I could watch forever ... #LorenzAttractor #ButterflyEffect #JavaScript #p5js #DifferentialEquations #math #visualization #computergraphics #dynamicsystems
I could watch forever ... #LorenzAttractor #ButterflyEffect #JavaScript #p5js #DifferentialEquations #math #visualization #computergraphics #dynamicsystems
Das Histogramm des Clifford-Attractors bei Variation des Parameters a zwischen 0 und 4 und Beibehalten der Parameter
b=1.7
c=0.6
d=1.2
#generative #generativeart #dynamicsystems #nonlinear #chaos #fractal #fractalart
Differential Logic • Overview 2
• https://inquiryintoinquiry.com/2024/11/25/differential-logic-overview-a/
Introduction
• https://oeis.org/wiki/Differential_Logic_%E2%80%A2_Part_1#Introduction
Cactus Language for Propositional Logic
• https://oeis.org/wiki/Differential_Logic_%E2%80%A2_Part_1#Cactus_Language_for_Propositional_Logic
Differential Expansions of Propositions
• https://oeis.org/wiki/Differential_Logic_%E2%80%A2_Part_1#Differential_Expansions_of_Propositions
Propositional Forms on Two Variables
• https://oeis.org/wiki/Differential_Logic_%E2%80%A2_Part_2#Propositional_Forms_on_Two_Variables
Transforms Expanded over Ordinary and Differential Variables
• https://oeis.org/wiki/Differential_Logic_%E2%80%A2_Part_2#Transforms_Expanded_over_Ordinary_and_Differential_Variables
Field Picture
• https://oeis.org/wiki/Differential_Logic_%E2%80%A2_Part_3#Field_Picture
Differential Fields
• https://oeis.org/wiki/Differential_Logic_%E2%80%A2_Part_3#Differential_Fields
Propositions and Tacit Extensions
• https://oeis.org/wiki/Differential_Logic_%E2%80%A2_Part_3#Propositions_and_Tacit_Extensions
Enlargement and Difference Maps
• https://oeis.org/wiki/Differential_Logic_%E2%80%A2_Part_3#Enlargement_and_Difference_Maps
Tangent and Remainder Maps
• https://oeis.org/wiki/Differential_Logic_%E2%80%A2_Part_3#Tangent_and_Remainder_Maps
Resources —
Logic Syllabus
• https://inquiryintoinquiry.com/logic-syllabus/
Survey of Differential Logic
• https://inquiryintoinquiry.com/2024/02/25/survey-of-differential-logic-7/
#Peirce #Logic #Mathematics #LogicalGraphs #DifferentialLogic #DynamicSystems
#Inquiry #PropositionalCalculus #BooleanFunctions #BooleanDifferenceCalculus
#EquationalInference #MinimalNegationOperators #CalculusOfLogicalDifferences
Differential Logic • Overview 1
• https://inquiryintoinquiry.com/2024/11/25/differential-logic-overview-a/
A reader once told me “venn diagrams are obsolete” and of course we all know how unwieldy they become as our universes of discourse expand beyond four or five dimensions. Indeed, one of the first lessons I learned when I set about implementing Peirce's graphs and Spencer Brown's forms on the computer is that 2‑dimensional representations of logic quickly become death traps on numerous conceptual and computational counts.
Still, venn diagrams do us good service at the outset in visualizing the relationships among extensional, functional, and intensional aspects of logic. A facility with those connections is critical to the computational applications and statistical generalizations of propositional logic commonly used in mathematical and empirical practice. All things considered, then, it is useful to make as visible as possible the links between variant styles of imagery in logical representation — and that is what I hoped to do in the sketch of Differential Logic outlined below.
Note. I'll give just the links to the main topic heads in the next post. Please follow the link at the top of this post for the full outline.
