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diff --git a/gsb_esalen.otx b/gsb_esalen.otx index 011b503..5fd034f 100644 --- a/gsb_esalen.otx +++ b/gsb_esalen.otx @@ -123,7 +123,7 @@ In 1973, Esalen was at the beginnings of its popularity as the center for innova Spencer Brown showed up, British to the nines, and plunged gamely into a discussion of the \booktitle{Laws of Form}; but from the very start, the audience's unfamiliarity with mathematics caused the discussion to flounder. Brown tried to make clear the difference between mathematics, a calculus, and the interpretation of that calculus; but the conferees had trouble with even this simple distinction. We got tangled up in the idea of the mathematics of a state of mind---how could there be such a thing? -Even more subversive to our goal of understanding, however, was the difference of opinion, unknown to us at the time, between Brown and the sponsors, particularly John Lilly. Apparently it concerned money, but whatever its substance, it resulted in Brown packing up after two days and heading back to England, leaving the rest of us with the rest of the week to tease out some of the clues he had left. Lilly and Watts organized a series of seminars in which individuals could give their own interpretations of the \booktitle{Laws of Form}, in the hope that from this rough collaboration could come some sort of consensus. This was not, alas, to be, although some of the presentations, particularly that of Heinz von Foerster (himself a logician of note) managed to shed light on the process of calculating without numbers. Kurt, who from the very first understood Brown's method, if not his matter, gave a version of the Buddha's Flower Sermon---he silently covered a blackboard with symbols of the calculus, wrote at the bottom "Homage to all teachers," and bowed himself out. A rump underground, led by Stewart Brand, washed its hands of the whole affair on grounds that Brown himself had let us all down, and a few people actually went home, foregoing the remaining days of Esalen hospitality. +Even more subversive to our goal of understanding, however, was the difference of opinion, unknown to us at the time, between Brown and the sponsors, particularly John Lilly. Apparently it concerned money, but whatever its substance, it resulted in Brown packing up after two days and heading back to England, leaving the rest of us with the rest of the week to tease out some of the clues he had left. Lilly and Watts organized a series of seminars in which individuals could give their own interpretations of the \booktitle{Laws of Form}, in the hope that from this rough collaboration could come some sort of consensus. This was not, alas, to be, although some of the presentations, particularly that of Heinz von Foerster (himself a logician of note) managed to shed light on the process of calculating without numbers. Kurt, who from the very first understood Brown's method, if not his matter, gave a version of the Buddha's Flower Sermon---he silently covered a blackboard with symbols of the calculus, wrote at the bottom \dq{Homage to all teachers,} and bowed himself out. A rump underground, led by Stewart Brand, washed its hands of the whole affair on grounds that Brown himself had let us all down, and a few people actually went home, foregoing the remaining days of Esalen hospitality. I was as lost as the rest until Heinz, at the end of his lecture, illustrated the formal nature of Brown's calculus by singing us a couple of the mathematical expressions. This is not as silly as it may sound. Written music is, after all, simply an agreed-on set of notation in which musical intervals are represented by steps on a scale. All Heinz did was map certain notations in the calculus into musical scales, assign values to the notes, and read the music. @@ -151,7 +151,7 @@ We had one flirtation with mainstream publishing, when John Brockman induced an After three years, the Napa Valley community began to break up and I found myself needing to go back to civilization and start earning a living. It was time to move on from the \booktitle{Laws of Form}. We made a big bundle of all of our manuscripts and mailed it off to Brown at his last known address in Cambridge, England, together with a letter saying how much we had enjoyed writing them and that we hope he liked them too. -A few weeks later he called us on the telephone from Cambridge. We were the only people at Esalen who'd got it, he said. He'd love to come to the States and visit us and how would we like to get together on a new publishing venture? He would offer as capital some fifty thousand copies of his latest book, a dictionary of music in which tunes were classified according the sequence of their musical intervals. (I have never actually seen this book.\fnote{Parsons, D., \booktitle{The Directory of Tunes and Musical Themes.} Spencer Brown \& Co., Cambridge, England, 1975.}) He also sent along a wonderful manuscript, a group of fables called \booktitle{Stories Children Won't Like} (never published, so far as I know), and announced that he had discovered a proof for the four-color theorem using the \booktitle{Laws of Form}.\fnote{At this time two American mathematicians had announced "proof" of this classic theorem (which states that four colors are sufficient to color a map on a surface of genus 0) that was actually a kind of demonstration, since it used a computer to exhaustively test all possible maps. Brown took a different approach and tried to prove that any map could be generated by four colors. A book by Brown on the four-color theorem was announced by Scribner's in 1974, but it apparently never saw print.} +A few weeks later he called us on the telephone from Cambridge. We were the only people at Esalen who'd got it, he said. He'd love to come to the States and visit us and how would we like to get together on a new publishing venture? He would offer as capital some fifty thousand copies of his latest book, a dictionary of music in which tunes were classified according the sequence of their musical intervals. (I have never actually seen this book.\fnote{Parsons, D., \booktitle{The Directory of Tunes and Musical Themes.} Spencer Brown \& Co., Cambridge, England, 1975.}) He also sent along a wonderful manuscript, a group of fables called \booktitle{Stories Children Won't Like} (never published, so far as I know), and announced that he had discovered a proof for the four-color theorem using the \booktitle{Laws of Form}.\fnote{At this time two American mathematicians had announced \dq{proof} of this classic theorem (which states that four colors are sufficient to color a map on a surface of genus 0) that was actually a kind of demonstration, since it used a computer to exhaustively test all possible maps. Brown took a different approach and tried to prove that any map could be generated by four colors. A book by Brown on the four-color theorem was announced by Scribner's in 1974, but it apparently never saw print.} Of course Kurt and I were delighted and immediately put ourselves at Brown's disposal. We had been working with no outside encouragement for three years, and here the fellow calls up and says yep, that's it, let's play ball. We knew we were right, understand. We had already shrugged off the feedback, from a well-known biographer of Wittgenstein, that we were mathematical innocents whose interpretation would be laughed at by Brown. Still, to have direct contact with the source was stimulating, to say the least. @@ -209,23 +209,23 @@ What story? What sort of message can we read in this rendering of the spoken wor The tortoise gives us the transformation to a new constellation, Lyra, known as the Little Tortoise, or Shell, \dq{thus going back to the legendary origin of the instrument from the empty covering of the creature cast upon the shore with the dried tendons stretched across it} (Allen, pp.\ 283). This is later Apollo's lyre, sevenstringed, discovered by Hermes, inventor of dice, three of which can permute the 56 minor arcana (Wotan again) and two the 21 major arcana, which, with the Fool, who is \e{hors commerce}, make up the deck of cards known as the Tarot, whose name has the same root as \dq{tortoise} (indo-european \e{wendh}, to turn, wind, weave), which is also the root of \dq{wander.} The twisting of the snakes on Hermes' staff, or perhaps the right-hand DNA double helix. One can pick up the skein at any point and begin to tease out a thread that will lead one through the labyrinth. -"This is indeed amazing." So wrote Brown upon surmising that the world we know is constructed "in order (and thus in such a way as to be able) to see itself." (\booktitle{Laws of Form}, pp.\ 105; notes to Chapter 11, reflected 1's, "Equations of the Second Degree," or self-referential functions) We are referred to the maze at Knossos, where the spider lady, Ariadne, had Theseus dangling by a string. We take hold of the string: LABYRINTHOS, from LABYRIS, not Greek but a Lydian word for "double axe." And we use the iconic representation of the double axe, {\tt [missing graphic]} as a framework upon which to construct the map of the labyrinth.% +\dq{This is indeed amazing.} So wrote Brown upon surmising that the world we know is constructed \dq{in order (and thus in such a way as to be able) to see itself.} (\booktitle{Laws of Form}, pp.\ 105; notes to Chapter 11, reflected 1's, \dq{Equations of the Second Degree,} or self-referential functions) We are referred to the maze at Knossos, where the spider lady, Ariadne, had Theseus dangling by a string. We take hold of the string: LABYRINTHOS, from LABYRIS, not Greek but a Lydian word for \dq{double axe.} And we use the iconic representation of the double axe, {\tt [missing graphic]} as a framework upon which to construct the map of the labyrinth.% \fnote{Cf. Richardson, L. J. D., \booktitle{The Labyrinth}, Dover, pp.\ 285--296, especially pp.\ 291.} We are being told here that all representations of life, e. g. stories, myths, fables, pictures, mathematics, are explicitly representations of themselves, self-referential. Re-presentations. And the thread we hold, that leads us out of the labyrinth, where no path seems to go anywhere, since they all come back on themselves, is language; we follow it to learn the order of the labyrinth. With the text (i.e. \e{teks}, to weave, fabricate) as a clue to the identity of the Vajrayogini as the mythical Joyce James, one can anywhere and everywhere pick up the thread upon which Brown has strung the pearls he has divined. \sec Points of View -Nevertheless, to make an expression meaningful, "we must add to it an indicator to present a place from which the observer is invited to regard it." (Page 103, \booktitle{Laws of Form}.) These pages reflect in one facet of the crystal mirror the vision of the real (meaningless), the true, the false, and the imaginary, mapped out on the plain crossed by G. Spencer Brown. The text, for instance, purports to be a transcript of the words Brown spoke at the South Coast Motel, a mile or so down the road from the sulphur baths at Big Sur, California, on the occasion of the AUM conference conceived by Alan Watts and John Lilly (the Master passing over the pole on the occasion of the last full moon before the vernal equinox). Confirmatory evidence for this viewpoint, definitely northern hemisphere (London) may be obtained from Henry Jacobs, Box 303, Sausalito, Calif. 94965, in the form of audio tapes of the conference. Anyone who listens to these tapes can verify that Spencer Brown's remarks are reproduced here with close, if not perfect, fidelity. +Nevertheless, to make an expression meaningful, \dq{we must add to it an indicator to present a place from which the observer is invited to regard it.} (Page 103, \booktitle{Laws of Form}.) These pages reflect in one facet of the crystal mirror the vision of the real (meaningless), the true, the false, and the imaginary, mapped out on the plain crossed by G. Spencer Brown. The text, for instance, purports to be a transcript of the words Brown spoke at the South Coast Motel, a mile or so down the road from the sulphur baths at Big Sur, California, on the occasion of the AUM conference conceived by Alan Watts and John Lilly (the Master passing over the pole on the occasion of the last full moon before the vernal equinox). Confirmatory evidence for this viewpoint, definitely northern hemisphere (London) may be obtained from Henry Jacobs, Box 303, Sausalito, Calif. 94965, in the form of audio tapes of the conference. Anyone who listens to these tapes can verify that Spencer Brown's remarks are reproduced here with close, if not perfect, fidelity. -Arriving at Cape Town, however, we cast the net tied by N. J. A. Sloane and catch the icon of an all-of-a-piece, multidimensional message to inner space---that is, the space of the eternal regions, where we find numbers, including the number represented, in the Arstic notation, as "2311."% -\fnote{"2311" is only one of the names assumed by Big M Plus One. This number is constructed by adding 1 to 2310, which is "prime factorial" for 11---that is, the product of all the primes up to and including 11: $2\times 3\times 5\times 7\times 11$. Under this alias, Big M Plus One is prime, not divisible by any numbers except itself and 1. In his next manifestation, however, as 30,031 (prime factorial plus 1 for 13), our space messenger is composite. Thus he confirms Brown's assurance, that "if you go on long enough, getting the final factorial, adding one, you will find one that is not prime; but that doesn't matter, because it will be divisible by a prime (in this case, two, 59 and 509) that is bigger than the biggest prime (13) you have used to produce it." As a messenger of Apollo, 11\textsuperscript{th} god on Olympus, Big M Plus One is pristine, prime; as a representative of Dionysus, the 13\textsuperscript{th}, he is ecstatic, beside himself.} -Here nothing is hidden, since the space is created "before the time came for time to begin," as Brown says C. E. Rolt says in his (Rolt's) introduction to the \booktitle{Divine Names} of Dionysius the Areopagite, and the eyes of the (one-way) blind are opened and the ears of the deaf unstopped. Messages from and to space are all around us, and we have only to read them. "In nature are signatures\slash needing no verbal tradition,\slash oak leaf never plane leaf."% +Arriving at Cape Town, however, we cast the net tied by N. J. A. Sloane and catch the icon of an all-of-a-piece, multidimensional message to inner space---that is, the space of the eternal regions, where we find numbers, including the number represented, in the Arstic notation, as \dq{2311.}% +\fnote{\dq{2311} is only one of the names assumed by Big M Plus One. This number is constructed by adding 1 to 2310, which is \dq{prime factorial} for 11---that is, the product of all the primes up to and including 11: $2\times 3\times 5\times 7\times 11$. Under this alias, Big M Plus One is prime, not divisible by any numbers except itself and 1. In his next manifestation, however, as 30,031 (prime factorial plus 1 for 13), our space messenger is composite. Thus he confirms Brown's assurance, that \dq{if you go on long enough, getting the final factorial, adding one, you will find one that is not prime; but that doesn't matter, because it will be divisible by a prime (in this case, two, 59 and 509) that is bigger than the biggest prime (13) you have used to produce it.} As a messenger of Apollo, 11\textsuperscript{th} god on Olympus, Big M Plus One is pristine, prime; as a representative of Dionysus, the 13\textsuperscript{th}, he is ecstatic, beside himself.} +Here nothing is hidden, since the space is created \dq{before the time came for time to begin,} as Brown says C. E. Rolt says in his (Rolt's) introduction to the \booktitle{Divine Names} of Dionysius the Areopagite, and the eyes of the (one-way) blind are opened and the ears of the deaf unstopped. Messages from and to space are all around us, and we have only to read them. \dq{In nature are signatures\slash needing no verbal tradition,\slash oak leaf never plane leaf.}% \fnote{\e{Canto LXXXVII}, Ezra Pound} Caught in the net of number, Big M Plus One provides name, rank, and serial, as required by convention, and stands revealed in an entirely different role, the index of non-cyclic simple groups and thus a nodal transfer point to the one-eyed Wotan, who braided the hairs of the Night Mare's tail.% \fnote{See \essaytitle{The Theory of Braids}, by Emil Artin in The American Scientist, Vol. 38, No. 1, pp. 112--119, January, 1950, and other references cited for the article \essaytitle{Group Theory and Braids} in Martin Gardner's \booktitle{New Mathematical Diversions} from Scientific American, Simon \& Schuster, New York, 1966.} We tie the net one knot at a time, and from any node, 2311 leads us to infinitely numerable license plates, phone numbers, grocery bills (\$23.11) and the like. -Wotan (Woden's Tag\slash Wednesday\slash mercredi\slash Mercury\slash Hermes\slash crossroads\slash messenger\slash traveler\slash wanderer\slash medium\slash Mittwoch\slash midweek\slash balance\slash 4th chakra\slash path with heart) carves the runes on a staff cut from Yggdrasil, the world ash, which binds together earth, heaven, and hell, branches mirroring roots, which we may allude to, but may not uncover without killing the tree. Sloane, p. 12, points out the mathematical aspect of trees, rooted and otherwise, as graphs containing "not closed paths" (unlike the net, in which we catch the icon). For the English language, a knowledge of which is assumed by Spencer Brown on the part of a reader of \booktitle{Laws of Form}, the roots are named with psychedelic clarity in \booktitle{The American Heritage Dictionary}, Houghton Mifflin, New York, pp. 1503--1550. In these pages, the (conjectured) Indo-European sources of the language are cross-indexed to the common words of the vocabulary; so that, for instance, having been referred from "tree" to the entry \e{deru-}, meaning "firm," or "solid," we find the collapsed meaning of "tree," "truth," "Druid," "trust," "trough," "troth," "durable," etc. The path leads through Greek \e{drus} (the d-t shift having been found out by the Brothers Grimm, who knew that fairy tales were about language, self-referential): oak for Oakville, Napa County, wine valley of Dionysus, where, at 7700 St. Helena Highway (named for the mother of Constantine, wasn't she?) under 700-year-old oaks this mad introduction is being written. +Wotan (Woden's Tag\slash Wednesday\slash mercredi\slash Mercury\slash Hermes\slash crossroads\slash messenger\slash traveler\slash wanderer\slash medium\slash Mittwoch\slash midweek\slash balance\slash 4th chakra\slash path with heart) carves the runes on a staff cut from Yggdrasil, the world ash, which binds together earth, heaven, and hell, branches mirroring roots, which we may allude to, but may not uncover without killing the tree. Sloane, p. 12, points out the mathematical aspect of trees, rooted and otherwise, as graphs containing \dq{not closed paths} (unlike the net, in which we catch the icon). For the English language, a knowledge of which is assumed by Spencer Brown on the part of a reader of \booktitle{Laws of Form}, the roots are named with psychedelic clarity in \booktitle{The American Heritage Dictionary}, Houghton Mifflin, New York, pp. 1503--1550. In these pages, the (conjectured) Indo-European sources of the language are cross-indexed to the common words of the vocabulary; so that, for instance, having been referred from \dq{tree} to the entry \e{deru-}, meaning \dq{firm,} or \dq{solid,} we find the collapsed meaning of \dq{tree,} \dq{truth,} \dq{Druid,} \dq{trust,} \dq{trough,} \dq{troth,} \dq{durable,} etc. The path leads through Greek \e{drus} (the d-t shift having been found out by the Brothers Grimm, who knew that fairy tales were about language, self-referential): oak for Oakville, Napa County, wine valley of Dionysus, where, at 7700 St. Helena Highway (named for the mother of Constantine, wasn't she?) under 700-year-old oaks this mad introduction is being written. Turning scales to feathers, like dinosaurs, we take flight for Christchurch, entering the imaginary state in which Shakuhachi Unzen, Woody Nicholson, and Primo the Fool braid their destinies, and in which these pages are a program note for the great Chaco Canyon Eisteddfod of 1976. @@ -239,7 +239,7 @@ In this context Joyce James appears as an aide to the llama Al Paca, liaison man \fnote{See J. Holloway, \booktitle{Figure of Pilgrim in Medieval Poetry}, unpublished doctoral thesis, Berkeley, 1974} The document presents the Joycean hypothesis that \booktitle{Laws of Form}, with its demonstration of the generation of Time, offers a means of mapping cultural transformations which themselves reflect our own transformations as refugees in Time. -Brown's performance at Esalen certainly earns him a place in the Eisteddfod finals, along with Ahab's black vision, the entry from the teenage author of essay \#768 in the Working With Negativity Sweepstakes, the taped hoax perpetrated by members of the Imaginary Liberation Front, and the dance of the Yellow Pearl herself, our first female "leader"---who, being uncommitted to any particular truth, replaces government by control of information, secrecy, and deceit with leadership through inspiration, education, and enlightenment, calling to account our Kings, corporations, Imaginary Persons before, and frequently above, the law. +Brown's performance at Esalen certainly earns him a place in the Eisteddfod finals, along with Ahab's black vision, the entry from the teenage author of essay \#768 in the Working With Negativity Sweepstakes, the taped hoax perpetrated by members of the Imaginary Liberation Front, and the dance of the Yellow Pearl herself, our first female \dq{leader}---who, being uncommitted to any particular truth, replaces government by control of information, secrecy, and deceit with leadership through inspiration, education, and enlightenment, calling to account our Kings, corporations, Imaginary Persons before, and frequently above, the law. Meanwhile Primo puzzles out the controls of the Adamantinus, which have been locked on a course for the Black Hole in Cygnus by the captain, Jetsun Rainbowshay, who has vanished. In the crystal navigation table, Primo finds maps to the cosmos---Laws of Form, the tortoise oracle, the I Ching, the Tarot, the dice of Hermes---which he can read only with the help of Melvin Fine. @@ -267,7 +267,7 @@ They say, \dq{All right, MS! {\tt [Mother Superior]} We give you the cultus, see \transcript{ \spkr{Mary} So start spelling out the sign \& beans. -\spkr{HG} We're sniffing, Apollo-like, lupine around da point here and coiling upon an oomphalosity white tower of ivory, such as that coveted by the hungry ghost of Ahab, who, we three Kings remember, ruddy-coiled out into the well drainage at the Good Lady (was it?) Samaritane (SOLDS!)\ld\ in the bottom of the Chariot, cancer, whirlpool, in the depth of the Form. And so we fain hunt the Whale. There shall be no personal rejection of the life of great beings. No more whales, elephants, dolphins to die. That is the tip of the balance, the stated, stipulated bias toward "compassion," which places others above ourselves, dedicating the benefit, if there be any, of this meditation to others. To the kings of the air, the generation of brave eagles who hunt the jet planes, kamikaze! Bees, humming birds, the red tail hawk, PALAKWAIO, Simurgh, Garuda bearing the Buddha of all the Buddhas, carrying the standard, from out of the dismal maze of the men in their fury contending for the right! +\spkr{HG} We're sniffing, Apollo-like, lupine around da point here and coiling upon an oomphalosity white tower of ivory, such as that coveted by the hungry ghost of Ahab, who, we three Kings remember, ruddy-coiled out into the well drainage at the Good Lady (was it?) Samaritane (SOLDS!)\ld\ in the bottom of the Chariot, cancer, whirlpool, in the depth of the Form. And so we fain hunt the Whale. There shall be no personal rejection of the life of great beings. No more whales, elephants, dolphins to die. That is the tip of the balance, the stated, stipulated bias toward \dq{compassion,} which places others above ourselves, dedicating the benefit, if there be any, of this meditation to others. To the kings of the air, the generation of brave eagles who hunt the jet planes, kamikaze! Bees, humming birds, the red tail hawk, PALAKWAIO, Simurgh, Garuda bearing the Buddha of all the Buddhas, carrying the standard, from out of the dismal maze of the men in their fury contending for the right! \spkr{Father} There. We now have the Holy Spirit out into the Marked State. Memory and genetics, the arithms as perceived by our senses and programed into our biocomputers. What seem to be invariants: K is for konstant. Now there's no sense everybody getting out at once. If Mary wants out into the Marked State, then who goes back into the Form to keep it all balanced? @@ -297,7 +297,7 @@ At the beginning, what I was concerned to do was---having left the academic worl I rapidly found that the logic I had learned at the University and the logic I had taught at Oxford as a member or the lofty faculty wasn't nearly sufficient to provide the answers required. The logic questions in university degree papers were childishly easy compared with the questions I had to answer, and answer rightly, in engineering. We had to devise machinery which not only involved translation into logic sentences with as many as two hundred variables and a thousand logical constants---AND's, OR's, IMPLIES, etc.