Esalen Institute and the AUM Conference
As is recounted in The Center of the Cylone, I spent two years, 1969 to 1971, at Esalen Institute in Big Sur. Among a fair number of people in the United States, Esalen has a certain kind of reputation. It apparently was the origin of encounter group work with William Schutz and of the Gestalt psychology type of therapy under Fritz Peris. As is recounted in The Center of the Cyclone, the Esalen Institute hot baths were one of the main attractions at the location in Big Sur. These were natural hot springs in the cliffs above the Pacific, used by the Indians for many years before Michael Murphy's grandfather bought the property in 1910, before California Highway One was put through. In 1938, Highway One was constructed and it went by this property between the Pacific on the west and the Santa Lucia mountains on the east. A motel was then constructed and over the years the motel grew, using the hot baths as its main attraction.
Mike Murphy and Dick Price, the founders of Esalen, met in a course on Asiatic studies at Stanford University. Mike Murphy then went to India and spent eighteen months at the Sri Aurobindo Ashram in Pondicherry, working with the cosmic
Mother. The life in the ashram was active with physical sports, physical exercises and yogic techniques being taught to the students. After Mike returned, he and Dick made an arrangement with his family and they started the Esalen Institute. Everyone concerned had to pitch in and help. Dick and Mike were washing dishes, gardening and so forth in the early days of the Institute.
As time went on, they became better known. The catalog expanded over the last twelve years; the influence of Esalen on the established community become prominent. As a consequence, well over a hundred copies of Esalen were set up around the United States and called "human potential movement growth centers."
I arrived at Esalen in 1969, and like many people before me, had my personality rescued for the use of my body, brain and mind to become a more integrated individual. I started my Esalen experience at a nude weekend conducted by Bill Schutz. He talked sixty people (including me) out of their clothes within fifteen minutes.
Dick Price laid out my schedule, and for the next six weeks I went through various samples of the main tent and sideshows at Esalen. I took the hurdle of the nude baths by the sea, saw a dolphin in the ocean and watched whales go by; I saw the sea otters swimming at the surface, on their backs, with their prey of clams to be pounded open against their chests. As was detailed in The Center of the Cyclone, I had left the confines of a laboratory and tropical existence where I had been working with dolphins and doing research on the problems of communication with humans and dolphins.
While I was at Esalen, the first seeds of the AUM Conference were planted when in 1969 Stewart Brand of The Whole Earth Catalog gave me G. Spencer Brown's book The Laws of Form. Stewart asked me to do a review for the catalog. I read it and immediately realized that I knew only one person in the United States, possibly in the world, who was capable of reviewing this book, justly and in depth. I suggested that he send the book to Heinz Von Foerster, who is Director of the Biological Computer Lab at the University of Illinois. Heinz is preeminent among the world's cyberneticists and computer logicians. He grew up in
Austria where, as Ludwig Wittgenstein's nephew, he had early exposure to the ideas and philosophy that Brown has further developed. Heinz's review and commentary (reproduced at the end of this chapter) on The Laws of Form appears in The Last Whole Earth Catalog and provides a doorway into Brown's work.
In the following years I continued to read The Laws of Form and, at odd times, tried to master it . . . with little success. I referred it to Alan Watts, who read it with such excitement that he quickly traveled to England to meet and talk with G. Spencer Brown. When Alan got back he suggested that we organize a conference on The Laws of Form. The purpose was to expose the works of G. Spencer Brown to leading thinkers in America in the hopes that the implications of the work could be discussed and explored from many different points of view. We wanted a number of people to meet Brown, and also felt that the exposure to his peers in America would be useful and stimulating to him.
As part of a larger generalization, Alan suggested that the conference be the initial grouping of the "American University of Masters" (AUM). He purposely chose the acronym AUM as the Sanskrit mantra form (commonly miscalled OM) meaning the Universe and the highest beings of that Universe. He felt the Western yogi could learn from the Eastern one, and vice versa. We planned to make the AUM into an ongoing ad hoc institution. Sadly, these plans have been stalled (at least temporarily) by Alan's sudden death. The organization, ephemeral as it might have been, proved to be a vital and invigorating experience in our lives.
He and I wrote to G. Spencer Brown. After several telephone calls, Brown agreed to come for forty-eight hours from London. Toni and I picked him up at the San Francisco airport in our motor home. For the three-hour drive to Big Sur he rested in bed in the back. It was impressive that in the midst of jet lag and with very little rest, he was quite ready to present his new calculus to his American colleagues.
