G. Spencer Brown & The Laws of Form
November 11, 2001 1:50 PM Subscribe
Laws of Form In 1969, George Spencer-Brown published a mathematical book called Laws of Form, which has inspired explorations in philosophy, cybernetics, art, spirituality, and computation. The work is powerful and has established a passionate following as well as harsh critics. This web site explores these people, their ideas and history, and provides references for further exploration. I read this then, didn't understand much of the math due to my innumeracy, but was struck by a passage in passing... I especially am curious to see what the numerate in MetaFilter have to say.
I disagree vehemently (though probably at much less length), on several fronts.
First, as a mathematician, I've got to tell you that the first paragraph is mostly wrong. Great discoveries in mathematics (if you must take the view that mathematics is discovered, rather than created, or simply "done") have two basic flavors. There are the solved conjectures, and there are the cosmic surprises.
The solved conjectures can sometimes fall into the camp that GSB is talking about: after years of withstanding assault, a problem sometimes falls to an argument that a grad student can follow, one that is transparently the "right" proof. Far more often, however, it is by years of incremental progress that conjectures are solved. Fermat's Last Theorem is the poster-child for this; a couple of hundred years, dozens of reductions, three or four whole new fields of mathematics, startling connections painstakingly worked out, and the final proof is still in the thousands of pages. This is much closer to the norm than what GSB is talking about.
He's probably thinking of the cosmic surprises, though. The work of Grothendieck is the best example here: his unification of algebraic geometry, topology, and commutative algebra in the sixties was something that you might have imagined only with the help of a bucketful of LSD. Nowadays, it seems like the most natural thing in the world, but that's because it changed the way we teach all three of those subjects. For forty-odd years, it's seemed "extremely simple and obvious", but only because we didn't have the words before then.
I have other things to say about the "sin of pride" and how misguided that is, but I'll quit now (it seems I wasn't as concise as I'd hoped). Do like the bit about Newton and contemplation, though.
posted by gleuschk at 2:15 PM on November 11, 2001
First, as a mathematician, I've got to tell you that the first paragraph is mostly wrong. Great discoveries in mathematics (if you must take the view that mathematics is discovered, rather than created, or simply "done") have two basic flavors. There are the solved conjectures, and there are the cosmic surprises.
The solved conjectures can sometimes fall into the camp that GSB is talking about: after years of withstanding assault, a problem sometimes falls to an argument that a grad student can follow, one that is transparently the "right" proof. Far more often, however, it is by years of incremental progress that conjectures are solved. Fermat's Last Theorem is the poster-child for this; a couple of hundred years, dozens of reductions, three or four whole new fields of mathematics, startling connections painstakingly worked out, and the final proof is still in the thousands of pages. This is much closer to the norm than what GSB is talking about.
He's probably thinking of the cosmic surprises, though. The work of Grothendieck is the best example here: his unification of algebraic geometry, topology, and commutative algebra in the sixties was something that you might have imagined only with the help of a bucketful of LSD. Nowadays, it seems like the most natural thing in the world, but that's because it changed the way we teach all three of those subjects. For forty-odd years, it's seemed "extremely simple and obvious", but only because we didn't have the words before then.
I have other things to say about the "sin of pride" and how misguided that is, but I'll quit now (it seems I wasn't as concise as I'd hoped). Do like the bit about Newton and contemplation, though.
posted by gleuschk at 2:15 PM on November 11, 2001
Not being numerate I think I'll just go and see the A Beautiful Mind movie. ;-)
I read the book of the same title about two years ago and it was riveting. Though very sad, as John Nash was. The recent Paul Erdos(pronounced "air dish")biography is much more amusing. Coffee and amphetamines, no suitcase, no private life, no nothing except mathematical problems.
Sorry I can't link to the actual books, y2karl(or umlaut that E!) but my browser won't let me leave this very spot, grrr.
