Common time aside, time is a mere fancy. Generalized time is a myth, the skeleton of all myths. There are no clocks or calendars in nature; the only real time anywhere in the universe is now. The fact that you can remember yesterday and anticipate to-morrow conspires with your superstitious love of the unknown to keep you from realizing this obvious fact, just as the fact that you pace the ground conspires with your ignore-ant fear of the unknown to keep you from realizing that there is no place but here. Though you mounted a sunbeam and road for a year, now would still be now and here would still be here; — though beyond the blue, you would still be you. Common-sense is of all things the most uncommon, and disillusionment is incredible to the credulous victims of illusion. Time-space is the greatest and most imposing illusion. It is pure mirror land. There is but one, real place duration, –the three-dimensional here-now, — the universal manifold of the omnipresent. Obvious. But who can realize the obvious? Mythomaniacs prefer religious-scientific fairy tales to the simple, immediate and knowable facts. The Evolutionist and the Seventh Day Adventist share the same delusion, — that fictions about the past are anything more than fiction. The Fourth Dimension is the scientist’s version-vision of heaven, but instead of a harp he fingers a formula, and his paradisical houri are the abstract skeletons of flesh-less figures. Buddha, mounted on an absolute negation, went Nowhere and arrived at his destination, but Einstein, mounted on an asymptote to asininity, powered by a formula of relativity, is still on his way: if the two ever meet, there will be a head-on collision of Absolute Nothing and Nothing Absolute, but nothing, — not even deified Nothing, — will happen, and the smoke will go up the chimney just the same.
The Fourth Dimension is absolutely pure delusion-hallucination, all fool and the square root of minus 1 wide. It has imaginary reality, and if you can seduce yourself into imagining two or more different present-s as existing simultaneously, you can actually imagine formulas that really will prove exactly that what you imagined you really did imagine. Real time is one, indivisible; relative time-s are imaginary, matters of memory-record or, as in the speculations of mathematical mystics, pure fancy. In no in-stance has real time, which is the one here now, ever been used as a fourth dimension; it hasn’t been used because it couldn’t be used: what has been used is imaginary, different time-s. This abuse of the imagination only opens new vistas in mirror land, only proves what childish dreamers and pansophists of physics are, only demonstrates how desperately determined most men are to believe any mysterious mystifying notion, to credit anything but the obvious facts. It is no wonder that the Pope now says that Science is proving the in-fallibility of the Pope. It is, relatively speaking, of course.
There is an end to reflections in mirrors. If you hold a mirror to a mirror, and then back of this hold a third mirror, you see in the second mirror a vague reflection in the reflection of the third mirror, but such reflections go off along an arc in to the “nowhere” of the real where behind the mirrors. There is no such end to mental reflections; the only end to mental reflections is the physical or mental exhaustion of the human reflector. The physicists are nearly physically inexhaustible and relatively mentally non compos; they go on imagining the unimaginable indefinitely, though not in-finitely, — minus 1 always pops up in the end as our dear, old friend, simple 1. A simple soul could do this without mirrors. The obvious fact is that you can “have” as many dimensions as you care to mention-imagine, — thought-forms and symbols for their computation are end-less, — but in reality there are only three dimensions, and these are one-indivisible. You can imagine any number of space-time-things, and concoct mathematical formulas to prove them that actually will prove them as long as you can imagine them. You can imagine a centaur or a chimera, and you can draw on paper outline reconstructions of such fancies that will impose on the minds of credulous morons, so that they actually believe that such fancies really exist; and of this nature are all the mathematics of relativity.
You can imagine that space-time, a thing that doesn’t exist anywhere save in your imagination, is curved, and you can imagine actual observations the inferential evidence of which will prove your fancy correct to all those who don’t know an inference from a real fact. You can imagine you have measured the distance to the planet Jupiter by observations-calculations based on inference, and then you can imagine-devise other observations-calculations the result of which will inferentially prove that the light reflected from Jupiter’s moons traveled from there to here at a definite speed, so many thousand miles per second. You can imagine-infer such things, and many, many others like unto them, but all you really know in any such case is a fancy-supposition. You can imagine almost anything, and imagine ways of making reality seem to fit your imaginary designs. You can delude yourself with imaginary facts almost endlessly. Great is the power of the imagination, and all but all men are utterly deceived thereby.
* * *
BUT imagination is subject to a number of obvious limitations.
You can’t really imagine being anyone save yourself, or being anywhere save where you really are right here and now. You can’t really imagine two or more concrete objects occupying the same present-place. Not really. You cannot imagine anything that is not finite, that does not have the irreducible, non-multiple three dimensions. You cannot imagine “infinite space” or “infinite time”. You cannot imagine a solid that has less than four plane surfaces. You cannot imagine a cube that is also a sphere. You cannot imagine a thing that is not either One or Many ones. You cannot really imagine a marble statue of a pretty girl coming to life, — not really. You cannot really imagine anything that you yourself have not experienced. You cannot really imagine either the historic or the prehistoric past. You cannot really imagine what anyone save yourself is imagining, has imagined or will imagine. If you can really imagine anything other than the things you are presently aware of, you have a more realistic imagination than “me”. Strange as it may seem, the imagination cannot really go beyond reality. Men just imagine that it can.