Resources —
Logic Syllabus
• https://inquiryintoinquiry.com/logic-syllabus/
Survey of Differential Logic
• https://inquiryintoinquiry.com/2024/02/25/survey-of-differential-logic-7/
#Peirce #Logic #Mathematics #LogicalGraphs #DifferentialLogic #DynamicSystems
#Inquiry #PropositionalCalculus #BooleanFunctions #BooleanDifferenceCalculus
#EquationalInference #MinimalNegationOperators #CalculusOfLogicalDifferences
Differential Logic • 1
• https://inquiryintoinquiry.com/2024/10/30/differential-logic-1-a/
Introduction —
Differential logic is the component of logic whose object is the description of variation — focusing on the aspects of change, difference, distribution, and diversity — in universes of discourse subject to logical description. A definition that broad naturally incorporates any study of variation by way of mathematical models, but differential logic is especially charged with the qualitative aspects of variation pervading or preceding quantitative models. To the extent a logical inquiry makes use of a formal system, its differential component governs the use of a “differential logical calculus”, that is, a formal system with the expressive capacity to describe change and diversity in logical universes of discourse.
Simple examples of differential logical calculi are furnished by “differential propositional calculi”. A differential propositional calculus is a propositional calculus extended by a set of terms for describing aspects of change and difference, for example, processes taking place in a universe of discourse or transformations mapping a source universe to a target universe. Such a calculus augments ordinary propositional calculus in the same way the differential calculus of Leibniz and Newton augments the analytic geometry of Descartes.
Resources —
Survey of Differential Logic
• https://inquiryintoinquiry.com/2024/02/25/survey-of-differential-logic-7/
cc: https://www.academia.edu/community/lJX2qa
cc: https://www.researchgate.net/post/Differential_Logic_The_Logic_of_Change_and_Difference
#Peirce #Logic #Mathematics #LogicalGraphs #DifferentialLogic #DynamicSystems
#Inquiry #PropositionalCalculus #BooleanFunctions #BooleanDifferenceCalculus
#EquationalInference #MinimalNegationOperators #CalculusOfLogicalDifferences
Survey of Differential Logic • 7
• https://inquiryintoinquiry.com/2024/02/25/survey-of-differential-logic-7/
This is a Survey of work in progress on Differential Logic, resources under development toward a more systematic treatment.
Differential logic is the component of logic whose object is the description of variation — the aspects of change, difference, distribution, and diversity — in universes of discourse subject to logical description. A definition as broad as that naturally incorporates any study of variation by way of mathematical models, but differential logic is especially charged with the qualitative aspects of variation pervading or preceding quantitative models. To the extent a logical inquiry makes use of a formal system, its differential component treats the use of a differential logical calculus — a formal system with the expressive capacity to describe change and diversity in logical universes of discourse.
Please follow the above link for the full set of resources.
Articles and blog series on the core ideas are linked below.
Differential Logic • The Logic of Change and Difference
• https://inquiryintoinquiry.com/2023/08/22/differential-logic-the-logic-of-change-and-difference/
Differential Propositional Calculus
• https://inquiryintoinquiry.com/2023/11/12/differential-propositional-calculus-overview-a/
• https://oeis.org/wiki/Differential_Propositional_Calculus_%E2%80%A2_Overview
Differential Logic
• https://inquiryintoinquiry.com/2020/03/20/differential-logic-overview/
• https://oeis.org/wiki/Differential_Logic_%E2%80%A2_Overview
Differential Logic and Dynamic Systems
• https://inquiryintoinquiry.com/2023/03/04/differential-logic-and-dynamic-systems-overview-a/
• https://oeis.org/wiki/Differential_Logic_and_Dynamic_Systems_%E2%80%A2_Overview
#Peirce #Logic #LogicalGraphs #DifferentialLogic #DynamicSystems
#BooleanFunctions #BooleanDifferenceCalculus #QualitativePhysics
#CactusCalculus #MinimalNegationOperators #NeuralNetworkSystems
#CalculusOfLogicalDifferences
New blog post! I review a dynamic systems model of pursuing happiness. Zerwas and Ford find that the system of happiness and goal pursuit can potentially lead to paradoxical effects. Pursuing happiness too intensely can make you less happy!
