George Spencer Brown

George Spencer Brown
Gesetze der Form

Übersetzung: Thomas Wolf
Bohmeier Verlag 1997

Vorstellung der internationalen Ausgabe Seite IX
Der gesamte Text der Laws kann auf ein Prinzip reduziert werden, welches wie folgt aufgezeichnet werden könnte.
Kanon Null. Koproduktion
Was ein Ding ist, und was es nicht ist, sind in der Form, identisch gleich.
Das heißt, die identische Form oder Definition oder Unterscheidung agiert als die Grenze oder Beschreibung sowohl des Dinges als auch dessen, was es nicht ist.
Daraus ist das Kollorar, das alles und nichts formal identisch sind, leicht zu beweisen. (Beweis: Beiden fehlt jegliche Form überhaupt.)

Spencer Brown GdF 192:
Last Word
Existence is a selective blindness.
Use „blindness“ as paradigmatic of any sense, e.g.“deafness“, „tastlessness“, etc.
We notice one side of a thing-boundary at the expense of paying less attention to the other side. We notice a dish to be washed up in the sink by paying scant attention to the not-dish universe that our definition of the dish-boundary equally defines. Were we to pay equal attention to both sides, we would have to attribute to them equal value, and then the dish boundary would disappear. The dish‘s existence would cease, and there would be nothing to wash up.
Wenn wir sagen, wir spülen das Geschirr, tun wir diesem tatsächlich überhaupt nichts: Wir tun es dem Rest des Universums, welches wir abkratzen, um dem Geschirr eine saubere Grenze zu geben.
We do exactly the same with ourselves. When we die the self-boundary eventually disappears. Before it did so, we described a huge value to what we called „inside“ of ourselves, and comparatively little value to what we called „outside“.
The death experiences thus ultimately the loss of selective blindness to see both sides of every distinction equally.

Preface to the 1994 Limited Edition
page VII
: A generation has grown up since Laws of Form was first published in English. Human awareness has changed in the meantime, and what could not be said then it can be said now. In particular, I can now refer to the falseness of current scientific doctrine, what I call scientific duplicity: that appearance and reality are somehow different.
Since there is no means, other than appearance, for studying reality, they are definitely the same.

Any indication implies duality, we cannot produce a thing without coproducing what it is not, and every duality implies triplicity: what the thing is, what it isn't, and the boundary between them. Thus you cannot indicate anything without defining two states, and you cannot define two states without creating three elements. None of these exists in reality, or separately from the others.

pg 90: Thus we cannot escape the fact that the world we know is constructed in order (and thus in such a way as to be able) to see itself.
This is indeed amazing. Not so much in view of what it sees, although this may appear fantastic enough, but in respect of the fact that it can see at all. But in order to do so, evidently it must first cut itself up into it least one state which sees, and it least one other state which is seen. In this severed and mutilated condition, whatever the sees is only partially itself. We may take it that the world undoubtedly is itself (i.e. is indistinct from itself), but, in any attempt to see itself as an object, it must equally undoubtedly, act* (actor, antagonist. We may note the identity of action with agony.) so as to make itself distinct from, and therefore false to, itself. In this condition it will all this partially elude itself. spencer-brown-LoF90
Thus the world, whenever it appears as a physical universe* (unus = one, vertere = turn. Any given (or captivated) universe is what is seen as the result of a making of one turn, and thus is the appearance of any first distinction, and only a minor aspect of all being, apparent and non-apparent. Its particularity is the price we pay for its visibility.), must always seem to us, its representatives, to be playing a kind of hide and seek with itself. spencer-brown-LoF90

Boe: Wie ich das verstehen soll - oder verstehen können sollte - ist mir trotz jahrelanger Versuche zu "verstehen" erst beim Verarbeiten des folgenden Buches aufgedämmert. Es geht um die Erkenntnis der grundlegenden Form "Unterscheiden-Unterscheidung" (Beobachten).
Ohne Beobachter - ohne Unterscheider - ist Alles und Nichts un-unterschieden, identisch.


