14 Jan
2022
14 Jan
'22
7:18 p.m.
I'm quite confused on why people are interested in Laws of Form.
What is LOF trying to do? Is it just rewriting logic or is there something more
fundamental e.g. a universal algebraic system?
What does GSB has to do with DNA, or DNA computing?
What does Lou's work in topology has to do with GSB?
What does GSB's theory has to do with knot theory?
What does GSB's theory has to do with quaternions?
How can GSB's theory be used for designing circuits?
What's wrong with Frege?
14 Jan
14 Jan
11 p.m.
New subject: Laws of Form
Hi Gary,
I am deep in the middle of other work right now,
but here's a smattering of resources relevant to
the relation between Peirce's logical graphs and
Spencer Brown's calculus of indications, at least
so far as the core subjects of boolean functions
and propositional calculus are concerned.
Survey of Animated Logical Graphs
https://inquiryintoinquiry.com/2021/05/01/survey-of-animated-logical-graphs…
As far as the extension to relations and quantification,
I start from where Peirce started in 1870 and follow up
several of his more radical ideas, ones he himself did
did not fully develop. That is what I'm doing on the
1870 Logic of Relatives thread.
Peirce’s 1870 “Logic of Relatives” • Overview
https://inquiryintoinquiry.com/2019/09/24/peirces-1870-logic-of-relatives-o…
Regards,
Jon
On 1/14/2022 1:18 PM, garyzhubc(a)gmail.com wrote:
I'm quite confused on why people are interested in
Laws of Form.
What is LOF trying to do? Is it just rewriting logic or is there
something more fundamental e.g. a universal algebraic system?
What does GSB has to do with DNA, or DNA computing?
What does Lou's work in topology has to do with GSB?
What does GSB's theory has to do with knot theory?
What does GSB's theory has to do with quaternions?
How can GSB's theory be used for designing circuits?
What's wrong with Frege?
16 Jan
16 Jan
1:09 a.m.
Laws of Form is something more fundamental. In his introduction, George Spencer-Brown
writes: "A principal intention of this essay is to separate what are known as
algebras of logic from the subject of logic, and to re-align them with mathematics."
Later on in the Introduction, GSB writes: "One of the motives prompting the
furtherance of the present work was the hope of bringing together the investigations of
the inner structure of our knowledge of the universe, as expressed in the mathematical
sciences, and the investigations of its outer structure, as expressed in the physical
sciences. Here the work of Einstein, Schrodinger, and others seems to have led to the
realization of an ultimate boundary of physical knowledge
in the form of the media through which we perceive it. 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."On the nature of mathematics, GSB writes: "A major aspect of the
language of mathematics is the degree of its formality. Although it is true that we are
concerned, in mathematics, to provide a shorthand for what is actually said, this is only
half the story. What we aim to do, in addition, is to provide a more general form in which
the ordinary language of experience is seen to rest. As long as we confine ourselves to
the subject at hand, without extending our consideration to what it has in common with
other subjects, we are not availing ourselves of a truly mathematical mode of
presentation.
"What is encompassed, in mathematics, is a transcedence 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."
Louis Kauffman's work, as he says, is "A presentation of the topology of curves
in the plane and how moves on these curves embody the themes of the Calculus of
Indications of Laws of Form." He also has a section on "A presentation and
discussion about idemposition (the principle that common boundaries cancel). How
idemposition of curves in the plane reproduces the calculus of indications and how the
calculus of idemposition is related to the Four Color Theorem". Now this process of
common boundaries cancelling appears, to me, to have application in the chemistry of cells
and cell membranes, but that is many levels of abstraction away from the mathematical and
topological roots.
Knot theory is a part of Topology, so it is covered as well by Laws of Form.
As for its applicability to computing, in Laws of Form, GSB develops everything that is
needed to build Finite State Machines and Turing Machines. In living creatures, the DNA
and RNA form the Turing Tapes, which are Universal Turing Tapes as they contain the
program as well as data, and the various enzymes are the Finite State Machines that
operate on the tapes. Again this is many levels of abstraction away from the roots in the
Laws of Form.
