Sources

• Slides of the CAS 2025 talk: https://file.notion.so/f/f/45ee1816-226b-4b32-9fbc-65cccb822418/79e1516c-5675-4a4c-b31d-f589c6c78c69/ScaleComplexAnarchismSlides.pdf?table=block&id=222f4647-7642-8096-84c6-e863601293ef&spaceId=45ee1816-226b-4b32-9fbc-65cccb822418&expirationTimestamp=1754359200000&signature=vqnEeKSFkBs-uq1oqEpJ_WKLwMyhApmeU386jHWUopM&downloadName=ScaleComplexAnarchismSlides.pdf
• Scale Anarchism paper https://www.its.caltech.edu/~matilde/ScaleAnarchy.pdf
• related publications on category theory: arXiv:2204.11931, arXiv:1409.5531, arXiv:1504.03661

Prototype Brainstorm

Open Questions

(This is a collection of questions, some of them probably due to not fully understanding the math in the papers. Feel free to add more questions or to answer them.)

1. There are many optimization algorithms out there. Depending on the application area, we should to pick an algorithm that is the best fit (at least I’m not aware of a general purpose optimization algorithm). E.g. for logic problems CP-SAT is a good choice. I understood that classic Pareto-based swarm algorithms are good for non-linear multi-objective problems that are based on numeric values. I also understood that the category theory version proposed in the above sources is for problems in which there are non-quantifiable resources or objectives. Question: What are concrete application use cases that would be best solved by this (and could not better be solved by e.g. CP-SAT, or graph-based algorithms (e.g. shortest path)).
   1. If I understood the prototype brainstorm correctly, the application area was peer-to-peer teaching. Isn’t that solved by CP-SAT assignment?
   2. We agree, that we don’t want prices. However, I still see quantities of resources and thus numeric problems in many economy related questions I can think of. What are examples of non-numeric ones, that are not solved by logic or graph algorithms?
2. In the talk and prototype brainstorm there was the idea of running the algorithm distributed in a network with multiple nodes (mentioning e.g. Urbit).
   1. Running it distributed is not strictly needed, right?
   2. If it would run distributed, was the idea that one node represents one particle? And/or one community in the network of communities?

Reflections

Those are some reflections by Evo on the “The problem of scale in anarchism” and the “PARETO OPTIMIZATION IN CATEGORIES” papers (without having understood all the math). (I did also make some summary and other notes, can share if wanted, but will try to keep focused here)

• On the ‘integrated information’ measure: to me, this is a too abstract measure to optimize, that does not really relate to satisfying people's needs (what economy should be about) - just as profit is. So I think blindly trying to optimize this, can give unwanted effects, like always when the aim becomes to optimize a measure instead of the thing it is supposed to capture (see academic measures). The unwanted effects are difficult to predict, but could create a dependency relation, a 'collectivity' that ignores individuals,... Also, I do not see how to optimize this in a decentralised way, as this is a quite overal-system property (as opposed to profit, that can still be optimized individually, decentralised).
  • I do think we can extract some general guidelines behind it, which is to increase connectivity (railway, information networks,...) and complexity (philosophy, art,science,...) (see ‘Instruments and mechanisms’ section). Hence to go for qualitative connections. It could maybe also be used as an analysis tool: to calculate the integrated complexity of an initiative, to gain some insights on it.
• On Multi-layered networks: people can be part of different cooperatives (so cooperatives can overlap), and membership can be fuzzy, not just a binary in/out. The larger network structure can also influence their form, so you cannot just take them as fixed and given.
  • Actually, in general the network-concept puts clear boundaries between 'nodes', while often those do not exist/are blurry. The world is more like (a painting of) a landscape. Can be interesting to think of mathematical models that could capture this (the concept of space could be useful, where there is continuity instead of discreteness, but it misses some relationality. I’m thinking something like a continuous version of a network (that is discrete).
• Pareto optimization: the issue is that the frontier is often large; so how to choose within? Sure, certain choices are worse in all respect to other choices; usually the issue is to choose when better in one aspect and worse in another. (Like if we have (0,1) and (1,0) in the frontier). Plus, an issue is how to assign those categories/values (the more people can add their values, the larger the frontier probably).
• Category theory: I don’t yet understand which morphism is used instead of the ≤ one (there is a morphism between s and s’ if s ≤ s’); so I do not yet understand how this differs from classical optimization. I tried to gain some understanding at https://chatgpt.com/share/689df762-3530-800c-8275-780fe9b368fd (sharing because it may be helpful for others). Probably should dive back in, as I’m no longer sure I’ve read the whole paper actually (first wanted to make sense I think). But a basic example could help.

Take-aways

This is a collection of quotes and insights that go beyond the math but followed from it.