George Spencer-Brown sounds very interesting though...
posted by MiguelCardoso at 2:19 PM on November 11, 2001
I read the book of the same title about two years ago and it was riveting. Though very sad, as John Nash was. The recent Paul Erdos(pronounced "air dish")biography is much more amusing. Coffee and amphetamines, no suitcase, no private life, no nothing except mathematical problems.
Sorry I can't link to the actual books, y2karl(or umlaut that E!) but my browser won't let me leave this very spot, grrr.
George Spencer-Brown sounds very interesting though...
posted by MiguelCardoso at 2:19 PM on November 11, 2001
Wouldn't it be the "numerati"? Also, Erdos with the Hungarian umlaut on the "o" is pronaunced "airdush", the "u" is as in church.
posted by semmi at 3:00 PM on November 11, 2001
posted by semmi at 3:00 PM on November 11, 2001
The Innumerati
A trilogy about a group who don't secretly control anything.
posted by y2karl at 3:14 PM on November 11, 2001
A trilogy about a group who don't secretly control anything.
posted by y2karl at 3:14 PM on November 11, 2001
The recent Paul Erdos(pronounced "air dish")biography is much more amusing.
careful -- I've read The Man Who Loved Only Numbers, and, like some friends and relations (I have one whose Erdos number is 1) found it trite and unsatisfying. I haven't read the more recent My Brain is Open but expect that its authors greater understanding of mathematics (compared to the encyclopedist (if I recall right) who wrote TMWLONs) must have helped.
The end of the GSB passage reminds my of a line by Roethke, that I've actually quoted on MeFi before:
What's madness but nobility of soul
at odds with circumstance?
In many ways he's insightful, but there're so many assumptions and presumptions behind it it's really hard to comment on. Food for thought, in any case.
posted by mattpfeff at 3:33 PM on November 11, 2001
careful -- I've read The Man Who Loved Only Numbers, and, like some friends and relations (I have one whose Erdos number is 1) found it trite and unsatisfying. I haven't read the more recent My Brain is Open but expect that its authors greater understanding of mathematics (compared to the encyclopedist (if I recall right) who wrote TMWLONs) must have helped.
The end of the GSB passage reminds my of a line by Roethke, that I've actually quoted on MeFi before:
What's madness but nobility of soul
at odds with circumstance?
In many ways he's insightful, but there're so many assumptions and presumptions behind it it's really hard to comment on. Food for thought, in any case.
posted by mattpfeff at 3:33 PM on November 11, 2001
Sheesh, I first heard about the "Laws of Form" about 6 years ago in a glowing gee-whiz front page review in electrical engineering trade journal EE Times, raving about how Spencer-Brown's analysis techniques were going to revolutionize the world of integrated circuit design. Young and curious with too much free time, I tracked down his hard-to-find book, studied over it for weeks, and annoyed all my friends with it. Ultimately, I couldn't figure out what all the fuss was about. As I recall, the main innovation of the book was an alternative notation of Boolean algebra somwehat akin to Venn diagrams. That, and the idea of representing the logical equivalent of square-root-of-minus-1, "the-root-of-x-equal-not-x" or somesuch as a spiral (which could be interpreted as an oscillator if you wished). The only part of the book that appeared promising from a mathematical perspective at all was the last chapter, in which he had perhaps three examples applications of his technique, two of which were trivial, and the third of which was a completely baffling full-page diagram that appeared to be missing a few terms, offered without any accompanying explanation.
Needless to say, the world of integrated circuit design has not been revolutionized (despite it desperately needs it), nor have I heard any more on the subject in an engineering context. Recently I happened on a couple of web sites discussing the Laws of Form. Revisiting the subject, I still failed to find any real meat. No rigor, no depth. His admirers seem more taken up with his philosophical points than his mathematics. One mathematician's opinion I read compared his boolean algebra scheme somewhat disparagingly to other more generalized schemes of multivariate logic.