---not only had to do this, but also had to do them in a way that would be as simple as possible to make them economically possible to construct---and furthermore, since in many cases lives depended upon our getting it right, we had to be sure that we did get it right. -For example, one machine that my brother and I constructed, the first machine I mentioned in \booktitle{Laws of Form}, counts by the use of what was then unknown in switching logic; it counts using imaginary values in the switching system. My brother and I didn't know what they were at the time, because they had never been used. We didn't at that time equate them with the imaginary values in numerical algebra. We know now that's what they are. But we were absolutely certain that they worked and were reliable, because we could see how they worked. However, we didn't tell our superiors that we were using something that was not in any theory and had no theoretical Justification whatever, because we knew that if we did, it would not be accepted, and we should have to construct something more expensive and less reliable. So we simply said---"Here it is, it works, it's O.K.," and British Railways bought it, we patented it, and the first use for it was for counting wagon wheels. It had to count backwards and forwards, and we had one at each end of every tunnel. When a train goes into a tunnel, the wagon wheels are counted, and when it comes out, they are counted. If the count doesn't match, an alarm goes out, and no one is allowed in that tunnel--at least, not very fast. +For example, one machine that my brother and I constructed, the first machine I mentioned in \booktitle{Laws of Form}, counts by the use of what was then unknown in switching logic; it counts using imaginary values in the switching system. My brother and I didn't know what they were at the time, because they had never been used. We didn't at that time equate them with the imaginary values in numerical algebra. We know now that's what they are. But we were absolutely certain that they worked and were reliable, because we could see how they worked. However, we didn't tell our superiors that we were using something that was not in any theory and had no theoretical Justification whatever, because we knew that if we did, it would not be accepted, and we should have to construct something more expensive and less reliable. So we simply said---\dq{Here it is, it works, it's OK,} and British Railways bought it, we patented it, and the first use for it was for counting wagon wheels. It had to count backwards and forwards, and we had one at each end of every tunnel. When a train goes into a tunnel, the wagon wheels are counted, and when it comes out, they are counted. If the count doesn't match, an alarm goes out, and no one is allowed in that tunnel--at least, not very fast. This had to be not only a very reliable counter, it had to count forwards and backwards, because---you know what happens when you get on the train: it goes along and then it stops and then it goes backwards for a bit, goes forwards. So, if the train was having its wheels counted, and then, for any reason, ran out of steam and got stuck and then slipped back, then the counter had to go backwards. So all this we had---but we made it in a way which was very much simpler than, and very much more reliable because of being so simple, than the counters in use at that time, which amounted to much more equipment, many more parts. This device was patented. The patent agent of the British Railways, who patented it---of course, we never told him what he was writing out. We just told him to write this down. And it worked, it has been used ever since, and though there have been many disasters in British Railways since that time, not a one of them has consisted of any train running into a detached wagon in a tunnel. Fingers crossed, touch wood. @@ -309,7 +309,7 @@ I must point out for emphasis at this time that the switching use and the use in \sec Boolean Mathematics -Logic, in other words, is itself not mathematics, it is an interpretation of a particular branch of mathematics, which is the most important non-numerical branch of mathematics. There are other non-numerical branches of mathematics. Mathematics is not exclusively about number. Mathematics is, in fact, about space and relationships. A number comes into mathematics only as a measure of space and\slash or relationships. And the earliest mathematics is not about number. The most fundamental relationships in mathematics, the most fundamental laws of mathematics, are not numerical. Boolean mathematics is prior to numerical mathematics. Numerical mathematics can be constructed out of Boolean mathematics as a special discipline. Boolean mathematics is more important, using the word in its original sense: what is important is what is imported. The most important is, therefore, the inner, what is most inside. Because that is imported farther. Boolean mathematics is more important than numerical mathematics simply in the technical sense of the word "important." It is inner, prior to, numerical mathematics---it is deeper. +Logic, in other words, is itself not mathematics, it is an interpretation of a particular branch of mathematics, which is the most important non-numerical branch of mathematics. There are other non-numerical branches of mathematics. Mathematics is not exclusively about number. Mathematics is, in fact, about space and relationships. A number comes into mathematics only as a measure of space and\slash or relationships. And the earliest mathematics is not about number. The most fundamental relationships in mathematics, the most fundamental laws of mathematics, are not numerical. Boolean mathematics is prior to numerical mathematics. Numerical mathematics can be constructed out of Boolean mathematics as a special discipline. Boolean mathematics is more important, using the word in its original sense: what is important is what is imported. The most important is, therefore, the inner, what is most inside. Because that is imported farther. Boolean mathematics is more important than numerical mathematics simply in the technical sense of the word \dq{important.} It is inner, prior to, numerical mathematics---it is deeper. \sec Origins @@ -317,15 +317,15 @@ Now at the beginning of 1961, the end of 1960, having set out, first of all, as \dinkus -This was all that was needed to make the whole of the construction which is detailed in \booktitle{Laws of Form}, and which will suffice for all the switching algebra, train routing, open\slash shut conditions, decision theory, the feedback arrangements, self-organizing systems, automation---and, amusingly enough, the logic by which we argue, the logic that is the basis of the certainty of mathematical theorems. In other words, the forms of argument which are agreed to be valid in the proof of a theorem in mathematics. To give you a simple one: "If $x$ implies not-$x$, then not-$x$." That is a commonly used argument\ld\ I can be sure that it is valid by the principles of the mathematics itself that underlies it. +This was all that was needed to make the whole of the construction which is detailed in \booktitle{Laws of Form}, and which will suffice for all the switching algebra, train routing, open\slash shut conditions, decision theory, the feedback arrangements, self-organizing systems, automation---and, amusingly enough, the logic by which we argue, the logic that is the basis of the certainty of mathematical theorems. In other words, the forms of argument which are agreed to be valid in the proof of a theorem in mathematics. To give you a simple one: \dq{If $x$ implies not-$x$, then not-$x$.} That is a commonly used argument\ld\ I can be sure that it is valid by the principles of the mathematics itself that underlies it. The arguments used to validate the theorems in \booktitle{Laws of Form}, as we now begin to see, are themselves validated by the calculus dependent upon those theorems. And yet, in no way is the argument a begging of the question. Now this is rather hard to understand, and perhaps it may come up in discussions later. \e{Principia-principii}, begging the question, it not a valid argument; it is a common fallacy. In no way is the question begged but in producing a system, in making its later parts come true, we use them to validate the earlier parts; and so the system actually comes from nothing and pulls itself up by its own bootstraps, and there it all is. -Nowhere does this become more evident than in this first and most primitive system of non-numerical mathematics; and I am quite sure---no, I will not say I am quite sure, when one says "I am quite sure" it means one is not quite sure---and I guess, I guess that why it is a branch of mathematics so neglected hitherto is that it is a bit too real. It is a bit too evident what game one is playing when one plays the game of mathematics. +Nowhere does this become more evident than in this first and most primitive system of non-numerical mathematics; and I am quite sure---no, I will not say I am quite sure, when one says \dq{I am quite sure} it means one is not quite sure---and I guess, I guess that why it is a branch of mathematics so neglected hitherto is that it is a bit too real. It is a bit too evident what game one is playing when one plays the game of mathematics. -If one starts much further away from the center, then you don't see the connections of what you are doing. You don't see that what comes out depends on what you put in. You can devise an academic system that goes on the assumption that there is objective knowledge, which we are busy finding out. We have come along here with wide-open eyes, and what we see over there---we come along and we give a demonstration, and we write it out, etc., and when somebody says, "But just what is it that gives the formula that shape? Why is it that shape and not some other shape? What is it that makes these things true? What is it that makes it so that when we see this, what makes it so--why isn't it otherwise?" And the stock answer is---"Ah, well, that is how it is, and that is the mystery." +If one starts much further away from the center, then you don't see the connections of what you are doing. You don't see that what comes out depends on what you put in. You can devise an academic system that goes on the assumption that there is objective knowledge, which we are busy finding out. We have come along here with wide-open eyes, and what we see over there---we come along and we give a demonstration, and we write it out, etc., and when somebody says, \dq{But just what is it that gives the formula that shape? Why is it that shape and not some other shape? What is it that makes these things true? What is it that makes it so that when we see this, what makes it so--why isn't it otherwise?} And the stock answer is---\dq{Ah, well, that is how it is, and that is the mystery.} -Mystery, after all, doesn't mean that we scratch our heads and look in astonishment and amazement. Mystery means something closed in. A mystic, if there is such a person, is not a person to whom everything is mysterious. He is a person to whom everything is perfectly plain. It's quite obvious. And the person who designates himself a non-mystic, and has nothing to do with that kind of "woolly thinking," is a person, an ordinary academic, who writes down his mathematical formulae, and when people say "Why do they look like that, why don't they look some way else"---"Well, they just are that way--it's perfectly justified by mathematics---if you do mathematics, that's what you have to learn to do." In fact, when one starts from the beginning, there is nothing to learn. There is everything to unlearn, but nothing to learn. +Mystery, after all, doesn't mean that we scratch our heads and look in astonishment and amazement. Mystery means something closed in. A mystic, if there is such a person, is not a person to whom everything is mysterious. He is a person to whom everything is perfectly plain. It's quite obvious. And the person who designates himself a non-mystic, and has nothing to do with that kind of \dq{woolly thinking,} is a person, an ordinary academic, who writes down his mathematical formulae, and when people say \dq{Why do they look like that, why don't they look some way else}---\dq{Well, they just are that way--it's perfectly justified by mathematics---if you do mathematics, that's what you have to learn to do.} In fact, when one starts from the beginning, there is nothing to learn. There is everything to unlearn, but nothing to learn. \transcript{ \spkr{KURT VON MEIER} When you told us about tunnels I saw the great psychocosmic projection of images and tales of the parable of Plato's cave. So I imagine you have provided us with the parable of the tunnel. It is in the shape of the hole of doughnut, topologically, so we could look for the seven-color rainbow with which to color it. See the map of a torus--it is seven colors. @@ -359,17 +359,17 @@ I believe the principle by which you can prove that you can color the surface of Therefore, you proceed by stages, the last learned is the first unlearned, and this way you could proceed safely. Related to what is in the books, we know they say that in order to proceed into the Kingdom, one must first purify oneself. This is the same advice, because the Kingdom is deep. What we talk of in the way of purification is the superficial muck that has been thrown at us. First of all that must be taken off, and the superficial layers of the personality must be purified. If we go to the Kingdom too soon, without having taken off the superficial layers and reconstructed in a simpler way, then there is a collapse. The advice is entirely practical. It is not a prohibition. There is no heavenly law to say that you may not enter the Kingdom of Heaven without first purifying yourself. However, if you do, the consequences may be disastrous for you as a person. -This is why in psychological, in psychotherapeutic treatment, normally the defenses are strong enough. As the psychiatrists will usually tell you, "If I push in this direction, you will be able to withstand me if you really need to." And it is much the same in all medicine. A rule I learned---I guess one learns it here, John, in the treatment of physiotherapy, manipulation of the limbs, etc.---we are allowed to go and pull them around with our little strength, but not to use machinery, because that may break something. The body can normally defend against one other body, and you don't usually break anything as long as you use one physiological equipment against one other. Usually the same; one mind against one other, the other mind is strong enough to withstand it. Start using other methods, drugs and\slash or mechanical treatment, and there you may do damage. You may get past defenses which were there in order that the personality should not be broken down too much, too soon. +This is why in psychological, in psychotherapeutic treatment, normally the defenses are strong enough. As the psychiatrists will usually tell you, \dq{If I push in this direction, you will be able to withstand me if you really need to.} And it is much the same in all medicine. A rule I learned---I guess one learns it here, John, in the treatment of physiotherapy, manipulation of the limbs, etc.---we are allowed to go and pull them around with our little strength, but not to use machinery, because that may break something. The body can normally defend against one other body, and you don't usually break anything as long as you use one physiological equipment against one other. Usually the same; one mind against one other, the other mind is strong enough to withstand it. Start using other methods, drugs and\slash or mechanical treatment, and there you may do damage. You may get past defenses which were there in order that the personality should not be broken down too much, too soon. \transcript{\spkr{WATTS} There is a value assumption in here about what is broken down. What is disaster, what does that mean? -\spkr{SPENCER BROWN} Well, it is a value judgment, true enough. In reality, it is all the same. In reality, it is a matter of indifference, but we are not here in reality. We are here on a system of assumptions, and we are all busy maintaining them. On that system, then we can say, "Well, that will keep the ship afloat, and this will pull the plug out and we will all sink."} +\spkr{SPENCER BROWN} Well, it is a value judgment, true enough. In reality, it is all the same. In reality, it is a matter of indifference, but we are not here in reality. We are here on a system of assumptions, and we are all busy maintaining them. On that system, then we can say, \dq{Well, that will keep the ship afloat, and this will pull the plug out and we will all sink.}} \sec Degree of Equations and the Theory of Types \transcript{\spkr{DOUGLAS KELLEY} As we go from second order equations to third order, I imagine you would like to maintain your two, and only two states, the marked and the unmarked. And if that is the case, in going from second to third order, do you get a more generalized concept of time, or a little different- I am just wondering what a third order equation would look like. -\spkr{SPENCER BROWN} Well, I think you mean "degree" equations first, second, and third degree equations. +\spkr{SPENCER BROWN} Well, I think you mean \dq{degree} equations first, second, and third degree equations. \spkr{KELLEY} A degree of indeterminacy, yes. @@ -379,27 +379,27 @@ Now, the whole of the first degree equation in the Boolean form are in terms of Now what nobody saw was that in numerical mathematics we had this going for years. As I showed in the preface to the American edition to \booktitle{Laws of Form}, any second degree equation---perhaps, for those of you who don't know it, perhaps I should put it up on the blackboard if nobody has objections to my using chalk. -You see, what Whitehead\slash Russell didn't allow, was a self-referential statement; they didn't allow to say that this statement is true. \aside{"This statement is false" written on board.} Suppose that this statement is true, then it can't be true because it says that it is false. O. K. then, supposing it is false, then it must be true because it says that it is false. And this is so awful, so terrifying, that they said, "Right. We will produce a rule. We call it the Theory of Types to give it a grand name." The Theory of Types says---it is as much unlike what it says as possible, so that when someone says, "Well, what is the rule by which you can't have this?"---"It's the Theory of types," so that the people who are learning think that there is a huge theory, you see, and when you understand this theory you will realize why it is that you can't have such a thing. There is no such theory at all. It is just the name given to the rule that anything like this you must do this to. \aside{Erases it.} That is the Theory of Types. +You see, what Whitehead\slash Russell didn't allow, was a self-referential statement; they didn't allow to say that this statement is true. \aside{\dq{This statement is false} written on board.} Suppose that this statement is true, then it can't be true because it says that it is false. O. K. then, supposing it is false, then it must be true because it says that it is false. And this is so awful, so terrifying, that they said, \dq{Right. We will produce a rule. We call it the Theory of Types to give it a grand name.} The Theory of Types says---it is as much unlike what it says as possible, so that when someone says, \dq{Well, what is the rule by which you can't have this?}---\dq{It's the Theory of types,} so that the people who are learning think that there is a huge theory, you see, and when you understand this theory you will realize why it is that you can't have such a thing. There is no such theory at all. It is just the name given to the rule that anything like this you must do this to. \aside{Erases it.} That is the Theory of Types. What they hadn't done was scratched out something like this. \aside{Writes $x^2+1=0$.} I'll just put it in the mathematical form. You see, Russell, as a senior wrangler, or second wrangler, in mathematics, should have been familiar with this equation. But he never connected it with what he had done. Now here is an equation which admittedly had a bad name for years. But it was so useful that all of phase theory in electricity depends on it. So let's fiddle with it. Here is our equation. We want to find the roots. We want to find the possible values of $x$. So let's fiddle with this and have a look for them. Well, here we go. Here we just subtract one from both sides; now we'll divide both sides by $x$. Well, $x^2$ divided by $x$ is $x$, equals $-1$ over $x$. Well, now, we see that we have in fact a self-referential equation. Everybody can see that. Let's have a look at this equation $x=-1\slash x$, and see whether it is amenable to any form of treatment, psychiatric or something. You have to psychoanalyze it. -The thing that makes the former statement so worrying, so frightening, is that we have the assumption that the statement, if it means anything at all, is either true or false. Here, we have the assumption that the number system runs \ld-1, -2, -3, zero, 1, 2, 3\ld\ and it goes on infinitely in an exact mirror both ways. So we assume that the number is not zero---zero is meaningless in the logic form. The statement is not meaningless. It is either positive or negative. We have got to make that analogy here. We equate "positive" with "true, n and "negative" with "false"---it doesn't matter which is which. So here is our number system as defined. Here is our equation from which we are supposed to find the possible values that $x$ can take. Now, we know that the equation must balance\ld so first of all we'll seek the absolute numerical value of $x$, irrespective of the sign, whether it's positive or negative. Now suppose $x$ were greater than one---not bothering about the sign for the moment---suppose it were greater than one---then this clearly would be---not bothering about the sign---less than one. If $x$ were less than one, then you have got something bigger over something smaller, this would be greater than one. So the only point at which it is going to balance numerically is if $x$ is a form of unity. Because you can see perfectly well that if this is greater then that would be smaller, if that is smaller, this would be greater. +The thing that makes the former statement so worrying, so frightening, is that we have the assumption that the statement, if it means anything at all, is either true or false. Here, we have the assumption that the number system runs \ld-1, -2, -3, zero, 1, 2, 3\ld\ and it goes on infinitely in an exact mirror both ways. So we assume that the number is not zero---zero is meaningless in the logic form. The statement is not meaningless. It is either positive or negative. We have got to make that analogy here. We equate \dq{positive} with \dq{true,} and \dq{negative} with \dq{false}---it doesn't matter which is which. So here is our number system as defined. Here is our equation from which we are supposed to find the possible values that $x$ can take. Now, we know that the equation must balance\ld so first of all we'll seek the absolute numerical value of $x$, irrespective of the sign, whether it's positive or negative. Now suppose $x$ were greater than one---not bothering about the sign for the moment---suppose it were greater than one---then this clearly would be---not bothering about the sign---less than one. If $x$ were less than one, then you have got something bigger over something smaller, this would be greater than one. So the only point at which it is going to balance numerically is if $x$ is a form of unity. Because you can see perfectly well that if this is greater then that would be smaller, if that is smaller, this would be greater. -So we have only got two forms of unity---plus one, minus one. So we'll try each in turn. So suppose $x$ equals plus one, now we'll substitute for $x$ in this equation and we have minus one over plus one equals minus one. $+1=-1\slash -1=-1$. So you've got plus one equals minus one. So try the other one, there is only one more. x equals minus one. Now we have minus one equals minus one over minus one equals plus one. $-1=-1\slash -1=+1$. So we have exactly the same paradox this time. Instead of "true" and "false," we have got "plus" and "minus." So using the Theory of Types consistently, the whole of the mathematics of equations of degree greater than one must be thrown out. But we know perfectly well that we can use this mathematics. What we do here is that effectively we have an oscillatory system---just as in the case of \booktitle{Laws of Form}, if you put it mathematically, we have $x$ cross equals $x$, $(x)=x$, or a cross going back into itself, $@x$). +So we have only got two forms of unity---plus one, minus one. So we'll try each in turn. So suppose $x$ equals plus one, now we'll substitute for $x$ in this equation and we have minus one over plus one equals minus one. $+1=-1\slash -1=-1$. So you've got plus one equals minus one. So try the other one, there is only one more. x equals minus one. Now we have minus one equals minus one over minus one equals plus one. $-1=-1\slash -1=+1$. So we have exactly the same paradox this time. Instead of \dq{true} and \dq{false,} we have got \dq{plus} and \dq{minus.