Felix Lau
Die Form der Paradoxie

Eine Einführung in die Mathematik und Philosophie
der „
Laws of Form“ von G. Spencer Brown
Carl-Auer 2008
Lau Form 23
Die Methode von Befehl und Betrachtung
Der deutschen Auflage der Laws of Form, die 1997 erschien, stellt George Spencer Brown eine Diskussion der Unterscheidung zwischen den Methoden „Befehl und Betrachtung“ sowie „Gerede und Interpretation“ voran.(Man findet diese Unterscheidung in der ersten Vorbemerkung zu den Gesetzen der Form, überschrieben mit „Vorstellung der internationalen Ausgabe“, die sich in keiner anderen Ausgabe der Laws of Form findet.)
Da die Darstellungsmethode einen inneren Zusammenhang mit dem Thema der Laws of Form aufweist, wird sie hier kurz dargestellt. Der Unterschied der beiden Methoden beruht auf einer unterschiedlichen Sprachverwendung (anweisend – beschreibend), die mit einer Erkenntnis über Sprache korreliert:
Gesagtes kann man glauben – aber nicht wissen.
Die von George Spencer Brown verwendete Methode beruht darauf, dass der Lernende bzw. Noch-nicht-Wissende Aufforderungen befolgt, bestimmte Operationen selbst durchzuführen und dann zu betrachten, wohin er mit ihnen gelangt. In herkömmlichen mathematischen Texten findet man keine Aufforderung, etwas selbst zu tun. (Ausgenommen natürlich die floskelhafte Aufforderung: „Den einfachen Beweis möge der interessierte Leser selbst finden.“
Die dort verwendete Formulierung „Es sei...“ verschleiert die Herkunft einer Unterscheidung. Es wird also unentwegt unterstellt, dass bestimmte Dinge so-und-so sind (tatsächlich und von sich aus). Die Sprachform ist dann beschreibend und lässt insofern einen Spielraum für Meinungen und Interpretationen.

Boe:...dass Erkenntnisleistungen immer Konstruktionsleistungen sind.

Lau Form 32:
Seite 32: 1. Vor dem Eintritt (
entry):
Seite 46: 2. Der Eintritt in die Form
Im Folgenden wird unter „Eintritt“ (entry)
das Treffen einer (ersten) Unterscheidung verstanden. Der Begriff veranschaulicht ein Durchschreiten, eine Veränderung, ein Losgehen oder Anfangen. Beim Eintreten wird eine Grenze überschritten. Zudem verweist der Begriff auf eine Tätigkeit, da immer jemand eintritt, sowie auf jemanden, der die Grenze kreuzt, und schließlich auf eine eigene Aktivität, da man nicht eingetreten werden kann.
Seite 34:Wesentlicher Inhalt dieses Kapitels sind dementsprechend die
Ideen der Unterscheidung und Anzeige, die Definition der Unterscheidung und die sich daraus ergebenden Axiome (Seite 40), welche später formal umgesetzt werden und als grundlegende Gesetze der Manipulation bzw. Veränderung von Ausdrücken dienen.
Mit dem ersten Satz des ersten Kapitels der Laws of Form werden die für den Kalkül grundlegende Unterscheidung und die entsprechenden Anzeigen (indication) in Form von Benennungen eingeführt:

Wir nehmen die Idee der Unterscheidung und die Idee der Bezeichnung [Anzeige; F. L.] als gegeben an, und dass wir keine Bezeichnung [Anzeige; F. L.] vornehmen können, ohne eine Unterscheidung zu treffen.“ (SPENCER BROWN 1997: 1)
We take as given the idea of distinction and the idea of indication, and that we cannot make an indication without drawing a distinction.
(SPENCER BROWN 1969: 1)
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George Spencer Brown
Only Two Can Play This Game
Bantam Books 1974