For two solid days of approximately six hours a day he gave polished performances, the like of which I have rarely seen. He not only went through some of the bases of The Laws of Form,
but also went through his ideas on the five levels of eternity as given in footnote number one of his book Only Two Can Play This Came, under the pseudonym James Keys.
After his departure, the other participants each lectured on the work. Heinz Von Foerster summarized the conference in his own unique way.
In his summary Heinz recapitulated some of the philosophical marvels in The Laws of Form, and ended with another piece of magical logic and biological significance by showing that Spencer Brown's logical operation of the "Cross" is constructed so as to miraculously recreate itself when operating on the "Void." Finally, however, Heinz drew our attention to a most touching relation between G. Spencer Brown and two other men who all are tied to one another by a state of melancholy that befalls those who know that they know. These men are Ludwig Wittgenstein and Carlos Castaneda's teacher, don Juan. To see this relation and to feel this melancholy, one should remember the last words of The Laws of Form. After G. Spencer Brown went through the incredible tour de force that Bertrand Russell called "a new Calculus of great power and simplicity," Spencer Brown ends his book by saying: "Thus we see that our journey was in its preconception unnecessary although its formal course once we had set out upon it was inevitable." This sounds so much like Ludwig Wittgenstein in his Tractatus Logico-Philosophicus. The famous last proposition is a resignation; it reads: "Whereof one cannot speak, thereof one must be silent."
To close the circle, Heinz now read us from a few of the last paragraphs of Castaneda's Journey to Ixtlan. The situation is that don Genaro, don Juan's brujo friend, has just ended his description of what he had left when he entered "the realm of knowledge" with the metaphor of always traveling but never or at best almost reaching Ixtlan. Don Genaro, don Juan and Carlos Castaneda are sitting around in a triangular formation and Castaneda writes:
For an instant I sensed a wave of agony and an indescribable loneliness engulfing the three of us. I looked at don Genaro and I knew that, being a passionate man, he must have had so many ties of the heart, so many things he cared for and left behind.
I had the clear sensation that at that moment the power of his recollection was about to landslide and that don Genaro was on the verge of weeping.
I hurriedly moved my eyes away. Don Genaro's passion, his supreme loneliness, made me cry.
... I gazed at the two of them, each in turn. Their eyes were clear and peaceful. They had summoned a wave of overwhelming nostalgia, and when they seemed to be on the verge of exploding into passionate tears, they held back the tidal wave. For an instant I think I saw. I saw the loneliness of man as a gigantic wave which had been frozen in front of me, held back by the invisible wall of a metaphor.
I derived from Heinz's summary of the AUM Conference the following explanation behind Brown's little symbol that looks like the inverted, capital L ( Ï ), which can be used as an operator at the same time as a signal. When one feeds the signal through the operator it generates an endless series of the marked state alternating with the unmarked state. In other words, the operator itself, the cross, the marked state, then the unmarked state (the Void, in other words, a blank space that lies outside any universe), the marked state, etcetera. This series was entitled a "flippety": an automatic oscillator that can be considered the basis of all communication, of all calculation, of all creation. Later, such considerations (after three years of study of The Laws of Form) led Francisco Varela, working with Heinz, to develop a three-valued logic: the unmarked state, a self-referential operator, and the marked state.
This new development of Varela, published since the AUM Conference, may eventually be used to solve the dilemma left in me by study of The Laws of Form since it was first published. This dilemma was not solved at the Conference, nor in my own work since that time.
All too simply the dilemma is this:
Where is the mathematician and his reader in all this high-powered calculus? Brown, apparently to his own satisfaction, relegates "the observer" as follows (The Laws of Form, p. 76) :
We see now that the first distinction, the mark, and the observer are not only interchangeable, but, in the form, identical.
This is the only reference in the main body of the work to "the observer." I ask the question: Who is making the above quoted statement? Is this statement self-referential in regard to its creator? Is the creator equivalent to "the observer," or is there more here than is stated?
Brown says, in a footnote to Chapter Two, The Laws of Form, p. 77, that:
. . . the primary form of mathematical communication is not description, but injunction. In this respect it is comparable with practical art forms like cookery, in which the taste of a cake, although literally indescribable, can be conveyed to the reader in the form of a set of injunctions called a recipe ... a set of commands, which if obeyed by the reader can result in a reproduction, to the reader of the [writer's] original experience.
My dilemma then arises anew: The Laws of Form, as written (as an injunctive set) postulates the creator, his injunctions, the reader, the creator's experience and its reproduction in the reader.