Your bring up quaternions is interesting. As written, Laws of Form covers only scalar
forms. Forms that have one inside. This leads to all of the possible scalar numbers. It
leads to numbers as measurement of length and angles. I am currently exploring what it
takes to add vectors, and matrices to the scalar Laws of Form. Forms of Distinctions that
have one or more inside boundaries. That is where spinors, and quaternions will come in.
Chapter 11, of Laws of Form is devoted to Equations of the Second Degree that develops
imaginary states and circuitry.
As to what is wrong with Frege, I will quote Louis Kauffman: "We urge the reader to
read or reread Laws of Form. In our view Spencer-Brown’s book is the most wonderful
addition to philosophy, foundations of mathematics, logic and epistemology since the
advent of symbolic logic with Boole, Frege, Peirce, Russell-Whitehead and Wittgenstein.
Laws of Form begins with the injunction “make a distinction!” This leads directly to the
epistemology of things (another name for distinctions) and the understanding that “A thing
is identical with what it is not.” A distinction occurs when a space or whole is
apparently taken apart (into an inside and an outside) and these two parts cohere into the
whole. By choice we designate one side and call it the thing, but it could just as well
have been the other side that was the thing. You, indeed, are what you are not. And if you
carry this further and ask that the whole Universe be a thing, why then what the Universe
is not is Nothing and so the Universe is identical with Nothing. This is paradoxical. Form
is emptiness, emptiness is form. The form we take to exist arises from framing nothing.
“We take as given the idea of a distinction, and that one cannot make an indication
without drawing a distinction. We take therefore the form of distinction for the form”
(Spencer-Brown, 1969, p.1)."
By ignoring the "imaginary" states in logic, all of the symbolic logicians have
limited themselves to an incomplete subject.
Hope this helps. Best regards,
Lyle Anderson
6:54 a.m.
Hi Lyle,
Thank you so much for your very detailed response, as this will be
tremendously helpful to my understanding. I'm quite interested in your
research, maybe we can connect in person? I'm curious to know what you
think about how algebraic systems are created? For example, from classical
gravity theory to general relativity is a change of algebraic system that
captures the geometric invariance that was not captured before. I'm quite
interested in thinking about how this shift happens and to formalize it in
some way.
Best regards,
Gary
On Sat, Jan 15, 2022 at 4:10 PM <lylephone(a)cox.net> wrote:
Laws of Form is something more fundamental. In his
introduction, George
Spencer-Brown writes: "A principal intention of this essay is to separate
what are known as algebras of logic from the subject of logic, and to
re-align them with mathematics." Later on in the Introduction, GSB writes:
"One of the motives prompting the furtherance of the present work was the
hope of bringing together the investigations of the inner structure of our
knowledge of the universe, as expressed in the mathematical sciences, and
the investigations of its outer structure, as expressed in the physical
sciences. Here the work of Einstein, Schrodinger, and others seems to have
led to the realization of an ultimate boundary of physical knowledge
in the form of the media through which we perceive it. 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."On the nature of mathematics,
GSB writes: "A major aspect of the language of mathematics is the degree of
its formality. Although it is true that we are concerned, in mathematics,
to provide a shorthand for what is actually said, this is only half the
story. What we aim to do, in addition, is to provide a more general form in
which the ordinary language of experience is seen to rest. As long as we
confine ourselves to the subject at hand, without extending our
consideration to what it has in common with other subjects, we are not
availing ourselves of a truly mathematical mode of presentation.
"What is encompassed, in mathematics, is a transcedence 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."