pg 11 ...Traditionally, there is a place called paradise. Instead of regarding it as a place, it is equally true, and sometimes practical, to consider it as a state of mind. Looking at it this way, it may be easier to see the possibility of any being attaining it any where and at any time....The state, or the place, whichever you like to call it, is frequently attained by the artist while alone, removed as far as possible from the distracting influences of the world. What has become clear to me now is that it need not be alone. Two people can, but quite a different way, take a trip to paradise together.
pg 16 The whole manifest world, with poor serious pompous important little man perched somewhat tatteringly out at the seventh level, counting down from the centre, which is everywhere, all comes spinning out of the nothingness in the middle of it all in the most indescribably inevitable way which is in fact, in form, and in content the only possible way. Nothing is left to chance, precisely because if we insist on making nothing into some thing, all this nonsense is the only thing nothing can really be.
pg 18 ...it looks as if the male is so afraid of the fundamentally different order of being of the female, so terrified of her huge magical feminine power of destruction and regeneration, that he daren't look at her as she really is, he is afraid to accept the difference, and so has repressed into his unconscious the whole idea of her as another kind of being, from whom he might learn what he could not know of himself alone, and replaced her with the idea of a sort of second-class replica1 of himself who, because she plays the part of a man so much worse than a man, he can feel safe with because he can despise her.
pg 19 All man's philosophy is a rationalization of his inner experience (or lack of it). And a lack of inner experience of the archetypal woman is expressed in a very obvious manner, by academic materialism, or its modern offshoot, logical positivism.
pg 23 The principle of Heisenberg was not clearly understood in western science until 1925, although the Chinese had already realized2 it as long ago as the fourth century BC, and possibly before. It amounts to this.

"What a man desires to know is that (i.e. the external world).
But his means of knowing is this (i.e. himself).
How can he know that!
Only by perfecting this."
Kuan Tsu.


To observe anything in the outside world, we have to interfere with it, for example by shining a light on it. And the more sensitive it is, the more the interference changes it. In respect of the most sensitive reality, what we actually see can bear no resemblance to what it really is. In any objective investigation, this principle operates at every level. The social sciences are perhaps too young to be very conscious of its effects in their fields, but it operates here in two ways. First, if you publish what you suppose (from your investigations) people will do, they read it and do something else. Or they do it because you suppose they will. Secondly, in any case, people (like other things) that are being watched don't behave like people who aren't being watched. In a very material sense, the eye of the investigator alienates whatever it rests on, from the electron upwards.

pg 24 It is still possible (although the out-and-out materialist of course denies it) to reveal, to ourselves at least, what this ultimate reality is by looking not outwards but inwards. This way we do not disturb it because here we are it. Indeed the faculty by which we do this is utterly familiar. It is called, appropriately enough, insight. Like any other faculty, the faculty of insight can be developed. If you are to become a mathematician, or an artist of any kind, you must develop it to a very high degree. And indeed, when we have developed our insight far enough, we can begin to see how the excessively "real" appearance of the physical world is in fact brought about.
pg 26 In the whole science of physics there is no such thing as a thing. Hundreds of years ago we carefully forgot this fact, and now it seems astonishing even to begin to remember it again. We draw the boundaries, we shuffle the cards, we make the distinctions. In physics, yes physics, super-objective physics, solid reliable four-square dam-buster physics, clean wholesome outdoor fresh-air family-entertainment sciencefiction superman physics, they don't even exist. It's all in the mind.
If you separate off this bit here (you can't really, of course) and call it a particle (that's only a name, of course, it's not really like that, more like waves really, only not really like that either, not really (space is not what you think, more a sort of mathematical invention, and just as real, or just as unreal, as the particle. In fact the particle and the space are the same thing really (except that we shouldn't really say "thing"), the sort of hypothetical space got knotted up a bit somewhere, we don't know exactly where because we can't see it, we can only see where it was before we saw it, if you see what I mean, I mean even that's not what it was really like, it was waves (or rather photons) of light carrying a message that may well be very unlike the thing, sorry, particle (remember this is only an abstraction, so that we can talk about it (it? sorry, we don't have an it in physics) ) it (sorry !) came from.
After all, we don't know that a thing (pardon !) is telling the truth about itself (would you mind looking the other way while I change into something formal?) when it emits (excuse me !) a blast (do forgive me !) of radiation, do we?, THEN (if you have followed the argument so far) this (I mean all these mathematical formulae, of course. What did you think I meant ?) is how it happens to come out. Of course, if you start in a different place (no, I'm afrald I can't tell you what a place is, although I could of course draw you a graph) and do it a different way (do please stop interrupting, darling, or we shall never get done), it (it? What we are talking about, my dear. It is convenient to at least pretend we are talking about something otherwise there would not be much point in doing physics, would there?) would naturally come out different. The significance of this way of talking, which, as everybody knows, is called modern science4, is maintained by means of a huge and very powerful magic spell cast on everybody to put us all to sleep for a hundred years, like that nice Miss Sleeping Beauty, while the amusements are being rigged up. We don't want people strolling all over the place asking awkward questions and making it collapse before it is ready do we? All in good time, when we have carefully finished building ourselves this nice big house of cards, we can, if we all keep our eyes shut tight and hold our breath and wish hard enough, we can all play this nice game of houses and all go and live in it before it all falls down. Except of course there isn't enough room there for everybody all at once, so we all have to not be too greedy and take it in turns
.