Looking back, I'd say the ideas still look stylish and intriguing, but clicking on the link above I'd say so far noone's yet managed to develop GSB's pipe smoke into anything worthwhile. If I've missed something good, by all means prove me wrong!
John Nash, Erdos, Grothendieck, those are men to admire.
posted by krebby at 3:35 PM on November 11, 2001
Needless to say, the world of integrated circuit design has not been revolutionized (despite it desperately needs it), nor have I heard any more on the subject in an engineering context. Recently I happened on a couple of web sites discussing the Laws of Form. Revisiting the subject, I still failed to find any real meat. No rigor, no depth. His admirers seem more taken up with his philosophical points than his mathematics. One mathematician's opinion I read compared his boolean algebra scheme somewhat disparagingly to other more generalized schemes of multivariate logic.
Looking back, I'd say the ideas still look stylish and intriguing, but clicking on the link above I'd say so far noone's yet managed to develop GSB's pipe smoke into anything worthwhile. If I've missed something good, by all means prove me wrong!
John Nash, Erdos, Grothendieck, those are men to admire.
posted by krebby at 3:35 PM on November 11, 2001
What krebby said. I fell for the first round of GSB hype back in the seventies at the hands of the Whole Earth Catalog, and failed then to see (and still fail) how it's different from Boolean algebra, which is itself simply a particularization of some more general mathematical objects. I don't see any deep connections beween hitherto unconnected truths there, nor any surprising, unsuspected results. I would love to hear otherwise.
I think that in some ways, Laws of Form should be viewed as the last gasp of mathematical foundationalism, which has a powerful glamor but, since the "disasters" of the twentieth century (Gödel et al.), has more or less ceased to occupy the attention of working mathematicians. Its value seems to be that, for some reason, it creates an image of Boolean algebra that some people in other fields find more congenial than the standard logical notation. It's no accident that it's popularity has been restricted almost completely to autodidacts and scholars in nonmathematical fields looking to borrow some rigor (or the appearance thereof) for their own.
posted by rodii at 4:59 PM on November 11, 2001
I think that in some ways, Laws of Form should be viewed as the last gasp of mathematical foundationalism, which has a powerful glamor but, since the "disasters" of the twentieth century (Gödel et al.), has more or less ceased to occupy the attention of working mathematicians. Its value seems to be that, for some reason, it creates an image of Boolean algebra that some people in other fields find more congenial than the standard logical notation. It's no accident that it's popularity has been restricted almost completely to autodidacts and scholars in nonmathematical fields looking to borrow some rigor (or the appearance thereof) for their own.
posted by rodii at 4:59 PM on November 11, 2001
...autodidacts and nonmathematical scholars, hmmm... Well, I'm lucky if I'm half of one and none of the other, and am not surprised at the response. Have any of the people mentioned or linked to had anything to contribute?
I'm leery, or perhaps Leary, of the whole New Age connection and it was in the first edition of the Whole Earth Catalog. He writes well, at least, and it looks like he has an interesting biography.
And then there are all the stories that could be urban legends of the literate, like Kekule's dream in front of the fire place, which is not mathematics entirely, but employs it certainly, and I have a vague memory of Einstein described as experiencing deep thought, working out problems in terms of internal physical sensations. I just don't know the truth of these stories.
The elegant otherworldly language of the first few laws in the book is attractive but it might as well be Big Voo Doo In Hyped Mumbo Jumbo to me, sympathetic magic, for the quantum level--in terms of container size only--amount I know.
And, speaking of that, when I hear people who know as little as I know start going on with the quantum physics, I cringe. I mean, aren't we talking about events that happen on a scale so infinitesimal as to be us in size as we are, say, to the Milky Way galaxy? Which is impossible for me to conceive.
I'm still waiting for the Flash animation. But then, that's true in any area of my life that I can think of.
posted by y2karl at 6:36 PM on November 11, 2001
I'm leery, or perhaps Leary, of the whole New Age connection and it was in the first edition of the Whole Earth Catalog. He writes well, at least, and it looks like he has an interesting biography.