About 99.9999999999999999999999999 per cent. of the know-ledge known to men on earth today is imaginary knowledge, pure fancy, mystical malarky, scientific hocus-pocus and religious razzle-dazzle (not to mention patriotic piffle), and true peace and true science and true religion will never bless this planet until a dominant minority of men realize this fact and consign the count-less fiends of fancy to the countless hells of oblivion.
* * *
NOW, if you haven’t tossed these pages into the flames of righteous indignation or those of the fireplace, I imagine you are either very puzzled or very critical-skeptical. On the other hand, if you agree with what I have been saying, it is I who might be puzzled or skeptical, for I have found that anyone who agrees with me is either an X (about which the least said the better) or a Y (about which you can’t say too much) like “me”. There is so much that I have seemingly ignored, and so much of what I have said is so utterly unheard-of in the realms of King Fancy, Emperor of AllFolderol and the Isles of Sciolism, that I myself have been compelled to write at least one mental page for each sentence in order to make sure every sentence really reflected verbally a true facet of the structure of thought-reality involved in the Order of the Whole of this lengthy note. The least I can say is that I have not really ignored anything, but have postponed direct consideration of certain matters as long as possible, in the hope of stimulating and preparing you to understand aright that which I am essaying to communicate to you in the code of English, verbal symbolism. There is no rational reason why you should either agree or disagree with what I have not said.
At length, the crucial node in this brief discourse has arrived. No longer can I put off saying that which I have to say about a) the more and b) the most subtle and abstruse factors in this formulation of the simple-complex Mysteries of the Obvious. The central question is: What really happens when U and I geometrize-mathematize? What really happens when U or I account for Things:-Forms/Energies: Matters by what we call counting? I dare say you imagine you know what you are doing when you count money, count sheep, calculate interest or demonstrate the Pythagorean theorem. You are right; unless you are an unusually perceptive person, you only imagine that you know. If all you know is what you have been told or have read in the books, then all you really know is hearsay information, a matter of faith-fancy; it may be fairly reliable information, as far as it goes, but it is not real knowledge. Theory, tradition, custom and authority cannot substitute for real knowledge. If you really desire to know the real facts, you must go beyond the generally accepted formulations and explanations, — go on to do your own thinking-demonstrating-knowing. All real knowledge is personal and absolutely empirical. So, with your indulgent co-operation, let us now swing the cat of real calculus in a few antics of simple, honest, intelligent, down-to-earth “charlatanism” with a view to discovering the bedrock Facts so deeply hidden in the mazes of Fiction, — the Realities back of the symbolic Imaginings of mathematics.
I I I
Physical Numbers and Metaphysical Sawdust
FIRST, simply look at all the Many real things in the world around you. You can’t really count them all. If you undertook to do so, you could spend the remainder of your life simply counting, and at the end would still be far from the end of your ac-count of all the Many. The first, simple, general ac-count of Reality is seemingly no count at all. The first, realistic, universal count is Many, or All, or Whole, and at first glance, this is no count. However, upon realistic reflection, you will perceive that it is a true count: no matter which of the three terms you use, the term is one (1), and the equation implicit in your verbal account an integration. The universe conceived as a Whole (1) is an integration of All the Many things it contains (all the many as a whole equals one-1). The first realistic count is the making of One out of Many.
Now focus your attention on one of the many things, — a desert willow, for example. It is one tree, one part of the whole universe. Examining the one tree, you discern that it, like the universe, is One whole composed of Many parts (such as leaves, blossoms, twigs, branches, trunk, roots). For another example, consider a book; it also is One composed of Many parts (so many pages, so many chapters, so many paragraphs, so many words, so many letters, so many non-verbal signs, such as commas, semicolons, periods, etc.).The second realistic count is the making of Many out of One.
Believe it or not, in essence that is all there is to real mathematics, and insofar as Imaginary Mathematics refers to Reality, it conforms to these two, the First and the Last count-s. There isn’t a problem in all the volumes of imaginary mathematics that cannot be reduced to this formula, — the making of One out of Many/-the making of Many out of One. The simplest version of the unified field formulation of Reality reads: Many : (Whole/Part-s; Part-s/Whole): One
At all times, you count Many-one-s or One-many; at all times, in ac-counting for reality, you either think of a thing as being One composed of Many part-s or as being a part of Many things that com-pose a greater One. The basic real counts are One and Many; that is all. The one is the many, and the many is the one, so the one real, first and last count is One-Many. In prime reality, you can-not count anything but One-Many, because you can never count all the parts of any one thing, not even the least. You can count the exact number of letters on this page of print, but that doesn’t account for the total reality of either this page of print or for the least character on it considered as a real one. To account in reality for a period (.), you would have to ac-count for the whole universe. The reality of all physics and all psychology, –the reality of the whole Objective-Subjective Universe, — is involved in the least part of the whole universe, — involved even in the period that concludes this sentence.