Brown goes on (p. 77, continued) mentioning the same proposition quoted by Heinz above:
Where Wittgenstein says (proposition 7, of Tractatus Logico-Philosophicus)
Whereof one cannot speak, thereof one must be silent.
(Wovon man nicht sprechen kann,
daruber muss man schweigen. (p. 150 of Tractatus)
he seems to be considering descriptive speech only. He notes elsewhere that the mathematician, descriptively speaking, says nothing.
I include my own, bracketed, interpolations within Brown's next statements:
The same may be said of the [cook], who, if he were to attempt a description (i.e., a limitation) of the set of [taste] ecstasies apparent through (i.e., unlimited by) his [recipe] would fail miserably and necessarily. But neither the [cook] nor the mathematician must, for this reason, remain silent.
Bertrand Russell, in his introduction to Tractatus, expressed "what thus seems a justifiable doubt in respect of the rightness of Wittgenstein's last proposition [number 7]," when he says (p. xxi) :
What causes hesitation is . . . Mr. Wittgenstein manages to say a good deal about what cannot be said, thus suggesting to the sceptical reader that possibly there may be a loophole through a hierarchy of language, or by some other exit.
The exit, as we have seen it here, is evident in the injunctive faculty of language.
This is a long tortuous road to understanding, necessarily complex for completion of a domain of discourse. Russell is suggesting that there is a loophole that is not present in Mr. Wittgenstein's explicit directions. He is looking for an exit. Brown maintains that the exit is in the external injunctive use of language beyond the internal injunctive use of language in Wittgenstein's system. Brown is attempting to open up this philosophical problem of the closure of Wittgenstein's system so that it extends further than merely the descriptive use of language as Russell makes clear. In my own work, I have enunciated the following format (cf The Mind of the Dolphin; The Human Biocomputer; Simulations of God: The Science of Belief):
1) Communication is the process of inviting another mind to participate in constructing a set of instructions for the construction of a simulation, of a model, of: how to think, and/or to build, and/or to feel, and/or to do an externally real new object, another simulation, a state of being, a state of one's central processes, a model of communication itself, a new language, a new calculus, or whatever.
2) Information exists exclusively in a mind in a central nervous system (C.N.5.).
3) Signals (including verbal, nonverbal, and unknown) exist outside the mind and transfer information from a mind-C.N.S. through the body, through the external reality to another body-ñ.N.5.-mind.
4) An observer-participant lives within his program domains within the central processes of a central nervous system.
5) An observer-participant is limited by his simulations within his program domains.
6) The program domains of the observer-participant can be enlarged beyond its current limits by his participation in searching for new simulations not yet in these domains.
7) The activities within the program domains of the observer-participant, within certain limits (unknown/known), can be self-programmed, and hence can be self-referential.
8) The observer-participant currently can be considered a property of the program domains: the satisfactory definition of this "entity" (observer-participant) is yet to be made fully and completely.
9) The observer-participant uses a set of operations as follows (regarding any language, any mathematics, any representation regarding his own inner reality ["inner simulations of inner experience"] and/or/including any representation of his outer reality ["simulations of outer experience"] or any representation lying within his program domain, bridging these "inner-outer" domains) :
a) A simulation is descriptive-injunctive (not one, but both).
b) A direct experience of newness, of uniqueness (arising within central processes or from incoming signals or both) is experienced by the observer-participant through a filter-screen-processing domain beyond his conscious observation-participation capacity: a very large fraction of perception requires a processing-^computation delay in which he cannot participate consciously.
c) The observer-participant is always delayed behind the signals generating the computations soon to become "informative" to him.
d) Information is central processing of signals coming in to the C.N.S. and going out from the C.N.S.
e) What appears to be "transfer of information” from one mind to another exists through each simulating the other.
f) Direct experience [inner, outer, inner—outer) cannot be transmitted directly from one mind to another: only
simulations can be analyzed and mutually transformed into appropriate signals for transfer to another participating mind.
g) In a dyad of two bodies (two separate minds within) only that which is contained in mutually compatible simulations can become appropriate communicative simulations generating appropriate signals and hence "shared" information.
h) Among all possible sets of simulations, mutual dyadic search can be done so as to develop or find elsewhere appropriate simulations.
i) Simulations and/or metasimulations are of several types (both in one mind and/or in more than one mind) :
iii "As if True"
iv "As if False"
vi "As if meaningless"
j) True in the injunctive-descriptive mode expresses a high degree of goodness-of-fit of simulation to direct experience-participation (inner, outer, inner-outer).
k) False (in the same mode) expresses a null or low degree of goodness-of-fit.
l) The "as if" values are used in the construction phase of simulations in evaluating simulations, in the recognition that all simulations are programs in a limited mind. (In the deeper analysis any and all simulations are "as if true/false".)
m) Meaningless is used in regard to simulations that are not useful in the program domain of the observer-participant.
n) "As if meaningless" is used in regard to simulations not yet one's own.