#Psychology #PsychologyToday #Happiness #DynamicSystems #Cyberntics #SystemsThinking #Emotion #EmotionRegulation
a dynamic existence- Haiku meditation with generative art is posted on medium (no paywall)
https://sophiawood.medium.com/in-dynamic-existence-3205a9bc6e07
#haiku #meditaion #strangeAttractor #creativeCoding #poetry #dynamicSystems #radialSymmetry
Survey of Differential Logic • 6
• https://inquiryintoinquiry.com/2023/11/10/survey-of-differential-logic-6/
This is a Survey of work in progress on Differential Logic, resources under development toward a more systematic treatment.
Differential logic is the component of logic whose object is the description of variation — the aspects of change, difference, distribution, and diversity — in universes of discourse subject to logical description. A definition as broad as that naturally incorporates any study of variation by way of mathematical models, but differential logic is especially charged with the qualitative aspects of variation pervading or preceding quantitative models. To the extent a logical inquiry makes use of a formal system, its differential component treats the use of a differential logical calculus — a formal system with the expressive capacity to describe change and diversity in logical universes of discourse.
Please follow the above link for the full set of resources.
Articles and blog series on the core ideas are linked below.
Differential Logic • The Logic of Change and Difference
• https://inquiryintoinquiry.com/2023/08/22/differential-logic-the-logic-of-change-and-difference/
Differential Propositional Calculus
• https://inquiryintoinquiry.com/2023/11/12/differential-propositional-calculus-overview-a/
Differential Logic
• https://inquiryintoinquiry.com/2020/03/20/differential-logic-overview/
Differential Logic and Dynamic Systems
• https://inquiryintoinquiry.com/2023/03/04/differential-logic-and-dynamic-systems-overview-a/
cc: https://www.academia.edu/community/lQX66L
#Peirce #Logic #LogicalGraphs #DifferentialLogic #DynamicSystems
#BooleanFunctions #BooleanDifferenceCalculus #QualitativePhysics
#CactusCalculus #MinimalNegationOperators #NeuralNetworkSystems
#CalculusOfLogicalDifferences
Comparison of Bootstrap Methods for Estimating Causality in Linear Dynamic Systems: A Review https://www.mdpi.com/1099-4300/25/7/1070 #timeseries #dynamicsystems
@NicoleCRust @kristinmbranson @neuroecology @zamakany
Einstein recommended we stop trying to reckon familiar 3-dimensional space on its own. We must also factor time.
One of the themes in this paper by Esther Thelen and Linda B. Smith is that behaviour on its own and frozen in time is not a worthwhile object of study. #dynamicSystems
Survey of Differential Logic • 5
• https://inquiryintoinquiry.com/2023/04/25/survey-of-differential-logic-5/
This is a Survey of work in progress on Differential Logic, resources under development toward a more systematic treatment.
Differential logic is the component of logic whose object is the description of variation — the aspects of change, difference, distribution, and diversity — in universes of discourse subject to logical description. A definition as broad as that naturally incorporates any study of variation by way of mathematical models, but differential logic is especially charged with the qualitative aspects of variation pervading or preceding quantitative models. To the extent a logical inquiry makes use of a formal system, its differential component treats the use of a differential logical calculus — a formal system with the expressive capacity to describe change and diversity in logical universes of discourse.
Please follow the above link for the full set of resources.
Articles and blog series on the core ideas are linked below.