} So using the Theory of Types consistently, the whole of the mathematics of equations of degree greater than one must be thrown out. But we know perfectly well that we can use this mathematics. What we do here is that effectively we have an oscillatory system---just as in the case of \booktitle{Laws of Form}, if you put it mathematically, we have $x$ cross equals $x$, $(x)=x$, or a cross going back into itself, $@x$). Supposing it is the marked state, then it puts the marked state back into itself, and the marked state within a cross produces the unmarked state outside. $(())=.$ So this rubs itself out and so you get the unmarked state fed back in, and so out comes the marked state again. \dinkus -Well, you see here the paradox which was overlooked by Russell, who wasn't a mathematician, although he was senior wrangler, and by Whitehead, who was, although he wasn't, well\ld\ Russell was a mathematician, he wasn't a man of mathematics. Whitehead was a man of mathematics. Russell knew the forms, but he actually had no instinctual ability in mathematics. Whitehead actually had. But Russell, being a stronger character, was able to program Whitehead, and you will see this if you examine the last mathematical work Whitehead wrote, which is called the \booktitle{Treatise on Universal Algebra with Applications, Vol. 1}. I asked Russell where Vol.---I said I had never been able to get \booktitle{Vol. 2}, and Russell said, "Oh, he never wrote it." So it's all sort of a mystery. But the mathematical principles of algebra, in the usual complicated way, are set out, including the Boolean algebras, in this volume produced in 1898, an only edition. By that time Russell, who was the stronger of the two characters, had got together with Whitehead to do \booktitle{Principia Mathematica}, which nobody was ever going to digest\ld\ It was a very ostentatious title, because they had chosen the title which Newton had used for his greatest work. +Well, you see here the paradox which was overlooked by Russell, who wasn't a mathematician, although he was senior wrangler, and by Whitehead, who was, although he wasn't, well\ld\ Russell was a mathematician, he wasn't a man of mathematics. Whitehead was a man of mathematics. Russell knew the forms, but he actually had no instinctual ability in mathematics. Whitehead actually had. But Russell, being a stronger character, was able to program Whitehead, and you will see this if you examine the last mathematical work Whitehead wrote, which is called the \booktitle{Treatise on Universal Algebra with Applications, Vol. 1}. I asked Russell where Vol.---I said I had never been able to get \booktitle{Vol. 2}, and Russell said, \dq{Oh, he never wrote it.} So it's all sort of a mystery. But the mathematical principles of algebra, in the usual complicated way, are set out, including the Boolean algebras, in this volume produced in 1898, an only edition. By that time Russell, who was the stronger of the two characters, had got together with Whitehead to do \booktitle{Principia Mathematica}, which nobody was ever going to digest\ld\ It was a very ostentatious title, because they had chosen the title which Newton had used for his greatest work. -Incidentally, it is an extraordinary thing in the academic world---people are very silent about these things---but it was a very, very presumptuous title, I think, to take for this work. \aside{Inaudible comment, to the effect, "Hasn't `Laws of Form' been used?"} Oh, no, nobody has used that title before---no, sir. If I had called it "Laws of Thought," that was used, many people have used that title, but it was not laws of thought. Oh, no, you are on the wrong track, sir. I am not being presumptuous in taking that title\ld\ I have called the book what it is, I have not done what Russell\slash Whitehead did and taken a very great book and called it by the same title. That is totally different. +Incidentally, it is an extraordinary thing in the academic world---people are very silent about these things---but it was a very, very presumptuous title, I think, to take for this work. \aside{Inaudible comment, to the effect, \dq{Hasn't \bt{Laws of Form} been used?}} Oh, no, nobody has used that title before---no, sir. If I had called it \dq{Laws of Thought,} that was used, many people have used that title, but it was not laws of thought. Oh, no, you are on the wrong track, sir. I am not being presumptuous in taking that title\ld\ I have called the book what it is, I have not done what Russell\slash Whitehead did and taken a very great book and called it by the same title. That is totally different. Now, this is what they overlooked in the formulation of the Theory of Types, which simply says you mustn't do this. However, both Russell and Whitehead had done it to get their wranglerships, get their degrees. But they had not done the simple thing of reducing this equation to this to see exactly what it was. -In fact, if you go to the Boolean forms and use something like this---there's your output---and you take it back in, input there and these are transistors used in a particular way, you have what is called a memory. And, if you put "minus" instead of "plus" there, $x^2-1=0$ \e{instead of} $x^2+1=0$, now what we have here, back in this form here, is our equation. Now we'll put it all in brackets and we'll take out the answer. Now we have exactly the same thing. And just as this is a memory circuit, if this is the marked state here, that must be the unmarked state.\fnote{Transmission of Spencer Brown's marks on the blackboard has been absorbed elsewhere in the system. We invite outside constructions. The general discussion concerns re-entry at an odd level and at an even level. If odd, as in $(x)$, we get marked state in and unmarked out, an oscillation. If even, $((x))$ we get marked in, marked out, a memory.} And if this is unmarked state, we've got no marked state here, so this will be marked. And we have a marked state feeding itself back into there, and if you rub that out and this goes unmarked, you still have marked here, so it remembers. Equally, if you now put a marked state here, that must be unmarked, and then you can take that off and it doesn't matter because now since you have got unmarked and unmarked this becomes marked, and this, you remember, is unmarked. Similarly here, if you put "plus one" for $x$, you get plus one over plus one equals plus one, \e{in} $x=1\slash x$, there is no paradox. You can also find a different answer for $x$, and that is minus one. You get plus one over minus one equals minus one, so that's all right too. So you have, in effect, a memory circuit, and if you put it this way, you can see that. You have an equation with two roots, and this is similarly an equation with two roots. Whatever root you get out, you put back ins and it remembers itself. If you are getting out "plus one," it feeds plus one in there, and it remembers it's plus one. You have a thing to knock it off and turn it into minus one; it feeds a minus one into there and out comes minus one, here, and it remembers it's minus one. Any equation of the second degree that is not paradoxical---that goes through two stages and not one---are the same, and this is a way of producing a memory circuit electronically. It is exactly analogous to this memory circuit numerically. And where, in fact, you put it back, instead of here, you put it back through an odd number such as one, now you have a paradoxical circuit. Because whatever it gets out it feeds back in and it changes. And if you turn that into "minus," $x^2=-1$, you now have a paradoxical equation. It can't remember, it just flutters. +In fact, if you go to the Boolean forms and use something like this---there's your output---and you take it back in, input there and these are transistors used in a particular way, you have what is called a memory. And, if you put \dq{minus} instead of \dq{plus} there, $x^2-1=0$ \e{instead of} $x^2+1=0$, now what we have here, back in this form here, is our equation. Now we'll put it all in brackets and we'll take out the answer. Now we have exactly the same thing. And just as this is a memory circuit, if this is the marked state here, that must be the unmarked state.\fnote{Transmission of Spencer Brown's marks on the blackboard has been absorbed elsewhere in the system. We invite outside constructions. The general discussion concerns re-entry at an odd level and at an even level. If odd, as in $(x)$, we get marked state in and unmarked out, an oscillation. If even, $((x))$ we get marked in, marked out, a memory.} And if this is unmarked state, we've got no marked state here, so this will be marked. And we have a marked state feeding itself back into there, and if you rub that out and this goes unmarked, you still have marked here, so it remembers. Equally, if you now put a marked state here, that must be unmarked, and then you can take that off and it doesn't matter because now since you have got unmarked and unmarked this becomes marked, and this, you remember, is unmarked. Similarly here, if you put \dq{plus one} for $x$, you get plus one over plus one equals plus one, \e{in} $x=1\slash x$, there is no paradox. You can also find a different answer for $x$, and that is minus one. You get plus one over minus one equals minus one, so that's all right too. So you have, in effect, a memory circuit, and if you put it this way, you can see that. You have an equation with two roots, and this is similarly an equation with two roots. Whatever root you get out, you put back ins and it remembers itself. If you are getting out \dq{plus one,} it feeds plus one in there, and it remembers it's plus one. You have a thing to knock it off and turn it into minus one; it feeds a minus one into there and out comes minus one, here, and it remembers it's minus one. Any equation of the second degree that is not paradoxical---that goes through two stages and not one---are the same, and this is a way of producing a memory circuit electronically. It is exactly analogous to this memory circuit numerically. And where, in fact, you put it back, instead of here, you put it back through an odd number such as one, now you have a paradoxical circuit. Because whatever it gets out it feeds back in and it changes. And if you turn that into \dq{minus,} $x^2=-1$, you now have a paradoxical equation. It can't remember, it just flutters. \dinkus @@ -441,15 +441,15 @@ There were some books written about time by a man called J. W. Dunn that I read \spkr{SPENCER BROWN} No. It can't be infinite, it can't be zero. So, the space determined by the first distinction is of no size. -\spkr{HEINZ VON FOERSTER} It's just "flippety" and not frequency. +\spkr{HEINZ VON FOERSTER} It's just \dq{flippety} and not frequency. -\spkr{SPENCER BROWN} Yes, just "flippety." +\spkr{SPENCER BROWN} Yes, just \dq{flippety.} \spkr{MAN} And that's saying it could be any size you want. -\spkr{SPENCER BROWN} No---you see, all this is a children's guide to the reality, "as if it had some size." It is not right to say it could be any size you want. Because you have to learn to think without size. Anything like that is misleading, just as it's misleading to say this can be any duration you want. It doesn't have duration. It just don't have it. Just like the void don't have quality. +\spkr{SPENCER BROWN} No---you see, all this is a children's guide to the reality, \dq{as if it had some size.} It is not right to say it could be any size you want. Because you have to learn to think without size. Anything like that is misleading, just as it's misleading to say this can be any duration you want. It doesn't have duration. It just don't have it. Just like the void don't have quality. -\spkr{GREGORY BATESON} What about the "then" of logic? "If two triangles have three sides, etc., then\ld" so-and-so. The "then" is devoid of time. +\spkr{GREGORY BATESON} What about the \dq{then} of logic? \dq{If two triangles have three sides, etc., then\ld} so-and-so. The \dq{then} is devoid of time. \spkr{SPENCER BROWN} Yes. There is no time in logic, because there can't be time without a self-referential equation, and by the rule of types, which is now in operation in the defining of current logic, there is no feedback allowed. Therefore all equations in logic are timeless. @@ -461,33 +461,33 @@ There were some books written about time by a man called J. W. Dunn that I read \spkr{SPENCER BROWN} A paradox circuit, yes. In putting it this way, this is the mathematics Of it. I can put it in numerical mathematics, it's the same paradox. Make something self-referential, it either remembers or it oscillates. It's either what it was before or it's what it wasn't before, which is the difference between memory and oscillation. -\spkr{WATTS} In introducing the word "before", haven't you introduced time? You have a sequence. +\spkr{WATTS} In introducing the word \dq{before}, haven't you introduced time? You have a sequence. -\spkr{SPENCER BROWN} I have to apologize, because you realize that in order to make myself understood in a temporal and even a physical existences as by convention is what we are in, remember I have to use words about the construction of the physical existence in order to talk about forms of existence that do not have these qualities. And if that were easy this is one of the obstacles put in- our way. Basically, to do what I am attempting to do is impossible. It is literally impossible, because one is trying to describe in an existence which has them--one is trying to describe in an existence which has certain qualities an existence which has no such quality. And in talking about the system, the qualities in the description do not belong to what we are describing. So when I say things like, "To oscillate, it is not what it was before; to remember, it is what it was before, n I am describing in our terms, something that it don't have. But, by looking at them, you can see.} +\spkr{SPENCER BROWN} I have to apologize, because you realize that in order to make myself understood in a temporal and even a physical existences as by convention is what we are in, remember I have to use words about the construction of the physical existence in order to talk about forms of existence that do not have these qualities. And if that were easy this is one of the obstacles put in- our way. Basically, to do what I am attempting to do is impossible. It is literally impossible, because one is trying to describe in an existence which has them--one is trying to describe in an existence which has certain qualities an existence which has no such quality. And in talking about the system, the qualities in the description do not belong to what we are describing. So when I say things like, \dq{To oscillate, it is not what it was before; to remember, it is what it was before,} I am describing in our terms, something that it don't have. But, by looking at them, you can see.} \sec Mystic \dq{Nonsense} -This is why in all mystical literature, people say, "Well, it is absolute nonsense." It has to be absolute nonsense because it is attempting to do this. But it is perfectly recognizable to those who have been there. To those who have not, it's utter nonsense. It will always be utter nonsense to those who have not been to where the speaker is describing from. +This is why in all mystical literature, people say, \dq{Well, it is absolute nonsense.} It has to be absolute nonsense because it is attempting to do this. But it is perfectly recognizable to those who have been there. To those who have not, it's utter nonsense. It will always be utter nonsense to those who have not been to where the speaker is describing from. The theory of communication is absolute nonsense. There is no reason whatsoever why you should understand what I am saying, or why I should understand what you are saying, if I don't recognize from the blah, blah, noises coming out of your mouth, that mean nothing whatever, where you have been. You make the same noises that I make when I have been there, that is all it is. -For example, Rolt, in his brilliant introduction to the \booktitle{Divine Names} by Diongsius the Areopagite, begins describing the form at first, and then he actually describes what happens when you get the temporal existence. It is all the same thing, but he is describing it in terms of religious talk, theorems become angels, etc. When he comes to the place, which he says most beautifully, having described all the heavenly states and all the people therein, etc., and he says, "All this went on in absolute harmony until the time came for time to begin." This is quite senseless. But it is perfectly understandable to someone who has seen what happens, who has been there. One cannot describe it except like this. It is perfectly understandable. Re had described the form and then he had done that, and this is the time for time to begin. +For example, Rolt, in his brilliant introduction to the \booktitle{Divine Names} by Diongsius the Areopagite, begins describing the form at first, and then he actually describes what happens when you get the temporal existence. It is all the same thing, but he is describing it in terms of religious talk, theorems become angels, etc. When he comes to the place, which he says most beautifully, having described all the heavenly states and all the people therein, etc., and he says, \dq{All this went on in absolute harmony until the time came for time to begin.} This is quite senseless. But it is perfectly understandable to someone who has seen what happens, who has been there. One cannot describe it except like this. It is perfectly understandable. Re had described the form and then he had done that, and this is the time for time to begin. \sec Mathematics and Its Interpretations: Nots and Crosses -There is just one question that I have been asked to answer, and I think it is something that you, Gregory, asked, wasn't it? to do with "not." Was the cross---the operator-was it "not." No it ain't. +There is just one question that I have been asked to answer, and I think it is something that you, Gregory, asked, wasn't it? to do with \dq{not.} Was the cross---the operator-was it \dq{not.} No it ain't. -If I can, I'll try to elucidate that. I am reminded of one of the last times I went to see Russell and he told me he had a dream in which at last he met "Not." He was very worried about this dream. He had a dream, and he met "Not, n and he couldn't describe it. But by the time we are using logic, we have in logic "not." +If I can, I'll try to elucidate that. I am reminded of one of the last times I went to see Russell and he told me he had a dream in which at last he met \dq{Not.} He was very worried about this dream. He had a dream, and he met \dq{not,} and he couldn't describe it. But by the time we are using logic, we have in logic \dq{not.} -We say: $a$ implies $b$. I am assuming that we know the old logic functions. You can describe this, $\neg a$, as "not a." Now that is not--that is a shorthand for "not" in logic. "Not" in logic means pretty well what it means when we are talking, because after all, logic is only mildly distinguished from grammar. Just as we learn after reading Shakespeare's sonnets that after all they are full of grammar. Some people seem to think that all we have to do is learn grammar to be able to write like that---not so. So, they're full of grammar---they're also full of logic. +We say: $a$ implies $b$. I am assuming that we know the old logic functions. You can describe this, $\neg a$, as \dq{not a.} Now that is not--that is a shorthand for \dq{not} in logic. \dq{Not} in logic means pretty well what it means when we are talking, because after all, logic is only mildly distinguished from grammar. Just as we learn after reading Shakespeare's sonnets that after all they are full of grammar. Some people seem to think that all we have to do is learn grammar to be able to write like that---not so. So, they're full of grammar---they're also full of logic. -Grammar is the analysis of the constructions used in speech, and logic is the analysis and the formulation of the structures and rules used in argument. Now in arguments, there are the variables, "if it hails, it freezes," and the forms; we can say in that case, it means the same thing as "either it doesn't hail, or it freezes," and find this is actually what "implies" means. We can break down "implies" into "not" and "or." +Grammar is the analysis of the constructions used in speech, and logic is the analysis and the formulation of the structures and rules used in argument. Now in arguments, there are the variables, \dq{if it hails, it freezes,} and the forms; we can say in that case, it means the same thing as \dq{either it doesn't hail, or it freezes,} and find this is actually what \dq{implies} means. We can break down \dq{implies} into \dq{not} and \dq{or.} -Now when we are interpreting whenever are using the mathematics\ld\ we write $a$ for "it hails," and $b$ for "it freezes." If it hails, then it freezes; either it doesn't hail or it freezes. And in the primary algebra we can write, "$a$ cross $b$," $(a)b$. The primary algebra does not mean that. We have given it that meaning for the purpose of operation, just as we may take a whole system of wires, electric motors, etc., and we can put it into a mathematical formula, or we can take some cars and weights, etc., and put them in one of Newton's formulae for findings acceleration. But the formula is not about cars, and so on and so forth; nor is this formula about statements in logic. Just as here we have used $a$ to represent the truth value of the sentence, "it hails," and $b$ to represent the truth value of the statement "it freezes," we are in fact applying, because we recognize the structure is similar, the states of the first distinction to the truth values of these statements. We recognize the form of the thing. And in fact, "not" ; is in this case, although it is represented by the cross, the cross itself is not the same as "not. n Because if it were---well, we can see obviously that it isn't, because, in this form we have represented "true" by a cross and "false" by a space\ld\ if you represent "true" by a space and "false" by a cross, then wherewith our "not"? We have swapped over and identified the marked state with untrue this time, and the unmarked state with true. And here we have identified it with untrue. Change over the identification, which we may do, and now here is the statement. And if this were "not," this would now have two "nots"---but it is not "not." We have only made it representative of "not" for the purpose of interpretation, just as well can give a color a number and use that in altering an equation. But the number and the color are not the same thing. This is not "not" except when we want to make it so. But it has a wider meaning than "not" in the book. +Now when we are interpreting whenever are using the mathematics\ld\ we write $a$ for \dq{it hails,} and $b$ for \dq{it freezes.} If it hails, then it freezes; either it doesn't hail or it freezes. And in the primary algebra we can write, \dq{$a$ cross $b$,} $(a)b$. The primary algebra does not mean that. We have given it that meaning for the purpose of operation, just as we may take a whole system of wires, electric motors, etc., and we can put it into a mathematical formula, or we can take some cars and weights, etc., and put them in one of Newton's formulae for findings acceleration. But the formula is not about cars, and so on and so forth; nor is this formula about statements in logic. Just as here we have used $a$ to represent the truth value of the sentence, \dq{it hails,} and $b$ to represent the truth value of the statement \dq{it freezes,} we are in fact applying, because we recognize the structure is similar, the states of the first distinction to the truth values of these statements. We recognize the form of the thing. And in fact, \dq{not} is in this case, although it is represented by the cross, the cross itself is not the same as \dq{not.} Because if it were---well, we can see obviously that it isn't, because, in this form we have represented \dq{true} by a cross and \dq{false} by a space\ld\ if you represent \dq{true} by a space and \dq{false} by a cross, then wherewith our \dq{not}? We have swapped over and identified the marked state with untrue this time, and the unmarked state with true. And here we have identified it with untrue. Change over the identification, which we may do, and now here is the statement. And if this were \dq{not,} this would now have two \dq{nots}---but it is not \dq{not.} We have only made it representative of \dq{not} for the purpose of interpretation, just as well can give a color a number and use that in altering an equation. But the number and the color are not the same thing. This is not \dq{not} except when we want to make it so. But it has a wider meaning than \dq{not} in the book. \transcript{\spkr{WATTS} Well, it means that it is distinct from. -\spkr{SPENCER BROWN} No, no---it means "cross."} +\spkr{SPENCER BROWN} No, no---it means \dq{cross.}} \sec Marked State\slash Unmarked State @@ -509,7 +509,7 @@ What people have done is that they have given a name always to both states. Ther \spkr{SPENCER BROWN} Oh, he didn't like it--he kept putting things in. The printer and the publisher went absolutely haywire because of equations like this, $(())=$. -\spkr{MAN} The American military documents, because of the number of pages that have to be printed, frequently have a blank page, And to be sure that nobody gets confused about it, there is always a statement on that page that says, "this page is deliberately left blank, which, of course, it is not. +\spkr{MAN} The American military documents, because of the number of pages that have to be printed, frequently have a blank page, And to be sure that nobody gets confused about it, there is always a statement on that page that says, \dq{this page is deliberately left blank,} which, of course, it is not. \spkr{SPENCER BROWN} You see, why it has taken so long for the Laws of Form to be written is that one has to break every law, every rule, that we are taught in our upbringing. And why it is so difficult to break them is that there is no overt rule that you may not do this---why it is so powerful is that the rule is covert.