohn, the anthropologist, “A whole is different from the sum of its parts,” and it is restated by Koestler, “A whole is defined by the pattern of relations between its parts, not by the sum of its parts…”

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It is also worth noting that the rhyme has also been interpreted as representing the second law of thermodynamics in that after his fall and shattering, the inability of the most powerful men in the world to reassemble Humpty is representative of the high unlikeliness to return him to his previous state of lower entropy as the entropy of an isolated system never decreases.

And in the nursery, those on the side of four, insisting upon the qualitative aspects of the whole, were reminded that time changes the aspects:

Hickory, dickory, dock.

The mouse ran up the clock.

The clock struck one, the mouse ran down.

Hickory, dickory, dock.

In these rhymes both the devotees of three and the devotees of four were given the clue: the whole must be described in terms of one, whole, and one must be seen as a working principle through which as time changes the arrangement of material forces within and without, one remains, itself a unity and the measure of unity.

This is to say, the answer to the dilemma of three and four rests in the answer to the mystery of one. This answer must be given in a mathematical statement that describes the composition and inner operation of one, itself. Jesus stated the Equation of One which must be seen against the briefly sketched background of the dilemma of three and four in order to appreciate the magnitude of His thought, for He transcends the dilemma, giving as the measure of one or wholeness, the number five.

We will begin to look at “Jesus the mathematician” in our next post. Until then, peace.