* * *
THAT is the core of Real Mathematics, but of course there are many other, ponder-able parts of the whole to be considered and formulated, even in a brief and simple survey of the field. We must now ask: What is the real relation of Imaginary Form/Energy: Number-s to Real Form/Energy: Thing-s? The first answer-s to that question are most obvious, and from the first word in this discourse I have been giving them. Imaginary number-s and geometrical abstractions are subjective realities, — real reflections-creations in your psychosomatic mirror of apprehension-comprehension, the most general term for which is Mind. These real fictions enable you to mold and control the phenomena of overall reality practically. What true insight into the structure-nature of Reality these Fictions may give remains to be discovered, and to get at that ultimate consideration we must clearly understand what really happens when we geometrize-mathematize. We must convert geometric-mathematical Fictions into Real operations. We must be empiricists, prepared to thumb our noses merrily at any eminent X who condescends to heave a metaphorical brickbat labeled charlatan in our direction.
Very well. Take this pencil, this ruler, and this piece of paper. Now draw on the paper a right-angle triangle, the base of which is 4, the perpendicular of which is 3 inches in length. As you draw the hypotenuse, the ruler will tell you that it is five inches in length. In doing this, you have made one empirical proof of the Pythagorean theorem, — the hypotenuse of any right-angle triangle is the square root of the sum of the square of the base and the square of the perpendicular. You have carried out the instructions in the books, and got the predicted result; all that you have done, in reality, is to prove that the information in the book is practically correct. But you have learnt nothing about the reality back of the abstract-symbolic formulation. Triangles appear in Art, never in Nature. Any triangle you see in nature is always an abstract Part of some three-dimensional Whole. Even if an accidental configuration of leaves casts a triangle of light upon a smooth wall, the triangular design is a Part of the Whole three-dimensional manifold of Light: Form/Energy;-Matter, and cannot be fully-really understood a-part from the Order of the Whole and all its part-s. So the question arises: What does your abstract-symbolic triangle, seemingly a proof of something not purely imaginary, have to do with the solid facts of overall reality? You have been an imaginary empiricist; you must now become really empirical.
* * *
LET us go out to the carpenter shop, where there are tools, such as a power saw and an old-fashioned balance scales, and some lumber. There we find or, better still, make a cube of clear, smooth red-wood, roughly 12 by 12 by 12 inches in dimension. We are going to cut this cube in a way to obtain 8 smaller cubes, each exactly 6 by 6 by 6 inches in dimension, so we must make the one, large cube enough larger than 12 inches square to allow for the sawdust the saw is going to make to make the required cuts. With a pencil and square we divide each of the six faces of the cube into four equal squares; then we switch on the saw, and proceed to do our work in empirical mathematics and geometry. The real saw converts the “one-dimensional” lines on the cube into three-dimensional sawdust, and in the end we reduce One large cube to Eight small cubes. Just to be imaginatively thorough and realistic, we reassemble the 8 ones so that they compose 1 cube eight times larger than any of the small ones. We have made Many of One, and then One of the Many, not in imagination, but in reality. To do this, we had to allow for the difference between the subjective Ideal and the objective Real. The evidence of the difference is to be found in the sawdust. I am not going to count the grains of sawdust we made, and neither are you. The realistic ac-count of them is many, and if there is any one in the world so unrealistic as not to accept that account of the matter we really don’t have to take that one into account. The One large cube was a manufactured fiction, from which we manufactured Eight smaller fictions; to project these 1-8 fictions into reality, we had to reduce the original One to Many (countless) Parts. You can manufacture Fictions from Reality, but you cannot convert Reality into Fiction. (Note this; it is of prime importance.)
We have now completed half of the projected experiment. From the same kind of wood we make a cube similar to the first one, but this time allowing for one, diagonal cut. With the real saw doing its real work of reducing One to Many real parts, we manufacture Two real fictions, — two blocks alike in shape and size. They are not real halves of the original, second block(don’t forget the meta-physical sawdust), but if you put them together they will form a cube 12 by 12 by 12 inches in dimension, exactly the same size as the cube composed of the eight small cubes. Each of these two “halves” has 5 plane surfaces, 3 of which are rectangular, 2 of which are triangular. We have manufactured 4 right-angle triangles; to get 1 right-angle triangle into Reality,we had to make 4. In three-dimensional reality, there is no such thing as an isolated, rectangular or triangular plane surface. The four triangles on our two blocks are like the abstract design you drew on paper a few minutes ago, but they are also very unlike it: there are Many things that accompany any One real triangle that an abstract-outline triangle does not take into account. However, the triangles at the ends of our two blocks are enough like the abstract to verify the Pythagorean theorem; the sides of each right angle are equal in length, 12 inches; the sum of 12 squared and 12 squared is 288; the ruler on the hypotenuse 17 shows a practical 17 inches, which is the square root of 289, — close enough to cause the shade of Pythagoras to smile and rub18 his palms together. The imaginary square root of 288 is either 16.97057 . . . or 16.97056 . . . , about which I will have something more to say in a few minutes. Now, just to be thorough in our real demonstration, we weigh each of the odd 19 “halves” in the scale against 4 of the small cubes, proving that “halves” are“halves” no matter what form they may be in. We conclude by cutting 4 of the small cubes in half diagonally so that from the parts of the first large cube we can assemble two “halves” similar to the “halves” we manufactured from the second large cube.
So what? U ask. The answer is, – – Manifold. The experiment in meta-physical sawdust is complete, but the full realization of it has just begun.
* * *
WE must go slowly here, if this fiction is to have a ghost of a chance to cause you to realize the full significance of what we just did in the carpenter shop. We must construct an ideal of the real experiment, resolutely restraining the imagination from taking off into the mirror-lands of merely shadow mathematics. The best way to do this here is to formulate, with illustrative comment, the major facts realized in the course of the experiment.
