This document discusses using category theory, topic maps, and knowledge gardens to facilitate peaceful interactions and build trust between groups. It proposes representing shared topics of interest and relationships between participants using topic maps. These topic maps would federate information across "knowledge garden condos" where groups explore topics together. Category theory could help model the topological space defined by these peace-building interactions and relationships. The goal is for participants to discover shared interests, build understanding through structured conversations, and develop trust.

1. Peace through Peaceful
Interactions, Knowledge
Gardens, Topic Maps,
and Category Theory
Jack Park
jackpark@topicquests.org
Stanford⟺Carnegie Mellon University Silicon Valley
Peace Innovation Workshop, © 2012, TopicQuests This work is
9 April, 2012 Licensed under a Creative Commons Attribution-NonCommercial-
.
ShareAlike 3.0 Unported License

2. Peirce: Categories Writ Large
Thirdness
UX: Habits
Secondness
Reactions
Firstness
Possibilities
Diagram co-created with Mary
Keeler and Howard Liu http://en.wikipedia.org/wiki/Categories_%28Peirce%29

3. Peace: Categories Writ Large
UX: Peace
Topic-centric
Trust Building
Peace Data
MAPI
https://docs.google.com/present/view?id=dckf69cs_28c3k2t4f8

4. Peace Mapping
Palestine Israel
Shared
Topic* Peace
Republicans Democrats
Peaceful
Interaction For category diagrams drawn this way, see, e.g.
Lawvere, F.William & Stephen H. Schanuel (1997).
*Shared topics relate to Issue-based Information Systems Conceptual Mathematics: A first introduction to
http://en.wikipedia.org/wiki/Issue- categories. Cambridge, UK: Cambridge University
Based_Information_System Press

5. Category Theory and Topic Maps
• Goal
– A global Knowledge Garden engaged in trust building for peace
• Trust built on shared topics of interest
– “Let’s discover or co-create topics on which we agree, and build on that…”
• Features
– Topic maps federate topics shared during peace interactions
• Represents links (trails) to other individuals with similar interests
– Facilitates trust growth
– Category theory facilitates exploration of the topological space
entailed by peace interactions*
• Multiple ways to discover, study, and enhance relations among participants
• Conjecture
– Topic maps can play roles in category theoretic knowledge
representation
*Some ideas: http://sites.google.com/site/howdowestop/topology-in-this-work

6. Inspiration: Robert Rosen
Metabolism
Environment Repair Replication
A canonical organism
expressed in category- Figure 10C.6.
theoretic representation Rosen, Robert(1991). Life Itself: A
Comprehensive inquiry into the Nature, Origin,
and Fabrication of Life. New York: Columbia
University Press. Page- 251

7. What is a Knowledge Garden?
A Knowledge Garden federates Social with Technical and Political
Condo Condo
(Topic (Topic
Garden) Garden)
Federated
Information
Resources
(Topics)
Collections of participants Condo
at topic-centric portals (Topic
(condos) with all Garden)
information resources
federated

8. What’s In a Condo
• A Social Contract Federation
– Sensemaking
– Discovery
– Learning Games
– Peace Interactions
• User Experience Topic
– Epistemic games Other Map
– Structured conversations
– Social gardening Research
• Tagging Tools
• Annotating Conversation
• Connecting Tools

9. Closing Thought: Topic Maps
• A Topic Map is like a library*
– A Topic Map is indexical
• Like a card catalog
– Each topic has its own representation
• Improving on a card catalog, a topic can be identified many
different ways
– A Topic Map is relational
• Like a good road map
– Topics are connected by associations
– Topics point to their occurrences in the territory
– A Topic Map is organized
• Multiple records on the same topic are co-located in the
map
*A library without all the books: a map is not its territory

10. Completed Representation
Compromised Host
Appropriate For
Bacterial Infection Contraindicates Antioxidants
Because
macrophages use antioxidants
free radicals to kill
Let’s Co-create a Garden and
kill bacteria free radicals
Federate Peace Interactions