Differential Propositional Calculus
• https://oeis.org/wiki/Differential_Propositional_Calculus_%E2%80%A2_Overview
1 https://oeis.org/wiki/Differential_Propositional_Calculus_%E2%80%A2_Part_1
2 https://oeis.org/wiki/Differential_Propositional_Calculus_%E2%80%A2_Part_2
• https://inquiryintoinquiry.com/2020/02/16/differential-propositional-calculus-overview/
Differential Logic
• https://oeis.org/wiki/Differential_Logic_%E2%80%A2_Overview
1 https://oeis.org/wiki/Differential_Logic_%E2%80%A2_Part_1
2 https://oeis.org/wiki/Differential_Logic_%E2%80%A2_Part_2
3 https://oeis.org/wiki/Differential_Logic_%E2%80%A2_Part_3
• https://inquiryintoinquiry.com/2020/03/20/differential-logic-overview/
Differential Logic and Dynamic Systems
• https://oeis.org/wiki/Differential_Logic_and_Dynamic_Systems_%E2%80%A2_Overview
1 https://oeis.org/wiki/Differential_Logic_and_Dynamic_Systems_%E2%80%A2_Part_1
2 https://oeis.org/wiki/Differential_Logic_and_Dynamic_Systems_%E2%80%A2_Part_2
3 https://oeis.org/wiki/Differential_Logic_and_Dynamic_Systems_%E2%80%A2_Part_3
4 https://oeis.org/wiki/Differential_Logic_and_Dynamic_Systems_%E2%80%A2_Part_4
5 https://oeis.org/wiki/Differential_Logic_and_Dynamic_Systems_%E2%80%A2_Part_5
• https://inquiryintoinquiry.com/2023/03/04/differential-logic-and-dynamic-systems-overview-2/
#Peirce #Logic #LogicalGraphs #DifferentialLogic #DynamicSystems
#BooleanFunctions #BooleanDifferenceCalculus #QualitativePhysics
#CactusCalculus #MinimalNegationOperators #NeuralNetworkSystems
Differential Logic and Dynamic Systems • Review and Transition 1
• https://oeis.org/wiki/Differential_Logic_and_Dynamic_Systems_%E2%80%A2_Part_1#Review_and_Transition
This note continues a previous discussion on the problem of dealing with change and diversity in logic-based intelligent systems. It is useful to begin by summarizing essential material from previous reports.
Table 1 outlines a notation for propositional calculus based on two types of logical connectives, both of variable \(k\)-ary scope.
• A bracketed list of propositional expressions in the form \(\texttt{(} e_1 \texttt{,} e_2 \texttt{,} \ldots \texttt{,} e_{k-1} \texttt{,} e_k \texttt{)}\) indicates that exactly one of the propositions \(e_1, e_2, \ldots, e_{k-1}, e_k\) is false.
• A concatenation of propositional expressions in the form \(e_1 ~ e_2 ~ \ldots ~ e_{k-1} ~ e_k\) indicates that all of the propositions \(e_1, e_2, \ldots, e_{k-1}, e_k\) are true, in other words, that their logical conjunction is true.
All other propositional connectives can be obtained in a very efficient style of representation through combinations of these two forms. Strictly speaking, the concatenation form is dispensable in light of the bracketed form but it is convenient to maintain it as an abbreviation of more complicated bracket expressions.
#Peirce #Logic #LogicalGraphs #DifferentialLogic #DynamicSystems
#BooleanFunctions #BooleanDifferenceCalculus #QualitativeChange
#MinimalNegationOperators #NeuralNetworkSystems #Semiotics
newest version! no more messing around: this one is headed over to @PLOS
Differential Logic and Dynamic Systems • Overview
• https://inquiryintoinquiry.com/2023/03/04/differential-logic-and-dynamic-systems-overview-2/
• https://oeis.org/wiki/Differential_Logic_and_Dynamic_Systems_%E2%80%A2_Overview
❝Stand and unfold yourself.❞
— Hamlet • Francisco • 1.1.2
In modeling intelligent systems, whether we are trying to understand a natural system or engineer an artificial system, there has long been a tension or trade-off between dynamic paradigms and symbolic paradigms. Dynamic models take their cue from physics, using quantitative measures and differential equations to model the evolution of a system’s state through time. Symbolic models use logical methods to describe systems and their agents in qualitative terms, deriving logical consequences of a system’s description or an agent’s state of information. Logic-based systems have tended to be static in character, largely because we have lacked a proper logical analogue of differential calculus. The work laid out in this report is intended to address that lack.
This article develops a differential extension of propositional calculus and applies it to the analysis of dynamic systems whose states are described in qualitative logical terms. The work pursued here is coordinated with a parallel application focusing on neural network systems but the dependencies are arranged to make the present article the main and the more self-contained work, to serve as a conceptual frame and a technical background for the network project.
