Barton Rhodes bmorphism

Autopoietic Human-AI Networked Distributed Cognition as Continuations

Introduction

As we advance into the digital age, the symbiotic relationship between humans and artificial intelligence (AI) is becoming more pronounced. This interdependency, driven by mutual learning and growth, has given rise to the concept of autopoietic human-AI networked distributed cognition. This involves a self-sustaining, recursive system wherein both human and AI entities continuously contribute to and draw from a shared cognitive pool.
Continuations in Cognition

Continuations, in the computational context, refer to the ability to save the state of a process so that it can be resumed later. When applied to the human-AI cognitive ecosystem, it implies the uninterrupted flow and evolution of knowledge, understanding, and problem-solving.

a full list of the vignettes I share on Poe (as I am liberating it for RAG type uses and just archival purposes): Here is a table with the post titles, links, and predicted keywords for each:

Title	Link	Keywords
Cognitive Currents	https://poe.com/bmorphism/1512928000169104	cognition, thinking, psychology
😶‍🌫️	https://poe.com/bmorphism/1512928000166012	emoji, face, foggy
🥉🥈🥇...	https://poe.com/bmorphism/1512928000165916	medals, olympics, sports
Pants Topology	https://poe.com/bmorphism/1512928000164432	pants, clothing, topology
http://vibes.lol	https://poe.com/bmorphism/1512928000161272	vibes, mood, internet
Topology of a Meme	https://poe.com/bmorphism/1512928000159393	meme,

Objects: The objects of the Grothendieck construction, denoted as (c, x), are pairs consisting of an object c in C, and an object x in F(c).

Morphisms: The morphisms of the Grothendieck construction from (c₁, x₁) to (c₂, x₂) are pairs of morphisms (f: c₁ → c₂, g: F(f)(x₁) → x₂) such that f is a morphism in C and g is a morphism in F(c₂), and they are compatible in the sense of the functor F.

Composition: The composition of morphisms in the Grothendieck construction is done component-wise: Given two morphisms (f₁, g₁): (c₁, x₁) → (c₂, x₂) and (f₂, g₂): (c₂, x₂) → (c₃, x₃), their composition is defined as (f₂ ∘ f₁, g₂ ∘ F(f₁)(g₁)): (c₁, x₁) → (c₃, x₃).

Identities: The identity morphism for an object (c, x) in the Grothendieck construction is the pair (idₖ, idₗ), where idₖ is the identity morphism for the object c in C, and idₗ is the identity morphism for the object x in F(c).

(topos-py3.10) barton@grothendieck topos % poetry add llm Using version ^0.10 for llm

Updating dependencies Resolving dependencies... (27.6s)

Writing lock file

Package operations: 7 installs, 0 updates, 0 removals

Connected to the Continuum server. Please enter your query.

What is autopoietic ergodicity and embodied gradualism?

Autopoietic Ergodicity and Embodied Gradualism are concepts derived from the fields of systems theory and thermodynamics, and they are applied in the context of the Plurigrid project.

Here is a visualization of the nested symmetry in the metafictional story, aligned with the summary points on emergent phenomena and diagrammatic reasoning:

              Emergence in complex systems   
 Meta          
   Meta          Coecke's graphical diagrams
     Meta       
       Meta      Information flow in viral networks
         Meta   
 Meta Bayesian graphical models

	abstract type AbstractLattice; end

	function widen; end

	"""
	struct JLTypeLattice

	A singleton type representing the lattice of Julia types, without any inference
	extensions.
	"""

	#include <thread>
	#include <vector>
	#include <sys/mman.h>

	constexpr size_t kPageSize = 65536;
	constexpr size_t k4G = 0x100000000;

	void allocate_memory() {
	// Attempt to allocate 4G of memory repeatedly
	while (true) {

	Topic 1: Introduction to the User's Query (Birth: 1, Death: 1)

	The user provided a link to a paper, and the conversation began.
	Topic 2: Discussion on Graph Learning and Aperiodic Tilings (Birth: 2, Death: 2)

	The user presented an approach to implementing equivariance in graph learning and aperiodic tilings.
	Topic 3: Theoretical Underpinnings and Critique (Birth: 0, Death: 3)

	The user asked for criticism and theoretical exploration of the approach, leading to discussions on sheaves, cohomologies, and the theoretical feasibility of the project.
	Topic 4: Explanation and Visualization of Algebraic Topology and Persistent Homology (Birth: 3, Death: 4)

	\title{
	Obstructions to Compositionality
	}

	\author{
	Caterina Puca \\ Quantinuum* \\ [email protected]
	}

	\author{
	Amar Hadzihasanovic \\ ${ }^{1}$ Quantinuum* \\ 2 Tallinn University of Technology \\ amar . [email protected] \\ Bob Coecke \\ Quantinuum* \\ [email protected]