Thus one can see that Wittgenstein's Proposition 7 above ("Whereof one cannot speak, thereof one must be silent") is an injunction to search, in silence, until one has the simulations necessary to emit the information one knows internally to be
true—simulations shared with other disciplined minds who either have, can find or create, or can be given the necessary instructions to construct, sufficiently corresponding simulations to receive the new information. (Brown spent several weeks working with Russell to demonstrate The Laws of Form as a new calculus.) The ultimate human test of one's simulations is their usefulness in communication with others: the construction of new consensus simulations shared among increasingly greater numbers of minds (hopefully, over the whole planet).
Studies of injunctive-descriptive simulations and their deep basic structure is rewarding in the inner-outer realities. The trend expressed in this conference (and, we hope, in future exchanges) is that disciplined minds hunt for and need more appropriate, more useful, more efficient simulations in every field. Mathematics and logic are the metasimulations that bring increased efficiency of operation to each of our inner program domains. It is less complex and more efficient mentally to understand simulations (and belief systems constructed from them) than it is to defend a belief system as if one's survival depended upon it. Defense-attack based upon belief systems is a meaningless simulation possibly leading, in the present era, to the end of humankind as we know it. The power of words, of language, of beliefs, of simulations can be deadly—especially if unshared and unreal in regard to consensuses separated from one another, growing in isolation with poor or missing communication between them.
Other participants taught The Laws of Form as found in the book. Douglas Kelley, a mathematician from Chicago, gave a series of explicative lectures for those who needed it. Gregory Bateson gave his wise advisories in the same region, connecting some of Brown's ideas to his own work in Steps to an Ecology of Mind. Gregory, who has had a persisting influence on many of us for years, is just becoming discovered (at age seventy) by the general intelligent reading public. His time seems finally to have arrived; we will all be the richer for it.
John Brockman contributed his usual humor, showing that "there is Nothing in the screen of words," i.e., the Void is inexpressible. The Brockman Void is generated in Afterwords,
a book in which blankness of page is interspersed with words which undo themselves.
(Baba) Ram Dass gave a warm presentation of his beliefs epitomized in his guru; he said that each of us is his guru; his guru is of universal extent. He said he loved him [us] deeply.
Alan Watts gave many wondrous remarks including one that Toni will never forget . . . "There is no substance, all is form/' even as in his version of physics. Part of The Lazos of Form (page 31, the Primary Algebra, Chapter One) was put to music by Kurt Von Meier and Company toward the end of the conference. The entire AUM proceedings were recorded. We have Brown's part transcribed: it is a clear presentation linking the laws to his "five levels of eternity."
Brown has been running his own publishing company, G. Spencer Brown, Limited, of Cambridge, England. Brown's books have been published in this country by Arthur Ceppos (Julian Press) at Toni's and my recommendation. The Lazos of Form is now available in paperback (Bantam Books). I recommend the United States edition over the British edition, as it contains a new introduction, which somewhat simplifies one's absorption of "Laws."
Many Esalen people attended the AUM Conference: Bill Schutz, Dick Price and several others. Heinz Von Foerster received a three-hour massage from Jane Milletich, which I am sure he will never forget. The conference, which lasted five days beyond Brown's departure, prospered in the Esalen atmosphere and the California sun. Most of the participants eventually got into the rhythm, taking advantage of the hot baths, massage, etcetera, as well as meals at the lodge.
"My first awareness of G. Spencer Brown/'James Keys,' as a person, the man behind the theory presented at the AUM Conference, came in the mail from my old friend Alan Watts.
"John and I had been together for about a year when we received the manuscript Only Tzoo Can Play This Game. Brown's work The Lazos of Form had been given to Alan originally by John. Alan returned from his visit to Brown in England with the
new manuscript, which he then sent to us. We were about to fly to New York and we took the manuscript with us.
We read the manuscript together on the plane. I was laughing and crying all the way, much to the distraction of fellow passengers. I loved the mystical, romantic and cosmic humor of the story. I remember asking him if they ever got back together (James Keys and the girl in the story, that is). I don't remember the precise wording, but it never was a yes or no.