#Peirce #Logic #LogicalGraphs #DifferentialLogic #DynamicSystems
#BooleanFunctions #BooleanDifferenceCalculus #QualitativeChange
#MinimalNegationOperators #NeuralNetworkSystems #Semiotics
The Phantom of the Operators • η
• https://oeis.org/wiki/Differential_Logic_and_Dynamic_Systems_%E2%80%A2_Part_3#The_Phantom_of_the_Operators_:_.CE.B7
❝I was wondering what the reason could be, when I myself raised my head and everything within me seemed drawn towards the Unseen, which was playing the most perfect music!❞
— Gaston #Leroux • “The Phantom of the Opera”
#DifferentialLogic #DynamicSystems
#DifferentialLogicAndDynamicSystems
Skywing: #OpenSource software aids collaborative #autonomy applications
https://www.miragenews.com/skywing-open-source-software-aids-collaborative-935255/
Good evening #Fediverse :fediverse: ! It's time for my not-quite-daily #ConnectionList #Introduction #FollowFriday post, where I use my large number of followers to more closely connect the Fediverse together, and help people find their people in the #TwitterMigration.
Please meet:
@effye does #DevOps and #DuctTape, connecting together various systems. I've followed their work for a long time, huge fan.
@davidasboth is one half of the #HalfStackDataScience #podcast and is into #DataScience and #SoftwareEngineeering
@ConserveChange is a human #ecologist and #StoryTeller at #Guelph, and is host of the #SecondTransition #podcast. Interests in #Food #FoodSystems #ClimateAction #Science and #Sustainability
@ststefany is from 🇺🇦 and is into #epistemology, #ethics and #feminism. Writes in en and ua, for any #Ukrainian #українська speakers in your network.
@futilityfunc is a #DataScientist and interested in #ComplexityScience #Complexity and does #research on stochastic #GraphModels #DynamicSystems and #Cybernetics
@CIT is Carolin and they toot in both 🇩🇪 and 🇬🇧. Carolin studies #systems and #OrganisationDevelopment, #Anthropology and #Psychology #researcher
@monad is #Professor Paul Feigelfeld who works in #KnowledgeCultures at HBK #Braunschweig, Uni Vienna and Uni Basel. Researches 🇨🇳
That's it for tonight, don't forget to curate your own #ConnectionList ❤️
Good evening #Fediverse :fediverse:! In tonight's #Introduction #ConnectionList #TwitterMigration post, where I help to more richly connect the Fediverse, I'd like you to meet:
@unsw_ai is #UNSW #AI research centre 👋
@oj_gstrein is the Director of #DataScience and society at the University of #Groningen #researcher #academic 👋
@hollie is enthusiastic about #nature, #puns, the #IndieWeb, #reading, #sewing and #knitting (me, too Hollie! 🧶 👋 )
@futilityfunc is a #DataScience person who is interested in #complexity, #DynamicSystems, #systems and #cybernetics 👋
@mythopoetica is a Senior #Lecturer #researcher in #Literature and #CreativeWriting and is into #CriticalTheory 👋
@peridragon designs colourful #knitting patters and is into #history #biology and #StarTrek Knit long and prosper, Peridragon! 👋
@HackingDave is the #founder of Binary Defense and TrustedSec and works in #infosec and is a #hacker 👋
@Ellopunk is into #Linux 🐧, #infosec and is into #ThreatModeling 👋
@ErikC is an #academic #researcher at UniSA and is into #DigitalHumanities, #VirtualHeritage and #SeriousGames 👋
Don't forget to build your own #ConnectionList #FollowFriday so we can more richly connect the Fediverse ❤️
#introduction I've been here for a few weeks, but have yet to introduce myself! I'm a #cogneuro & #quantpsych researcher at The University of Utah studying #pain #perception & #emotion with a focus on how perceptual and emotional processes interact over time using #psychophysics #intensivelongitudinalmethods #DynamicSystems #bayesianestimation . Lover of all things time #timeperception #temporalanalysis and quant. I love #Stats & #Programming , and enjoy teaching these methods to others.