An Esoteric Guide to Spencer Brown’s Laws of Form #1
George Spencer Brown (in his spirit, I would like to say: “Let George Spencer Brown = GSB”), a logician, engineer, and teacher, wrote a curious little book called Laws of Form, that inspired countless interesting people of widely varying backgrounds. The book is not a book of mathematics, nor is it a book of logic, although if you were to read it this is likely what you’d say. It is, rather, an attempt to enact something prior to both. Indeed, GSB feels that his work actually forms (meaning both “is” and “shapes”) “the basic forms [same double-meaning] underlying linguistic, mathematical, physical, and biological science” (p. v of the 1972 edition).
If you haven’t read Laws of Form (LoF), I quite recommend it, and it is actually quite short. Even if you don’t want to follow along with the meaty theorems and proofs, the prose and context is definitely worth chewing on. What is fascinating to me is that the work can also be read with an esoteric eye, which is to say, with a sensitivity to the form and nature of spiritual experiences. This is not at all a departure from what GSB intended: in his other works he quite openly discusses this connection (see Only Two Can Play This Game published under his pen name, James Keys). Even in LoF he prefaces the preface with this quote from Blake:
“Tho’ obscur’d, this is the form of the Angelic land.”
So what I would like to do is to show that within the LoF are a number of coherent relations to principles that are rightly considered esoteric: they are hidden, but very important when considering actual spiritual development. Of course as a whole LoF can be taken as a cosmological treatise, and in this sense could be read alongside works such as those by Ibn Arabi, Nagarjuna, Lao Tzu, or Eckhart, among many others.
Because I doubt most of the people reading this (hi people!) already have a copy of LoF (I don’t know why you are waiting), I’m going to keep things pretty informal: I’m going to cite passages from LoF and then write comments on esoteric connections, including some connections to second-order cybernetics and cybernetic epistemology. The esoteric connections I will be pointing out rely heavily upon my own experience, which is primarily informed by the spiritual science of Rudolf Steiner’s anthroposophy. The reason I am writing about this here is that in my PhD dissertation work I am connecting anthroposophy to second-order cybernetics and related disciplines, and LoF played an influential, although not central, role in the unfolding of second-order cybernetics.
Excellent. Hopefully the context provided up to this point is sufficient for me to begin, but before I do, I want to warn you that this journey is not for the faint of heart or the unstable in mind, and will be neither easy nor brief (there are six installments in this series), but it WILL be worth it. Let us dive in:
LoF p. v (all page numbers are from the 1972 version by The Julian Press, Inc.)
- Although all forms, and thus all universes, are possible, and any particular form is mutable, it becomes evident that the laws relating such forms are the same in any universe. It is this sameness, the idea that we can find a reality which is independent of how the universe actually appears, that lends such fascination to the study of mathematics. That mathematics, in common with other art forms, can lead us beyond ordinary existence, and can show us something of the structure in which all creation hangs together, is no new idea.
This corresponds with Steiner’s view that mathetmatics is a spiritual activity, par excellance. However, it must be recognized that it is not the CONTENT of mathematics alone which is what makes it spiritual, it is the PROCESS of mathematics.
LoF p. v
- A mathematical text is thus not an end in itself, but a key to a world beyond the compass of ordinary description.
This “world beyond the compass of ordinary description” can be taken to refer to the spiritual world. As we learn elsewhere from GSB (I suggest reading the transcript of his presentation at Esalen in 1973’s American University of Masters Conference: http://www.lawsofform.org/aum/index.html), the world he is trying to describe is not formally describable. This is a problem, obviously, and it is the same problem that pretty much every mystic of every tradition has run into in one form or another. Of course I could cite the Tao Te Ching’s “the way that can be spoken of is not the constant way; the name that can be named is not the constant name”, or reference the whole point of the koan in Zen, or the Sufi’s Wujud (the incomparable, incommensurable nature of God, which Ibn ‘Arabi points out is “absolutely incomparable with every declaration of incomparability that delimits”). Basically, say anything and you are already off the mark, as it were.
