While I agree that nitty gritty formalizations are important to grasp, it's been made clear that the formal sciences were often insufficient in facilitating insight on the type of complexity cyberneticians cared about -- especially that of process oriented circular causality, which often involved paradox and self-reference.
> Shannon was like Spencer-Brown a mathematician and electrical engineer. In his study of data transmissions, he has demonstrated how any medium generates background noise that interferes with the transmitted characters. To this day, mathematics has not perceived or not wanted to perceive the elementary consequences of this for mathematics and logic. To this day, mathematics is regarded as a teaching that is independent of the medium in which it is written and through which it is transmitted. Nobody can imagine that the medium could have an influence on the signs and their statements. Mathematics is regarded as a teaching that is developed in a basically motionless mind.
Having taken the last 2 years to really go through the discourse surrounding second order cybernetics beyond Ashby's introduction and Stafford Beer, I learned of a pivotal text called Laws of Form, which was at the heart of second order cybernetics. The formal system was directly incorporated in Varela and Maturana's thesis of autopoiesis, and Niklas Luhmann was also /obsessed/ with Laws of Form for much of his academic career. This is a progenitor of our current interest of enaction and embodied cognition!
With the book's 50th anniversary in 2019, the discourse has been seeing a rejuvenation thanks to some small conferences at https://lof50.com. I've seen some intriguing applications. Some are a bit far out, but that's the nature of systems thinkers, yeah?
A couple that may be of interest:
William Bricken's work on Iconic Mathematics, a system that covers K-12 math and bridges it to purely physical manipulation, shedding matters of complexity difficult that fuel general mathphobia such as: associativity, commutativity, division by 0, bases, functions, order of operations, the disambiguated meaning of equality. Instead, everything is a /structure/.
Bricken's work on computational implementations of Iconic Logic. One example includes a novel SAT algorithm / tautology verification algorithm called Virtual Insertion, which makes extensive use of the notion of semipermeable boundaries, in which the context of a boundary still pervades its content.
Gitta and Ralf Peyn on FORMWELT, a yet-released system aiming to facilitate precise, clear communication of nebulous natural language concepts through the use of injunction and self reference.
>While I agree that nitty gritty formalizations are important to grasp, it's been made clear that the formal sciences were often insufficient in facilitating insight on the type of complexity cyberneticians cared about -- especially that of process oriented circular causality, which often involved paradox and self-reference.
I wholeheartedly agree. Hence why I think we are dealing with an entirely new type of science, the basic principles and theorems are yet to be discovered.
Lots of interesting pointers and links throughout. Thanks again!
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.
(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!
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.
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.
See Stuart Umpleby's lectures on the History of Cybernetics: https://www.youtube.com/playlist?list=PLB81F4FC0EDC4DECC
Or Walter Tydecks on the cultural understanding of mathematics as a sign system: http://www.tydecks.info/online/themen_e_spencer_brown_logik....
> Shannon was like Spencer-Brown a mathematician and electrical engineer. In his study of data transmissions, he has demonstrated how any medium generates background noise that interferes with the transmitted characters. To this day, mathematics has not perceived or not wanted to perceive the elementary consequences of this for mathematics and logic. To this day, mathematics is regarded as a teaching that is independent of the medium in which it is written and through which it is transmitted. Nobody can imagine that the medium could have an influence on the signs and their statements. Mathematics is regarded as a teaching that is developed in a basically motionless mind.
Having taken the last 2 years to really go through the discourse surrounding second order cybernetics beyond Ashby's introduction and Stafford Beer, I learned of a pivotal text called Laws of Form, which was at the heart of second order cybernetics. The formal system was directly incorporated in Varela and Maturana's thesis of autopoiesis, and Niklas Luhmann was also /obsessed/ with Laws of Form for much of his academic career. This is a progenitor of our current interest of enaction and embodied cognition!
With the book's 50th anniversary in 2019, the discourse has been seeing a rejuvenation thanks to some small conferences at https://lof50.com. I've seen some intriguing applications. Some are a bit far out, but that's the nature of systems thinkers, yeah?
A couple that may be of interest:
William Bricken's work on Iconic Mathematics, a system that covers K-12 math and bridges it to purely physical manipulation, shedding matters of complexity difficult that fuel general mathphobia such as: associativity, commutativity, division by 0, bases, functions, order of operations, the disambiguated meaning of equality. Instead, everything is a /structure/.
Bricken's work on computational implementations of Iconic Logic. One example includes a novel SAT algorithm / tautology verification algorithm called Virtual Insertion, which makes extensive use of the notion of semipermeable boundaries, in which the context of a boundary still pervades its content.
Gitta and Ralf Peyn on FORMWELT, a yet-released system aiming to facilitate precise, clear communication of nebulous natural language concepts through the use of injunction and self reference.