pg 111
Other Books: G. Spencer Brown, Laws of form: An account of the emergence of physical archetypes, presented as a rigorous essay in mathematics.
Starting with nothing and making one mark, we trace first of all the eternal forms.
From these we obtain two axioms, and proceed from here to develop theorems.
The word angel, as we find if we look it up, means messenger, and the algebraic consequences that spring from any mathematical system are always the "Angels" through which the mathematics, which is basically structured in the eternal regions may be interpreted or applied in everyday life.
In this particular system, the consequences enable us to construct logic and to build computers. They turn out to be, in other words, the principles underlying Boolean algebra. It thus appears that accounts of the creation of the world, from Genesis back to Yin-Yang and beyond, turn out to be more or less evident, if incomplete, accounts of certain fundamental properties of Boolean mathematics.
Having arrived, then, at a point where we have reconstructed Boolean algebra, we then proceed to take it considerably further than the ordinary textbooks, into equations of the second and higher degrees, which Boole found no way of doing. What in fact we do now is extend the disciplines of Boolean algebra as in the ordinary numerical algebras, to include both real and imaginary values, thus introducing into Boolean mathematics what turns out to be an exact analogue of the arithmetical i = root(-1).
In the Boolean form, of course, the imaginary value is not in any way numerical, but does behave in all other essentials like its numerical counterpart, enabling us to solve equations and to reason in ways we could not manage without it. Most astonishing of all, the use of this imaginary value reproduces, in the forms necessary to represent it, recognizable archetypes (what I calI "precursors») of particle and quantum physics, thereby constructing, without any outside help, the ground of what we call material existence.
It is constructed from nothing other than an unbroken sequence of argument whereby we see that, if we distinguish anything at all, then "all this" - including in the end the physical universe - is how it must eventually appear. In short, what I prove is that all universes, whatever their contents, are constructed according to the same formal principles.


pg 127 Notes
Note 1:
...Space is a construct. In reality there is no space. Time is also a construct. In reality there is no time. In eternity there is space but no time. In the deepest order of eternity there is no space. It is devoid of any quality whatever. This is the reality of which the Buddhas speak. Buddhists call it Nirvana. Its order of being is zero. Its mode is completeness. Its sex-emblem is female.
It is known to western doctrine, sometimes as the Godhead, sometimes as JHVH, or that which was in the beginning, is now, and ever shall be. This way of describing it, like any other, is misleading, suggesting that it has qualities like being, priority, temporality. Having no quality at all, not even (except in the most degenerate sense) the quality of being, it can have none of these suggested properties, although it is what gives rise to them all. It is what the Chinese call the unnamable Tao, the Mother of all existence. It is also called the Void.
...It is known to eastern doctrine, as it is to western, as the Triune God or Trinity. In western books of magic it is called The One Thing. In China' it is called the namable Tao. In Tibetan Buddhism it is called the densely-packed region.
...The explanation of the Trinity in fact turns out to be simple enough. When you make a distinction of any kind whatever, the easiest way to represent its essential properties mathematically is by some sort of closed curve like a circle. Here the circumference distinguishes two sides, an inside and an outside. The two sides, plus the circumference itself, which is neither the inside nor the outside, together make up three aspects of one distinction. Thus every distinction is a trinity. Hence the First Distinction is the First Trinity.
page 137
"What a man desires to know is that (i.e. the external world).
But his means of knowing is this (i.e. himself).
How can he know that!
Only by perfecting this." Kuan Tsu
.
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George Spencer Brown
A Lion's Teeth