But here’s the important esoteric bit, expressed well in this quote from author John Barth’s novel Chimera:
“The key to the treasure is the treasure.”
Strictly speaking, the Laws of Form cannot be written, but in attempting to write them, they can be indicated by the marks: what is not in the mark is indicated by the mark, although it is also in the mark. If you think this is a paradox, then you are correct, but it is a functional paradox in that it can actually accomplish something by its existence, which is exactly why so many mystical or cosmological traditions utilize the paradox as a central form of learning and communication. This is true even of Jesus Christ, as Parker Palmer elucidates:
“The promise of paradox is the promise that apparent opposites–like order and disorder–can cohere in our lives, the promise that if we replace either-or with both-and, our lives will become larger and more filled with light. It is a promise at the heart of every wisdom tradition I know, not the least the Christian faith. How else can I make sense of the statement ‘If you seek your life, you will lose it, but if you lose your life, you will find it’? Or ‘The first shall be last and the last shall be first’? Or the affirmation that Jesus Christ was fully human and fully divine? Or the notion that we know there is a God but we cannot claim to know the God that is?” -Parker Palmer, The Promise of Paradox, p. xxix (2008)
The point is that something happens when we engage with paradox. GSB, who recognized that Russell and Whitehead’s Theory of Logical Types, which explicitly excluded paradox, was in error, and the “problem” of the paradox wasn’t actually:
LoF p. x
- Put as simply as I can make it, the resolution is as follows. All we have to show is that the self-referential paradoxes, discarded with the Theory of Types, are no worse than similar self-referential paradoxes, which are considered quite acceptable, in the ordinary theory of equations.
He goes on to say that he found a way to deal with these paradoxes by incorporating them formally, which required the recognition of imaginary values,
LoF p. xi
- which means that a valid argument may contain not just three classes of statement, but four: true, false, meaningless, and imaginary. The implications of this, in the fields of logic, philosophy, mathematics, and even physics, are profound.
Indeed, as GSB will have it, the whole of Time and Space in a sense arise out of a paradox, but that’s much later. He continues by indicating that:
LoF p. xx
- we have a direct awareness of mathematical form as an archetypal structure. I try in the final chapter to illustrate the nature of this awareness. In any case, questions of pure probability alone would lead us to suppose that some degree of direct awareness is present throughout mathematics.
Rudolf Steiner would indicate that this direct awareness is spiritual in nature, and arises through a free activity of the spirit. In any case, such direct awareness must be considered both real and essential to epistemology. That is to say, a science of knowing cannot discard (as Russell and Whitehead tried in their failed Principia Mathematica) the role of intuitive knowing. This is a knowing that cannot be achieved through deductive or inductive processes; it is of a completely different type. GSB explicitly recognizes this difference in his discussion of the distinction between a proof and a demonstration in mathematics (re: 1973 Esalen conference, session 2): a computer can do a demonstration, because it relies only upon manipulation of what is already known, while a proof can only arise on the basis of what is not already known, and which cannot be reduced to mere calculations.
LoF p. xxi
- It becomes apparent that if certain facts about our common experience of perception, or what we might call the inside world, can be revealed by an extended study of what we call, in contrast, the outside world, then an equally extended study of this inside world will reveal, in turn, the facts first met with in the world outside: for what we approach, in either case, from one side or the other, is the common boundary between them.
Put simply, this is simply a recapitulation of the central tenet of alchemy, “As Above, so Below; as Below, so Above”. Steiner clearly indicates that if you want to know yourself, you need to look into the world, and if you want to know the world, look into yourself. Know the world to know yourself; know yourself to know the world. What GSB usefully adds to this principle, which is often overlooked in esoteric circles, is that the link between this inner and outer takes the functional form of a shared boundary. It is not the case in a simple way that what is inner is outer; it’s just not very useful to say inner=outer. The point is that there is a boundary between inner and outer, but that this boundary is where all the interesting bits happen, because it is the domain of action by virtue of which inner and outer become so. Or more seriously, is the place upon which, and through which, one must work if one is to transform, because this is what transformation means: to cross the boundary (which is coincident with creating the boundary, as we will see momentarily). For anyone that has read LoF, you know that this language of “crossing” is quite deliberate; the activity of crossing changes what is crossed. More on this later.