Louis Kauffman's work, as he says, is "A presentation of the topology of
curves in the plane and how moves on these curves embody the themes of the
Calculus of Indications of Laws of Form." He also has a section on "A
presentation and discussion about idemposition (the principle that common
boundaries cancel). How idemposition of curves in the plane reproduces the
calculus of indications and how the calculus of idemposition is related to
the Four Color Theorem". Now this process of common boundaries cancelling
appears, to me, to have application in the chemistry of cells and cell
membranes, but that is many levels of abstraction away from the
mathematical and topological roots.
Knot theory is a part of Topology, so it is covered as well by Laws of
Form.
As for its applicability to computing, in Laws of Form, GSB develops
everything that is needed to build Finite State Machines and Turing
Machines. In living creatures, the DNA and RNA form the Turing Tapes,
which are Universal Turing Tapes as they contain the program as well as
data, and the various enzymes are the Finite State Machines that operate on
the tapes. Again this is many levels of abstraction away from the roots in
the Laws of Form.
Your bring up quaternions is interesting. As written, Laws of Form covers
only scalar forms. Forms that have one inside. This leads to all of the
possible scalar numbers. It leads to numbers as measurement of length and
angles. I am currently exploring what it takes to add vectors, and
matrices to the scalar Laws of Form. Forms of Distinctions that have one
or more inside boundaries. That is where spinors, and quaternions will come
in.
Chapter 11, of Laws of Form is devoted to Equations of the Second Degree
that develops imaginary states and circuitry.
As to what is wrong with Frege, I will quote Louis Kauffman: "We urge the
reader to read or reread Laws of Form. In our view Spencer-Brown’s book is
the most wonderful addition to philosophy, foundations of mathematics,
logic and epistemology since the advent of symbolic logic with Boole,
Frege, Peirce, Russell-Whitehead and Wittgenstein. Laws of Form begins with
the injunction “make a distinction!” This leads directly to the
epistemology of things (another name for distinctions) and the
understanding that “A thing is identical with what it is not.” A
distinction occurs when a space or whole is apparently taken apart (into an
inside and an outside) and these two parts cohere into the whole. By choice
we designate one side and call it the thing, but it could just as well have
been the other side that was the thing. You, indeed, are what you are not.
And if you carry this further and ask that the whole Universe be a thing,
why then what the Universe is not is Nothing and so the Universe is
identical with Nothing. This is paradoxical. Form is emptiness, emptiness
is form. The form we take to exist arises from framing nothing. “We take as
given the idea of a distinction, and that one cannot make an indication
without drawing a distinction. We take therefore the form of distinction
for the form” (Spencer-Brown, 1969, p.1)."
By ignoring the "imaginary" states in logic, all of the symbolic logicians
have limited themselves to an incomplete subject.
Hope this helps. Best regards,
Lyle Anderson
_______________________________________________
CG mailing list -- cg(a)lists.iccs-conference.org
To unsubscribe send an email to cg-leave(a)lists.iccs-conference.org
8:36 a.m.
Gary,
There is an eclectic group discussing this on https://groups.io/g/lawsofform/messages
You are welcome to join us.
If you haven't read the 2011 edition of Laws of Form, please get a copy and do so.
GSB recommended a guide for the journey, and Leon Conrad, who actually knew GSB, has a
YouTube series of lectures on the book. https://www.youtube.com/watch?v=VvHYDjkp9Qc
The other resource that you may find useful is Bernie Lewin's "Enthusiastic
Mathematics, Reviving Mystical Emanationism in Modern Science." Bernie connects Laws
of Form to pre-Enlightenment science, which was quite mystical, of course.
As for physics and cosmology that is totally consistent with Laws of Form, the Unified
Theory of Everything developed by Burkhard Heim is described in a PDF at
http://heim-theory.com/wp-content/uploads/2016/03/I-v-Ludwiger-The-New-Worl…
Heim's Theory encompasses general relativity as an included approximation, but totally
recasts gravitation in a way that eliminates the need for the Big Bang. Also, everything
is quantized by areas, i.e., in two dimensional pairs, so the physical world is complex
integer based, but the irrationals and transcendental numbers are presents as limits of
infinite series/fractions.