And then there are all the stories that could be urban legends of the literate, like Kekule's dream in front of the fire place, which is not mathematics entirely, but employs it certainly, and I have a vague memory of Einstein described as experiencing deep thought, working out problems in terms of internal physical sensations. I just don't know the truth of these stories.
The elegant otherworldly language of the first few laws in the book is attractive but it might as well be Big Voo Doo In Hyped Mumbo Jumbo to me, sympathetic magic, for the quantum level--in terms of container size only--amount I know.
And, speaking of that, when I hear people who know as little as I know start going on with the quantum physics, I cringe. I mean, aren't we talking about events that happen on a scale so infinitesimal as to be us in size as we are, say, to the Milky Way galaxy? Which is impossible for me to conceive.
I'm still waiting for the Flash animation. But then, that's true in any area of my life that I can think of.
posted by y2karl at 6:36 PM on November 11, 2001
*brain implodes, then leaks out ears in thin grey stream*
Although I have no problem at all imagining quantum mechanics. But as someone who couldn't get past Taylor series, real math hurts.
posted by solistrato at 8:20 PM on November 11, 2001
Although I have no problem at all imagining quantum mechanics. But as someone who couldn't get past Taylor series, real math hurts.
posted by solistrato at 8:20 PM on November 11, 2001
real math hurts
If we could only have personal taglines... I want this one for mine.
posted by rodii at 8:46 PM on November 11, 2001
If we could only have personal taglines... I want this one for mine.
posted by rodii at 8:46 PM on November 11, 2001
...autodidacts and nonmathematical scholars, hmmm...
hmm indeed. There isn't much to say about the mathematics on the website linked, because there isn't really any mathematics there -- just definitions and hand-waving. To say anything interesting, one would have to see some theorems and proofs. There are indefinitely many calculi one could invent (or discover -- whichever); to demonstrate that one is actually more interesting than another you'd have to prove something significant with it, and elegantly, too....
As for the quoted theory of learning, well, it's not mathematics, is it? And gleushk offers a mathematician's response quite adequately, as far as the claim about mathematics offered therein. It's hard to see how the passage on learning is in any way pertinant to mathematics as it's studied today: there is no fear of ignorance; rather, what is not yet known is the entire focus. And as for "pride" of knowledge, well, I suppose you could call it that if you wanted, but the whole point of mathematics is to prove things. It's not like there's any doubt once they've been proved (and to be proud of some abstract truth would be silly), except in those rare cases where the proof is so complex and inaccessible that one has to trust other mathematicians' claims as to its veracity. But very few mathematicians indeed are proud of those proofs; rather, they are troubled and skeptical, from my experience.
(I only have a very little graduate-level mathematics, and that a few years ago, I should say.)
posted by mattpfeff at 8:54 PM on November 11, 2001
hmm indeed. There isn't much to say about the mathematics on the website linked, because there isn't really any mathematics there -- just definitions and hand-waving. To say anything interesting, one would have to see some theorems and proofs. There are indefinitely many calculi one could invent (or discover -- whichever); to demonstrate that one is actually more interesting than another you'd have to prove something significant with it, and elegantly, too....
As for the quoted theory of learning, well, it's not mathematics, is it? And gleushk offers a mathematician's response quite adequately, as far as the claim about mathematics offered therein. It's hard to see how the passage on learning is in any way pertinant to mathematics as it's studied today: there is no fear of ignorance; rather, what is not yet known is the entire focus. And as for "pride" of knowledge, well, I suppose you could call it that if you wanted, but the whole point of mathematics is to prove things. It's not like there's any doubt once they've been proved (and to be proud of some abstract truth would be silly), except in those rare cases where the proof is so complex and inaccessible that one has to trust other mathematicians' claims as to its veracity. But very few mathematicians indeed are proud of those proofs; rather, they are troubled and skeptical, from my experience.