LoF p. xxiii
- What is encompassed, in mathematics, is a transcendence from a given state of vision to a new, and hitherto unapparent, vision beyond it. When the present existence has ceased to make sense, it can still come to sense again through the realization of its form.
Mathematics, as a spiritual activity, can change the way we see; it can help us transform spiritually. GSB is implicitly indicating something that is found in many esoteric traditions: that there are many ways of viewing the world (and ourselves in the world), but that not all views are equivalent, nor can they all be relativized at the same level (Wilber’s “Flatland”). Rather, there is structure to be found in the various views, and the structure is significant with respect to the content of the view itself. I’m just restating GSB’s quote in different words. The important thing here is the distinction between thecontent (GSB’s “sense”) and the form of the content. The reason why things change from being senseless to sense-full has to do not with the change at the level of the content, but a change at the level of form. THIS is the key that is the treasure. It is not enough to “think different” — we must think differently, in a new way. Herein lies the power of mathematics as part of a spiritual discipline: its ability to transform our capacity to see, not simply what we see.
LoF p. xxiv
- In general, the more universal the law, the more it seems to resist expression in any particular mode.
When speaking of universal law, we can recognize what is meant esoterically by the word “archetype”. The principle that GSB relates here is in accord with the features of the archetype, conceived in general (we could say, the archetype of archetypes). The more we attempt to encompass it in particulars, the more it squeezes through the cracks and eludes our grasp. This is in obvious relation to the previously discussed limitations of language.
What is interesting, esoterically, is that this inverse relation is a general characteristic of the boundary between the physical and spiritual worlds. It is something like Heisenberg’s Uncertainty Principle: you can’t pin down both the nature of an archetype and its manifestation at the same time, and you can swing (depending upon how you draw your distinctions) more towards the side of exactitude or more to the side of generality. Alchemically, this is a manifestation of the Air principle (see http://www.spiritalchemy.com/p6-metaphors.html), and is a state that we will encounter again and again on our journey.
On a more mundane note, this polarity has long been with us in the form of the tension between induction and deduction. Historically these views were championed by Plato (induction) and his pupil, Aristotle (deduction). If you are a Platonist at heart you will have the feeling that the generalities are somehow more real than the particular, while if you are an Aristotelian at heart you will feel that the particulars are more real than the generalities, obviously.
The point is that both are correct, and neither are complete. I would suggest, in this vein, the introduction of the process of abduction, championed by Charles Sanders Peirce, which is another form of reasoning that is perpendicular to both induction and deduction, and which fleshes out a logical “space” that allows it to slip very well into the palm offered by esoteric methods.
In the preface to the 1994 edition of the Laws of Form, Spencer-Brown explains the ground of the work, which is “the point” so to speak (sorry, I don’t have the page numbers):
- All I teach is the consequences of there being nothing. The perennial mistake of western philosophers has been to suppose, with no justification whatever, that nothing cannot have any consequences. On the contrary: not only it can: it must. And one of the consequences of there being nothing is the inevitable appearance of “all this”.
- The idea that the creation must be a consequence of ‘something’ is moronic. No thing can have any consequence whatever. If there were originally something, it would poison the whole creative process. Only nothing is unstable enough to give origin to endless concatenations of different appearances.
Obviously GSB is getting into territory that has a long esoteric history, beginning at least as far back as the ancient Greek’s identification of Chaos as the mother of Gaia, and thus the source of the difference between the Heavens and the Earth, the Above and Below. Now, things can get really interesting and complicated here very quickly, because we are being taken into pretty deep territory with these claims about nothing and something. But we have to go there because GSB’s essential insight, that nothing cannot NOT have any consequences, is very important, as he is making a fundamental metaphysical, cosmological, epistemological and esoteric point all at the same time, and indeed (as he indicates) this is actually the only thing he is trying to communicate, so it bears some scrutiny.
