Recently we held a workshop in Edinburgh titled Mathematics for Governance Design, consisting of a roughly 50/50 split between social scientists and category theorists.

In which we connect the physics Nobel Prize to machine learning and economic design.

In this post we will make probably the single most important step from a generic type theory to one specialised to bidirecional programming.

In this post we'll begin designing a kernel language in which all programs are optics. What I mean by a "kernel language" is that it will serve as a compiler intermediate representation, with a surface language compiling down to it. I intend the surface language to be imperative style like the current Open Game Engine (with an approximately Python-like syntax), but the kernel language will reflect the category theory as closely as possible. I plan the kernel language to be well typed by construction, something that seems like overkill until I think about the problem of figuring out how pattern matching should work in a bidirectional language.

In which we learn why "flat earth" is a perfectly sound scientific proposition and why being wrong two thirds of the time can actually be quite lucrative.

This is the first post in a new series documenting my work developing a bidirectional programming language, in which all programs are interpreted as optics. This is something I've been thinking about for a long time, and eventually I became convinced that there were enough subtle issues that I should take things extremely slowly and actually learn some programming language theory. As a result, this post will not be about categorical cybernetics at all, but is a foundation to a huge tower of categorical cybernetics machinery that I will build later.

In which we try to capture all the ways how beliefs can shape social and economic interaction.

Are economic models useful for making decisions? One might expect that there is clear answer to this simple question. But in fact opinions on the usefulness or non-usefulness of models as well as what exactly makes models useful vary widely. In this post, I want to explore the question of usefulness. Even more so, I want to explore how the usefulness ties into the modelling process. The reason for doing so is simple: Part of our efforts at CyberCat is to build software tools to improve and accelerate the modelling process.

Suppose we have some category, whose morphisms are some kind of processes or systems that we care about. We would like to be able to talk about contexts (or environments) in which these processes or systems can be located.

This is an overview of the 'RL lens', a construction that we recently introduced to understand some reinforcement learning algorithms like Q-learning

In which we bring back together the estranged fraternal disciplines of economics and operations research and map out how we can combine them to design cybernetic economies.

I explore the effect of players following their best response dynamics in large random normal form games.

The first installment of a multi-part series demistifying the underlying mechanics of the open games engine in a simple manner.

In this post we will look at how dependent types can allow us to effortlessly implement the category theory of machine learning directly, opening up a path to new generalisations.

I'm going to record something that I think is known to everyone doing research on categorical cybernetics, but I don't think has been written down somewhere: an even more general version of mixed optics that replaces the backwards actegory with an enrichment. With it, I'll make sense of a curious definition appearing in The Compiler Forest.

Dependent lenses are useful for general-purpose programming, but in which way exactly? This post demonstrates the use of dependent lenses as input/output-conversion processes, using parsing and error location reporting as a driving example.

In which we discuss how knowledge travels thru the economy, and how, when and where it forms clusters.

In Towards Foundations of Categorical Cybernetics we built a category whose objects are selection functions and whose morphisms are lenses. It was a key step in how we justified open games in that paper: they're just parametrised lenses weighted by selection functions. In this post I'll show that by adding dependent types and stirring, we can get a nicer category that does the same job but has all colimits, and comes extremely close to having all limits. Fair warning: this post assumes quite a bit of category-theoretic background.

In which we describe organization and organizations as tectonic plates shaped by clashing beliefs.

A system whose architecture has invariant preferences will act in a way to bring about or avoid certain states of the world, no matter what it learns. A lot of people have already put a lot of thought into the issue of good and bad world-states, including very gnarly issues of how to agree on what they should be - what I'm proposing is a technological missing link, how to bridge from that level of abstraction to low-level neural network architectures.

In which we establish an underlying model for human behavior and claim that all economies are just a variation of the attention economy.

An Economic Pattern Language (@econpatterns for short) takes the economy and disassembles it into its constituent parts. But first, this blog post describes the economy as a whole.

In this post I'll describe the theory of how to add iteration to categories of optics. Iteration is required for almost all applications of categorical cybernetics beyond game theory, and is something we've been handling only semi-formally for some time. The only tool we need is already one we have inside the categorical cybernetics framework: parametrisation weighted by a lax monoidal functor. I'll end with a conjecture that this is an instance of a general procedure to force states in a symmetric monoidal category.

This post is a writeup of a talk I gave at the Causal Cognition in Humans and Machines workshop in Oxford, about some work in progress I have with Toby Smithe. To a large extent this is my take on the theoretical work in Toby's PhD thesis, with the emphasis shifted from category theory and neuroscience to numerical computation and AI. In the last section I will outline my proposal for how to build AGI.

Suppose your name is x and you have a very important state machine that you cherish with all your heart. Because you love this state machine so much, you don't want it to malfunction and you have a subset which you consider to be safe. If your state machine ever leaves this safe space you are in big trouble so you ask the following question.

Advanced AI making economic decisions in supply chains and markets creates poorly-understood risks, especially by undermining the fundamental concept of individuality of agents. We propose to research these risks by building and simulating models.

This is a short summary of the post. It is meant to explain how to write for our blog.

Some time ago, in a previous blog post, we introduced our software engine for game theoretic modelling. In this post, we expand more on how to apply the engine to use cases relevant for the Ethereum ecosystem. We will consider an analysis of a simplified staking protocol. Our focus will be on compositionality – what this means from the perspective of representing protocols and from the perspective of analyzing protocols.

Categorical cybernetics, or CyberCat to its friends, is – no surprise – the application of methods of (applied) category theory to cybernetics. The "category theory" part is clear enough, but the term "cybernetics" is notoriously fluid, and throughout history has meant more or less whatever the writer wanted it to mean. So, let’s lay down some boundaries.