I. Mathematics, as presently generally understood, is purely imaginary, with none save a profoundly misunderstood, artificial reference to reality. The world has yet to discover Real Mathematics. To reproduce in three-dimensional reality any mathematical proposition, we must resort to artifice, and at every point make allowance for the material difference between the Ideal and the Real.
II. That difference is manifold and obvious, actually most important and radical, though often seemingly negligible. (The mathematicians who blow away the metaphorical sawdust blow away the evidence of their vast ignorance of truth-reality, — an ignorance that makes it possible for them to “talk of many things” as unreal as anything in the Alice books.) The more you reflect on the fact that in objective reality there is neither number nor geometric design, the more you see how significant this fact is, how delusively illusive mathematical-geometric abstractions really are. The hairs on your head are not numbered, though doubtless, if you are not totally bald, there is a definite number of them. The sands of the seashore are finite, not infinite, but they are absolutely unnumbered and practically end-less. There are analogues to geometrical forms in nature, the most obvious of which are crystals, the sun, the moon, and the planets as seen through telescopes, but geometry merely reflects an outline abstract of each of these. So far as is generally known, sun, moon and planets are actual spheres, and different substances crystallize20 in different characteristic forms (the most familiar examples of which are the six-sided salt crystal and the 21six-pointed snowflake), but, unless nature is informed by creative imagination, these are no more than analogues to the forms of imaginary geometry. Even if creative imagination does inform nature, the geometry in Euclid and in the texts on crystallography presents nothing more than symbolic abstracts of its products, –symbols that have no direct reference to the processes and operations of universal, real-creative geometry. Mathematical fictions are practical interpretations, not demonstrations of reality. (Note this, also, for reference when other facets of this thought-form again occupy the unfolding present of this discourse.)
III. Divorced from objective reality, counting is illusion-delusion, and only shot-gun marriages can get concrete form and abstract number together. Even so the numbers won’t stick, or if stuck will not endure very long. We made 8 small cubes of the large 1 by the saws of eye and hand, but the actual cubes are indifferent to numeration; we can assign any number to any of them, but each is just 1 cube. The pyramids, the most impressive Fictions manufactured in material Reality, are slowly wearing away, and it is not impossible that there will be 49 or 0 states in the United States someday. Many blossoms have 5 petals, but each 5 unfolded as 1, and are present in 1 configuration; and none of them are numbered. They are like snowflakes: counting does not really account for their forms. You can pick up 8 pebbles and hold them in your hand, but you have not subtracted 22 the 8 from the sum of all the pebbles in the universe; you have merely manufactured a group of 8, distinguished by your artifice-design from all the others. In imaginary mathematics, as in art, everything is a say and a make, not a prime reality. Mathematics is an art, not a science.
IV. In reality, there are no fractions; everything is just 1 thing. (Each of the Many grains of sawdust we made is One.)Each of our 8 small cubes is 1 cube; it is only artifice that says-makes it one-eighth of the large 1. Though seemingly ignoring it, imaginary mathematics reflects this prime reality at every point. Every number is 1 number, every term 1 term, every operation 1 operation. From a kindergarten to the School for Advanced Study, there is not a mathematical operation that, in essence, is not either a) a design to produce Many from One or b) a design to find formulate the One that accounts for Many. Engineers of imaginary mathematics overlook, but cannot utterly ignore 1. One is the ghost of Reality that haunts every term and factor in their imaginary operations. The fountainhead of human ignorance is the ignorance of 23 the obvious, and 1 is the most obvious of all Forms/Formulations. The Science of One in the ears of an ignoramus sounds nonsensical; the simpleton is unimpressed by the simple, and is incredulous of any-thing save mysterious and in-comprehensibly complex multiplicities: he delights in the long ago, the far away, the infinite, the inscrutable, the invisible, — in any myth that will enable him to pretend to be superior to honest ignorance. The race at present is so low in psycho-somatic, moral-intellectual integration that only a few prefer obvious fact-truth to religious-scientific myth-delusion.
V. All e-numeration/mathematics not rigorously related to the One-Many of Reality is illusion, but zero and the endless decimal fraction are delusion. In reality, 0 is a symbol for the brilliant blankness of the mental mirror considered as the Whole, the in-different potential of All, and an “infinite” decimal fraction is merely the mental mirror turned in upon itself in a series of endless reflections approaching unity (1). There is no end to subjective reflections (short of the end of the reflector), and the endless decimal reflects that subjective reality: it is the mental-abstract analogue to objective-concrete perspective, an attempt to approximate the Vanishing point; and zero is the complementary attempt to fix the Vanishing point. In reality, there is no no-thing, every vanishing point is a real illusion, and something always remains some-thing. 0 is a convenience in the mathematical short-hand of computation, but the formulation of equations to equal 0, not 1, is illogical and unrealistic. All reality is absolutely positive; the verbal-mathematical negative is merely the sign of differentiation and relative distribution: you are not in New York because you positively are in Palm Springs, and when you are in Palm Springs you are no-where else; a monkey is not a monkey-wrench, but both positively are, the one a monkey and the other one a monkey-wrench.
