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.

A Musical “Number”

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Merriam-Webster’s Dictionary defines music as “the science or art of ordering tones or sounds in succession, in combination, and in temporal relationships to produce a composition having unity and continuity.” Notice how “science” is used as part of this definition, along with the usual category music falls under, “art.” Any musician knows that music’s aural qualities can be described in terms of numbers, for instance the way rhythm or time is notated – ¾, 4/4, 6/8, etc. Most western music is based on a 12 tone chromatic scale, with numbered intervals denoting the spaces between the tones. There are major thirds, minor thirds, flatted fifths, dominant sevenths, etc. Numbers play a major role in how musicians communicate with one another and notate their compositions. Of course music cannot be reduced to numbers as they leave out the emotional and immaterial impacts of the SOUND, which can lead us to a higher plane. As a musician myself I know the importance of understanding theory, but also understand the fact that theory must be secondary to the actual aural experience and feelings invoked by the tones themselves.

Preston Harold explains the dilemma of the three and four and how it manifests in music.

The dilemma of the three and four is not confined to the world of science. One comes upon the play between three and four in the world of art. Here one sees that musicians, like ancient alchemists, strive to bring together four “elements” to make possible the quinta essentia, the lapis, that brings forth a new element or a whole new statement. Although musicians do not discuss this in terms of the dilemma of three and four, one can hear the play between the two numbers in Beethoven’s Symphony #5 in C Minor.

This symphony begins with a four-note rhythm, described by the composer as “destiny knocking on the door.”  Deems Taylor calls it an “ominous” signal. This signal announces an agitated main theme which changes to suppressed tragedy, to resignation, to a lyrical movement during which the dread reminder of the four-note rhythm is played. It continues as a sinister reminder throughout the work. The third movement is a dream of terror wherein the four-note beat “sounds noble,” but the nobility fades and it becomes a caricature – the restated theme becomes a “macabre joke.” Reduced to its original skeleton, it becomes suppressed tension, increasing in rhythmical intensity, releasing tightly harnessed fury which becomes a bridge to the last movement. Here triplet note rhythms are introduced, artistic unity is achieved, the symphony ends on a one-two-three beat and a magnificent chord in a triumph of grandeur. In that chord is expressed wholeness: one sound based upon the number man’s hand is based upon – five. Abt Vogler says of music:

“I know not if, save in this, such gift is allowed to man

That out of three sounds he frame, not a fourth sound but a star.”

Perhaps Sibelius was trying to say this in another way in his mighty Seventh Symphony – here, symphonic expression is not given in four movements following each after the other, posed the one against the other: one movement encompasses the whole expression that transcends the dilemma of three and four.

The question becomes – how does life transcend its play between triad and tetrad to produce one, wholeness?

This we will begin to explore in our next post. Until then, peace.

Four Dimensions

Picking up where we last left off, our dilemma of the three and four continues into the realm of mathematics. Preston Harold explains:

In the mathematician’s view, the physicist deals with four continua, or – more precisely – with four dimensions. In geometry, four dimensions would mean that one has four independent directions. For example, this could be seen by drawing four lines through a given point, all perpendicular to the others. In this narrow sense the universe has only three dimensions. The mathematicians extended the concept of dimensions to any situation where events can be described by independent coordinates, and where certain simple laws hold. In this broader sense Einstein found it convenient to use four independent coordinates, with time playing the role of a fourth dimension. In pure mathematics, as well as in its applications to physics, it is often convenient to use many more dimensions, even infinitely many.

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But the idea of wholeness, or of continua itself, as one dimension greater than any number of dimensions has not broken through the tetragrammaton – through the confines of four. For example, Einstein speaks of the “bold” interpretation of the modern quantum theory associated with de Broglie, Schrodinger, Dirac, and Born – he says their interpretation “is logically unobjectionable and has important successes to its credit. Unfortunately, however, it compels one to use a continuum the number of whose dimensions is not that ascribed to space by physics hitherto (four) but rises indefinitely with the number of the particles constituting the system under consideration.”

For how long does the number not ascribed to space rise? Is it infinite? Jesus will have something to teach us here but before we get to him, we will detour into the world of music.

Until next time, peace.

Triad or Tetrad?

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Difference emphases on either the three or the four can be found within varying cultures, the beginnings of which are lost in the sands of time.

