Re: [PEIRCE-L] Theme One • A Program Of Inquiry
Cf: Theme One Program • Motivation 4 https://inquiryintoinquiry.com/2018/05/20/theme-one-program-motivation-4/ All, From Zipf’s Law and the category of “things that vary inversely to frequency” I got my first brush with the idea that keeping track of usage frequencies is part and parcel of building efficient codes. In it’s first application the environment the Learner had to learn was the usage behavior of its user, as given by finite sequences of characters from a finite alphabet which might as well be called “words” and as given by finite sequences of those words which might as well be called “phrases” or “sentences”. In other words, Job One for the Learner was the job of constructing a “user model”. In that frame of mind we are not seeking anything so grand as a Universal Induction Algorithm but simply looking for any approach that gives us a leg up, complexity wise, in Interactive Real Time. Resource • Survey of Theme One Program https://inquiryintoinquiry.com/2020/08/28/survey-of-theme-one-program-3/ Regards, Jon _ _ _ _ _ _ _ _ _ _ ► PEIRCE-L subscribers: Click on "Reply List" or "Reply All" to REPLY ON PEIRCE-L to this message. PEIRCE-L posts should go to peirce-L@list.iupui.edu . ► To UNSUBSCRIBE, send a message NOT to PEIRCE-L but to l...@list.iupui.edu with UNSUBSCRIBE PEIRCE-L in the SUBJECT LINE of the message and nothing in the body. More at https://list.iupui.edu/sympa/help/user-signoff.html . ► PEIRCE-L is owned by THE PEIRCE GROUP; moderated by Gary Richmond; and co-managed by him and Ben Udell.
Re: [PEIRCE-L] Theme One • A Program Of Inquiry
Cf: Theme One Program • Motivation 3 https://inquiryintoinquiry.com/2018/05/19/theme-one-program-motivation-3/ All, Sometime around 1970 John B. Eulenberg came from Stanford to direct Michigan State’s Artificial Language Lab, where I would come to spend many interesting hours hanging out all through the 70s and 80s. Along with its research program the lab did a lot of work on augmentative communication technology for limited mobility users and the observations I made there prompted the first inklings of my Learner program. Early in that period I visited John’s course in mathematical linguistics, which featured Laws of Form among its readings, along with the more standard fare of Wall, Chomsky, Jackendoff, and the Unified Science volume by Charles Morris which credited Peirce with pioneering the pragmatic theory of signs. I learned about Zipf’s Law relating the lengths of codes to their usage frequencies and I named the earliest avatar of my Learner program XyPh, partly after Zipf and playing on the xylem and phloem of its tree data structures. Resource • Survey of Theme One Program https://inquiryintoinquiry.com/2020/08/28/survey-of-theme-one-program-3/ Regards, Jon _ _ _ _ _ _ _ _ _ _ ► PEIRCE-L subscribers: Click on "Reply List" or "Reply All" to REPLY ON PEIRCE-L to this message. PEIRCE-L posts should go to peirce-L@list.iupui.edu . ► To UNSUBSCRIBE, send a message NOT to PEIRCE-L but to l...@list.iupui.edu with UNSUBSCRIBE PEIRCE-L in the SUBJECT LINE of the message and nothing in the body. More at https://list.iupui.edu/sympa/help/user-signoff.html . ► PEIRCE-L is owned by THE PEIRCE GROUP; moderated by Gary Richmond; and co-managed by him and Ben Udell.
Re: [PEIRCE-L] Theme One • A Program Of Inquiry
Cf: Theme One Program • Motivation 2 https://inquiryintoinquiry.com/2018/05/17/theme-one-program-motivation-2/ All, A side-effect of working on the Theme One program over the course of a decade was the measure of insight it gave me into the reasons why empiricists and rationalists have so much trouble understanding each other, even when those two styles of thinking inhabit the very same soul. The way it came about was this. The code from which the program is currently assembled initially came from two distinct programs, ones I developed in alternate years, at first only during the summers. In the Learner program I sought to implement a Humean empiricist style of learning algorithm for the adaptive uptake of coded sequences of occurrences in the environment, say, as codified in a formal language. I knew all the theorems from formal language theory telling how limited any such strategy must ultimately be in terms of its generative capacity, but I wanted to explore the boundaries of that capacity in concrete computational terms. In the Modeler program I aimed to implement a variant of Peirce’s graphical syntax for propositional logic, making use of graph-theoretic extensions I had developed over the previous decade. As I mentioned, work on those two projects proceeded in a parallel series of fits and starts through interwoven summers for a number of years, until one day it dawned on me how the Learner, one of whose aliases was “Index”, could be put to work helping with sundry substitution tasks the Modeler needed to carry out. So I began integrating the functions of the Learner and the Modeler, at first still working on the two component modules in an alternating manner, but devoting a portion of effort to amalgamating their principal data structures, bringing them into convergence with each other, and unifying them over a common basis. Another round of seasons and many changes of mind and programming style, I arrived at a unified graph-theoretic data structure, strung like a wire through the far‑flung pearls of my programmed wit. But the pearls I polished in alternate years maintained their shine along axes of polarization whose grains remained skew in regard to each other. To put it more plainly, the strategies I imagined were the smartest tricks to pull from the standpoint of optimizing the program’s performance on the Learning task I found the next year were the dumbest moves to pull from the standpoint of its performance on the Reasoning task. I gradually came to appreciate that trade-off as a discovery ... Regards, Jon _ _ _ _ _ _ _ _ _ _ ► PEIRCE-L subscribers: Click on "Reply List" or "Reply All" to REPLY ON PEIRCE-L to this message. PEIRCE-L posts should go to peirce-L@list.iupui.edu . ► To UNSUBSCRIBE, send a message NOT to PEIRCE-L but to l...@list.iupui.edu with UNSUBSCRIBE PEIRCE-L in the SUBJECT LINE of the message and nothing in the body. More at https://list.iupui.edu/sympa/help/user-signoff.html . ► PEIRCE-L is owned by THE PEIRCE GROUP; moderated by Gary Richmond; and co-managed by him and Ben Udell.