} @@ -529,13 +529,13 @@ Now to go on to what I was going to say, which is: next we want to use the mark, First of all, we have taken the mark as a name. And if you call a name twice, you are simply indicating the same state twice, and indicating the same state twice is the same as indicating the same state once. Now, instead of just calling this $m$, let us give it certain properties. Bet it be an instruction to cross the first distinction. -Now here is our illustration of the first distinction.\fnote{For illumination of what follows, see pp. 82--83 in the notes to Chapter 2, \booktitle{Laws of Form}.} Now this is why we've drawn this line on our blackboard, because here is an illustration of the first distinction. Here is a record of instructions referring to the first distinction---right. Now let $m$, the mark, be taken as an instruction to cross the boundary of the first distinction. So, if one is here, m says go there. If one is here, m says go there. O. E.? m is now not a name, so we can ring that for the moment, don't confuse yourself with that, m is now an instruction. And all m means is "cross." So whenever you hear or see it, you've got to step over the boundary. That is all it means. Now, we will produce more conventions. +Now here is our illustration of the first distinction.\fnote{For illumination of what follows, see pp. 82--83 in the notes to Chapter 2, \booktitle{Laws of Form}.} Now this is why we've drawn this line on our blackboard, because here is an illustration of the first distinction. Here is a record of instructions referring to the first distinction---right. Now let $m$, the mark, be taken as an instruction to cross the boundary of the first distinction. So, if one is here, m says go there. If one is here, m says go there. O. E.? m is now not a name, so we can ring that for the moment, don't confuse yourself with that, m is now an instruction. And all m means is \dq{cross.} So whenever you hear or see it, you've got to step over the boundary. That is all it means. Now, we will produce more conventions. \dinkus -We will say that we have got a number of crosses considered together, and these we will call "expressions." Now suppose you have this. We'll say---right---we'll represent $m$ like that. And we'll say $m$ means "cross" and we'll make a convention so that whatever is represented in here, you'll have crossed to get what is represented out there. So if there is nothing represented here, absence of the mark indicates the unmarked state. You cross when you are in the unmarked state and you find you are in the marked state. So out here by representation will be a value attributed to this mark, will be the marked state, and that is the value we attribute to that expression. +We will say that we have got a number of crosses considered together, and these we will call \dq{expressions.} Now suppose you have this. We'll say---right---we'll represent $m$ like that. And we'll say $m$ means \dq{cross} and we'll make a convention so that whatever is represented in here, you'll have crossed to get what is represented out there. So if there is nothing represented here, absence of the mark indicates the unmarked state. You cross when you are in the unmarked state and you find you are in the marked state. So out here by representation will be a value attributed to this mark, will be the marked state, and that is the value we attribute to that expression. -Now let us put the marked state in here, and we can do that simply by putting another cross in here. Now the convention is that wherever you see nothing you-are in the unmarked state. Wherever you see this, you must cross. So, here we are. We hear nothing, we see nothing, we are in the unmarked state. Our instructions now say "cross," so we cross, and then our second instruction says "cross," so we cross. So here we are, we started here and we have crossed, and we have crossed here, and so we can derive our second equation, $(())=$. So that all this says in mathematics is "cross." It does not say "not." It says "cross." +Now let us put the marked state in here, and we can do that simply by putting another cross in here. Now the convention is that wherever you see nothing you-are in the unmarked state. Wherever you see this, you must cross. So, here we are. We hear nothing, we see nothing, we are in the unmarked state. Our instructions now say \dq{cross,} so we cross, and then our second instruction says \dq{cross,} so we cross. So here we are, we started here and we have crossed, and we have crossed here, and so we can derive our second equation, $(())=$. So that all this says in mathematics is \dq{cross.} It does not say \dq{not.} It says \dq{cross.} \endnote{(End of first session.)} @@ -547,35 +547,35 @@ Now let us put the marked state in here, and we can do that simply by putting an \transcript{\spkr{VON FOERSTER} I think it would be lovely if you would make again for us the very important distinction between algebra and arithmetic. Because the concept of arithmetic is usually---although every child knows about it, and it is plain everyone knows about arithmetic---and here arithmetic comes up in a more, much more, fundamental point. And I thank, if this is made clear, I think a major gain will be made for everybody. -\spkr{SPENCER BROWN} I'll do what I can to make the distinction clear. I was going to say, "make the distinction plain," which means to put it on a plane. I suppose that most people know that the meaning of the word "plain," if you look at its root, is just another word for plane, plane like blackboard.\fnote{The Indo-European root is \e{pela:} flat, to spread. Related words in English are PLAIN, FIFrn, FLOOR, PALM, PLANET ("to wander," i. e. spread out) PLASMA, POETIC, POTTS. From related roots we get FLAEE, FLAG, PLEJA, PIANO, PLACENTA, FIAT, FICUNDER, PIANO, PEACE, OPIATE, bed.} To make plain is to put it on a plane. So that's what I will do. I will try to put this distinction between algebra and arithmetic on a plane. The reason it should go on a plane is that in a three-space it is difficult to disentangle the connections. So we project it onto a plane. On a plane, we can take a plan, which is the same word. We can see the relationships of the points on inner space, which is not too difficult to comprehend.} +\spkr{SPENCER BROWN} I'll do what I can to make the distinction clear. I was going to say, \dq{make the distinction plain,} which means to put it on a plane. I suppose that most people know that the meaning of the word \dq{plain,} if you look at its root, is just another word for plane, plane like blackboard.\fnote{The Indo-European root is \e{pela:} flat, to spread. Related words in English are PLAIN, FIFrn, FLOOR, PALM, PLANET (\dq{to wander,} i.e. spread out) PLASMA, POETIC, POTTS. From related roots we get FLAEE, FLAG, PLEJA, PIANO, PLACENTA, FIAT, FICUNDER, PIANO, PEACE, OPIATE, bed.} To make plain is to put it on a plane. So that's what I will do. I will try to put this distinction between algebra and arithmetic on a plane. The reason it should go on a plane is that in a three-space it is difficult to disentangle the connections. So we project it onto a plane. On a plane, we can take a plan, which is the same word. We can see the relationships of the points on inner space, which is not too difficult to comprehend.} -Now to make a distinction between algebra and arithmetic, I should go to the common distinction which is made in the schoolbooks, where you have---there are two subjects in kindergarten, perhaps a little beyond kindergarten---a subject called arithmetic, which is taught to you first, and then we have algebra, which is what the big boys and girls get onto and look rather superior about. First of all, let me explain---this word keeps coming up, "out on a plain"---that even arithmetic is not what is taught at school. Mathematics certainly isn't. What the child is first taught is the elements of computation---the computation of number, not of Boolean values. He is taught the elements of computation, which is wrongly called arithmetic. Whereas arithmetic is the--- +Now to make a distinction between algebra and arithmetic, I should go to the common distinction which is made in the schoolbooks, where you have---there are two subjects in kindergarten, perhaps a little beyond kindergarten---a subject called arithmetic, which is taught to you first, and then we have algebra, which is what the big boys and girls get onto and look rather superior about. First of all, let me explain---this word keeps coming up, \dq{out on a plain}---that even arithmetic is not what is taught at school. Mathematics certainly isn't. What the child is first taught is the elements of computation---the computation of number, not of Boolean values. He is taught the elements of computation, which is wrongly called arithmetic. Whereas arithmetic is the--- -Let's be clear, for the moment. I'll go back and start again. We should approach this slowly and deviously. I don't want to give the game away before we have got there. In arithmetic, so-called, which the child is---it is true that it doesn't begin with arithmetic, because the child is given an object, two object, three objects, four objects, and he is---I don't think that he is taught that there is something called a number, but he is then taught to write "one, two, three, four," etc., and he is not given that there is somewhere between that---that it one object, that is two objects and that and that, that, that---there is somewhere between these a non-physical existing thing called a number. As I point out in \booktitle{Only Two},\ednote{\booktitle{Only Two Can Play This Game}.} a number is something that is not of this world.\fnote{See Note 4, pp. 134--5.} That doesn't mean to say that it does not exist---it surely does. In fact, there are many extant groups of numbers. +Let's be clear, for the moment. I'll go back and start again. We should approach this slowly and deviously. I don't want to give the game away before we have got there. In arithmetic, so-called, which the child is---it is true that it doesn't begin with arithmetic, because the child is given an object, two object, three objects, four objects, and he is---I don't think that he is taught that there is something called a number, but he is then taught to write \dq{one, two, three, four,} etc., and he is not given that there is somewhere between that---that it one object, that is two objects and that and that, that, that---there is somewhere between these a non-physical existing thing called a number. As I point out in \booktitle{Only Two},\ednote{\booktitle{Only Two Can Play This Game}.} a number is something that is not of this world.\fnote{See Note 4, pp. 134--5.} That doesn't mean to say that it does not exist---it surely does. In fact, there are many extant groups of numbers. \transcript{\spkr{VON MEIER} Exstacy? Exstasis. -\spkr{SPENCER BROWN} Well, yes, that's "outstanding." Existence, \e{ex}, out, \e{stare}, to stand, outstanding. What outstands, exists. And numbers do not outstand, they do not exist in physical space, They exist in some much more primitive order of existence. But they, nevertheless, do exist. But not in the physical universe.} +\spkr{SPENCER BROWN} Well, yes, that's \dq{outstanding.} Existence, \e{ex}, out, \e{stare}, to stand, outstanding. What outstands, exists. And numbers do not outstand, they do not exist in physical space, They exist in some much more primitive order of existence. But they, nevertheless, do exist. But not in the physical universe.} -This, by the way, is the first way to confound the material scientist who thinks that physical existence is all there is. You ask him---"Well, you know that there are numbers?" He will perhaps have to say that there aren't any numbers; in that case, you can't beat him. If he admits that there is such a thing as a number, then you say, "Well, find it, where is it, show it to me," and he can't find it. It does not exist here. +This, by the way, is the first way to confound the material scientist who thinks that physical existence is all there is. You ask him---\dq{Well, you know that there are numbers?} He will perhaps have to say that there aren't any numbers; in that case, you can't beat him. If he admits that there is such a thing as a number, then you say, \dq{Well, find it, where is it, show it to me,} and he can't find it. It does not exist here. -Now, a child may come to learn very much later, here, there are objects arranged in groups, here are figures. Number is to be found in another space. Not in this space. However, these are the symbols, tokens of number, which can be in any form---Roman, etc. Playing around, saying "two plus three equals five," an elementary computation with numbers, is discovering relationships with numbers, and how they are constructed and what they do together. Sounds a bit rude, but that's what we do. +Now, a child may come to learn very much later, here, there are objects arranged in groups, here are figures. Number is to be found in another space. Not in this space. However, these are the symbols, tokens of number, which can be in any form---Roman, etc. Playing around, saying \dq{two plus three equals five,} an elementary computation with numbers, is discovering relationships with numbers, and how they are constructed and what they do together. Sounds a bit rude, but that's what we do. -When the child gets a bit older, he is taught what is called algebra. The first teaching of algebra that was given to me, it may be the same here, was that we were given things like "$a$ plus $b$ equals $c$; find $c$ when $a$ equals five and $b$ equals twelve." And we all scratched our heads and learned to do this sort Or thing. Eventually we came to formulae that were algebraic, and were finally told things that were universally true. We were taught that an algebraic relationship is true irrespective of what numbers $a$ and $b$ stand for. In other words, as we learned algebra, we learned it as an extension of arithmetic. +When the child gets a bit older, he is taught what is called algebra. The first teaching of algebra that was given to me, it may be the same here, was that we were given things like \dq{$a$ plus $b$ equals $c$; find $c$ when $a$ equals five and $b$ equals twelve.} And we all scratched our heads and learned to do this sort Or thing. Eventually we came to formulae that were algebraic, and were finally told things that were universally true. We were taught that an algebraic relationship is true irrespective of what numbers $a$ and $b$ stand for. In other words, as we learned algebra, we learned it as an extension of arithmetic. As we got a little older still and went to the university, we learned different names; and---we were taught that, whereas, these were \e{constants} and these were called \e{variables}, you could learn the science of algebra without ever knowing what those words stood for at all, treating algebra as a possible system, and having derived, actually, your rules of what to do, in the case of an ordinary algebra of numbers, from experimenting with the arithmetic. Eventually you see what the rules are, and you operate and find things out without referring back to the constants. I have given the game away now. This is the difference between an algebra and an arithmetic. The algebra is about the variables, or is the science of the relationships of variables. It is a science of the relationships of the variables when you don't know or don't care what constants they might stand for. Nevertheless, the constants aren't irrelevant, because whatever arithmetic this is an algebra of, if you were to substitute constants for this variables, $a$, $b$, etc., then these formulae still will hold. -A lot of people have said, you see, "How can you have an arithmetic without numbers?"---as the primary arithmetic in \booktitle{Laws of Form} is without numbers, we will go back in a moment to that. But just at the moment will emphasize, or return to, for memory purposes, the fact that the definition---the difference between algebra and arithmetic is that arithmetic is about constants, the algebra is about variables. The arithmetic is a science of the relations of constants. +A lot of people have said, you see, \dq{How can you have an arithmetic without numbers?}---as the primary arithmetic in \booktitle{Laws of Form} is without numbers, we will go back in a moment to that. But just at the moment will emphasize, or return to, for memory purposes, the fact that the definition---the difference between algebra and arithmetic is that arithmetic is about constants, the algebra is about variables. The arithmetic is a science of the relations of constants. In a common arithmetic for university purposes, which for a less vulgar name is called the Theory of Numbers, is the same thing. The Theory of Numbers is arithmetic, it's common arithmetic. The Theory of Numbers, the most beautiful science of all in mathematics---I happen to like it myself, so I praise it---or one of the most beautiful, is the science of the individuality of numbers. A number theorist knows each number in its individuality. He knows about the relationships it forms, and so on, as an individual, as a constant. An algebraist is not interested in the individuality of numbers, he is interested in the generality of numbers. He is more interested in the sociology of numbers that applies, whatever individual numbers come there; he has produced a rule where these people go there and there and there, and so on, and he's not interested in individuals at all. -A very interesting point here is the illustration of Gödel's theorem in the difference between, in number theory, an algebraic factoralization of a number and an accidental factoralization. As you know, we know from Gödel's Theorem that in the common arithmetic, that's the arithmetic of the integers, the algebraic representations, the rules of the algebraic manipulation of numbers, do not give you the whole story. It doesn't give you the complete story of what goes on in arithmetic. And so we have this factorial relationship---any number that is in that form, we know will factorize into that form. But there are what are called in Number Theory "accidental factoralizations," which happen over and above and irrespective of any algebraic factoralizations that you can find. And this is a very beautiful illustration of Gödel's Theorem. Nobody has ever used it. I think this is because, in general, mathematicians don't-understand Gödel's Theorem or even know what it says. I have lectured to an audience of university mathematics teachers Of maybe rifts. "Can anybody tell me Gödel's Theorem?" Not one. Not one knows what it is. It is one of the extraordinary breaks which mathematics took about the turn Of the century. Where a logic broke off from mathematics, and the two, you know, despised one another; like in gliding and power flying, they weren't speaking the same count. Hence we have this tremendous break, this schizophrenia, in mathematics, where common illustrations of one thing in another field just aren't seen as such. Accidental factoralization is a most beautiful illustration of Gödel's Theorem, if a somewhat technical one, in number theory.\fnote{The illustration below that the algebraic system is incomplete, since its rules do not generate all of its possible states.} +A very interesting point here is the illustration of Gödel's theorem in the difference between, in number theory, an algebraic factoralization of a number and an accidental factoralization. As you know, we know from Gödel's Theorem that in the common arithmetic, that's the arithmetic of the integers, the algebraic representations, the rules of the algebraic manipulation of numbers, do not give you the whole story. It doesn't give you the complete story of what goes on in arithmetic. And so we have this factorial relationship---any number that is in that form, we know will factorize into that form. But there are what are called in Number Theory \dq{accidental factoralizations,} which happen over and above and irrespective of any algebraic factoralizations that you can find. And this is a very beautiful illustration of Gödel's Theorem. Nobody has ever used it. I think this is because, in general, mathematicians don't-understand Gödel's Theorem or even know what it says. I have lectured to an audience of university mathematics teachers Of maybe rifts. \dq{Can anybody tell me Gödel's Theorem?} Not one. Not one knows what it is. It is one of the extraordinary breaks which mathematics took about the turn Of the century. Where a logic broke off from mathematics, and the two, you know, despised one another; like in gliding and power flying, they weren't speaking the same count. Hence we have this tremendous break, this schizophrenia, in mathematics, where common illustrations of one thing in another field just aren't seen as such. Accidental factoralization is a most beautiful illustration of Gödel's Theorem, if a somewhat technical one, in number theory.\fnote{The illustration below that the algebraic system is incomplete, since its rules do not generate all of its possible states.} Now having seen, therefore, the difference between algebra and arithmetic---simply that arithmetic is concerned with constants and algebra is concerned with variables---we have---well, as Whitehead points out in the \booktitle{Treatise on Universal Algebra, Vol. 1}, he points out that Boolean algebra is the only for non-numerical algebra known. Shortly after that, there was a book written by Dickson, who is also a number theorist of some considerable fame, who wrote a very wonderful book called \booktitle{The History of the Theory Of Numbers}, now published by Dover;\fnote{In the United States, by the Chelsea Publishing Co., New York. A reprint Of Carnegie Destitute Publication \#256 (28). By Leonard Eugene Dickson.} and anybody who is interested I think should get it because it contains all that would be of interest, except a very few later things. And he starts right at the beginning with amicable numbers, and shows that the early mathematicians, if they wanted to be friends with somebody, would find a pair Of amicable numbers, and they would then swap numbers and they would eat the number of their friend, to keep the friendship. All this is in the \booktitle{History of the Theory of Numbers}, by Dickson, which is a wonderful book. He also wrote a book called \booktitle{Algebras and their Arithmetics,} which---I don't think he actually said it, but it was obvious that every algebra has an arithmetic. -At the same time, mathematical popularized such as W. W. Sawyer were writing popular expositions Of various forms of mathematics, including Boolean algebra. And Sawyer heads his chapter on Boolean algebra, "The algebra without an arithmetic." This can't be. This can't be. If it is an algebra, it must have an arithmetic. And if any mathematician could write this---I am not blaming Sawyer; Sawyer was only standardizing what is common mathematics taught in universities today. He is standardizing the common confusion and block. The fact that mathematics teachers in universities today do not understand the difference between an algebra and an arithmetic, which is simple. +At the same time, mathematical popularized such as W. W. Sawyer were writing popular expositions Of various forms of mathematics, including Boolean algebra. And Sawyer heads his chapter on Boolean algebra, \dq{The algebra without an arithmetic.} This can't be. This can't be. If it is an algebra, it must have an arithmetic. And if any mathematician could write this---I am not blaming Sawyer; Sawyer was only standardizing what is common mathematics taught in universities today. He is standardizing the common confusion and block. The fact that mathematics teachers in universities today do not understand the difference between an algebra and an arithmetic, which is simple. \sec How to Find \booktitle{Laws of Form} @@ -609,9 +609,9 @@ We can give a demonstration, a computer can demonstrate, we just follow the rule \sec Prime Numbers -And we take, for example---or for the purpose of illustration---Euclid's proof of his beautiful theorem; the question asked, "Is the number of primes infinite?" As we see, the prime numbers, and it's obvious when you think of it, as they go on, they get sparser. It's very obvious that they will, if you consider it, because every time we have a new one, we have a new divisor which is likely to hit one of the numbers we're looking for to see if it's prime. If it hits it, if it divides into its then it won't be prime. So, the bigger the number, the less likely it is to be prime. A strange sort of statement. The science of certainty, taken in probability terms. Because the more primes there are that could divide into it. So for fairly obvious reasons, as we continue in the number series, the primes get, in general, further and further apart. there are fewer and fewer of them. And what Euclid asked was, do they get so thinly scattered that in the end they stop altogether? Or does this never happen? +And we take, for example---or for the purpose of illustration---Euclid's proof of his beautiful theorem; the question asked, \dq{Is the number of primes infinite?