Name: Laws of form
ISBN: 9780963989901

What Hacker News says

2snakesSep 2025

An alternative to abstraction is to use iconic forms and boundary math (containerization and void-based reasoning). See Laws of Form and William Bricken's books recently. Using a unary operator instead of binary (Boolean) does indeed seem simpler, in keeping with Nature. Introduction: https://www.frontiersin.org/journals/psychology/articles/10....

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carapaceJun 2024

I would say that the first-order Cybernetics (as exemplified IMO in Ashby's book) is all about symbolic formalism for "circular loops in causality", and that Second-Order Cybernetics is a species of mysticism (I hasten to add that I don't mean that in a derogatory way. I'm a Mystic myself.)

You could imagine a spectrum from logic to cybernetics to philosophy to mysticism. It's all fine, just I believe that it's important to be clear where on the spectrum you're working. If you want to build machines that do things use Cybernetics and feedback/control theory, if you want to grok reality and self eat a mushroom and read "Gödel, Escher, Bach" or Tao Te Ching.

In re: "Laws of Form", yeah, he identifies the boundary or distinction between the mystic realm (non-form, non-distinct, non-dual) and symbolic logic, and then builds a lovely binary Boolean logic directly off of that. It's a tour de force.

The really interesting thing is that George Spencer-Brown figured out how to deal with circular logical systems by introducing the concept of imaginary Boolean values.

It's a formal system for symbolic logic, and you can indeed build a lovely and efficient SAT solver with it using Bricken's Basis. E.g.: https://ariadne.systems/pub/~sforman/Thun/notebooks/Correcet...

(For reference, here's the LoF/Bricken formalism)

    Arithmetic

    (()) =
    ()() = ()

    Calculus

    A((B)) = AB
    A() = ()
    A(AB) = A(B)

(That third rule in the calculus, discovered by Bricken, is the kicker!)

cf. "The Markable Mark" George Burnett-Stuart http://www.markability.net/ GBS (not GSB, they're two different people) has managed to extend the system to Predicate Logic as well!

William Bricken's home page: https://wbricken.com/

His Iconic Math Page (a wonderland!) https://iconicmath.com/

To sum up, we need symbolic formalism to communicate and build machines, otherwise we're just sort of reading poetry to each other, which can still be helpful, but in a different way than building machines. (And when I say machines in the context of Cybernetics I mean to include those made out of people! "Human use of Human Beings", eh?)

As an aside, there is a fascinating talk and book "My Stroke of Insight: A Brain Scientistʼs Personal Journey" by Dr. Jill Bolte Taylor:

> In it, she tells of her experience in 1996 of having a stroke in her left hemisphere and how the human brain creates our perception of reality and includes tips about how Dr. Taylor rebuilt her own brain from the inside out.

https://en.wikipedia.org/wiki/My_Stroke_of_Insight

https://youtu.be/UyyjU8fzEYU (TED Talk)

When "Laws of Form" talks about the beginning of logic from the pre-logical non-distinct or non-distinguished realm, the "mark" that divides the world into A and Not-A, it turns out to be quite literal, purely biological: the brain does it. When the part of her brain that "does logic" was rendered inoperative due to the stoke she was having, she reports an inability to tell herself from the world around her accompanied by oceanic bliss...

Mysticism is real, you just can't talk about it. The very first chapter of the Tao Te Ching says it right off: the Tao that can be talked about is not the Tao.

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2snakesMay 2023

LLMs are more like a natural language interface for computers that do symbolic calculation of bytes aka computer science. Statistical madlibs for text generation, but useful for understanding people. There is a deeper and simpler logic of nonphysical consciousness that is perhaps best outlined in George Spencer Brown’s Laws of Form. LoF can do boolean logic but goes beyond it as well, towards the resolution of antinomy paradox with the logic of distinction andedness. It is also an interesting philosophy when it comes to Systems Theory of Luhmann. As well as used to do other very interesting things. There is an intro on Youtube by Leon Conrad.

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9214May 2020

• "Laws of Form" by George Spencer-Brown, a little book that describes how to bootstrap the Universe from nothing. Louis Kauffman [1] has a lot of papers/writeups on it, from knot theory to quantum physics. If you ever wanted to make a pancake truly from scratch, this is a place to start.

• "The Unconscious as Infinite Sets" by Ignacio Matte Blanco. Reformulates Freud in logico-mathematical terms and establishes a formal system (bi-logic) to describe unconsciousness phenomena: in case you ever wanted to apply category theory to study yourself.

• "The Protracted Game" by Scott Boorman. Interprets Maoist's revolutionary strategies during 1927 - 1949 period as a game of Go. Interesting both from historical, military, and game-theoretical perspective; raised an appreciation of Eastern wisdom and 'board games as a tool of thought' [2] for me.

• "The Unwritten Laws of Engineering" by W. J. King. Written in 1944, but the advice is still relevant, more so to the software engineering field. Should be at least skimmed at any part of your career.

• "The Myth of Sisyphus" by Alber Camus. Unequivocally answers the most important question there is — does life have meaning, and if not, should you kill yourself over it? I read it in my teens while wrestling with existential dread, and lived a somewhat happy and interesting life ever after.

[1]: http://homepages.math.uic.edu/~kauffman/Form.html

[2]: There's also "Laws of the Game" by Eigen & Winkler that describes natural phenomena as glass-bead games with various rules.

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carapaceNov 2018

If you liked that you'll like this: http://www.markability.net/

It's a walk-through of George Spencer-Brown's Laws of Form.

It turns out all logic can be modeled by simple containment, and there's a complete basis (discovered by Bricken):

    A() = ()
    ((A))B = AB
    A(AB) = A(B)

One interesting thing about LoF notation is that every expression is also a schematic of a logic circuit. The letters are inputs, the expression is the output, and each container represents a logical (multi-input) NOR gate.

Another interesting thing about it is that it's significantly more efficient to derive proofs in LoF notation than conventional notation. (Often a proof that takes several pages in conventional notation will be less than a dozen lines in LoF.)

You can write a simple SAT solver that doesn't require the input expressions to be put into a Normal Form first.

- - - -

As Wolfram and others have pointed out: It's relatively easy to program computers to search for new proofs and such[1], the trick is making it "surface" the human-interesting ones.

[1] E.g. DeepAlgebra https://arxiv.org/abs/1610.01044 https://github.com/przchojecki/deepalgebra

> We outline a program in the area of formalization of mathematics to automate theorem proving in algebra and algebraic geometry. We propose a construction of a dictionary between automated theorem provers and (La)TeX exploiting syntactic parsers. We describe its application to a repository of human-written facts and definitions in algebraic geometry (The Stacks Project). We use deep learning techniques.

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aldoushuxley001Nov 2018

Yeah the Laws of Form notation is very elegant and provides a really profound conceptual foundation. Always loved the book and the people who've tried to take it even further (some surprisingly good discussion on the LoF yahoo group over the years)

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