Bohmeier Verlag 1995
page 12
Part 1 Heaven
0. One Who Came Thus (the word 'tathagata' means suchness (literally 'thus come' or 'thus gone') is all of us and none of us. For we all came exactly the same way, that is, thus. One Who Came Thus knows everything and never makes a mistake, and no one can know everything, and nothing never made a mistake, so One Who Came Thus is none of us.
1. Can there be any one who is nothing and no one? Can any one aspire to the nature, or lack of it, of nothing, and thus attain the absolute freedom of no one?
2. The idea is so contradictory that ordinary logic does not allow us to attempt it. Indeed to "attempt" it would not bring it about, for no act of creation attempts itself, but is what happens of its own accord.
3. That is, by its own laws, the laws that are themselves self-created because they accord with one another.
4. Creation, or all that appears, does not come from anywhere - how could it? If it came from somewhere, then that somewhere would be elsewhere, and what appeared would not be all. So
all that appears simply has nowhere to come from, and that is how we know it comes from nowhere.
5. We learn this profound secret because we can see it is self-evident. Scientific knowledge, attained by studying the appearance of what are called things, gives no account of their fundamental nature and origin, how they came to exist and what they really are. It explains things in terms of other things, far ever putting the question back a step, without ever actually answering it. Religious explanations in terms of a supernatural "creator" are equally helpless, giving an account of the creation at the expense of an ignorance of the imagined creator.
6.
We tend to forget that animals don't ask this question, because they don't possess the elaborate descriptive languages that we do. When we see the problem as one that our language has constructed for us, is when we begin to realize that, by an extremely profound analysis of what the language has done, we might answer the question in a way that "natural" science and "revealed" religion never have, and never could.
7. We made the mistake of thinking our questions must have religious or scientific answers, where in fact the answers are so simple, such obvious truisms, that people spend their whole lives failing to notice them. They look for something more complicated, and whereas, deep down, they "knew" the simple answer, they are brought up to believe it "must" be more complicated than it is, and so caretully continue to look for answers in every direction but the right one.
8. How we, and all appearance that appears with us, appear to appear is by conditioned coproduction, which I and my immediate predecessor, who was the last person to explain it correctly, have each given accounts of elsewhere.

page 134
...
Of course we cannot follow these instructions, we cannot carry out the act of creation they decide, without becoming identical with what is created. When the creator identifies with what is created, the creation must appear miraculous. And this 'must' is a mathematical must, it is purely definitional. If two "different" creators realize this identity at "different" times, there really can be no distinction between them, for what they "both" realize cannot be other than the same creation.

We say that the "two" creators are "each" a manifestation of the "one" Tathagata. And we say the Tathagata is not exactly the creation itself, but the underlying principle by which it appears. The principle, conditioned coproduction operating through the laws of form, can never be different from what it is, and that is why the teaching of the Tathagata is ever the same. But whenever it appears, it appears different, each time like a first time, pristine, new, delightful, because this is how time is made.

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G. Spencer Brown AUM Conference: Esalen Conference March 1974
Heinz von Foerster - Gregory Bateson - Alan Watts

G. Spencer Brown AUM Conference

Transcript Session One
Monday Morning, March 19, 1973

Mathematics and Logic - The Form - Feedback:
A positive feedback remembers itself, a negative feedback oscillates. We have got the mathematics of the oscillator. How often do you use this operator, i = sqrt(-1), which is derived from the paradoxical equation? Now, why is it used so much? Because i is the state that flutters, is the oscillation. This has been totally overlooked in mathematics, that i is in an oscillatory state. Because in order to get over this paradox of x-squared equals minus one, we see that we can't use any ordinary form of unity so we invent in mathematics another form of unity and we-call it i, which is the root that satisfies that equation. And the root that satisfies that equation is that you have plus one, minus one, and here's a state between; and the root that satisfies that equation, whatever it is, it isn't. And this is why i is so useful in dealing with that kind of curve--because it is, by its very nature, that kind of curve. i is an oscillation. -Time and Space: Space is only an appearance. It is what would be if there could be a distinction. Boe: vgl. Spencer Brown Only Two can Play this Game, Note 1
Similarly, when we get eventually to the creation of time, time is what there would be if there could be an oscillation between states. - the void doesn't have quality:.
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. - Mathematics and Its Interpretations
Nots and Crosses - Marked State/Unmarked State -

