Author Archives: Jon Awbrey

τὰ δὲ μοι παθήματα ἐόντα ἀχάριτα μαθήματα γέγονε

Posted on March 24, 2013 by Jon Awbrey

Croesus, addressing Cyrus, says — τὰ δὲ μοι παθήματα ἐόντα ἀχάριτα μαθήματα γέγονε. My sufferings, though painful, have been my lessons. — Herodotus • 1.207 Notes • (1) • (2) • (3) • (4) • (5)

Posted in Anthem | Tagged | 2 Comments

A Meno Acid

Posted on March 21, 2013 by Jon Awbrey

What answers to the Meno Paradox Comes in the moment of realizing — Gathering together the building blocks Is just the beginning of the building.

Posted in Artificial Intelligence, Cognitive Science, Education, Inquiry, Learning, Meno, Philosophy, Plato, Teaching, Verse | Tagged , , , , , , , , , | Leave a comment

Indicator Functions • 1

Posted on March 13, 2013 by Jon Awbrey

Re: R.J. Lipton and K.W. Regan • Who Invented Boolean Functions? One of the things it helps to understand about 19th Century mathematicians, and those who built the bridge to the 20th, is that they were capable of high abstraction … Continue reading →

Posted in Abstraction, Boole, Boolean Functions, C.S. Peirce, Category Theory, Characteristic Functions, Euler, Indicator Functions, John Venn, Logic, Mathematics, Peirce, Propositional Calculus, Set Theory, Venn Diagrams, Visualization | Tagged , , , , , , , , , , , , , , , | Leave a comment

Riffs and Rotes • 2

Posted on March 3, 2013 by Jon Awbrey

Re: Peter Cameron • Addition and Multiplication of Natural Numbers The interaction between addition and multiplication in the natural numbers has long been an interest of mine, leading to broader questions about the relationship between algebra and combinatorics.  My gropings … Continue reading →

Posted in Arithmetic, Combinatorics, Graph Theory, Group Theory, Logic, Mathematics, Number Theory, Riffs and Rotes | Tagged , , , , , , , | Leave a comment

Oracles

Posted on March 1, 2013 by Jon Awbrey

Computing, in its way, and science, in its broader way, both involve the relation between what appears limited and what appears not. Whether you believe in divinity or not, and whether you believe that humanity contains a spark of divinity … Continue reading →

Posted in Communication, Computability, Computing, Inquiry, Oracles, Relative Computability, Science, Universals | Tagged , , , , , , , | 3 Comments

Quotiens?

Posted on February 28, 2013 by Jon Awbrey

How many times do I repeat the same experience? Before I come to see it as the same experience?

Posted in Algorithms, Anamnesis, Arithmetic, Deja Vu, Education, Epistemology, Eternal Return, Inquiry, Learning, Meno, Music, Pattern Recognition, Plato, Poetry, Recursion, Repetition, Rhythm, Teaching | Tagged , , , , , , , , , , , , , , , , , | 2 Comments

Poems and Programs

Posted on February 27, 2013 by Jon Awbrey

Words that do … A trendy misunderstanding has reared its head as to what the discipline of computing, indeed the logic of science, are all about.  I blame Penrose, of course, but he is only the most recent promulgator of … Continue reading →

Posted in Aesthetics, Artistic Differences, Computability, Effective Description, Ethics, Existential Choice, Finitude, Form, Imagination, Information, Inquiry, Limitation, Logic of Science, Matter, Mortality, Poetry, Programming, Volition | Tagged , , , , , , , , , , , , , , , , , | 1 Comment

I Wonder, Wonder Who

Posted on February 25, 2013 by Jon Awbrey

Re: R.J. Lipton and K.W. Regan • Who Invented Boolean Functions? The question recalls recent discussions of discovery and invention in the mathematical field, bringing back to mind questions I’ve wondered about for as long as I can remember. Speaking … Continue reading →

Posted in Anamnesis, Aristotle, Boole, Boolean Functions, C.S. Peirce, Discovery, Invention, Learning, Logic, Mathematics, Meno, Model Theory, Peirce, Plato, Propositional Calculus, Recollection, Semiotics, Socrates, Teaching | Tagged , , , , , , , , , , , , , , , , , , | Leave a comment

Notes On Categories • 1

Posted on February 22, 2013 by Jon Awbrey

Continued from “Notes On Categories” (14 Jul 2003) • Inquiry List • Ontology List NB.  This page is a work in progress.  I will have to dig up some still older notes from the days of pen and paper before … Continue reading →

Posted in Abstraction, Category Theory, Computing, Graph Theory, Logic, Mathematics, Relation Theory, Type Theory | Tagged , , , , , , , | 10 Comments

Theme One • A Program Of Inquiry 4

Posted on February 14, 2013 by Jon Awbrey

Re: Next Polymath Project • What, When, Where? Here’s a bit of data on the Theme One Program I worked on all through the 1980s.  My aim was to develop fundamental algorithms and data structures to support an integrated learning … Continue reading →

Posted in Artificial Intelligence, C.S. Peirce, Cognition, Computation, Constraint Satisfaction Problems, Cybernetics, Formal Languages, Inquiry, Inquiry Driven Systems, Intelligent Systems, Learning Theory, Logic, Peirce, Semiotics | Tagged , , , , , , , , , , , , , | 8 Comments