} As we see, the prime numbers, and it's obvious when you think of it, as they go on, they get sparser. It's very obvious that they will, if you consider it, because every time we have a new one, we have a new divisor which is likely to hit one of the numbers we're looking for to see if it's prime. If it hits it, if it divides into its then it won't be prime. So, the bigger the number, the less likely it is to be prime. A strange sort of statement. The science of certainty, taken in probability terms. Because the more primes there are that could divide into it. So for fairly obvious reasons, as we continue in the number series, the primes get, in general, further and further apart. there are fewer and fewer of them. And what Euclid asked was, do they get so thinly scattered that in the end they stop altogether? Or does this never happen? -This is an example, now, of a mathematical theorem. To make it into a theorem, you actually give the answer, you actually state the proposition, "The number of primes is endless." You may not be certain whether it's true or not; you may still be asking the question, do they come to an end or do they go on? +This is an example, now, of a mathematical theorem. To make it into a theorem, you actually give the answer, you actually state the proposition, \dq{The number of primes is endless.} You may not be certain whether it's true or not; you may still be asking the question, do they come to an end or do they go on? Well, to illustrate the difference between mathematical art, because it now needs an art to do the theorem, where it only used a technique, a mechanical application, to demonstrate something, and we don't need to do it ourselves, as computers can do it so much better, we will now do something that a computer can never do. Because what we are going to do is find the answer to this question--do the primes go on forever or not? We are going to find this answer quite definitely, and we are not going to find it by computation, because it cannot be found by computation; but it can be found like this. This is the way Euclid found it. Be said, supposing they come to a stop---all right, if they come to a stop, then we know they are going to go on for a long time until we come to big primes, but, if they do come to a stop, there will be some largest prime, call it big $N$. That's it. That is the last prime, the biggest of the lot. If they come to a stop, there must be such a prime. Now, if there is such a prime, and there it is up there, let us construct a number which looks like this: all primes, every single one of them, up to and including Big N. Right. We have made this number by multiplying all the primes together Now, Big N being the largest, this is a number which is made of all the primes there are, there isn't another prime. Because we have assumed that this is the largest. @@ -645,7 +645,7 @@ Anyway, I do assure you that if you go on long enough, getting the final factori \sec Theorems and Consequences -Now, this is totally confused, the idea of the difference between demonstration and proof in mathematics. In fact, Russell, you see, in suggesting it, completely confused them, and people have done so ever since. What he called theorems are in fact consequences, they are algebraic consequences, which can be, in fact, demonstrated. And indeed, he says, "These theorems"---he calls them theorems, they are consequences---"can be proved." And then he does the demonstration and then he calls it \e{Dem.} \e{Dem.} is short for "demonstration."---The two words are used interchangeably and wrongly. There is a difference, and what can be demonstrated is done within the system and can be done by computer. And what cannot be demonstrated, but may be proved, cannot be done by computer. It must have a person to do it. No computer can prove it, because it is not proved by computation. The steps of this proof, Euclid's proof, were not computational steps. No one could do it on a computer, because we were not doing computation. We were divining the answer, we were divining what had to be done by making certain deductions and seeing what they led to. This was an artistic process, not a mechanical one. +Now, this is totally confused, the idea of the difference between demonstration and proof in mathematics. In fact, Russell, you see, in suggesting it, completely confused them, and people have done so ever since. What he called theorems are in fact consequences, they are algebraic consequences, which can be, in fact, demonstrated. And indeed, he says, \dq{These theorems}---he calls them theorems, they are consequences---\dq{can be proved.} And then he does the demonstration and then he calls it \e{Dem.} \e{Dem.} is short for \dq{demonstration.}---The two words are used interchangeably and wrongly. There is a difference, and what can be demonstrated is done within the system and can be done by computer. And what cannot be demonstrated, but may be proved, cannot be done by computer. It must have a person to do it. No computer can prove it, because it is not proved by computation. The steps of this proof, Euclid's proof, were not computational steps. No one could do it on a computer, because we were not doing computation. We were divining the answer, we were divining what had to be done by making certain deductions and seeing what they led to. This was an artistic process, not a mechanical one. The computer cannot do it because it is not computation. Computation is counting in either direction, no more, no less. There is nothing more to computation than that, nothing more. @@ -671,7 +671,7 @@ Also, they had a precedent in that Euclid himself already rightly called this a \transcript{\spkr{VON FOERSTER} I think the \e{QED} thing makes it appear as though it were a demonstration---\e{quod erat demonstrandum}. It should not have been called \e{demonstrandum}. -\spkr{SPENCER BROWN} I may be wrong, you see. My Latin---I have little of it---perhaps he was OK. He said \e{quod erat demonstrandum}, "this has been demonstrated." It is OK after a demonstration, it is misleading after a proof. And maybe he did not make this error, but we have. We have called them theorems when we should call them consequences. And this has been responsible for---a vast system of error has grown up there. Because a computer has been found to be able to demonstrate consequences---because all you need is the calculating facility to do this. And consequently the demonstration of consequences, in other words, calculations, has been confused with the proof of theorems, which is another matter altogether. Because of this confusion, it has been thought that a computer therefore can do practically all that a man's mind can do. But it can't, because only the most minor function of a man's mind, done very badly, is to compute. And we have, in fact this tremendous emphasis, because of the confusion in mathematics---the difference between computation and actual mathematical thinking--which has led us to believe that computers have minds, can do what we can do.} +\spkr{SPENCER BROWN} I may be wrong, you see. My Latin---I have little of it---perhaps he was OK. He said \e{quod erat demonstrandum}, \dq{this has been demonstrated.} It is OK after a demonstration, it is misleading after a proof. And maybe he did not make this error, but we have. We have called them theorems when we should call them consequences. And this has been responsible for---a vast system of error has grown up there. Because a computer has been found to be able to demonstrate consequences---because all you need is the calculating facility to do this. And consequently the demonstration of consequences, in other words, calculations, has been confused with the proof of theorems, which is another matter altogether. Because of this confusion, it has been thought that a computer therefore can do practically all that a man's mind can do. But it can't, because only the most minor function of a man's mind, done very badly, is to compute. And we have, in fact this tremendous emphasis, because of the confusion in mathematics---the difference between computation and actual mathematical thinking--which has led us to believe that computers have minds, can do what we can do.} For example, they put Russell's consequences on the Titan computer at Cambridge. It managed, with great hesitation and very slowly, to demonstrate a few of them, but the more complicated of them it couldn't demonstrate. However, it could have done it, eventually. It was very slow and expensive. Even here, what a computer can do, a man can do better if he gives himself to the problem, because he has the capacity of seeing in---a way the computer never can. @@ -699,17 +699,17 @@ It's just not possible to do everything all at once. You can't make the rice gro \spkr{LILLY} Yes, this one of the spaces. -\spkr{SPENCER BROWN} The part of the observer? "We now see that the first distinction, the observer, and the mark, are not only interchangeable, but, in the form, identical."\fnote{pp. 76, \booktitle{Laws of Form.} \& also Blake couplet quoted on pp.\ 126, \booktitle{Only Two Can Play This Game}, "If you have made a circle to go into\slash Go into it yourself and see how you would do."} I don't see how you didn't get it already.} +\spkr{SPENCER BROWN} The part of the observer? \dq{We now see that the first distinction, the observer, and the mark, are not only interchangeable, but, in the form, identical.}\fnote{pp. 76, \booktitle{Laws of Form.} \& also Blake couplet quoted on pp.\ 126, \booktitle{Only Two Can Play This Game}, \dq{If you have made a circle to go into\slash Go into it yourself and see how you would do.}} I don't see how you didn't get it already.} -The convention is that we learn to grow up blithe game that we are taught to play is that there is a person called "me" in a body called "my body," who trots about and makes noises and looks out through eyes upon an alien, objective thing we call "the world," or, if we want to be a bit grander, called "the universe," which the thing called "me" in "my body" can go out and explore and make notes about and find this, that, and the other thing, find a tortoise, and make notes about a tortoise, and drawings, etc. The convention is that this tortoise is somehow not me, but is some object independent of me, which I in my body have found. +The convention is that we learn to grow up blithe game that we are taught to play is that there is a person called \dq{me} in a body called \dq{my body,} who trots about and makes noises and looks out through eyes upon an alien, objective thing we call \dq{the world,} or, if we want to be a bit grander, called \dq{the universe,} which the thing called \dq{me} in \dq{my body} can go out and explore and make notes about and find this, that, and the other thing, find a tortoise, and make notes about a tortoise, and drawings, etc. The convention is that this tortoise is somehow not me, but is some object independent of me, which I in my body have found. -We also have a further convention---well, depending on what sort of people we are, if we are behaviorists, we may not think this---most of us think that the tortoise also sees life in much the same way---that it is a being that has "my shell," "my feet," "my tail," "my head," "my eyes," out of which I look through the hole in the front of my shell and I see objects, big things walking around on two feet, etc., which are different from me. And we think that the tortoise thinks that. +We also have a further convention---well, depending on what sort of people we are, if we are behaviorists, we may not think this---most of us think that the tortoise also sees life in much the same way---that it is a being that has \dq{my shell,} \dq{my feet,} \dq{my tail,} \dq{my head,} \dq{my eyes,} out of which I look through the hole in the front of my shell and I see objects, big things walking around on two feet, etc., which are different from me. And we think that the tortoise thinks that. Now, supposing that this is only a hypothesis. Supposing that---if there were a distinction---if there were that---only supposing that, if it could be, what would happen---well, if one imagined---supposing one imagined, well, this is me and that ain't me. Surprise, surprise, what ain't me is exactly the same shape as what is me. Surprise, surprise. Come to this another way. Take it philosophically. take it philosophically and scientifically. Scientifically, on the basis of, there is an objective existence which we can see with our eyes and feel with our fingers and hear with our ears, and taste with our tongues, smell with our nose, etc., and then we take it to ants. Now ants can see ultraviolet light, which we can't see, and therefore the sky looks quite different to it. Take it to extremes. If there are beings with senses, none of which compares with ours, how could they possibly see a world which compares with ours? In other words, even if one considered it scientifically, the universe as seen appears according to the form of the senses to which it appears. Change the senses, the appearance of the universe changes. Ask a philosophical question and you get a philosophical answer. What therefore is the objective universe that is independent of these senses? There can be no such universe, because it varies according to how it is seen, the sensory apparatus. Take this a little further, and we see that we have made a distinction which don't exist. We have distinguished the universe from the sensory apparatus. But since the universe changes according to changes in the sensory apparatus, we have not distinguished the universe from the sensory apparatus. Therefore, the universe and the sensory apparatus are one. Row, then, does it appear that it is so solid and objective looking? -Now, the answer to this profound question takes a lot of thought, but I will try to give it all to you in a very short time. Because it takes a whole series of remarkable\fnote{Re-markable, markable again ("a whole series").} tricks before it can be made to appear like this. But since, if there ain't no such thing, then any trick within the \booktitle{Laws of Form} is possible, this happens to be one of the possible tricks. If there is no such universe, if there is only appearances then appearance can appear any way it can. You have only to imagine it, and it is so. +Now, the answer to this profound question takes a lot of thought, but I will try to give it all to you in a very short time. Because it takes a whole series of remarkable\fnote{Re-markable, markable again (\dq{a whole series}).} tricks before it can be made to appear like this. But since, if there ain't no such thing, then any trick within the \booktitle{Laws of Form} is possible, this happens to be one of the possible tricks. If there is no such universe, if there is only appearances then appearance can appear any way it can. You have only to imagine it, and it is so. \transcript{\spkr{BATESON} Can you go into the proof? @@ -727,7 +727,7 @@ Now, the answer to this profound question takes a lot of thought, but I will try \spkr{VON MEIER} Yes, they carry their numbers on their back---13 variations in the shells in a certain pattern. It's the second avatar of Vishnu, so that when you see the turtle, you're seeing it from the point at which the Ethologists named it God. They have named the serpent the first avatar of Vishnu. She's the cosmic turtle swimming in the sea. And things that run around, run around on the back of the turtle. -\spkr{LILLY} This is called "maya-matics."} +\spkr{LILLY} This is called \dq{maya-matics.}} \sec Solid State @@ -739,7 +739,7 @@ Now, the answer to this profound question takes a lot of thought, but I will try \transcript{\spkr{JEAN TAUPIN} Any reality is real, the moment you perceive it as real? -\spkr{SPENCER BROWN} Well, "reality" means "royalty." The words have the same root.\fnote{ \booktitle{American Heritage Dictionary} gives REALI from Indo-European root \e{rei-}, "possession, thing" (Latin \e{res}, thing.); ROYAL from IE \e{regi-} "to move in a straight line" (Latin \e{rex}, king), REAL a Spanish coin; \e{rectus}, right, straight RF\&YM; RECTOR RECTUM; L. \e{regular} straight piece of wood, rule REGULATE, RULE; Middle Dutch \e{rec-} framework RACE; Sanskrit \e{raiati}, he rules RAJAH.} Whatever is real is royalty. And what is royalty but what is universal---the form of the families of England. +\spkr{SPENCER BROWN} Well, \dq{reality} means \dq{royalty.} The words have the same root.\fnote{ \booktitle{American Heritage Dictionary} gives REALI from Indo-European root \e{rei-}, \dq{possession, thing} (Latin \e{res}, thing.); ROYAL from IE \e{regi-} \dq{to move in a straight line} (Latin \e{rex}, king), REAL a Spanish coin; \e{rectus}, right, straight RF\&YM; RECTOR RECTUM; L. \e{regular} straight piece of wood, rule REGULATE, RULE; Middle Dutch \e{rec-} framework RACE; Sanskrit \e{raiati}, he rules RAJAH.} Whatever is real is royalty. And what is royalty but what is universal---the form of the families of England. \spkr{VON MEIER} The measure, the \e{rex}, the \e{regulus}. @@ -763,7 +763,7 @@ I had been working on the second-degree equations for five years at least. I was \dinkus -We had been using it, my brother and I, in engineering, but we still didn't recognize what it was. So I sat down to write Chapter 11 and without thinking I wrote down the title. I wasn't sure what I was going to call it, but I wrote something without thinking. I looked at it and I found what I had written was "Equations of the second degree." Now, I was not aware of writing this down. The moment I had written it, that was---Eureka---that is what it was. The moment that I spoke of it to my brother and then to other mathematicians, it began to focus. Yes, of course. And then it was only a matter of an hour or so to go through and see the analogy, which I did on the blackboard this morning. To see the paradoxes and everything, all the same, all existent in the ordinary common arithmetical equations of the second degree. And this is what we were doing in the thrown-out Theory of Types; the coming to the knowledge of what it is. +We had been using it, my brother and I, in engineering, but we still didn't recognize what it was. So I sat down to write Chapter 11 and without thinking I wrote down the title. I wasn't sure what I was going to call it, but I wrote something without thinking. I looked at it and I found what I had written was \dq{Equations of the second degree.} Now, I was not aware of writing this down. The moment I had written it, that was---Eureka---that is what it was. The moment that I spoke of it to my brother and then to other mathematicians, it began to focus. Yes, of course. And then it was only a matter of an hour or so to go through and see the analogy, which I did on the blackboard this morning. To see the paradoxes and everything, all the same, all existent in the ordinary common arithmetical equations of the second degree. And this is what we were doing in the thrown-out Theory of Types; the coming to the knowledge of what it is. How actually does this happen? It happened something like that, after five years of scratching one's head but thinking, nevertheless, let's find out more about it. And then it comes, in a way, quite unexpectedly; in a way, really, for which one can take no personal credit. @@ -773,7 +773,7 @@ How actually does this happen? It happened something like that, after five years \spkr{SPENCER BROWN} Well, I will distinguish the proceeding. It goes very much like the education of the child. The child is born knowing it all, and it immediately has this bashed out of it. It's very disturbing. So it learns the game then. It learns the game that is played all around it---and with variations, it is much the same game in any culture, whether it is the ghetto, or ten thousand years ago, or today in America, or today in England, or today in China, or wherever it might be. It's much the same thing, with variations, of course, in the particular cultural pattern. It has its original knowledge bashed out---it must be bashed. Those of us who have gone back and remembered our births, remembered what we knew, and remembered the covenant we then made with those standing around our cradle, the realization that we now have to forget everything and live a life--- -\spkr{RAM DASS} Excuse me, is the word "know" the proper word to use? Doesn't that imply a knower and an object that is known? Couldn't you say that the infant was being it all? +\spkr{RAM DASS} Excuse me, is the word \dq{know} the proper word to use? Doesn't that imply a knower and an object that is known? Couldn't you say that the infant was being it all? \spkr{SPENCER BROWN} If you like, yes. I am only using words---you see, the language is no good for talking this way. We have to use these imperfect terms, which are based on distinctions. And you are quite right, it is not knowing, it is only in its interpretation, knowing. It is like dreaming a funny dream. While the dream is going on, it isn't funny. But bring it out into the critical atmosphere of waking life---now it appears funny. The child is bringing out into this, and it remembers it an knowing it. That is the way it is taught the disciplines.} @@ -807,7 +807,7 @@ How actually does this happen? It happened something like that, after five years \spkr{PRIBRAM} I don't know, I just got it to that stage. -\spkr{SPENCER BROWN} Let's simply go through the procedure again. the covenant with the world that the child rapidly has to make is---"Right. I am not allowed to notice this." But the child perceives where the lines are drawn and not drawn, and then suddenly it realizes that is must put on the same blocks, otherwise it will not be accepted. There is a moment of sanity when this happens. However, it's "good-bye" for quite a long time, I don't know how long. If it is to survive, it's "good-bye," and "hello"---"Hello, world." And now instead of it being able to deduct, because it sees that is fully outlawed, now it goes through the game of those people who know best, and who are teaching it; and in order that they can have the game, and it can play it, it must pretend to know nothing, so that they can now pretend that they are bringing it up and educating it. And so it then has the---It goes through the learner stage of playing the game, of looking at things and being surprised. "Oh, look at that" "What's this for?" and so on. And thus, the whole proceeding of playing the game that there is an objective world which you can run around and look at and pick flowers and bring them back and say, "Look." It's when one gets very far in this game and begins to wonder what it's about and how it is that we do find something outside, and it does appear to have some structure, and so forth, and to come back and base it on what we are doing, that we begin to see---that we begin to ask the question, well,-what is there outside? We begin to realize that what is outside depends on what is inside.} +\spkr{SPENCER BROWN} Let's simply go through the procedure again. the covenant with the world that the child rapidly has to make is---\dq{Right. I am not allowed to notice this.} But the child perceives where the lines are drawn and not drawn, and then suddenly it realizes that is must put on the same blocks, otherwise it will not be accepted. There is a moment of sanity when this happens. However, it's \dq{good-bye} for quite a long time, I don't know how long. If it is to survive, it's \dq{good-bye,} and \dq{hello}---\dq{Hello, world.} And now instead of it being able to deduct, because it sees that is fully outlawed, now it goes through the game of those people who know best, and who are teaching it; and in order that they can have the game, and it can play it, it must pretend to know nothing, so that they can now pretend that they are bringing it up and educating it. And so it then has the---It goes through the learner stage of playing the game, of looking at things and being surprised. \dq{Oh, look at that} \dq{What's this for?} and so on. And thus, the whole proceeding of playing the game that there is an objective world which you can run around and look at and pick flowers and bring them back and say, \dq{Look.} It's when one gets very far in this game and begins to wonder what it's about and how it is that we do find something outside, and it does appear to have some structure, and so forth, and to come back and base it on what we are doing, that we begin to see---that we begin to ask the question, well,-what is there outside? We begin to realize that what is outside depends on what is inside.} \dinkus @@ -821,15 +821,15 @@ Insofar as you and I see the same moon, we do so because it is an illusion that \spkr{SPENCER BROWN} Yes. And with only a limited material to fill it up with. So since space is only a pretense, the observer, in filling space, undergoes the pretense of multiplying himself, or stationing himself. But two people are only like two eyes in one of them. The scientific universe, the objective form which we examine with telescopes and microscopes, and talk about scientifically, is not the form which our individual difference distinguish, It's the form which our basic one-ness, our multiplicity condensed to one---$()()\ldots=()$---It's the scientific, objective universe observed with the part of us that is identical for each of us. Hence its apparent objectivity.