Every thing, whether considered as one Part or one Whole, equals its-elf, 1, but endless decimals delusively flee from even as they approach 1. The hypotenuse on paper or manufactured in wood is 1, but in mathematics it is always more than 1 or not quite the ultimate 1. The square root of 288, carried to seven decimal points, is either 16.9705628 or 16.9705627; the square of the first produces the end-less figure, 288.00000174874364…, and the square of the second produces the endless figure, 298.99999835463139…: the first goes beyond the final 1, the second approaches it; the second is closer to the “real” square root because it is only .00000164536861 short of the final 1 (288), whereas the first is .00000174874364 more than that 1. The real, three-dimensional square root is neither one of these, nor yet the practical 17: it is the 1 that it actually is (+/- a few real grains of meta-physical sawdust), for which neither the fictions on the ruler nor the fictions on paper can ever exactly account. This is true even if the triangle is One of the Many whose hypotenuses can be stated in mechanical-mathematical integers. Mathematics is really a form of art, — the ultimate form of Abstract paint-drawing, and essentially as in-sane, though its insanity goes in the opposite direction, — in the direction of impracticability, not in the direction of impracticability; both have the real value of being negative signs of positive sanity: when the Ab-stractionists, painters/mathematicians, come to the end of their illusive abstractions, they will be either 0’s or real 1’s. I repeat, in reality there are no fractions. You can’t divide a sheep in to halves and quarters unless you kill it and manufacture the fractions; half a sun/son is no sun/son, and a silver dollar sawed in two is not two half-dollars. And here is the first paradox (which, you recall, is only a seeming contradiction): — there are no fractions in mathematics either.
Every term is 1 term, as witness:
1 2 3 4 5 6 7 8 9 etc. ½ ¼ etc. 1 1 1 1 1 1 1 1 1 1 1
The prime reality is that you and every other natural unit are 1’s, and every process of reality is a matter of Dis/Integration, for which there can be no exact mechanical-mathematical formula.
VI. Pythagorean triangles, and other formulations in geometry, reveal a notable symmetry in Idea-l forms and proportions. That the square of 3 plus the square of 4 equals the square of 5, that this configuration in numbers reflects the formal proportions of a right-angle triangle constructed according to the formula, –and does so no matter how large or small the unit of measurement used in its construction, — is no mere coincidence, but a real fact in the Subjective “half” of reality, — a fact that is a clue to the structure-nature of the Re-Creative Imagination, of the Mental Mirror,of the Mind that reflects, abstracts, projects, invents, creates.The fact that such subjective Idea-ls can be impressed upon and manufactured from portions of objective reality also is a clue to the structure-nature of the overall reality, — to the reality that integrates both subjective and objective “halves” of the uni(t) verse. The difference between Animate and Inanimate matter is almost but not quite absolute: the imagination reflects reality, and could not do so if reality were absolute other: numbers, degrees, angles, squares, cubes and ideal spheres are Fictions which do no perse exist in natural Fact, but there is that in the overall reality which does not utterly reject and does respond to a marked degree to these un-realities. Though mental fictions do not absolutely reflect reality, “mind” and “matter” are ultimate One.
VII. No matter how close the Ideal sometimes approaches the Real, it is confusing and stultifying to ignore the metaphysical sawdust created in every projection of the Ideal into the Real. In the carpenter shop, and in fields where the real is under perfect control you can practically forget the sawdust, but the moment you project a geometrical-mathematical Ideal beyond the field of immediate observation, — as in the calculation of interstellar space-s, — you are in no position to distinguish fiction from fact, metaphor from stardust. Only nos-es with no scent for the difference between demonstration and supposition could fail to realize that present texts on astronomy and astrophysics are full of the dust of in-definity thrown off by saws of inference and fiction. The sun, the moon and the stars are light-images, not so far away, reflected everywhere in the atmosphere, just as the light of a candle is reflected everywhere in a mirror; light-bearing ether is a hypothesis, and the actual means by which light is transmitted to earth is unknown: under such conditions, even a parallax “186,000,000” miles wide at the base is a toy-fiction that merely gives those with an unrealistic yen for guessing the shadow of a probable excuse for guessing. Guesses about the “speed of light” are even more unrealistic, — absurdly inferential-fictitious.
Any guess about the “velocity” of light which make it almost universally instantaneous (which it really is on earth) is a “good guess”, –a guess good enough to keep big and little morons in mystified awe long enough to permit the professor, the EA26 and the official X’s time to collect their pay and perhaps take a bow or two in the spotlight of academic-newspaper fame. The mob and the eminent authorities have much in common: they delight to hear and to tell big lies, — and the Biggest Lie is always the SOLEMN TRUTH. The scientist now competes with the priest and the mystic for the credulous wonder of ignorance. Geologists, physicists, biologists and astronomers in congress assembled have knocked their cyphers together, pooled their puerile profundities, and come up with a fairy tale about the past and the future of man, the earth and the universe as fantastic as any fathered by any hierophant of the ineffable. 0 is the technological crystal, and there is no end to what the mahatma of the modern mystification and mechanistic mumbo-jumbo can see in and conjure from it. Man is not only an ignore-amus; he is a seemingly incurable mythomaniac: when he tires of religious myths, he invents scientific ones. The latter are more holy than the holy. If you don’t believe in the religion of science and the Gospels of Darwin, Marx, Freud and Einstein, you are a dangerous heretic, and without trial the hyper spatial inquisitions will convict you of charlatanism, tomfoolery inferiority, subversive sanity, unauthorized ideology, social in-security, intelligent insubordination, and conduct unbecoming a moron, forthwith to be burnt at the stake of public ridicule with the fire of ecumenical scorn.