The Greek’s Chaos is generally taken to be a sort of formless void, but for some reason nobody seems to recognize that our habit is generally to take this phrase “formless void” and take the “void” aspect as a thing we are talking about. That is to say, we take “void” as a noun and “formless” as a modifier. But the whole point is that we are trying to talk about the source of “all this”, and as GSB indicates, it can’t be a thing, even a “void”. It is more appropriate to speak only of “formlessness” rather than a formless void, and if you are now hearing echoes of century’s worth of one-handed Buddhists clapping, you are in good company. There is a lot of good stuff to read on this, not least of which is Shankara’s commentaries on the Mandukya Upanishad (and of course the Upanishad itself), where the three syllables A U M are the waking, dreaming, and sleeping states that comprise all existence… but that there is a fourth state, which is SILENCE, which is the substratum for the other three. This fourth state is “unseen and ineffable, ungraspable, featureless, unthinkable and unnameable” — which should remind you of the Ibn ‘Arabi quote earlier.
This is GSB’s “nothing”; it is cosmological, because it is the origin of the (all/any) universe, it is metaphysical because all physics (all manifest laws of any kind) rests upon it, it is epistemological because all knowing rests precisely on this particular unknown, and it is esoteric because it allows the simultaneous integration of all of these other aspects in such a way as to provide the ground upon which actual spiritual evolution can occur individually and as a universe.
This “formless” (drop the ‘ness’ because that too makes it seem to “it”-like) is also the state referred to in Genesis 1:2 by the phrase “tohu wa bohu”, which is usually translated as “without form and void” or “formless and empty”. This phrase is pointing, explicitly, to what was there before the universe was there (obviously a kind of paradox, but we are comfortable with paradox, yes?). We read Genesis forwards in time, but don’t recognize that the ontological background of the question really leads us to consider that it is pointing backwards, to a state before time, which GSB indicates, quoting Roth (who wrote about Dionysius the Areopagite) “went on in perfect harmony until the time came, for time to begin” (Esalen conference session four).
So this phrase, “tohu wa bohu”, has become an idiom for both “confusion” and “commotion” in French, German, Estonian, and Hungarian, and here is preserved something of the flavor of GSB’s “nothing”. This confusion of meanings happens even the case of the Buddhist “śūnyatā“, which is translated either as “emptiness” or “voidness”. The actual root of the word is “svi” meaning swollen: this primal ground is not empty but is ready to burst at every moment. Thus the “nothing” is thus not best conceived of as a void, but more as a primal confusion or Chaos. Chaos is both empty and not empty, it is without form, but contains all form. It is thus very appropriate that in LoF, GSB indicates that the sign “=” may stand for the words “is confused with” (p. 69); at this level, identification and difference form a complex unity. This is the unity implicit in Jung’s enantiodromia, where a tendency or manifestation proceeds so far in one direction that it suddenly becomes its opposite (for example Love into Hate on an emotional spectrum). That this can happen is a direct consequence of the primal confusion: nothing gets confused about itself, thus becoming itself. GSB has a nice way of talking about this, when he says that existence is “what would appear if it could” (Esalen conference session four). This phraseology, rather than collapsing the distinction into one state or another (existence or non-existence), maintains the complex unity. That the phraseology is also a paradox is essential to its meaning.
I could even point out that we have an excellent geometric, and therefore completely thinkable, manifestation of this principle of the complex unity of multiplicity given in projective geometry. One need only think about the relation between a line, its single point at infinity, which can be reached in two directions (the directions along the line, of course), and how this line is nothing other than a circle whose center is at infinity. The topological structure, taken as a whole, of the line, is a circle, but to “take as a whole” requires the inclusion of infinity, which is not a place or a destination in any sense of the word. Yet it is precisely this infinity that makes the whole whole, and allows a point moving on the line to zoom out to infinity and then come back to its starting point again from the other side of infinity.
You see, all of this is connected. This is why we find God spoken of as an “infinite sphere whose center is everywhere and whose circumference is nowhere” (this is from a 12th century Neoplatonist work called The Book of Twenty-Four Philosophers, esoterically attributed to Hermes Trimegistus).
But before we reach infinity let us take a break. You have progressed now to the beginning of the actual Laws of Form themselves.