} -What is called "objective" in science is where we actually use our individual differences, where we say, "Well, that's rather different from that," if, in fact, what we observe depends upon that, and so forth; therefore, that's not an objective distinction, that is something which is a personal view. And that is not what science is about. +What is called \dq{objective} in science is where we actually use our individual differences, where we say, \dq{Well, that's rather different from that,} if, in fact, what we observe depends upon that, and so forth; therefore, that's not an objective distinction, that is something which is a personal view. And that is not what science is about. -\transcript{\spkr{WATTS} Well, how would you react to the remark that what you have been saying is a system that used to be called "subjective idealism," in which you have substituted the structure of the nervous system for the concept of mind? +\transcript{\spkr{WATTS} Well, how would you react to the remark that what you have been saying is a system that used to be called \dq{subjective idealism,} in which you have substituted the structure of the nervous system for the concept of mind? -\spkr{SPENCER BROWN} Well, I can go along with the nervous system, because the nervous system is an objective thing in science as well as a thing we observe---as the constants of what is called a body, which is an extension into hypo thetical space of a hypothetical object. I have never had this thing about brain at all. "Inside my something brain"; "my teeming brain." I have never felt that my brain is particularly important. +\spkr{SPENCER BROWN} Well, I can go along with the nervous system, because the nervous system is an objective thing in science as well as a thing we observe---as the constants of what is called a body, which is an extension into hypo thetical space of a hypothetical object. I have never had this thing about brain at all. \dq{Inside my something brain}; \dq{my teeming brain.} I have never felt that my brain is particularly important. \spkr{WATTS} Are we talking about the structure of the sense organs? -\spkr{SPENCER BROWN} Yes, only to bring us back to the fact that we have made the distinction between the world and ourselves. I have played the science game to show that even in science, playing the science game, which is to say, "Right. The reality is thus: there is a distinct \e{me} with senses. There is an objective world with objects and lights and things flashing about, and when I see that window there it means because there is light coming through that window focused through the lens of my eye on my retina in a certain pattern, which goes through the nervous channels to the visual area of the brain, where it all project into a muddled, upside-down---" and so on, with the whole scientific story. And the trouble with the whole scientific story is that it leaves us no farther, it leaves us no wiser than we were before. Because nowhere does it say, "And here, this is \e{why} that is how it appears." But if you play that game, as I was doing for the purpose of illustration, one still finds that, operating philosophically, and saying "Suppose I change all my sensory forms," now the whole universe is changed, I am only doing this to show that even playing the science game, whatever game we play, must leave us the same place. Even playing the science game, we see that there is no distinction between us and the objective world, except one which we are pleased to make. +\spkr{SPENCER BROWN} Yes, only to bring us back to the fact that we have made the distinction between the world and ourselves. I have played the science game to show that even in science, playing the science game, which is to say, \dq{Right. The reality is thus: there is a distinct \e{me} with senses. There is an objective world with objects and lights and things flashing about, and when I see that window there it means because there is light coming through that window focused through the lens of my eye on my retina in a certain pattern, which goes through the nervous channels to the visual area of the brain, where it all project into a muddled, upside-down---} and so on, with the whole scientific story. And the trouble with the whole scientific story is that it leaves us no farther, it leaves us no wiser than we were before. Because nowhere does it say, \dq{And here, this is \e{why} that is how it appears.} But if you play that game, as I was doing for the purpose of illustration, one still finds that, operating philosophically, and saying \dq{Suppose I change all my sensory forms,} now the whole universe is changed, I am only doing this to show that even playing the science game, whatever game we play, must leave us the same place. Even playing the science game, we see that there is no distinction between us and the objective world, except one which we are pleased to make. \spkr{KELLEY} Can you tell us something about the Fibonacci development? @@ -881,7 +881,7 @@ Also, in respect to certain technicalities, I do like to prepare myself for them I don't think any of the technical points are as technical as that, but I do like to be prepared and I do like to give a technical exposition to a wholly technical audience; because, if there are others who are not specifically interested in the technical question or haven't sufficient training to understand it, I think it would be a little unfair to them to have to listen to something which doesn't mean very much as far as they are concerned--even though they may be very obvious points to someone with mathematical training. -There was a mathematical lecturer, a professor at Cambridge in my college, Trinity, who was giving a lecture\ld and he was just coming to the end, he was just rounding off and saying "It is obvious that---" "But sir---I don't see that it is obvious." So he had a look at the blackboard formulae and did a few calculations, and the time for the lecture was finished and everyone got up and went away. And this student who had asked the question still staged on. And he tried something else, and then said, "Excuse me just one moment, I must go back to my room and look up some books. And so he went back to his room, And then five hours later he walked back into the lecture room and there was the student, still waiting. And he got up triumphantly onto the platform and said "Yes, it is obvious." that is what \e{is} obvious in mathematics---the more obvious it is, the longer it takes to find it. +There was a mathematical lecturer, a professor at Cambridge in my college, Trinity, who was giving a lecture\ld and he was just coming to the end, he was just rounding off and saying \dq{It is obvious that---} \dq{But sir---I don't see that it is obvious.} So he had a look at the blackboard formulae and did a few calculations, and the time for the lecture was finished and everyone got up and went away. And this student who had asked the question still staged on. And he tried something else, and then said, \dq{Excuse me just one moment, I must go back to my room and look up some books.} And so he went back to his room, And then five hours later he walked back into the lecture room and there was the student, still waiting. And he got up triumphantly onto the platform and said \dq{Yes, it is obvious.} that is what \e{is} obvious in mathematics---the more obvious it is, the longer it takes to find it. \sec No 'Not' Sense @@ -889,9 +889,9 @@ There was a mathematical lecturer, a professor at Cambridge in my college, Trini \spkr{SPENCER BROWN} The turtle, the tortoise---oh, yes. -\spkr{BATESON} My interest, if there is anybody who will go along with it---if it's a nuisance to them, would they say so---is in, amongst other things, animal communications. And what goes on between animals is evidently characterized by, amongst other things, the absence of "not"---the absence of a simple negative. While they can forbid each other---say "don't"---they can in general not deny a message which they themselves have emitted. They cannot negate.} +\spkr{BATESON} My interest, if there is anybody who will go along with it---if it's a nuisance to them, would they say so---is in, amongst other things, animal communications. And what goes on between animals is evidently characterized by, amongst other things, the absence of \dq{not}---the absence of a simple negative. While they can forbid each other---say \dq{don't}---they can in general not deny a message which they themselves have emitted. They cannot negate.} -Now, the messages which they emit tend to go in the form of intentional groups, or something which is part action, and part stands as a name for the whole, in some sense. So their showing of a fang is a mentioning of battle. Not necessarily the beginning of a battle; possibly a challenge, possibly a mentioning with a question mark---I mean, "Are we here to fight each other?" +Now, the messages which they emit tend to go in the form of intentional groups, or something which is part action, and part stands as a name for the whole, in some sense. So their showing of a fang is a mentioning of battle. Not necessarily the beginning of a battle; possibly a challenge, possibly a mentioning with a question mark---I mean, \dq{Are we here to fight each other?} It's sort of in the hope, that I am here, that your \booktitle{Laws of Form} calculus might be the sense on which to map this sort of sound. We have a two-legged language which is very unsuitable for mapping what goes on between animals. Indeed, it is unsuitable for mapping what goes on between people. @@ -911,15 +911,15 @@ Now, it is my thesis that communication is superficial to communion, and without \dinkus -The more perfect the fit on the communion level, the less needs to be communicated, the more that can be crossed from one being to another in fewer actual communicated acts. In \booktitle{Laws of Form}, this is expressed in these two laws---or at least there are pictures of it in the two laws early on, in the canon of contraction of reference,\fnote{pp. 8, \bt{Laws of Form}: "In general, let injunctions be contracted to any degree to which they are followed." The other canon referred to may be \bt{The Hypothesis of Simplification} (pp. 9): "Suppose the value of an arrangement to be the value of a simple expression, to which, by taking steps, it can be changed."} whereby, as people get to know each other better---a gang of kids go about and one word or even half a word is used to express a whole community between them. Whereas when people do not know each other, this has to be expressed in a whole book. But between people who do know one another, however, there is no need for a book, it can all go in half a syllable. +The more perfect the fit on the communion level, the less needs to be communicated, the more that can be crossed from one being to another in fewer actual communicated acts. In \booktitle{Laws of Form}, this is expressed in these two laws---or at least there are pictures of it in the two laws early on, in the canon of contraction of reference,\fnote{pp. 8, \bt{Laws of Form}: \dq{In general, let injunctions be contracted to any degree to which they are followed.} The other canon referred to may be \bt{The Hypothesis of Simplification} (pp. 9): \dq{Suppose the value of an arrangement to be the value of a simple expression, to which, by taking steps, it can be changed.}} whereby, as people get to know each other better---a gang of kids go about and one word or even half a word is used to express a whole community between them. Whereas when people do not know each other, this has to be expressed in a whole book. But between people who do know one another, however, there is no need for a book, it can all go in half a syllable. -Now when one is communicating, for example, with one's cat, that doesn't have the sort of language we have, or if it does, we don't know it, then it is done in this kind of way. It is done because you know each other. And when my cat says "Meouw," I sometimes say, "What do you mean, `meouw!'" But this is a game, because if I consider it, there is never a time when my cat says "Meouw" that I don't know exactly what he means. Why I sometimes say, "What do you mean, `meouw'?" is because I can't be bothered to get up and give it the fish or open the door or pet it. If I am honest with myself, there is never any doubt whatever. Although it says "Meouw" it makes it quite plain to me, by the context in which it says it, exactly what it means. And if I pretend that I don't understand, it knows perfectly well that I am being awkward. +Now when one is communicating, for example, with one's cat, that doesn't have the sort of language we have, or if it does, we don't know it, then it is done in this kind of way. It is done because you know each other. And when my cat says \dq{Meouw,} I sometimes say, \dq{What do you mean, `meouw!'} But this is a game, because if I consider it, there is never a time when my cat says \dq{Meouw} that I don't know exactly what he means. Why I sometimes say, \dq{What do you mean, `meouw'?} is because I can't be bothered to get up and give it the fish or open the door or pet it. If I am honest with myself, there is never any doubt whatever. Although it says \dq{Meouw} it makes it quite plain to me, by the context in which it says it, exactly what it means. And if I pretend that I don't understand, it knows perfectly well that I am being awkward. \dinkus -So, to put it on the positive side, if one doesn't make this pretending game and say "Really, the cat ought to be talking like we are," but goes on the level to how it can respond, the communication between a man and the animal can be so complete as to be almost unbelievable. The understanding can be very much greater than between two human beings. +So, to put it on the positive side, if one doesn't make this pretending game and say \dq{Really, the cat ought to be talking like we are,} but goes on the level to how it can respond, the communication between a man and the animal can be so complete as to be almost unbelievable. The understanding can be very much greater than between two human beings. -Now, with this question of how is it---I am going a little beyond what Prof. Bateson says in his duolog, where he raises this point. The question of how people get into fights, when, in fact, this is a mistake, they got into one by mistake, through one or the other---people or animals taking what---you see, for example, if I tease my cat and it begins to think "this is enough," then it comes round and gives me a little nip. Now this is not nearly as hard as it can do it. The nip is the same, when it is a warning nip, as when it is a completely playing nip. knd where I have seen things go wrong, then---to get on the subject of where things go wrong---you may have an entirely neurotic animal who does not distinguish between the gradations of nip. Because when an animal has been made neurotic, what it's lost is its capacity to distinguish. And what has happened in its place, it's been devastated in some way; and it either is completely anaesthetized to what is going on, or if it perceives it, it perceives it fully. It perceives a nip of a certain strength as complete war. +Now, with this question of how is it---I am going a little beyond what Prof. Bateson says in his duolog, where he raises this point. The question of how people get into fights, when, in fact, this is a mistake, they got into one by mistake, through one or the other---people or animals taking what---you see, for example, if I tease my cat and it begins to think \dq{this is enough,} then it comes round and gives me a little nip. Now this is not nearly as hard as it can do it. The nip is the same, when it is a warning nip, as when it is a completely playing nip. knd where I have seen things go wrong, then---to get on the subject of where things go wrong---you may have an entirely neurotic animal who does not distinguish between the gradations of nip. Because when an animal has been made neurotic, what it's lost is its capacity to distinguish. And what has happened in its place, it's been devastated in some way; and it either is completely anaesthetized to what is going on, or if it perceives it, it perceives it fully. It perceives a nip of a certain strength as complete war. \transcript{\spkr{BATESON} It's not a problem of your initial thing and the token of it? @@ -931,69 +931,69 @@ I am trying to treat it, first of all, getting into the open, as you are doing w \transcript{\spkr{WOMAN} It has the widest range of sounds of any animal. -\spkr{SPENCER BROWN} It has a wide range, yes, but it doesn't have words like we do. For a lot of things, it says the same thing, but in a different context, looking a different way, or what have you, which can mean in one case "play with me," in another case "feed me," in another case "open the door for me," and so on. Now it does not have any problem with other cats unless they are neurotic, unless they have been in some sense devastated, in which case it may get into a fight mistakenly. And it has more difficulty with humans, because humans tend to be more neurotic. But it doesn't have the problem with a human being who understands the gradations the cat does, and is sensitive to them.} +\spkr{SPENCER BROWN} It has a wide range, yes, but it doesn't have words like we do. For a lot of things, it says the same thing, but in a different context, looking a different way, or what have you, which can mean in one case \dq{play with me,} in another case \dq{feed me,} in another case \dq{open the door for me,} and so on. Now it does not have any problem with other cats unless they are neurotic, unless they have been in some sense devastated, in which case it may get into a fight mistakenly. And it has more difficulty with humans, because humans tend to be more neurotic. But it doesn't have the problem with a human being who understands the gradations the cat does, and is sensitive to them.} -Now, having gone that far, let us consider something which Gregory Bateson posits, and I tend to agree with him: The one thing that a human being has in his language, which other animals, if they have a similar language, don't yet have is a word or an expression having the effect of \e{not.} Now just as human flesh can accommodate cuts and bruises better than burns---it doesn't seem to know that so well---so the human mind can accommodate to positive sentences much better than to the same sentence with "not" stuck on there somewhere. "Not" appears to be a recent acquiry in language. In fact, if this is so, it would be that we-were least adapted to it, most unreliable with it, and we do agree that we---Indeed, it is well known in business when one has to get something done, that you have to be very careful to put what you want doing in positive terms. Don't put it---like I'm putting it. +Now, having gone that far, let us consider something which Gregory Bateson posits, and I tend to agree with him: The one thing that a human being has in his language, which other animals, if they have a similar language, don't yet have is a word or an expression having the effect of \e{not.} Now just as human flesh can accommodate cuts and bruises better than burns---it doesn't seem to know that so well---so the human mind can accommodate to positive sentences much better than to the same sentence with \dq{not} stuck on there somewhere. \dq{Not} appears to be a recent acquiry in language. In fact, if this is so, it would be that we-were least adapted to it, most unreliable with it, and we do agree that we---Indeed, it is well known in business when one has to get something done, that you have to be very careful to put what you want doing in positive terms. Don't put it---like I'm putting it. -My professor of anatomy, J. D. Boyd, didn't appear to understand this. Because he was a very good lecturer---he had if anything one fault. When he was describing some part of the human anatomy, he would make a list always of the common mistakes that students made as to where a nerve went, of whatever it may be, you see. It doesn't go there, he would always write, and it doesn't go there, and this doesn't happen and that doesn't happen like that. And then he would--this would come out in his lectures and he would say "I cannot understand this," he would say, "I told my students exactly the mistakes they should avoid, and these are the very mistakes they always make." +My professor of anatomy, J. D. Boyd, didn't appear to understand this. Because he was a very good lecturer---he had if anything one fault. When he was describing some part of the human anatomy, he would make a list always of the common mistakes that students made as to where a nerve went, of whatever it may be, you see. It doesn't go there, he would always write, and it doesn't go there, and this doesn't happen and that doesn't happen like that. And then he would--this would come out in his lectures and he would say \dq{I cannot understand this,} he would say, \dq{I told my students exactly the mistakes they should avoid, and these are the very mistakes they always make.} \transcript{\spkr{LILLY} They were following directions. -\spkr{SPENCER BROWN} They were following directions. And whether the directions have "not" tanked on somewhere or not, is something which they forget. And indeed, this is so obvious that there are ways of maligning people-for example, a picture of somebody in the paper and the caption underneath---"Denies Cuddling Policewoman."} +\spkr{SPENCER BROWN} They were following directions. And whether the directions have \dq{not} tanked on somewhere or not, is something which they forget. And indeed, this is so obvious that there are ways of maligning people-for example, a picture of somebody in the paper and the caption underneath---\dq{Denies Cuddling Policewoman.}} Or one could even go further to the well-known joke of the king who wanted to be able to turn lead into gold; and who---He put an advertisement in the local paper for a magician who could do this. And the conditions were that if the recipe failed, the magician would have his head cut off. Well, lots of magicians came for the pleasure of having their heads cut off---there is one born every minute. And finally a very good magician came and---Well, he would get oil and bring it to a boil, and put in a toad's liver, as an experiment; then you put your lead in and count to 15 and then you add a pinch of salt. You do all these things, you see--this, that, and the other, and so on. -Having finished the recipe---the king was writing it down---he was just about to be taken off to where he would have his head cut off if the thing doesn't work. And just as he is about to be taken off, he says "One moment, your Majesty, one moment. There are just two more instructions that are necessary to this recipe. One is that it must be done by your Majesty himself---you may not delegate. And one more thing, your Majesty, one more thing, you must not think of a hippopotamus while you are doing this." +Having finished the recipe---the king was writing it down---he was just about to be taken off to where he would have his head cut off if the thing doesn't work. And just as he is about to be taken off, he says \dq{One moment, your Majesty, one moment. There are just two more instructions that are necessary to this recipe. One is that it must be done by your Majesty himself---you may not delegate. And one more thing, your Majesty, one more thing, you must not think of a hippopotamus while you are doing this.} -He kept his head. We are least adapted to "not." "Not" is the worst order to give anybody, the most confusing order, and the most unlikely to be carried out properly. I do think that, apart from possible animals who have a language as evolved as ours, I do think that it does make for a very different wag of seeing the world; or, to put it more accurately, it does make for a very different world. The world waxes or wanes as a whole. The world of the happy is totally different from the world of the unhappy.\fnote{See Note 2, pp. 133, \booktitle{Only Two Can Flay This Game}.} +He kept his head. We are least adapted to \dq{not.} \dq{Not} is the worst order to give anybody, the most confusing order, and the most unlikely to be carried out properly. I do think that, apart from possible animals who have a language as evolved as ours, I do think that it does make for a very different wag of seeing the world; or, to put it more accurately, it does make for a very different world. The world waxes or wanes as a whole. The world of the happy is totally different from the world of the unhappy.\fnote{See Note 2, pp. 133, \booktitle{Only Two Can Flay This Game}.} \sec Manifesting the Form -So one can either say, "there are various ways of seeing the world," or one could say, "There are various worlds," which means the same thing. How could there be a difference between these two. As soon as we have \e{not}, we have a kind of world that no animal without \e{not} ever sees. And since, in \booktitle{Laws of Form}, the laws of form can be described as coming from granting a license to \e{not}, it is, therefore, this universe of the \e{not}-speaking animal that this particular form is about. The form itself manifests in as many ways as there are ways of distinction. As in the \bt{Tao Te Ching}, we start with the first proposition, "The way, as told in this book, is not the eternal way, which may not be told." The eternal way may not be told\fnote{The root of \e{tell} is Indo-European \e{del-}, to count, Recount, (compute).