Although scientists move away from the quantitative view toward the qualitative view and acknowledge the validity of both positions, the dilemma of three and four is by no means resolved – its beginning is lost in antiquity and its end is not yet in sight. As to its beginning, Jung says that number helps more than anything else to bring order into “the chaos of appearances…primitive patterns of order are mostly triads or tetrads,” and he points to I Ching, Book of Changes:

“…the experimental basis of classical Chinese philosophy…one of the oldest known methods for grasping a situation as a whole and thus placing the details against a cosmic background – the interplay of Yin and Yang… there is also a Western method of very ancient origin which is based on the same general principle as the I Ching, the only difference being that in the West this principle is not triadic but, significantly enough, tetradic…”

He refers also to the alchemists’ tackling of the problem of three and four, seeing the dilemma stated in the story that serves as a setting for the Timeaus and extending all the way to the “Cabiri scene in Faust, Part II…recognized by a sixteenth-century alchemist, Gerhard Dorn, as the decision between the Christian Trinity and the serpens quadricornutus, the four-horned serpent who is the Devil.”

Of course western religion and culture has been based on the tension between the three and the four, both being primary factors in the Holy Scriptures. The four is stated outright: YHVH, even translated into English as a four-letter word, LORD. The three is implied in the three visitors to Abrahm, the Christian Trinity, etc. Returning to alchemy’s approach of the problem, Preston Harold says:

Wolfgang Pauli discusses the controversy between Johannes Kepler, discoverer of the three famous laws of planetary motion, and Robert Fludd, in his day a famous alchemist and Rosicrucian. Pauli says that Kepler’s ideas “represent a remarkable intermediary stage between the earlier, magical-symbolical and the modern, quantitive-mathematical descriptions of nature,” indicating a way of thinking that produced the natural science which today is called classical. Kepler, a devotee of Euclid’s geometry, insisted upon strict mathematical methods of proof. His premise was that “Mathematical reasoning is ‘inborn in the human soul’…” His is a trinity-concept, his symbol “contains no hint of the number four or quaternity.” Fludd, however, was a mystic with great aversion to all quantitative mensuration: “It is significant for the psychological contrast between Kepler and Fludd that for Fludd the number four has a special symbolical character, which, as we have seen, is not true of Kepler.” Fludd drew his inspiration from Moses, and he brilliantly defends his stand on the nature of the soul. Kepler, however, appears to best him in all scientific argument until one realizes that Kepler considered the quantitative relations of the parts to be essential while Fludd considered the qualitative indivisibility of the whole. Pauli says, “modern quantum physics again stresses the factor of the disturbance of phenomena through measurement,” as Fludd (and Goethe) insisted upon. He concludes that the only acceptable point of view appears to be one that recognizes both the quantitative and the qualitative, “the physical and the psychical” as compatible, embracing them simultaneously.

This attitude eases the argument, but it does not resolve the dilemma of three and four, as may be seen in a mathematician’s explanation of continua.

We will explore this mathematical explanation in our next post. Until then, peace.

The Dilemma and the Pearl

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Chapter 8, “The Dilemma and the Pearl,” begins with Preston Harold asking us what type of outlook we bring to the world around us – are we a “three” or a “four?”

Wolfgang Pauli says that two types of minds have battled through history: first, the thinking type that considers the quantitative relations of the parts to be essential – and secondly, the intuitive type that senses the qualitative indivisibility of the whole.

The first type mind is posed on the side of three. This type took its stand with Euclid, resting upon his well-known axiom: the whole is equal to the sum of the parts. This axiom, along with the rest of Euclidian geometry, dominated Western thought until the late 19th century. One might say that Euclidian geometry still dominates, for the revolution in mathematics that tumbled it from sacred pre-eminence has not yet seeped down to the layman’s level, and many students will learn first, by rote, Euclid’s axioms, imbedding in the subconscious mind these fallible statements which have been presented as unquestionable truth…

One might say that the three represents Rene Guenon’s “reign of quantity,” the historical manifestation of the descent from form (quality) toward matter (quantity), and the “nothing but-ness” of stark materialism. Tradition calls this period the Kali Yuga, the age of the demon, Kali, or the iron age.