G. Spencer Brown AUM Conference

Transcript Session Two
Monday Afternoon, March 19, 1973
Original Transcript: http://www.lawsofform.org/aum/session2.html
distinction between algebra and arithmetic -
First Distinction, Observer. and Mark -
the universe as seen appears according to the form of the senses to which it appears - There is no enlightenment without un-enlightenment. -

G. Spencer Brown AUM Conference
Transcript Session Three
Tuesday Morning, March 20, 1973
Original Transcript:
AUM Conference III

Not - the negative:
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,
SPENCER bROWN: 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 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.
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 way 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 [2].
No 'Not' Sense: 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 not.

G. Spencer Brown AUM Conference
Transcript Session Four
Tuesday Afternoon Morning, March 19, 1973
Original of the transcription: http://www.lawsofform.org/aum/session4.html

Five Eternal Levels & the Generation of Time:
SPENCER BROWN: Well, it looks like an electron [Fig. 2]. Indeed, in some circles it is an electron. Level nought. Level one. Level two. Level Three. Level Four. There is a diagram of the five orders to eternity, the five levels. They are brought about--there is no about until they are brought so--by it being, it seeing, it being seeing being? it seeing being seeing being, it being seeing being seeing being, it seeing being seeing being seeing being, it being seeing being seeing being seeing being, and it finally seeing--it being seeing being seeing being seeing being-and if it tries to see that, it finds it can't without going half blind and coming out into time. -
Time is a one-way blindness, the blind side being called the future: 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.
Consciousness:
LILLY: Where does consciousness first appear in that setup? 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...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.
Existence:
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 to one side or the other of the boundary. It leaves you still in take 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 Paradoxy the forbidden contradiction. It has been created out of "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.
The Mathematics of Vibrations:
once you get to this stage, where you are once in time, now everything is a vibration of it.
Vibrations--as we know,
the mathematics of vibrations is always the equations with the imaginary value--if it is, it isn't, if it isn't it is. Whichever it is, it isn't.
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 Z 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.
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--"; 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.
The fifth crossing:
there is evidence all over the universe of a special state where you come to the fifth degree or the fifth whatever it may be, and bang, it changes [6]. It was all self-contained before that.
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Niklas Luhmann: Gesellschaft der Gesellschaft, S.866

Einen anderen Zugang bietet die Mathematik selbstreferentieller Systeme. Wenn das Gesellschaftssystem die Differenz von System und Umwelt nicht nur erzeugt, sondern sich außerdem noch daran orientiert, liegt ein Fall eines „re-entry“ einer Form in die Form (einer Unterscheidung in die Unterscheidung) vor, der das System in den Zustand einer „unresolvable indeterminacy“ versetzt. „Unresolvable“ heißt, dass die normalen mathematischen Operationen der Arithmetik und der Algebra nicht mehr zu eindeutigen Ergebnissen führen.
Das System braucht imaginäre Zahlen oder imaginäre Räume, um sich weiterzuhelfen
.

Boe: vgl. Sylvia Taraba

GG1148
Eine gleichermaßen radikale, postontologische Thematisierung von Zeit scheint dem Formenkalkül von George Spencer Brown zugrundezuliegen.
Form wird hier als Markierung einer Unterscheidung begriffen, also als eine Einheit mit zwei Seiten, von denen nur die eine bezeichnet wird und die andere unmarkiert bleiben muss. Der Übergang zu anderen Seite (das crossing) erfordert eine zweite Operation, setzt also Zeit voraus. Dies wird spätestens dann deutlich, wenn das Kalkül seine eigenen Voraussetzungen einzuholen versucht und zwischen marked und unmarked space zu oszilieren beginnt.

Während die klassische Formtheorie Form als statische Gestalt begriffen hatte, die nach gelungen/nichtgelungen zu beurteilen sei, wird Form jetzt als Dispositiv eines Beobachters begriffen und als Regulativ für die Entscheidung, zu bleiben, wo man ist, (sich zu wiederholen ) oder zur anderen Seite überzugehen. Ein Primat der Form gegenüber Instanzen, die in der Tradition Vernunft und Wille (Freiheit) genannt worden, scheint eine Temporalisierung der Formen zu erfordern.