These are some of the major realities uncovered by our chore in the carpenter shop.
* * *
THE brutal fact is that man sees Reality through a veil of Symbols-Imagination, and when he reaches an advanced stage of what is called civilization the veil becomes so heavily loaded with symbols piled on symbols that he finds it almost impossible to see through it a tall and catch a glimpse of unsophisticated fact. You could no more dis-illusion one infected with the Higher Mathematics than you could dis-illusion a true believer in any religion. It is ill-bred to make the attempt; the greater of two fools is the one who tries to prove to the other that he is a fool. But I am talking to You, and you’re no fool, — the proof of which is that you are reading these words without jumping to the conclusion that I am a fool. The wisest of two wise men is the one who first recognizes the other. So, before we complete our survey of the mathematics of number-s and come to the mathematics of mathematics, let us indulge in another trifle of honest charlatanism.
Here on the table are a blank sheet of typewriter paper and a pencil. Now, I desire you to do something with this paper and this pencil, and as you do it I will correlate what you do with clock-time. Take the pencil in hand. When I say go, you are to put down at random on the surface of the paper, but in arithmetical order, as I give you the count, the numbers from 1 to 60…. Ready?…..GO. 1, 2, 3, 4,5, 6, 7,8, 9………………………………………………………………….60. — Done. This paper now bears one record of 60 seconds, 1 minute, of what is usually called time. All the numbers from 1 to 60 are present, each a record of 1 second. Now write at the top of the page these words:
ONE MINUTE: 3.30-3.31 P.M., 22 May, 1958 Palm Springs
Now at the bottom of the page write, — FD-UI29. The UI stand for U and I. Quite a nice little graph. The fourth dimensionalists, cow-boys of hyperspace, could romp around on that diagram for the next sixty years, and keep all good romanticists guessing all the time. But we are neither hyperspatial cowboys nor cowboys of hyperspace;so we’ll confine our elucidations to the next few minutes. It ought not to take more than that to get at the real facts.
Now, first of all, note that this record is a Fiction; areal fiction, true enough, but still a fiction that doesn’t tell one real thing about the “past” time. Every number was set down in the present, — for the present in which you set it down was the present in which you set it down (that’s as clear as mud reflected in mud,isn’t it? Well, that’s what Fictions about Fictions come to, — mud about mud). Furthermore, all 60 symbols-fictions are right here-and-now on the paper in this present second. The minute in which you set down those 60 symbols no longer exists in reality, except in your present memory, and your memory is an imaginary reconstruction of all that you did in that minute. Any diagram you draw correlating these 60 symbols to any “past” or “future” will be a figure of pure imagination; any formula you concoct to ac-count for the expanded diagram will also be pure imagination, an asinine asymptote 30 to the real present which you deliberately ignore by focusing your attention on your memory of the past and anticipation of the future.
You can imagine 60 curved lines passing through the 60 points on this paper, expand them into cosmic geodesics, or any fancy configuration you fancy,correlate them to the fireless fire in the torch of the Goddess of Liberty, the tail of your grandmother’s old, black cat and the fourth minute after four o’clock on the Fourth of July, A.D.4444, and with telescope and theodolite and other instruments go out into the field and make observations to the end of your time, but at no time will you ever be able to get away from the personal, three-dimensional here-now of absolute reality. Unless your observations-formulations can be verified in that absolute reality, — in the personal, three-dimensional present place, — they are illusions-delusions, a schimerical as the chimera. You can fool yourself with fancies, and the figures that conform to the fancies will confirm you in your folly: reality bestows upon you that truly awful freedom.
What I have just said is a verbal reflection of the prime fact about reality, but it is a Fiction, a symbolic formulation, it-self; it rightly reflects the prime fact, but it doesn’t, — and it cannot, — prove it. Reality is its own proof, and the only demonstration thereof is a personal realization thereof. I have now subtracted abstractions and un-imagined the imagination to the point where the silver of negative hypostatization is nearly washed away from the back of the mental mirror, and we are almost face to face with Reality beyond-behind all reflections. It will be well if we put some of the silver back, and do a few more real-imaginary sums,before I undertake to engineer in Fiction the definitive revelation of Reality.
I V The Many/One
THE more clearly-completely-accurately I imagine three-dimensional reality, the more I realize just how imaginary Symbols:Names/Numbers;-Abstractions are. There are no things in nature like the things on this page. Mirror reflections and mirages are the only things in nature that resemble the things evoked in your mind by the things on this page. There are no abstractions in nature, and no pure or absolute abstractions in your mind; thought-forms, not matter how abstract, never escape the matrix of the concrete.(If you are of the unimaginative minority, you may opine you do sums “in your head” without being conscious of numbers and mathematical signs, but your head is concrete, and unconscious images of the numbers-signs are present or you wouldn’t be able to recall and recognize them when you see them in print or on the blackboard.)In general, words, as distinguished from numbers, evoke subjective,finite images-illusions, while numbers evoke subjective “in” finite images-illusions. (When you say, 2 times 2 equals 4, you use particular signs to formulate a generalization, seemingly but never really divorced from concrete example and application.) Images-illusion, evoked by numbers or names, are positively serviceable up to the point where you begin to mistake the Symbol for the Thing, the image for the reality. You pass that point any time you believe anything you read without making a personal effort to prove what you have read in your personal field of science-experience. Infants under the age of three are virtually the only persons in the world who live in reality, not in symbol-fiction-imagination.