Today, the second type of mind, posed on the side of four, insisting upon the qualitative indivisibility of the whole, regains much of the standing lost in recent centuries. As regards the sum of the parts in relation to whole being, scientists, dealing with one whole atom and the sum of its parts, have found that in the formation of a nucleus from protons and neutrons some of the mass of the particles apparently is converted to energy. The chemist sees that the combined action of several elements taken together is greater than the sum of them taken separately. Mathematicians working with transfinite number theory confront the concept that the whole can equal one of its parts. In short, one is forced to alter his concept that a discrete whole within the universe can be divided and its parts regathered to equal the sum of the whole…

Anyone wishing to look further into the “qualitative indivisibility of the whole” would do well to search out the works of the Goethean scientist Henri Bortoft. You can thank me later😉.

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Of course both the three and the four have their place in our world but how do we go about regaining the balance between the two? This is what we will continue to explore in Chapter 8. Until next time, peace.

Trinity or Tetragrammaton?

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At this point we are finishing up chapter 7 and getting ready to move on to chapter 8. In order to make the transition a smooth one, Preston Harold takes us from the mortal sin via blasphemy into pronouncing the name of God. I will leave the rest of this post to Harold as he transitions us so well.

That the mortal sin is nameless, that it is a derelict from the forgotten past which can be any sin a man has repressed or has been unable to forgive himself, rests upon Jesus’ contradictory words. He says any blasphemy will be forgiven – and He, Himself, blasphemed if “pronouncing the forbidden name of God” is to say, “Ani hu,” and if to say, “Ani hu,” is blasphemy.

The forbidden name of God is indeed a mystery. What is this name? The definition of blasphemy (from Webster’s Collegiate Dictionary) reads: “In Jewish law, cursing or reviling God or the king…pronouncing the forbidden name of God. See Tetragrammaton.” Tetragrammaton? “The four letters (variously written, without vowel points…) forming a Hebrew tribal name of the Supreme Being…too sacred to pronounce.” What is this mystery having to do with four “unpronounceable” letters, IHVH, or JHVH, etc.? Does the blasphemy rest in rendering the form of God in a four-dimensional concept such as consciousness can know? Could one state the forbidden name in numbers, for example:

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Could this be “blasphemy” because although the equation might bespeak a four-dimensional concept, it does not coincide with the “odd-even” division of a light wave group and thus it cannot truly and fully satisfy life’s situation? Is there anything in the realm of physics and mathematics that might explain this mystery?

The answer is yes. But to solve the riddle one must enter into an argument that engages the scientific world. The gist of the argument can be very simply told: it hangs upon what Jung calls, “the dilemma of three and four,” and one may grasp its general outline in Jung’s work and that of the physicist W. Pauli…The “dilemma of three and four” deals with a very old dispute, but it is one that is examined to this day. Trinity or Tetragrammaton? Triad or Tetrad?

Until next time, peace.

The Mortal Sin

“The LORD God will by no means leave the guilty unpunished, visiting the iniquity of fathers on the children and on the grandchildren to the third and fourth generations.” –Ex 34: 7

The esoteric interpretation of this verse from Exodus is that the children, grandchildren, and future generations refer to future incarnations of an individual spirit. The “father” is one’s current life. The “sins of the father” are “punished” by having to be rectified in later incarnations, meaning one has not completed their personal cycle of birth and death by way of, as Preston Harold says, obtaining “matter of his own.” This matter is spiritual matter, a “quantum of light’s radiant energy.” Before each of us can obtain “matter of our own,” we must go through the trials of life. One of the greatest trials we can go through is committing a mortal sin. But as Preston Harold asked at the end of our last installment, “what is the mortal sin?”

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In the view of this study, Jesus recognized that there will be one blaspheming of life itself which a man will be unable to forgive himself – this is the mortal sin. [Jesus] did not name this sin, because unto each is his own expression of it – it might be no more than kicking his dog: the sin as such has no name. In the great majority of cases, he is unable to forgive himself, because the sin is quickly repressed and forgotten; if not, he “spends his life” in remorse and dies still unable to forgive himself what he has done. Thus, in one way or the other Homo sapiens bears this unforgiven sin into the “world to come” which develops as his ego-group develops. Because man never recovers from infant amnesia, the newly stated ego-group does not and cannot know the name and nature of the sin he bears into the world at birth – thus, the sin cannot be forgiven in this life. For this reason, each man is committed to pay the wage of this nameless sin, each pays the wage that Judas paid – in one way or another he destroys himself: “O Israel, thou hast destroyed thyself…”

So here we see that no one can define a mortal sin except for the individual who commits it. No other person or institution can tell another human being exactly what a mortal sin is. Each person harbors it themselves in their own heart and mind. We can also glimpse from Harold’s words here the impetus for the doctrine of original sin. We all bear with us into this life something that needs to be rectified from our own previous life, or “Adam.”