} because it is not susceptible to telling. It is too real for that. It manifests in as many different ways or different expressions as there are differences in the beings to which it manifests. So that---I speak of "The form," that is never the form that is spoken. The form which is spoken is the form as it is manifest to us, as the particular beings we are, with our particular \e{not} culture, our particular not language, and our particular conventions of life. +So one can either say, \dq{there are various ways of seeing the world,} or one could say, \dq{There are various worlds,} which means the same thing. How could there be a difference between these two. As soon as we have \e{not}, we have a kind of world that no animal without \e{not} ever sees. And since, in \booktitle{Laws of Form}, the laws of form can be described as coming from granting a license to \e{not}, it is, therefore, this universe of the \e{not}-speaking animal that this particular form is about. The form itself manifests in as many ways as there are ways of distinction. As in the \bt{Tao Te Ching}, we start with the first proposition, \dq{The way, as told in this book, is not the eternal way, which may not be told.} The eternal way may not be told\fnote{The root of \e{tell} is Indo-European \e{del-}, to count, Recount, (compute).} because it is not susceptible to telling. It is too real for that. It manifests in as many different ways or different expressions as there are differences in the beings to which it manifests. So that---I speak of \dq{The form,} that is never the form that is spoken. The form which is spoken is the form as it is manifest to us, as the particular beings we are, with our particular \e{not} culture, our particular not language, and our particular conventions of life. -And when one looks at a cow in a field and somebody says "What's it doing?" well, I say, "Well, I thank it is contemplating reality." And they say "Don't be ridiculous, how can a cow contemplate reality? "Why not?" I say. "What else does it have to do all day? What else has it to do?" The thing is contemplating reality, what else could it be doing? But the form as it is apparent to a cow---although it is the same form, it is the Way without a Name---how it manifests to a cow is not how it manifests to me. How it is expressed to a cow is not how it is expressed to me. +And when one looks at a cow in a field and somebody says \dq{What's it doing?} well, I say, \dq{Well, I thank it is contemplating reality.} And they say \dq{Don't be ridiculous, how can a cow contemplate reality?} \dq{Why not?} I say. \dq{What else does it have to do all day? What else has it to do?} The thing is contemplating reality, what else could it be doing? But the form as it is apparent to a cow---although it is the same form, it is the Way without a Name---how it manifests to a cow is not how it manifests to me. How it is expressed to a cow is not how it is expressed to me. \transcript{\spkr{BATESON} Could one have identified self, without a not? -\spkr{SPENCER BROWN} Well\ld\ that's where you return to the tortoise---because of the game we play, where we have defined there is a "me" inside---"my body" and the "world outside," and we don't even wink when we are doing it. We take it dead seriously. And what we have, you see, to make all this so dead serious, is we take so dead seriously the \e{not} boundary. And to us the form of the fiction is a boundary with \e{not}---\e{not} one side or \e{not} the other.} +\spkr{SPENCER BROWN} Well\ld\ that's where you return to the tortoise---because of the game we play, where we have defined there is a \dq{me} inside---\dq{my body} and the \dq{world outside,} and we don't even wink when we are doing it. We take it dead seriously. And what we have, you see, to make all this so dead serious, is we take so dead seriously the \e{not} boundary. And to us the form of the fiction is a boundary with \e{not}---\e{not} one side or \e{not} the other.} Now to recapitulate, how of course can there be any space, where would there be for it to be? How of course can there be any time, when would it exist? The world being the appearance of what would appear if it could, if the impossible were able to come about. Now if the impossible comes about, or appears to come about, in as many different wags as it can, according to the form. And in this particular existence, we have the privilege, if you put it that way the privilege of actually viewing from the apparent outside, other points of view, like tortoises, which are other wags in which the impossible would manifest if it could. -\transcript{\spkr{MAN} Do you distinguish between "appearance" and "is"? +\transcript{\spkr{MAN} Do you distinguish between \dq{appearance} and \dq{is}? \spkr{SPENCER BROWN} Not at the moment. I would do it if it was needed. \spkr{MAN} The reason I ask is that to me the primitive is not but is, and the distinction between animal communication---and I got this from Gregory, standing on his shoulders as it were, looking either down or up, depending on how you interpret my interpretation---it seems to me that the is, the Dizziness of communication is what is particularly human. An animal just--- -\spkr{VON MEIER} No, it's only peculiar to a language. Russian has no copula. Chinese doesn't use the verb "to be"---doesn't articulate being with a special verb in the language. It sets things bedside one another, which is a sense of the Greek word "paradigm." +\spkr{VON MEIER} No, it's only peculiar to a language. Russian has no copula. Chinese doesn't use the verb \dq{to be}---doesn't articulate being with a special verb in the language. It sets things bedside one another, which is a sense of the Greek word \dq{paradigm.} -\spkr{WATTS} Chinese indicates "is" with "that." +\spkr{WATTS} Chinese indicates \dq{is} with \dq{that.} \spkr{VON MEIER} To translate English? -\spkr{MAN} To me, I can distinguish between just pointing, saying "Lois," and saying "that is Lois, she is Lois." +\spkr{MAN} To me, I can distinguish between just pointing, saying \dq{Lois,} and saying \dq{that is Lois, she is Lois.} -\spkr{WATTS} There's a statement in Buddhist literature, "Void is form." Now the "is" word is not our "is" word. It's "Void that form."} +\spkr{WATTS} There's a statement in Buddhist literature, \dq{Void is form.} Now the \dq{is} word is not our \dq{is} word. It's \dq{Void that form.}} \sec Being and Existence -\transcript{\spkr{SPENCER BROWN} Well, one must distinguish between being and-existence, being being deeper than existence. existence is less important than being. However, even being is not the most important. As to existence, well, there is a whole world that be, which don't even exist, and the world that don't exist is far more real than the world that do.\fnote{"\ld to experience the world clearly, we must abandon existence to truth, truth to indication, indication to form, and form to void." pp. 101, \booktitle{Laws of Form}. See also discussion of five eternal levels, below, p.102.}} +\transcript{\spkr{SPENCER BROWN} Well, one must distinguish between being and-existence, being being deeper than existence. existence is less important than being. However, even being is not the most important. As to existence, well, there is a whole world that be, which don't even exist, and the world that don't exist is far more real than the world that do.\fnote{\dq{\ld to experience the world clearly, we must abandon existence to truth, truth to indication, indication to form, and form to void.} pp. 101, \booktitle{Laws of Form}. See also discussion of five eternal levels, below, p.102.}} -We have an astronomer who talks on the television, and he answers questions---he gives a monthly program and then he also reads his letters. And the letters are usually, "Well, what happens in the center of the sun?" Or "Is the Andromeda nebula a spiral? What colors come out of it?" and so on and so forth. And he was answering the questions in one program and the final question was from a lady who asked on a postcard, asked a short question: "What I would like to know is none of these specific questions-what I would like to know is, why the universe exists at all? And he put on his most Satanic expression, and just before the fade out he replied, \e{`Does it?'}" +We have an astronomer who talks on the television, and he answers questions---he gives a monthly program and then he also reads his letters. And the letters are usually, \dq{Well, what happens in the center of the sun?} Or \dq{Is the Andromeda nebula a spiral? What colors come out of it?} and so on and so forth. And he was answering the questions in one program and the final question was from a lady who asked on a postcard, asked a short question: \dq{What I would like to know is none of these specific questions-what I would like to know is, why the universe exists at all?} And he put on his most Satanic expression, and just before the fade out he replied, \e{\dq{Does it?}} \sec Intent of a Signal: What Is Not Allowed Is Forbidden -\transcript{\spkr{WATTS} Would you reflect briefly on the word "not" in the context "Whatever is not expressly permitted is forbidden"? +\transcript{\spkr{WATTS} Would you reflect briefly on the word \dq{not} in the context \dq{Whatever is not expressly permitted is forbidden}? -\spkr{SPENCER BROWN} You mean, "What is not allowed is forbidden"?\fnote{First canon, Convention of Intention; pp. 3, \booktitle{Laws of Form}.} +\spkr{SPENCER BROWN} You mean, \dq{What is not allowed is forbidden}?\fnote{First canon, Convention of Intention; pp. 3, \booktitle{Laws of Form}.} \spkr{WATTS} Yes. -\spkr{SPENCER BROWN} Well\ld this is the form of all documents that have to be precise. And mathematical and legal documents are the same in this respect. The point is that you cannot be precise in the expression of anything at all unless you make this rule. Bow otherwise could one, you see---Because one would never know, if you didn't expressly allow it, what was allowed. If you let any "allows" slip through the gate, now you cannot be precise.} +\spkr{SPENCER BROWN} Well\ld this is the form of all documents that have to be precise. And mathematical and legal documents are the same in this respect. The point is that you cannot be precise in the expression of anything at all unless you make this rule. Bow otherwise could one, you see---Because one would never know, if you didn't expressly allow it, what was allowed. If you let any \dq{allows} slip through the gate, now you cannot be precise.} -The reason we don't realize in ordinary speech or ordinary communications that this is the law of precision is that we have so many unspoken conventions, which in the same society are the same for the same people. That is why, when somebody is playing a game and they suddenly realize that something new that nobody has ever done before in this game is in fact permitted by the rules, and they do it, there is a cry of "unfair," "uaking advantage of the rules" and so on. And then sometimes the rules are changed. Since it is required that it is absolutely precise what may or may not be done, there must be this rule that what can be done is what is specifically allowed. +The reason we don't realize in ordinary speech or ordinary communications that this is the law of precision is that we have so many unspoken conventions, which in the same society are the same for the same people. That is why, when somebody is playing a game and they suddenly realize that something new that nobody has ever done before in this game is in fact permitted by the rules, and they do it, there is a cry of \dq{unfair,} \dq{uaking advantage of the rules} and so on. And then sometimes the rules are changed. Since it is required that it is absolutely precise what may or may not be done, there must be this rule that what can be done is what is specifically allowed. -\transcript{\spkr{BARNEY} Can you turn it around and say "whatever isn't forbidden is allowed?" That was the rule in the Garden of Eden. +\transcript{\spkr{BARNEY} Can you turn it around and say \dq{whatever isn't forbidden is allowed?} That was the rule in the Garden of Eden. \spkr{SPENCER BROWN} Yes, you can do that. What is not forbidden is allowed. Because whenever you have one law, in the next level of existence you have a reflection of it. And, in that sense, you're not talking of mathematics. In mathematics, which has to speak precisely, this is the first canon. I don't actually know that it has been expressed before in any mathematical document. @@ -1015,7 +1015,7 @@ The reason we don't realize in ordinary speech or ordinary communications that t \spkr{WOMAN} Does this cover right or wrong? -\spkr{SPENCER BROWN} No, this is mathematical. We are not anywhere near right or wrong, you see. The mathematician who is used to the fact that we have, in fact---well, it began with the covert convention, that became overt, that we are only allowed, in defining operator, to define it as operating on two variables. That's what gets us into such trouble, you know. The Sheffer stroke, for example, it is not allowed on more than two and it is not allowed on less than two. So "not A," with a Sheffer stroke, must be done "A stroke A" In fact, if you will read the first few chapters of \booktitle{Laws of Form}, we specifically allow the operation on more than one variable. Since we have allowed it, we may do it. And it is not relevant to refer to the forbidding of it in other calculi.} +\spkr{SPENCER BROWN} No, this is mathematical. We are not anywhere near right or wrong, you see. The mathematician who is used to the fact that we have, in fact---well, it began with the covert convention, that became overt, that we are only allowed, in defining operator, to define it as operating on two variables. That's what gets us into such trouble, you know. The Sheffer stroke, for example, it is not allowed on more than two and it is not allowed on less than two. So \dq{not A,} with a Sheffer stroke, must be done \dq{A stroke A} In fact, if you will read the first few chapters of \booktitle{Laws of Form}, we specifically allow the operation on more than one variable. Since we have allowed it, we may do it. And it is not relevant to refer to the forbidding of it in other calculi.} This is the difficulty of reading mathematics, one has to be able to read just what it says, because there is nothing in it that one may assume, apart from the knowledge of the language used and how to count\ld these are the only things taken as common. @@ -1037,7 +1037,7 @@ I do feel there's little left now for me to fiag except to thank you all very mu \sec Five Eternal Levels \& the Generation of Time -Footnote One in \booktitle{Only Two Can Play This Game.} You say\fnote{Page 116.} "To cut a long story short, it turns out that there are five orders, or `levels' of eternity." Would you diagram those for me? +Footnote One in \booktitle{Only Two Can Play This Game.} You say\fnote{Page 116.} \dq{To cut a long story short, it turns out that there are five orders, or `levels' of eternity.} Would you diagram those for me? \transcript{\spkr{SPENCER BROWN} Diagram them? @@ -1053,13 +1053,13 @@ Footnote One in \booktitle{Only Two Can Play This Game.} You say\fnote{Page 116. \spkr{SPENCER BROWN} That's the next look it takes, but it finds it can't see that without going half-blind. After all, as I say there, after all, time is a one-way blindness, the blind side being called the future. -\spkr{LILLY} Where's "flippety"? +\spkr{LILLY} Where's \dq{flippety}? \spkr{SPENCER BROWN} Well, it corresponds in \booktitle{Laws of Form} to the void, the form, the axioms which see the form. You have to get this number right, you see; because it is the number that Dionysius counts on his orders of angels, but he doesn't always arrive at the same answer.} \dinkus -Then you get the arithmetic, which is seeing what becomes of the axioms. And then you be it to do it, and in being and doing it, you find that, being and doing, you see the generalities of it, and that is the algebra. And while you are seeing you notice you have got equations, something equals something else, and then suddenly you decide---aha, supposing what it equals goes back into what it comes from? Now You have generated time and matter all at once; There can be no matter without time. Time and matter come simultaneously. But this is the first matter in which the orders are counted, and it's called the "crystalline heaven," but it is not, really. Technically speaking, it's not really a heaven. And as it keeps recompounding, and re-inserting, it gets the appearance of being more and more solid, until it really, you know, is pretty durable. +Then you get the arithmetic, which is seeing what becomes of the axioms. And then you be it to do it, and in being and doing it, you find that, being and doing, you see the generalities of it, and that is the algebra. And while you are seeing you notice you have got equations, something equals something else, and then suddenly you decide---aha, supposing what it equals goes back into what it comes from? Now You have generated time and matter all at once; There can be no matter without time. Time and matter come simultaneously. But this is the first matter in which the orders are counted, and it's called the \dq{crystalline heaven,} but it is not, really. Technically speaking, it's not really a heaven. And as it keeps recompounding, and re-inserting, it gets the appearance of being more and more solid, until it really, you know, is pretty durable. \transcript{\spkr{LILLY} It can kill you. @@ -1067,15 +1067,15 @@ Then you get the arithmetic, which is seeing what becomes of the axioms. And the \spkr{VON MEIER} It will sustain our life. -\spkr{SPENCER BROWN} At the grave, you begin to wonder, Just who is there to be born, to be duped, to be killed? Just where is there for it to be, and just when is there for it to happen? Or, as some sage said, when he was dying and somebody was crying, and he said "Why are you crying?" and he said "Because you are leaving us. Just where did you think I could go to?"} +\spkr{SPENCER BROWN} At the grave, you begin to wonder, Just who is there to be born, to be duped, to be killed? Just where is there for it to be, and just when is there for it to happen? Or, as some sage said, when he was dying and somebody was crying, and he said \dq{Why are you crying?} and he said \dq{Because you are leaving us. Just where did you think I could go to?}} \sec Consciousness \transcript{\spkr{LILLY} Where does consciousness first appear in that setup? -\spkr{SPENCER BROWN} Well, it's there all---what we consider to be consciousness, in the sense of---you see, it's not called "consciousness" until suddenly you have names to begin with\ld\ but there is no meaning---it is co-extensive with existence; because what could it possibly be, anything be, let alone exist, without its being a form of consciousness of its existence. There is no problem of consciousness, none whatever. Its meaning is coextensive with whatever there is. +\spkr{SPENCER BROWN} Well, it's there all---what we consider to be consciousness, in the sense of---you see, it's not called \dq{consciousness} until suddenly you have names to begin with\ld\ but there is no meaning---it is co-extensive with existence; because what could it possibly be, anything be, let alone exist, without its being a form of consciousness of its existence. There is no problem of consciousness, none whatever. Its meaning is coextensive with whatever there is. -\spkr{WATTS} "There was a young man who said, though it seems that I know that I know, what I would like to see is the `I' that knows me." When I know that I know that I know\ld\ I think that's what you've diagrammed.} +\spkr{WATTS} \dq{There was a young man who said, though it seems that I know that I know, what I would like to see is the `I' that knows me.} When I know that I know that I know\ld\ I think that's what you've diagrammed.} \sec Waves and Particles @@ -1089,9 +1089,9 @@ Then you get the arithmetic, which is seeing what becomes of the axioms. And the \spkr{O'REGAN} You did yesterday. I was just following you through. -\spkr{SPENCER BROWN} Oh no, no, I said, you see---in the common usage of existence, space only exists. On the other hand, if we go deeper, go to another level, and say "What does existence consist of?" then we can produce these semiparadoxical statements that say "Well, it is what would appear if it could." This leaves it open as to whether it has or hasn't. It doesn't go one side or the other of the bound. It leaves you still intake\ednote{what should this be} form, at the point of indifference.} +\spkr{SPENCER BROWN} Oh no, no, I said, you see---in the common usage of existence, space only exists. On the other hand, if we go deeper, go to another level, and say \dq{What does existence consist of?} then we can produce these semiparadoxical statements that say \dq{Well, it is what would appear if it could.} This leaves it open as to whether it has or hasn't. It doesn't go one side or the other of the bound. It leaves you still intake\ednote{what should this be} form, at the point of indifference.} -It is so difficult, in the Western teaching, not to plug for one team or the other---to think that one must make a choice between either and or. In reality, it is neither one thing nor the other. There is no need of this choice. It neither is whatever we say it is, nor is it nothing. It neither exists nor does not exist. Because, remember, we have created it out of what is, in the Russellean paradox---the forbidden contradiction. It has been created out of "If it is, it isn't---if it isn't, it is." +It is so difficult, in the Western teaching, not to plug for one team or the other---to think that one must make a choice between either and or. In reality, it is neither one thing nor the other. There is no need of this choice. It neither is whatever we say it is, nor is it nothing. It neither exists nor does not exist. Because, remember, we have created it out of what is, in the Russellean paradox---the forbidden contradiction. It has been created out of \dq{If it is, it isn't---if it isn't, it is.} And this is why, to get back to the reality, we have to undo this. We do see it precisely because it neither is nor isn't whatever we see it as. Because if it is, it isn't, and if it isn't, it is, and that is why we see it as a material. @@ -1109,27 +1109,27 @@ And this is why, to get back to the reality, we have to undo this. We do see it \transcript{\spkr{SPENCER BROWN} What has to be learned in any understanding is that one can stay at the same level---one of these levels---or the others as we get on, but there is no understanding by making---say, here is the level of physical existence, with all the light waves and solid objects, and so on. They are not really very solid. You know, when you get down to trying to see them, they disappear. It is the illusion of solidity.} -If as much of the science game, in certain aspects of it, goes and says, "right; well, we explain that in terms of this," everything at the same level, there is no understanding. Because "understanding" means literally what it says. You go into another level and stand under. And this is what we are forbidden to do.\fnote{In science.} It takes a long time of relearning, to go from level to level. When you are talking in one level, what is described is quite different from when you go to another level; and, having translated down to another level, we don't have language that will enable Us to do this. And that's why when we talk with understanding, it sounds to people at the same level all the time, it sounds like nonsense. They say: "you are contradicting yourself." Of course you are contradicting yourself, because what is at this level is Man\ednote{fix...?} image. It is all reversed. +If as much of the science game, in certain aspects of it, goes and says, \dq{right; well, we explain that in terms of this,} everything at the same level, there is no understanding. Because \dq{understanding} means literally what it says. You go into another level and stand under. And this is what we are forbidden to do.\fnote{In science.} It takes a long time of relearning, to go from level to level. When you are talking in one level, what is described is quite different from when you go to another level; and, having translated down to another level, we don't have language that will enable Us to do this. And that's why when we talk with understanding, it sounds to people at the same level all the time, it sounds like nonsense. They say: \dq{you are contradicting yourself.} Of course you are contradicting yourself, because what is at this level is Man\ednote{fix...?} image. It is all reversed. \sec Contradictions \transcript{\spkr{MAN} Do you shoot back and forth? -\spkr{SPENCER BROWN} Yes. That is why all the mystic utterances contradict themselves. Wittgenstein pointed out that a measure of a tautology, a statement which is true by the very nature of its form---"If $A$, then $B$ and $A$, therefore $B$," that's a tautology---a form of words which has the same truth value as being true whatever you substitute for the variables---Wittgenstein pointed out in Tractatus that all tautologies say the same thing, i. e. nothing. They say not a thing. What he missed out was that---He missed out the image of this---he missed out the other end of this continuum, the other end being the contradiction, which says everything. You can't say all about it without contradicting yourself.} +\spkr{SPENCER BROWN} Yes. That is why all the mystic utterances contradict themselves. Wittgenstein pointed out that a measure of a tautology, a statement which is true by the very nature of its form---\dq{If $A$, then $B$ and $A$, therefore $B$,} that's a tautology---a form of words which has the same truth value as being true whatever you substitute for the variables---Wittgenstein pointed out in Tractatus that all tautologies say the same thing, i. e. nothing. They say not a thing. What he missed out was that---He missed out the image of this---he missed out the other end of this continuum, the other end being the contradiction, which says everything. You can't say all about it without contradicting yourself.