Scientific-religious-political-social illusions, myths and other unrecognized/uncontrolled errors have some positive values in a world strongly inclined to contented ignorance, mental sloth and craven conformity: they stimulate and instruct the wise, and keep the otherwise more-or-less pre-occupied and satisfied with their lot. Illusion is in-complete knowledge, a challenge to the truly knowledgeable; myth lurks in any symbol, an invitation to the daring to discover truth; and error can be the hero-villain who slays the enchantress of fancy to liberate the innocent and beautiful facts. Anything in words-numbers is fancy-fiction, and the honest as well as intelligent writer must recognize this fact, and slay the illusions his words inevitably create as often as necessary. Unless you see through my fiction to the intended reality, the tentative formulation of reality I rattled off in the preceding chapter contradicts itself at every word. Before this conversation with You ends, I shall fabricate another sieve of symbols about the Whole Matter, the mesh of which will be (or should be) considerably finer, better designed to retain positive sense and strain away non-sense. In the meantime I feel constrained to do a little more dis-enchanting.
The power of a symbol is general agreement, but before the end reality must break every agreement. You must realize that in reality anything can stand for anything, — that nothing in the word water or the symbol 7 really relates them to water and 7. If 2 had begun as the symbol for 3, 3 might now be the symbol for 2.FD (which we used a moment ago) could mean fascist deceptions, or fascinated doughnuts, or free delivery, or fourth dimension; or,as I now choose to think of it, it could stand for Factual Demonstration. Until recently UI, I dare say, has stood for unlimited insanity. Personally, I can’t stand for that any longer; so let us agree, U and I, that from now on UI stands for Universal Integration.
Very well. Applying UI to the question, What really happens when we count? let us discover, identify and formulate the facts.
* * *
WE begin by counting 1 in reality, and the best illustration of what really happens when you count 1 is a rigorous extension of a demonstration I used a few minutes ago. Imagine you stand on the shore of a beautiful, still lake as the full moon rises over the wooded hills across the waters. There is just one moon. The count is obvious. You count that 1 automatically, unconsciously, without thinking. In reality, how-ever, there are 4 moons involved in the 1 count. (There is even a fifth, a sixth and a seventh, but we must be content to master the simple square of real counting first.) There is the real, objective moon in the sky (A); there is the real, objective image of the moon in the lake (D); there is the real, subjective image of A in your mind (B); there is the real, subjective image of D in your mind (C). This is merely a parable of counting. To understand the parable, you walk with me to a place where you can’t see the reflection of the moon in the lake, and consider the following analysis.
There is the one moon up in the sky (A). You cannot count it without being aware of it, — without having the subjective image (B); furthermore, you cannot really count the 1 moon until you reflect upon the image (C), and identify it with an objective symbol (D), — 1 moon. Here is the simple square of the count of 1: .Objective Reality 1 . 1 subjective image (A) . . . . . . (B) .Objective Symbol 1 . 1 Sub.-Ob. Counter-Image (D). (C) M
The perpendicular M … stands for the Mental Mirror focused up on the outer, objective field; the horizontal M … when focused upon the inner, subjective field. The attention goes out to the moon (A), receives an impression (B), returns in to reflect upon B and thus becomes aware of C, in order to identify it with D, the projected word-symbol, one moon. In simplified symbols, the simple square of 1 real count reads: A, Object; B, Image; C, Counter-Image; D, Symbol. These 4 are involved in the evolution of every real count.“Pure” mathematics affects to transcend these basic, psycho-somatic realities; the “purest” mathematics are so relatively imaginary and unreal as to be actual delusion-hallucination.
* * *
NOW, before we ask the next, obvious question, let us cube the square. The square ac-counts for two dimensions and two axes, but in ultimate reality there are three dimensions and three axes. The simplest way to add the third dimension-axis and cube the square is to realize at once that You, the one counter, are the Integrator-Creator of the count. It is your Inner and Outer foci of conscious attention that project the two dimensions-axes of the simple count; it is your faculty of integrated attention-identification that projects the third dimension axis. All the while you are aware of observing-counting the moon you are also aware of observing-counting-being yourself. You are the One who integrates ABCD; to do this you have to re-create the moon, and to do this you have to employ your attention-empathy in three reflections, — 1) objective,2) subjective, 3) symbolic or subjective-objective projection. The six faces of the cube of 1 count may be defined thus: Object, Image, Counter-Image, Symbol, Identification, Recall. All of the six are You, the central 1. The ultimate reality of every count is the counter,– the three-dimensional (3), un/conscious (2), psycho-somatic (2)unit-integrator.