Re: [PEIRCE-L] Theme One • A Program Of Inquiry
Cf: Theme One Program • Motivation 1 https://inquiryintoinquiry.com/2018/05/15/theme-one-program-motivation-1/ All, The main idea behind the Theme One program is the efficient use of graph-theoretic data structures for the tasks of “learning” and “reasoning”. I am thinking of learning in the sense of learning about an environment, in essence, gaining information about the nature of an environment and being able to apply the information acquired to a specific purpose. Under the heading of reasoning I am simply lumping together all the ordinary sorts of practical activities which would probably occur to most people under that name. There is a natural relation between the tasks. Learning the character of an environment leads to the recognition of laws which govern the environment and making full use of that recognition requires the ability to reason logically about those laws in abstract terms. Regards, Jon _ _ _ _ _ _ _ _ _ _ ► PEIRCE-L subscribers: Click on "Reply List" or "Reply All" to REPLY ON PEIRCE-L to this message. PEIRCE-L posts should go to peirce-L@list.iupui.edu . ► To UNSUBSCRIBE, send a message NOT to PEIRCE-L but to l...@list.iupui.edu with UNSUBSCRIBE PEIRCE-L in the SUBJECT LINE of the message and nothing in the body. More at https://list.iupui.edu/sympa/help/user-signoff.html . ► PEIRCE-L is owned by THE PEIRCE GROUP; moderated by Gary Richmond; and co-managed by him and Ben Udell.
Re: [PEIRCE-L] Theme One • A Program Of Inquiry
Cf: Theme One Program • Discussion 4 https://inquiryintoinquiry.com/2021/10/15/theme-one-program-discussion-4/ All, I’ve been going back and looking again at the problems and questions which nudged me into the computational sphere as a way of building our human capacities for inquiry, learning, and reasoning. One critical issue, you might even say bifurcation point, came up again on the Peirce List almost a decade ago in discussing the so-called “Symbol Grounding Problem”, a problem I thought had long been laid to rest, at least, among readers of Peirce, who ought to have no trouble grasping how the problem dissolves as soon as placed in the medium of Peirce’s sign relations. Here is how the ghost of a problem returned to haunt us on that occasion ... • Peirce List • Jerry Chandler • Jon Awbrey • Gary Richmond • Christophe Menant • https://list.iupui.edu/sympa/arc/peirce-l/2012-12/thrd3.html#00063 All of which led me to recall the problems I worked on all through the ’80s ... I spent one of my parallel lives in the 1980s earning a Master’s degree in psychology, concentrating on the quantitative-statistical branch with courses in systems theory, simulation, and mathematical models, plus a healthy diet of courses and seminars in cognitive science and counseling psychology. Instead of the usual thesis I submitted a computer program which integrated a module for multi-level sequential learning with a module for propositional constraint satisfaction, the latter based on an extension of Peirce’s logical graphs. All the hottest topics of artificial intelligence and cognitive science from those days enjoy no end of periodic revivals, and though it brings me a twinge of nostalgia to see those old chestnuts being fired up again, those problems now seem to me as problems existing only for a peculiar tradition of thought, a tradition ever occupied with chasing will o’ th’ wisps Peirce dispersed long before the chase began. Regards, Jon _ _ _ _ _ _ _ _ _ _ ► PEIRCE-L subscribers: Click on "Reply List" or "Reply All" to REPLY ON PEIRCE-L to this message. PEIRCE-L posts should go to peirce-L@list.iupui.edu . ► To UNSUBSCRIBE, send a message NOT to PEIRCE-L but to l...@list.iupui.edu with UNSUBSCRIBE PEIRCE-L in the SUBJECT LINE of the message and nothing in the body. More at https://list.iupui.edu/sympa/help/user-signoff.html . ► PEIRCE-L is owned by THE PEIRCE GROUP; moderated by Gary Richmond; and co-managed by him and Ben Udell.