Tatjana Schönwälder/ Katrin Wille / Thomas Hölscher
Eine Einführung in die "Laws of Form"
Verlag für Sozialwissenschaften 2004
Dem Haupttext der Laws of Form ist eine Reihe von Schriftzeichen vorangestellt. Den meisten westlichen LeserInnen tritt damit zu Beginn des Textes ein fremdes Schriftbild entgegen, unübersetzt und unkommentiert. Die dieser Sprache unkundigen LeserInnen werden im Dunkeln gelassen über Bedeutung, Sinn, genauen Ort.'




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Arno Schöppe Theorie paradox
CarlAuer 1995

Die Erkenntnistheorie von G. Spencer Brown (LoF)
78
(Spencer Brown) beginnt die Konstruktion mit der Anweisung: Zeichne eine Unterscheidung!. Durch diese Instruktion entsteht eine Grenze (boundary), die einen gewählten Raum (space) in zwei willkürliche Teile trennt. Einer der beiden Abschnitte wird im Anschluss daran bezeichnet. Er erhält hierdurch einen Wert (value) zugesprochen, der mit einem Namen (name) belegt werden kann. Für den Vorgang der Unterscheidung und Bezeichnung ist es allerdings erst in zweiter Linie von Bedeutung, ob dieser Name hinzugefügt wird, wichtiger ist es hervorzuheben, dass sich eine Absicht (motive), eine Willkür hinter der Wahl der Unterscheidung und Bezeichnung verbirgt.
Unterscheidung und Bezeichnung sind somit in der Auswahl der Platzierung von Unterscheidung und Bezeichnung frei wenn es aber gleich-gültig ist, welche Präferenzen auf die beiden entstandenen Teilstücke verteilbar sind, man denke an die Bevorzugung von Vorder- und Hintergrund eines Tapetenmusters, dann kann die Grenze auch wieder überschritten (crossing) werden, um das bisher unberücksichtigte (ausgeschlossene) Teilstück zu bezeichnen.
Allerdings wird der Wert (value) nach der Rückkehr (recrossing) zum ursprünglich Bezeichneten ein anderer sein als vorher das erste Überwechseln hat schließlich eine Situation hinzugefügt, die vorher nicht gegeben war, nämlich die Erfahrung des Außenraumes, erzeugt durch die reine Absicht (intention) des ersten Überwechseln, die mit der zweiten Absicht des Zurückwechselns nicht übereinstimmt.
Anders hingegen der Fall, bei dem ein bezeichneter Wert ohne einen vorher erfolgten Grenzübertritt wieder aufgerufen wird (calling). Hier ändert sich der Wert des nocheinmal Bezeichneten nicht. Das Bezeichnete kann also so oft aufgerufen werden wie erwünscht, das Bezeichnete bleibt dann identisch in seinem Wert.
Das Zurückkehren (recrossing) wie auch das Wieder-Aufrufen (calling) setzen natürlich einen Raum (das Bezeichnete) voraus, in denen zurückgekehrt werden kann. In diesen Raum (form) treten diese Bewegungen also ein (Entry), ähnlich Personen, die ein Zimmer betreten. Sollten diese Rückkehrer ihrerseits ein Bezeichnetes sein, so nennt Spencer Brown diesen Vorgang
Reentry.


Peter Fuchs/ Niklas Luhmann
Reden und Schweigen
Suhrkamp 1989
fuchsschweigen46
Draw a distinction! ist dann die moderne Formulierung der Anweisung für die Operation des Sprunges im Rahmen einer formbildenden Logik10. Was immer dann nach dem Sprung geschieht (und mit welch unterschiedlichen Methoden auch gesprungen wird), geschieht post festum, als sich fortspulender Differenzgebrauch, geschieht als Entfernung vom unmarked space und ist untilgbarer Unschuldsverlust. Auf den Raum jenseits aller Differenzen, auf das Zuvor jeder differenz-benutzenden Operation bezieht sich Buddhas Formulierung.
10 Für diese Logik steht ein
George Spencer Brown, Laws of Form, New York 1972


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