The basic idea is, as Bernie writes, "It's Forms all the way down!"
Everything starts with the First Distinction.
Warning: It is really different from anything you have ever been taught in school.
Best regards,
Lyle
2:30 p.m.
Lyle - thank you so much for your splendid outline. As you say, ‘it’s forms all the way
down ‘ and this is Not a mechanical or reductionist view! My focus is on Peirce and I
think he’d agree.
Edwina
Sent from my iPad
On Jan 16, 2022, at 2:36 AM, lylephone(a)cox.net wrote:
Gary,
There is an eclectic group discussing this on https://groups.io/g/lawsofform/messages
You are welcome to join us.
If you haven't read the 2011 edition of Laws of Form, please get a copy and do so.
GSB recommended a guide for the journey, and Leon Conrad, who actually knew GSB, has a
YouTube series of lectures on the book. https://www.youtube.com/watch?v=VvHYDjkp9Qc
The other resource that you may find useful is Bernie Lewin's "Enthusiastic
Mathematics, Reviving Mystical Emanationism in Modern Science." Bernie connects Laws
of Form to pre-Enlightenment science, which was quite mystical, of course.
As for physics and cosmology that is totally consistent with Laws of Form, the Unified
Theory of Everything developed by Burkhard Heim is described in a PDF at
http://heim-theory.com/wp-content/uploads/2016/03/I-v-Ludwiger-The-New-Worl…
Heim's Theory encompasses general relativity as an included approximation, but
totally recasts gravitation in a way that eliminates the need for the Big Bang. Also,
everything is quantized by areas, i.e., in two dimensional pairs, so the physical world is
complex integer based, but the irrationals and transcendental numbers are presents as
limits of infinite series/fractions.
The basic idea is, as Bernie writes, "It's Forms all the way down!"
Everything starts with the First Distinction.
Warning: It is really different from anything you have ever been taught in school.
Best regards,
Lyle
_______________________________________________
CG mailing list -- cg(a)lists.iccs-conference.org
To unsubscribe send an email to cg-leave(a)lists.iccs-conference.org
5:15 p.m.
Edwina,
The work of Charles Sanders Pierce is very interesting, but he never discovered the
"imaginary" values of a complete logical system. I am sure that had he been
given a copy of Laws of Form, his reaction would have been the same as Bertrand
Russell's, "This is the book I wish I had written."
If your focus on Pierce is based on his introduction of new terminology to describe
things, semiotics, and such, then I sincerely invite you to read Illobrand von
Ludwiger's monogram on "The New Worldview of the Physicist Burkhard Heim."
Heim introduced a lot of new terms because he was describing things no one had thought of
before.
If you want to skip the physics and go to the heart of the matter, then start with page
81, "The aspect-related Logic for the unified Description of Body and Soul."
http://heim-theory.com/wp-content/uploads/2016/03/I-v-Ludwiger-The-New-Worl…
Here is a sample of what you will find there: "The interpretation of the two
additional dimensions in Heim’s theory as coordinates with qualitative character demanded
the alternative logic being expanded to an aspect-related logic. With his logical method
independent of a specific statement system Heim was then able to make quantitative and
qualitative statements in a unified formal way. This method is called syntrometry by Heim.
It is the combination of different metronic structures.
"The consequence is, we no longer need to try deriving life processes or
consciousness from physical quantum processes, but you start from a superior entity that
manifests itself in this logic method, the syntrometry."
What I am working on now is to demonstrate how Heim's "different metronic
structures" are specific Forms that were Indicated by the Creator for this specific
Universe.
Best regards,
Lyle
1036
days inactive
1038
days old
6 comments
5 participants
participants (5)
-
Edwina Taborsky -
garyzhubc＠gmail.com -
Jon Awbrey -
lylephone＠cox.net -
Peiyuan Zhu