I was so moved by the book that as soon as I arrived in New York I went to the home of Arthur and Prue Ceppos, handed it to Arthur, and didn't stop talking for hours about my reaction and why I thought he should publish it. He subsequently read it and agreed for his own reasons that it should be published. I received one of the first copies with the inscription "To the Godmother."
Whatever I have been able to assimilate from The Laws of Form has been through people like John and Alan. I understood it intuitively through my own experience. One can relate to "flippety," as he calls it:
—the dichotomy of: should I? shouldn't I?
—expansion and contraction.
—the cosmic balance game, or cosmic surfing, as I like to call it.
The last one I've known very well for some time (see end of Chapter Twelve, The Dyadic Cyclone).
We were both anxious to meet him after that, and coincidences seemed to line up so that the right amount of density focused on having the conference take place. Hence, the "American University of Masters" was instituted and the big brains came from around the country to hear the ex-Don from Oxford present his Laws of Form at Big Sur.
James, as he asked me to call him, is like an exotic rare bird with plumage that I had never seen before. His eccentric behavior has a great deal of style (at least in short doses, to which I've been exposed). I loved his voice. Just listening to his presentation was a privilege. He is in every sense a professional.
I was happy to have the memory of that last gathering with
Alan Watts who died shortly after that. He had such a wonderful time playing host to his peers. Every morning at 6 am he would ring a gong and awaken everyone for meditation. Most of us meditated in our own way. It was somehow comforting to hear the gong. Every evening, the last sign we would have would be the lonely figure of Alan walking up and down the motel corridor looking for another night bird to share yet another charming story over a glass of wine. At one point he lauded all of us for our patterns of regularity in sleeping and eating.
In a gathering of his peers, as opposed to disciples, Alan was at his lovable best. He so wanted to help James to be more sociable, which of course was not James' style.
Much of the glow of the conference came not from the official program and lectures, but from the interaction among the "Masters" and the interaction between our group and the regular Esalen people.
Here were a group of "super-heads" descending on Esalen, a place where many of the staff members feel that "the body is the temple of the mind." Just as the Esalen people were suspicious and even disdainful of the intellect, so too were the AUM members forgetful that they had something called a body. However, as the conference went along, the ice began to break, discussions sprang forth, the AUM people began drifting down to the baths, signing up for nude massages, and genuinely enjoying themselves in the ambience of Big Sur.
Some of the fondest memories are of the people and what they brought to the conference in the way of style and personality.
Kurt Von Meier, the Master American Shaman, and his musicians put the math to music. We had a concert at the end of the conference. The added dimensions of understanding it with the use of music made the "Glass Bead Game" of Hermann Hesse come to life (as in Magister Ludi).
(Baba) Ram Dass was his usual lovable bhakti non-self. He had a wonderful time appearing to resist the academic packaging of this new Western mystical math. We stayed up for hours one evening as mathematician Ted Glynn took a typical Western stance vis-`a-vis Ram Dass's Eastern trip. Ram Dass was very argumentative at first, even disconcerted, until all at once, he
came forth with a gleaming smile and turned to Ted and thanked him for being his guru.
Gregory Bateson and his lovely wife Lois were there with their beautiful daughter, Nora. Gregory, with his usual dignified English manner, "harumphed" his way through the sessions, quietly assimilating.
Heinz Von Foerster was charming and erudite, as usual. He is a rare combination of Austrian charm accompanied by an amazing ability to make even the most difficult proposition understandable. After Brown left, Heinz gave his dynamic interpretation of what had been presented (see above).
John Brockman's profound humor always makes it possible for me to catch a glimpse of myself turning a corner. Alan Watts, reading from the galleys of the now-published Afterwords at breakfast one morning, looked up and laughingly said, "He's like the man who draws a circle on a piece of paper to make a hole, then jumps in through the hole, and then pulls the circle, the paper and us in behind him, leaving nothing . . . just the Void."
George Gallagher and his wife Betty helped me to put some of this high-powered math in perspective. George has a beautiful ability to simplify with the use of short, precise analogy.
It was quite a show . . . some of the intellects ("mystics") of our culture all getting together to compare interpretations of a new mathematical theory ... in the midst of mineral baths, massage and sunshine.
Heinz Von Foerster's review of "The Laws of Form," by G. Spencer Brown, as it appeared in "The Last Whole Earth Catalog," p. 12, Portola Institute, Menlo Park, California 94025.