[PEIRCE-L] Theme One • A Program Of Inquiry
Peircers,
Discussion arose in the Laws Of Form Group about computational
explorations of George Spencer Brown's calculus of indications.
Readers of Peirce are generally aware that Spencer Brown revived
certain aspects of Peirce's logical graphs, focusing on the Alpha
level interpretable for Boolean Algebra and Propositional Calculus
but adding some hints of potential extension and generalization.
He used what amounts to Peirce's “entitative” interpretation of the
graphical forms in his exposition but was clear about the abstract
character of the forms themselves, as evidenced by their admitting
dual interpretations, dubbed “entitative” and “existential” by Peirce.
In computational context the question naturally arises how to code
the abstract formal structures used by the calculi of CSP and GSB
into the relatively concrete forms that a computer can process.
I began my response to that question as follows ...
Theme One • A Program Of Inquiry : 6
https://inquiryintoinquiry.com/2018/02/28/theme-one-%e2%80%a2-a-program-of-inquiry-6/
{A plaintext transcript follows, but see my blog copy
if the ASCII figure below gets mushed in this email.)
Programs are algorithms that operate on data structures (Wirth).
How do we turn abstract graphs like those used by C.S. Peirce
and Spencer Brown into concrete data structures that algorithms
can manipulate? There are many ways to do this, but one very
efficient way is through the use of “pointer data structures”.
The full documentation of my Theme One Program is still in progress,
but here's a link to a page of exposition, describing the family of
graphs used in the program, how to code the graphs as strings of
parentheses, commas, and letters, and how the program parses the
strings into pointer structures that live in computer memory.
Theme One Program • Exposition
http://intersci.ss.uci.edu/wiki/index.php/Theme_One_Program_%E2%80%A2_Exposition
Here's a link to a suitable point of entry for our present purpose:
Theme One Program • Expository Note 2
http://intersci.ss.uci.edu/wiki/index.php/Theme_One_Program_%E2%80%A2_Exposition#Expository_Note_2
2. Painted And Rooted Cacti And Conifers
=
Figure 1 depicts a typical example of a painted and rooted cactus (PARCA).
o
a | d
o---o o
\ / b c |
ooo b e
\ /
\ /
\ /
\ /
@ a c e
Figure 1. Painted And Rooted Cactus
The graph itself is a mathematical object and does not inhabit
the page or other medium before our eyes, and it must not be
confused with any picture or other representation of it, anymore
than we'd want someone to confuse us with a picture of ourselves,
but it's a fair enough picture, once we understand the conventions
of representation involved.
Let V(G) be the set of nodes in a graph G and let L be a set of
identifiers. We very often find ourselves in situations where we
have to consider many different ways of associating the nodes of G
with the identifiers in L. Various manners of associating nodes with
identifiers have been given conventional names by different schools of
graph theorists. I will give one way of describing a few of the most
common patterns of association.
• A graph is “painted” if there is a relation between its node set
and a set of identifiers, in which case the relation is called a
painting and the identifiers are called paints.
• A graph is “colored” if there is a function from its node set
to a set of identifiers, in which case the function is called
a coloring and the identifiers are called colors.
• A graph is “labeled” if there is a one-to-one mapping between
its node set and a set of identifiers, in which case the mapping
is called a labeling and the identifiers are called labels.
• A graph is said to be “rooted” if it has a unique distinguished node,
in which case the distinguished node is called the root of the graph.
The graph in Figure 1 has a root node marked by the “at” sign or
amphora symbol “@”.
The graph in Figure 1 has eight nodes plus the five paints in the set
{ a, b, c, d, e }. The painting of nodes is depicted by drawing the
paints of each node next to the node they paint. Observe that some
nodes may be painted with an empty set of paints.
The structure of a painted and rooted cactus (PARC) can be encoded
in the form of character string called a painted and rooted cactus
expression (PARCE). For the remainder of this discussion the terms
cactus and cactus expression will be used to mean the painted and
rooted varieties. A cactus expression is formed on an alphabet
consisting of the relevant set of identifiers, the paints, together
with three punctuation marks: the left parenthesis, the comma, and
the right parenthesis.
To be continued ...
Jon
On 2/26/2018 7:18 AM, Jon Awbrey wrote:
Peircers,
I started learning programming about the same time I first ran across
C.S. Peirce's Logical Graphs and Spencer