The un-conscious is the negative silver at the back of the mirror of conscious awareness that “divides the Whole field of attention and makes it possible for you to reflect-integrate the two “Halves”, Objective Thing/Subjective Image; your prime faculty of empathy-identity, — your re-creative Mind as an Un/Conscious Whole, — provides the third, inner dimension, making it possible for you to reflect-recreate the outer, three-dimensional Order of the Whole. Once you have seen the moon, you can turn your back to it and project an endless, but not infinite, series of conscious reflections of it into the inner, three-dimensional black-board-mirror of the sub-conscious. With this series of endless images you can do anything in imagination: you can arrange the units in any number of ways, cut them up, reassemble them, you can cor-relate them to a series of mathematical symbols, forget the moon images, and do sums with their abstractions: you can do anything in the imagination but really get away from the Prime Reality, –Yourself:Object/Image:1 Moon. What the moon really is apart from your personal ac-count of it, — apart from your re-creative, unconscious identification with it, — remains to be dis-covered, and about that I shall have more to say as we go on. It is now obvious that UI not only stands for Universal Integration, but for U, the objective “half”, and I, the subjective “half”, of the Whole One.
* * *
THE second obvious question is, What really happens when we count more than I? The not unexpected answer is, An orderly extension of the first count into the field of the Universal Many/One. This is obvious, and therefore not to be ignored, for science is the orderly discovery of the inner-outer nature-structure of the obvious. We learn nothing in reality by taking anything for granted. True-real knowledge is absolutely personal-empirical; at every node, we must be re-creative “charlatans”36, if we desire to be more than figure-heads and deluded technicians of teramorphous theory. So, now, imagine that you are the antique shepherd Abram,that you own 4 sheep, that you desire to count them, not automatic-ally-unconsciously, but realistically, with conscious UI. Very well.You tie the sheep in a row under a great yew tree beside the brook in your pasture, stand off at a little distance, and count them, reflecting thoroughly on each operation as you perform it. Here is a graph reflecting symbolically the Simple UI of what you did:
S . S . S . S . 1 . 1 . 1 . 1 . . 1 . 1 . 1 . A-1 . . 1 . 1 . . . . 1 . 1 M 2 M 3 M 4 M
S stands for objective sheep, M for mental-mirror, I, I, I … for subjective image-s, and A-1 for U, Abram, the one, prime counter. There are three major reconstructions of the real operation re-presented by the graph, — Simple, Complex and Dynamic. The simple explanation is not too complex, and will serve as an introduction to the Complex and the Dynamic.
To count the Many/One sheep, you reflected them in four groups, — 1 at once, 2 at once, 3 at once, 4 at once. The first reflection produced one image of one sheep and one numberical 38 symbol or counter-image, “1”; the second reflection produced one image of 1-1 sheep and one symbol or counter-image, “2”; the third reflection produced one image of 1-1-1 sheep and one symbol or counter-image, “3”; the fourth reflection produced one image of 1-1-1-1 sheep and one symbol or counter-image, “4”. The process was unitary throughout, a progressive Real-Imaginary (Objective-Subjective)disintegration-integration. To count 4 sheep you had to imagine 10 sheep in 4 groups, — 1-1, 1-2, 1-3, 1-4, — and you had to realize, at every node, the difference between Real and Imaginary sheep.
Moreover, you had to have ready 1 different symbol or counter-image for each group. The process was all a matter of 1’s and groups of 1’s. It is obvious that the count of more than 1 is an extension of the count of 1, but it is also obvious that our graph of the count of 4 does not give a full ac-count of this. A fuller account introduces the complexity involved in the use of One mental-mirror in a coherent series of Many, different reflections. The following graph will enable us to focus our attention on this complexity:
A-1(5*) 1 2 3 4 (Objective Symbol) S S S S (Objective Sheep) 1* . 2 . . . “½” “½”(Subjective-Objective . . 3 . . (Subjective-Objective Field) Field) . . . 4 . . . . . 5* UI ONE
The diagonal, 1*-2-3-4-5*, stands for the mirror-line of calculation, for the vital “division” of Abram’s Mind, by action of that Mind upon itself, into two “halves”, one a relative Subject, the other a relative Object. By this device we introduce in the graph itself the prime One, Abram, the Integrator of the Count-s. The graph may be read horizontally, perpendicularly, diagonally and progressively. In every count, all 4-5 prime factors, — Object, Image, Counter-Image, Symbol and Counter are present, ac-count-ed for. Reading progressively along the diagonal, 1* to 5*, each count is ac-counted for by the preceding square and is the source of the succeeding square. At every node-image-number, each Group-Count integrates the Order of the Whole (inner-outer/subjective-objective) Field. At every point, the Complex mirror of the re-creative imagination is reflecting objective, three-dimensional realities and re-re-reflecting upon its reflections. The Vital Factor that empowers it to do such Complex sums so un/consciously is, of course, the prime object of this ac-count of counting, — and about that I shall have considerable to say in the end of this discourse.
The Simple-Complex Square of Real Mathematics is now symbolically complete. The analogy to the Pythagorean Triangle is obvious. As a matter of fact, the correspondence is perfect. Every count is a Square, the “halves” of which are subjective reflections of objective right-angle triangles. The Ideal and the Real “divide” in order to “integrate” both the Symbolic and the Actual order of the UI One, Whole.
Continue to Part 3 http://planetarydynamics.com/2020/11/23/ignorance-of-one-part-3/