The laws of form have finally been written! With a "Spencer Brown" transistorized power razor (a Twentieth Century model of Occam's razor). G. Spencer Brown cuts smoothly through two millennia of growth of the most prolific and persistent of semantic weeds, presenting us with his superbly written Laws of Form. This Herculean task which now, in retrospect, is of profound simplicity rests on his discovery of the form of laws. Laws are not descriptions, they are commands, injunctions:
"Do!" Thus, the first constructive proposition in this book (page 3) is the injunction: "Draw a distinction!" an exhortation to perform the primordial creative act.
After this, practically everything else follows smoothly: a rigorous foundation of arithmetic, of algebra, of logic, of a calculus of indications, intentions and desires; a rigorous development of laws of form, may they be of logical relations, of descriptions of the universe by physicists and cosmologists, or of functions of the nervous system which generates descriptions of the universe of which it is itself a part.
The ancient and primary mystery which still puzzled Ludwig Wittgenstein (Tractatus Logico-Philosophicus, A. J. Ayer (ed), Humanities Press, New York, 1961, 166 pp.), namely that the world we know is constructed in such a way as to be able to see itself, G. Spencer Brown resolves by a most surprising turn of perception. He shows, once and for all, that the appearance of this mystery is unavoidable. But what is unavoidable is, in one sense, no mystery. The fate of all descriptions is ". . . what is revealed will be concealed, but what is concealed will again be revealed."
At this point, even the most faithful reader may turn suspicious: how can the conception of such a simple injunction as "Draw a distinction!" produce this wealth of insights? It is indeed amazing—but, in fact, it does.
The clue to all this is Spencer Brown's ingenious choice for the notation of an operator ~l which does several things at one time. This mark is a token for drawing a distinction, say, by drawing a circle on a sheet of paper which creates a distinction between points inside and outside of this circle; by its asymmetry (the concave side being its inside) it provides the possibility of indication; finally, it stands for an instruction to cross the boundary of the first distinction by crossing from the state indicated on the inside of the token to the state indicated by the token. (A space with no token indicates the unmarked state.) Moreover, these operations may operate on each other, generating a primary arithmetic, an opportunity which is denied us by a faulty notation in conventional arithmetic as pointed out by Karl Menger in "Gulliver in the Land Without One, Two, Three" (The Mathematical Gazette, voi. 53, pp. 224-250, 1959).
These operations are defined in the two axioms (no other ones are needed) given on pages 1 and 2. They are:
Axiom 1. The law of calling:
The values of a call made again is the value of the call. That is to say, if a name is called and then is called again, the value indicated by the two calls taken together is the value indicated by one of them. That is to say, for any name, to recall is to call. (In notation: _ _ _
the "form of condensation.") Axiom 2. The law of crossing:
The value of a crossing made again is not the value of the crossing. That is to say, if it is intended to cross a boundary and then it is intended to cross it again, the value indicated by the two intentions taken together is the value indicated by none of them.
That is to say, for any boundary, to recross is not to cross. (In notation: _
the "form of cancellation.")
For instance, take a complex expression
lb= =i Ë²HI Hll Ù
Then, by the two axioms
In the beginning this calculus is developed for finite expressions only (involving a finite number of “1 ), simply because otherwise any demonstration would take an infinite number of steps, hence would never be accomplished. However, in Chapter 11, Spencer Brown tackles the problem of infinite expressions by allowing an expression to reenter its own space. This calls for trouble, and one anticipates now the emergence of antinomies. Not so! In his notation the classical clash between a simultaneous Nay and Yea never occurs, the system becomes "bi-stable," flipping from one to the other of the two values as a consequence of previous values, and thus generates time! Amongst the many gems in this book, this may turn out to be the shiniest.
Sometimes the reading gets rough because of Spencer Brown's remarkable gift for parsimony of expression. But the 30 pages of "notes" following the 12 Chapters of presentation come to the reader's rescue precisely at that moment when he lost his orientation in the lattice of a complex crystal. Consequently, it is ad-
visable to read them almost in parallel with the text, if one can suppress the urge to keep on reading Notes.
In an introductory note Spencer Brown justifies the mathematical approach he has taken in this book: "Unlike more superficial forms of expertise, mathematics is a way of saying less and less about more and more." If this strategy is pushed to its limit, we shall be able to say nothing about all. This is, of course, the state of ultimate wisdom and provides a nucleus for a calculus of love, where distinctions are suspended and all is one. Spencer Brown has made a major step in this direction, and his book should be in the hands of all young people—no lower age limit required.