(I only have a very little graduate-level mathematics, and that a few years ago, I should say.)
posted by mattpfeff at 8:54 PM on November 11, 2001
Are we talking Deep Thoughts with Jack Handy here?
Oh great, the feel good book for ignoroids.
posted by y2karl at 9:18 PM on November 11, 2001
Oh great, the feel good book for ignoroids.
posted by y2karl at 9:18 PM on November 11, 2001
Why is it that the word "adequate" gets my hackles up, when it's clear no diss is intended? Reminds me of that TalkRadio episode where Bill McNeal gets rated Adequate and brags about it for the entire half-hour.
posted by gleuschk at 8:24 AM on November 12, 2001
posted by gleuschk at 8:24 AM on November 12, 2001
gets my hackles up
sorry 'bout that; I was trying to pick a neutral term and didn't think about it much. I didn't want to use a stronger term because, as you said, there are plenty more things one could say from your perspective (that you didn't include because you'd made the point).
posted by mattpfeff at 9:55 AM on November 12, 2001
sorry 'bout that; I was trying to pick a neutral term and didn't think about it much. I didn't want to use a stronger term because, as you said, there are plenty more things one could say from your perspective (that you didn't include because you'd made the point).
posted by mattpfeff at 9:55 AM on November 12, 2001
(which is kind of silly of me, actually, because I did like your response (and appreciated the historical perspective) -- and was even tempted to post a "what gleuschk said" comment)
posted by mattpfeff at 10:16 AM on November 12, 2001
posted by mattpfeff at 10:16 AM on November 12, 2001
Hackles down, cockles warmed. All better.
*mightily resists urge to smiley*
posted by gleuschk at 1:02 PM on November 12, 2001
*mightily resists urge to smiley*
posted by gleuschk at 1:02 PM on November 12, 2001
This thread has been archived and is closed to new comments
And here is the passage--excuse the length.
Discoveries of any great moment in mathematics and other disciplines, once they are discovered, are seen to be extremely simple and obvious, and make everybody, including their discoverer, appear foolish for not having discovered them before. It is all too often forgotten that the ancient word for the prenascence of the world is a fool, and that foolishness, being a divine state, is a condition to be either proud or ashamed of.
Unfortunately we find systems of education today which have departed so far from the plain truth, that they now teach us to be proud of what we know and ashamed of ignorance. This is doubly corrupt. It is corrupt not only because pride is a mortal sin, but also because to teach pride in knowledge is to put up an effective barrier against any advance upon what is already known, since it makes one ashamed to look beyond the bonds imposed by one’s ignorance.
To any person prepared to enter with respect into the realm of his great and universal ignorance, the secrets of being will eventually unfold, and they will do so in a measure according to his freedom from natural and indoctrinated shame in his respect of their revelation.
In the face of the strong, and indeed violent, social pressures against, few people have been prepared to take this simple and satisfactory course toward sanity. And in a society where a prominent psychiatrist can advertise that, given the chance, he would have treated Newton to electric shock therapy, who can blame a person for being afraid to do so?
To arrive at the simplest truth, as Newton knew and practiced, requires years of contemplation. Not activity. Not reasoning. Not calculating. Not busy behaviour of any kind. Not reading. Not talking. Not making an effort. Not thinking. Simply bearing in mind what it is one needs to know. And yet those with the courage to tread this path to real discovery are not only offered practically no guidance on how to do so, they are actively discouraged and have to set about it in secret, pretending meanwhile to be diligently engaged in the frantic diversions and to conform with the deadening personal opinions which are continually being thrust upon them.
In these circumstance, the discoveries that any person is able to undertake represent the places where, in the face of induced psychosis, he has, by his own faltering and unaided efforts, returned to sanity. Painfully, and even dangerously, maybe. But nonetheless returned, however furtively.
posted by y2karl at 1:52 PM on November 11, 2001 [1 favorite]