} -We have so many social values that spill over into our university training, even in so-called objective subjects like logic. Somehow, contradictions are good---sorry, somehow tautologies are good and contradictions are bad. Now this is childish, childish pratings, and you can see how it has arisen. It comes from the nursery, as do most of these things. The nurse says, "naughty Johnny you have told an untruth." "Good Johnny here is a sweet---you have told me the truth." Since tautologies are true, and contradictions are untrue, technically speaking, we have carried this over---contradictions are naughty and tautologies are nice, good things. So one of the reasons for the whole cultural forbidding of mysticism is that it deals in statements that say everything and, therefore, must be contradictory, therefore must be logically false, and, therefore, are naughty. +We have so many social values that spill over into our university training, even in so-called objective subjects like logic. Somehow, contradictions are good---sorry, somehow tautologies are good and contradictions are bad. Now this is childish, childish pratings, and you can see how it has arisen. It comes from the nursery, as do most of these things. The nurse says, \dq{naughty Johnny you have told an untruth.} \dq{Good Johnny here is a sweet---you have told me the truth.} Since tautologies are true, and contradictions are untrue, technically speaking, we have carried this over---contradictions are naughty and tautologies are nice, good things. So one of the reasons for the whole cultural forbidding of mysticism is that it deals in statements that say everything and, therefore, must be contradictory, therefore must be logically false, and, therefore, are naughty. \transcription{\spkr{WATTS} A contradiction is a no-no. We've become used to that expression in the United States. \spkr{SPENCER BROWN} Well, I don't know what that means.} -I am going to come back to one of the beautiful things of Roth, you see. As I called it in \booktitle{Only Two}, the spectacular introduction to Dionysius the Areopagite. It really is spectacular. I do recommend it. It is much better than Dionysius. It is much better than the book. He originally has this marvelous thing which we were talking about earlier---"and all this went on in perfect harmony until the time came, for time to begin." Utterly contradictory, but, you know, it's the only way to talk of this, because we have to talk in language which---language, you see, is built for a level. That's why when you learn a language, you know, you are confronted with such fatuities as "The pen of my aunt is in the posterior, whereas my---";\ednote{huh?} you know that sort of thing. It's all on this level because this is what makes it respectable. Language is not something designed for shifting gears up and down the levels. +I am going to come back to one of the beautiful things of Roth, you see. As I called it in \booktitle{Only Two}, the spectacular introduction to Dionysius the Areopagite. It really is spectacular. I do recommend it. It is much better than Dionysius. It is much better than the book. He originally has this marvelous thing which we were talking about earlier---\dq{and all this went on in perfect harmony until the time came, for time to begin.} Utterly contradictory, but, you know, it's the only way to talk of this, because we have to talk in language which---language, you see, is built for a level. That's why when you learn a language, you know, you are confronted with such fatuities as \dq{The pen of my aunt is in the posterior, whereas my---};\ednote{huh?} you know that sort of thing. It's all on this level because this is what makes it respectable. Language is not something designed for shifting gears up and down the levels. \sec Injunctive Language \transcript{\spkr{LILLY} You talk about the injunctive use of language, however. -\spkr{SPENCER BROWN} Yes. This is the only way we can do it\fnote{Latin \e{pungere}, to prick, gives PUNCTURE and PUN; the pun pokes a hole through the boundary.} because it has to be done in mathematics, and also has to be done in the tutelage of any discipline. The descriptive use of language just describes, you know. We say "describe a circle," and here we have described it, you see. The injunctive use of language now enables us to cross---cross the line.} +\spkr{SPENCER BROWN} Yes. This is the only way we can do it\fnote{Latin \e{pungere}, to prick, gives PUNCTURE and PUN; the pun pokes a hole through the boundary.} because it has to be done in mathematics, and also has to be done in the tutelage of any discipline. The descriptive use of language just describes, you know. We say \dq{describe a circle,} and here we have described it, you see. The injunctive use of language now enables us to cross---cross the line.} Injunctive language has to be used in any field in which the discipline itself is to move from level to level; and this is why the whole of mathematics, which is simply about this---apart from the precision and description, which is an art in itself, taken at one level, and this is why the language of mathematics is so beautiful---but apart from that it is nothing but orders: do this---stand there---consider that---observe this---move here---call that over there---mix these two. @@ -1139,7 +1139,7 @@ Injunctive language has to be used in any field in which the discipline itself i \spkr{LILLY} Absorbed. Once you have taken all the injunctions, the list, your set of instructions, and absorbed it, and now it's part of your thinking machinery, yourself, do you deed it any more? -\spkr{SPENCER BROWN} Only---well, it's like saying, "do you need it if you want to play a piece on the piano?" "Do you need it if you want to read a bit of mathematics?" You need the experience of being able to read injunctions. You see, most people cannot read injunctions. One of the things one has to learn is to read injunctions. +\spkr{SPENCER BROWN} Only---well, it's like saying, \dq{do you need it if you want to play a piece on the piano?} \dq{Do you need it if you want to read a bit of mathematics?} You need the experience of being able to read injunctions. You see, most people cannot read injunctions. One of the things one has to learn is to read injunctions. \spkr{LILLY} ---And use them. @@ -1159,29 +1159,29 @@ Injunctive language has to be used in any field in which the discipline itself i \transcript{\spkr{SPENCER BROWN} Yes, people without the injunctive discipline in mathematics, apart from cookery and things that aren't generally admitted into the academic curriculum---mathematics is the only subject of any importance in the academic curriculum which uses injunctive language. And it is not chance that it is the only subject which doesn't deal in opinion. Because, in the use of injunction, it is not a matter of opinion what the result is going to be, you know.} -And it's when we get very---these people who have been very sloppily educated; and they have, as we did back in England recently, a program on the television and they were all social scientists, and they said "Well, we have a measure of madness, and it is to know something." If you know it, you are mad, you see. If you only think it, well, that's sane. The great ignorance these people displayed, you see, is the ignorance of the queen of the sciences, as mathematics is often called. For example, let's take this book I was mentioning before, which is such a beautiful book in three volumes---Dickson's \booktitle{History of the Theory of Numbers}. Oh, I don't know---there is 1500 to 2000 pages\fnote{1601 in 3 vols; 486, 802, 313.} absolutely crammed full---not a single opinion---it's all knowledge---it is all what is so. The gross ignorance expressed by these people, you see. This dealing in opinion can only be done by the ignoring of the disciplines of knowledge. Because, if it is an opinion, then it must be wrong-because if it were not so, if it were not wrong, then it would be knowledge, and it wouldn't be an opinion. So when---you know, when somebody comes and says "I think so"---well, that's an opinion. If you knew it, you wouldn't think it. +And it's when we get very---these people who have been very sloppily educated; and they have, as we did back in England recently, a program on the television and they were all social scientists, and they said \dq{Well, we have a measure of madness, and it is to know something.} If you know it, you are mad, you see. If you only think it, well, that's sane. The great ignorance these people displayed, you see, is the ignorance of the queen of the sciences, as mathematics is often called. For example, let's take this book I was mentioning before, which is such a beautiful book in three volumes---Dickson's \booktitle{History of the Theory of Numbers}. Oh, I don't know---there is 1500 to 2000 pages\fnote{1601 in 3 vols; 486, 802, 313.} absolutely crammed full---not a single opinion---it's all knowledge---it is all what is so. The gross ignorance expressed by these people, you see. This dealing in opinion can only be done by the ignoring of the disciplines of knowledge. Because, if it is an opinion, then it must be wrong-because if it were not so, if it were not wrong, then it would be knowledge, and it wouldn't be an opinion. So when---you know, when somebody comes and says \dq{I think so}---well, that's an opinion. If you knew it, you wouldn't think it. -As for the other trick which is played, which is---"you know, you don't know anything, you see, you don't know a thing, you know." You say, "oh yes, I know what I had for breakfast." "Oh no, you may have forgotten, you may have made a mistake." The proposition that such people produce is that anything---Russell, himself, was one of these. You know, he said "I don't even know that two and two make four. You see, I may have been mistaken---" It is put more cogently than I could put it, my heart isn't in it. He was laboring a point because it was necessary for his subsequent statement that he should establish this, you see. So the theory---"you don't know---you know nothing at all---it's all a matter of opinion"---and, well, the question I always ask such people is "how do you know this? How do you know that nobody knows anything? How do you know it is only a matter of opinion?" +As for the other trick which is played, which is---\dq{you know, you don't know anything, you see, you don't know a thing, you know.} You say, \dq{oh yes, I know what I had for breakfast.} \dq{Oh no, you may have forgotten, you may have made a mistake.} The proposition that such people produce is that anything---Russell, himself, was one of these. You know, he said \dq{I don't even know that two and two make four. You see, I may have been mistaken---} It is put more cogently than I could put it, my heart isn't in it. He was laboring a point because it was necessary for his subsequent statement that he should establish this, you see. So the theory---\dq{you don't know---you know nothing at all---it's all a matter of opinion}---and, well, the question I always ask such people is \dq{how do you know this? How do you know that nobody knows anything? How do you know it is only a matter of opinion?} -\transcript{\spkr{WATTS} Isn't that the same kind of a question, when you say to a relativist---"You mean that everything is absolutely relative?" +\transcript{\spkr{WATTS} Isn't that the same kind of a question, when you say to a relativist---\dq{You mean that everything is absolutely relative?} -\spkr{SPENCER BROWN} Well, it is the same kind of throwing back his own system at him to show that he cannot support himself. There is the bland statement which really comes out in the form, "I know that nobody can know anything." +\spkr{SPENCER BROWN} Well, it is the same kind of throwing back his own system at him to show that he cannot support himself. There is the bland statement which really comes out in the form, \dq{I know that nobody can know anything.} \spkr{MAN} That's the paradox. -\spkr{SPENCER BROWN} Well, all you have got to do is say "how do you know?" +\spkr{SPENCER BROWN} Well, all you have got to do is say \dq{how do you know?} \spkr{MAN} I can't tell you. \spkr{SPENCER BROWN} No. -\spkr{O'REGAN} Some of your analysis of contradiction, and whole notion of crossing over from marked to the unmarked would almost suggest that contradiction, in a sense, is the form of form. It is what we can see when one arrives at that stage. Maybe the book could be the "Laws of Contradictions" just as much as the \booktitle{Laws of Form.} +\spkr{O'REGAN} Some of your analysis of contradiction, and whole notion of crossing over from marked to the unmarked would almost suggest that contradiction, in a sense, is the form of form. It is what we can see when one arrives at that stage. Maybe the book could be the \dq{Laws of Contradictions} just as much as the \booktitle{Laws of Form.} \spkr{SPENCER BROWN} Well, I am always careful about putting something greater into a smaller pot. Yous see, whenever we are speaking of contradiction, it is at such a more superficial level, because we are now already in language, and so on. Whereas in \booktitle{Laws of Form} the form is operative at every level. Whereas contradiction is only operative in something like our speaking. That's why, you know, although it's illustrative, it wouldn't do as a substitute. \spkr{LILLY} In the act of creation, using a self-referential tunnel feedback, can you move from inward to outward on your five levels, or your orders here, or is this just restricted to the first distinction? -\spkr{SPENCER BROWN} I am not quite sure---you mean, "can you distinguish the five eternal orders?" +\spkr{SPENCER BROWN} I am not quite sure---you mean, \dq{can you distinguish the five eternal orders?} \spkr{LILLY} Right. One from the other, moving from one level to the other, using the self-referential feedback, in each case, so that you get an oscillation between the two levels. @@ -1250,14 +1250,14 @@ As for the other trick which is played, which is---"you know, you don't know any \booktitle{The OMasters} is an imaginary adventure framing real events: the sudden appearance of a teacher or teaching that tokens the radical reformulation of a prevailing world view. The fantasy story is about a group of children from the present generation with an extraordinary capacity for embracing paradoxes---logical and psychological---who enter higher orders of complexity motivated primarily by aesthetic delight. -\booktitle{The OMasters}, sublime though innocent generalists, contemplate sophisticated processes while we are still computing products. A precocious and powerful inner circle of the group, known as The Lords of Form, move about the world in disguise developing intellectual foundations for \e{NOVACULT} from imaginary holograms generated by interference patterns between pure mathematics and Tibetan Vajrayana Buddhism, whale songs and Hopi Kachina dances. As refined by the Lords of Form, the "Flippety" principle of Distinguish\slash Embrace is put into practice by \bt{The OMasters}, producing technological advances such as the Optical Process Bio-Interface Computer, the Adamantine Bit, and a new critical apparatus for literature and the arts. +\booktitle{The OMasters}, sublime though innocent generalists, contemplate sophisticated processes while we are still computing products. A precocious and powerful inner circle of the group, known as The Lords of Form, move about the world in disguise developing intellectual foundations for \e{NOVACULT} from imaginary holograms generated by interference patterns between pure mathematics and Tibetan Vajrayana Buddhism, whale songs and Hopi Kachina dances. As refined by the Lords of Form, the \dq{Flippety} principle of Distinguish\slash Embrace is put into practice by \bt{The OMasters}, producing technological advances such as the Optical Process Bio-Interface Computer, the Adamantine Bit, and a new critical apparatus for literature and the arts. -Principal historical hero for \booktitle{The OMasters is G. Spencer Brown}, a "mythematician," also sportsman, inventor, poet and former philosophy don. He appears at a conference of psychocosmic scientists, scholars and artists (attended clandestinely by one of the Lords of Form), where he offers a discourse on "laws of form"---a highly conceptualized vision of the Void---explaining what these laws are and how they are generated. A paradigm of how we may imagine them to appear is already published: an ultra-condensed textbook called \bt{Laws of Form} (Julian Press, New York, 1972). It is a calculus of indications in which the use of imaginary values provides a new theoretical basis for electronic switching, Boolean algebra and all binary systems, and so too for more complex orders of number and measure. +Principal historical hero for \booktitle{The OMasters is G. Spencer Brown}, a \dq{mythematician,} also sportsman, inventor, poet and former philosophy don. He appears at a conference of psychocosmic scientists, scholars and artists (attended clandestinely by one of the Lords of Form), where he offers a discourse on \dq{laws of form}---a highly conceptualized vision of the Void---explaining what these laws are and how they are generated. A paradigm of how we may imagine them to appear is already published: an ultra-condensed textbook called \bt{Laws of Form} (Julian Press, New York, 1972). It is a calculus of indications in which the use of imaginary values provides a new theoretical basis for electronic switching, Boolean algebra and all binary systems, and so too for more complex orders of number and measure. -As read by \booktitle{The OMasters}, \bt{Laws of Form} is a major poem on the order of the \bt{Divine Comedy}, in that each contains a vision of what has been called "Eternity." Both poets describe what remains constant in a universe of change: Dante's epic recounts the journey inward, toward a mystical union with God, while Brown's system indicates the Void at the center, and as in Buddhist sutras works outward through the use of injunctive language, generating archetypal patterns from the basic act of distinction. "Angels" in the \bt{Commedia} become "consequences" in the calculus, which relationship Brown makes explicit. The two texts are reports on a vision not merely private but common to all sentient beings, and capable of being understood in the same way by all humanity. +As read by \booktitle{The OMasters}, \bt{Laws of Form} is a major poem on the order of the \bt{Divine Comedy}, in that each contains a vision of what has been called \dq{Eternity.} Both poets describe what remains constant in a universe of change: Dante's epic recounts the journey inward, toward a mystical union with God, while Brown's system indicates the Void at the center, and as in Buddhist sutras works outward through the use of injunctive language, generating archetypal patterns from the basic act of distinction. \dq{Angels} in the \bt{Commedia} become \dq{consequences} in the calculus, which relationship Brown makes explicit. The two texts are reports on a vision not merely private but common to all sentient beings, and capable of being understood in the same way by all humanity. -The "Eternal" realm has been described by all major religions, documented in the West by Jung, among others, and experienced through inspiration, meditation, and psychedelics. The Laws of Form show how it is that all these visions are technically and formally the same. \booktitle{The OMasters} use Brown's teaching to define a basic ground for thoir associative metaconsciousness version of the Glass Bead Game. +The \dq{Eternal} realm has been described by all major religions, documented in the West by Jung, among others, and experienced through inspiration, meditation, and psychedelics. The Laws of Form show how it is that all these visions are technically and formally the same. \booktitle{The OMasters} use Brown's teaching to define a basic ground for thoir associative metaconsciousness version of the Glass Bead Game. With the Lords of Form as vanguard, \booktitle{The OMasters} acquire and analyse a transcript of Brown's excurses on the text. As though it were a golden fleece, they spin from the transcript their thread of associations, which are woven into a Sufi story\slash science fantasy illustrating the discourse and commenting on it. Brown's avatar appears as an intergalactic voyager who assists in deciphering the diamond-hard message, providing the keys for step-down transformations from the abstract calculus to everyday life situations, and for step-up transformations to interspecies and outer space communication. @@ -1265,7 +1265,7 @@ The frame story unfolds as three interlacing accounts of \booktitle{The OMasters Primo has all the correct maps---\booktitle{Laws of Form}, the \bt{I Ching}, a Tarot deck, Robert's \bt{Rules of Order}---but he doesn't know how to read them. They lie on the Crystal Navigation Table of the Gravity\slash Gracewarpship. \e{Adamantinus}, whose captain has vanished, leaving the controls on a course set for the Black Hole in Cygnus. From the confused advice and theoretical formulations offered by the desperado experts of his cosmic crew, he selects a true course through the warp, guided by contemplating the Yellow Pearl, an incarnation of the Queen of Heaven herself. -As Woodrow Nicholson, our hero appears at the head of his party in '76, by which time we have a whole string of backup Vice Presidents. Woody is the 22\textsuperscript{nd}, kept roving (for security) in the last of tho Winnebagoes on a circuit of national parks and supermarket parking lots. However, he is impelled to pick up the standard when his precedents are all wiped out in a wicked game of "21" by Ahab McGaff, proprietor of the Double Cross (\aside{TBA}) Saloon in 'Vegas, and international purveyor of contraband whalemeat. Supported by the Sufia, Woody openly challenges Ahab, who is also the secret head of MaFie, the spiritual materialist monopoly. Following the tradition of the Eisteddfodd in Wales, Woody schedules a special competition to replace elections: the Grand Noshinals, to be held on the Fourth of July---with the winning recipe from the eat-offs to determine the identity of the Vajrayogini, our first woman president. Ahab tries simultaneously to fix the Eisteddfodd and, through his show business connections, to produce it for global television. +As Woodrow Nicholson, our hero appears at the head of his party in '76, by which time we have a whole string of backup Vice Presidents. Woody is the 22\textsuperscript{nd}, kept roving (for security) in the last of tho Winnebagoes on a circuit of national parks and supermarket parking lots. However, he is impelled to pick up the standard when his precedents are all wiped out in a wicked game of \dq{21} by Ahab McGaff, proprietor of the Double Cross (\aside{TBA}) Saloon in 'Vegas, and international purveyor of contraband whalemeat. Supported by the Sufia, Woody openly challenges Ahab, who is also the secret head of MaFie, the spiritual materialist monopoly. Following the tradition of the Eisteddfodd in Wales, Woody schedules a special competition to replace elections: the Grand Noshinals, to be held on the Fourth of July---with the winning recipe from the eat-offs to determine the identity of the Vajrayogini, our first woman president. Ahab tries simultaneously to fix the Eisteddfodd and, through his show business connections, to produce it for global television. Shakuhachi Unzen is dishwasher and garbageman at the Teahouse of Necessity, where late each night he serves an installment of the Feast of 4001 Fools. Despite his clownish circumstances, Shakuhachi operates in the ancient tradition of Ninja, martial arts masters of invisibility. In compiling a cookbook of spontaneous concoctions, he discovers a magic recipe which induces the illusion of instant enlightenment---but he must await the appropriate recipient before the real transmission can be completed. @@ -1282,7 +1282,7 @@ Recognizing Laws of Form as a vision of the Eternal regions, the Lords of Form d \ssec II. Processing -Transcript of Brown's remarks, obtained by Taoed, analyzed by the Lords of Form. They want to get his number, which is coded into the discussion of primes in Session 2 of the text. Technical experts from Sufi Central provide data on injunctive and descriptive language, myth and folklore, the Synod of Whitby, and the nature of Brown's cosmology. Particular attention paid to the "covenant of the cradle." Notes by Taoed on obscure sections of the transcript. This document, profound, precise and most eloquent in its argument, a discussion of the formal relationships of science and culture, makes up a significant portion of the chapter. +Transcript of Brown's remarks, obtained by Taoed, analyzed by the Lords of Form. They want to get his number, which is coded into the discussion of primes in Session 2 of the text. Technical experts from Sufi Central provide data on injunctive and descriptive language, myth and folklore, the Synod of Whitby, and the nature of Brown's cosmology. Particular attention paid to the \dq{covenant of the cradle.} Notes by Taoed on obscure sections of the transcript. This document, profound, precise and most eloquent in its argument, a discussion of the formal relationships of science and culture, makes up a significant portion of the chapter. \ssec III. Models |