As one’s work in this world draws to completion, Authority-Ego places upon the Judas-factor the burden of unknown sin. Through death the unknown sin is forgiven and the Judas-factor is redeemed. But as a person dies, he takes into the world to come another nameless, unknown sin that will command the price of death which the Authority-Ego and the Judas-factor will pay to redeem this evil. Because each person comes bearing his unknown, unforgiven sin, death is already stated in his being. Will man be forever in bondage to this wheel, to a nameless sin, to death?

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Only with the resurrection body does original sin end.

Scripture says: “O death I will be thy plagues; O grave I will be thy destruction.” If this scripture be true, man will not forever lay down his consciousness in the grave. This study concludes that as long as man commits sins he cannot in consciousness and good conscience forgive himself, death alone can reduce to dust his psychic “cities” of sin and his corrupted flesh. But death returns him to life to try again to learn how to live without corrupting himself and others. In each life experience, man can and does have done with error as his lust is recast into empathy. In death an iota of his evil purchases a bit of pure matter. Thus in time he will regenerate himself – will don incorruptible flesh born of incorruptible consciousness guided in life by empathy. Man will be free of the grave, but he will not be absolutely free of death – which is to say, death will be in his life as sleeping and waking is to his present consciousness, or as inhaling and exhaling is to his present body.

Until next time, peace.

The Resurrection of Damnation

When one hears and thinks of the word “resurrection,” one’s mind tends to immediately think of other concepts that surround and reinforce it; eternal life, God’s victory over death, glory, celebration. All of these thoughts usually congeal around a positive attitude. But what happens if we actually view the concept resurrection not just through Easter, but through the eyes, mind, and teaching of Jesus?

Marvel not at this: for the hour is coming in which all that are in the graves shall hear His voice and shall come forth; they that have done good unto the resurrection of life; and they that have done evil unto the resurrection of damnation. –John 5:28-29

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From this statement of Jesus we can surmise that for some or many, resurrection may not be all it’s cut out to be. But who among us really believes that they will be part of the resurrection of “damnation?” We automatically assume that we are part of the “life” camp. Preston Harold may give us pause to question our certainties on this issue. He begins by giving us an excellent theology of inevitable sins within the context of life:

There is that in every person’s life that he knows to be damnable, knows to be corrupting… But all his sinning is not so easily bedamned, so wantonly forgot – nor can it be ceased, for there is not the will in him to have done with it at the time; even when what might be called “an episode of sin” is over, he cannot truly regret it – the experience has raised the level of his understanding and he would not possess less.  He can say of such sin only this: “I did it knowing it was wrong, but I cannot regret that I did it; I know now, however, that I could not bring myself to do this again because I know its cost to me and to others.” Such experience represents, in truth, a lesson learned.

But here is where the rubber hits the road. Harold goes deep:

But there are other deeds that even though they have brought new understanding, one must regret to the end of his life and in the very-depths of his being, saying of them, “god be merciful to me, a sinner,” as though to pray, “forgive me this terrible toll of life I have taken, toll of my own life and of another’s, for which I shall be bitterly sorry in every breath I draw now and forever.” Or he quickly represses and forgets the sin he cannot forgive himself – the sin that must await the resurrection of damnation.

…there are sins that blaspheme the preciousness of life itself – these are unforgivable because a man cannot bring himself to forgive himself: they sever his connection with his own Authority-Ego and still the voice of the ego-member in the world of selves, as Judas’ voice was stilled.

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Jesus says…in part of a statement in itself contradictory: “I tell you, therefore, men will be forgiven any sin and blasphemy, but they will not be forgiven for blaspheming the Spirit. Whoever says a word against the Son of man will be forgiven, but whoever speaks against the holy Spirit will never be forgiven, neither in this world or the world to come.”

First, Jesus says man will be forgiven any sin and blasphemy. Then, any is contradicted – man is not forgiven for blaspheming the holy Spirit. Is the holy Spirit not life itself? Who can live without in some way at some time cursing or reviling life? Is true repentance of no account? What, exactly is the mortal sin?

It is this question we explore in the next installment. Until then, peace.