Rupert’s Property | Azimuth
You can cut a hole in a cube that’s big enough to slide an identical cube through that hole! Think about that for a minute—it’s kind of weird. Amazingly, nobody could prove any co…| Azimuth
You can cut a hole in a cube that’s big enough to slide an identical cube through that hole! Think about that for a minute—it’s kind of weird. Amazingly, nobody could prove any co…| Azimuth
When bad news gets me down, I often get insomnia. I wake up in the middle of the night, start thinking about how we’re all doomed, and can’t easily stop. To break out of these doom loop…| Azimuth
Today I’d like to dig a little deeper into some ideas from Part 2. I’ve been talking about causal loop diagrams. Very roughly speaking, a causal loop diagram is a graph with labeled edg…| Azimuth
In Part 2, I explained some stuff you can do with graphs whose edges are labeled by elements of a rig. Remember, a rig is like a ring, but it might not have negatives. A great example is the boolea…| Azimuth
I’m talking about ‘causal loop diagrams’, which are graph with edges labeled by ‘polarities’. Often the polarities are simply $latex +$ and $latex -$ signs, like here: But p…| Azimuth
Last time I explained ‘causal loop diagrams’, which are graphs with edges labeled by plus or minus signs, or more general ‘polarities’. These are a way to express qualitativ…| Azimuth
This is a progress report on some joint work with Xiaoyan Li, Nathaniel Osgood and Evan Patterson. Together with collaborators we have been developing software for ‘system dynamics’ mod…| Azimuth
guest post by David Spivak • Part 1: The problem. Creating a knowledge network In 2007, I asked myself: as mathematically as possible, what can formally ground meaningful information, includin…| Azimuth
Agent-based models are crucial in modern epidemiology. But currently, many of these models are large monolithic computer programs—opaque to everyone but their creators. That’s no way to…| Azimuth
I learned a lot from the comments on Part 3 and also this related thread on the Category Theory Community Server: • Coalgebras, operational semantics and the Giry monad. I’d like to than…| Azimuth
By next summer I need to understand agent-based models well enough to help people design better software for such models using category theory. And recently this project has been folded into an eve…| Azimuth
I’ve been explaining our software for agent-based models based on stochastic C-set rewriting systems. But my only example so far has been the Game of Life, which is not what most people would…| Azimuth
Today I’d like to wrap up my discussion of how to implement the Game of Life in our agent-based model software called AlgebraicABMs. Kris Brown’s software for the Game of Life is here: …| Azimuth
Last time I began explaining how to run the Game of Life on our software for stochastic C-set rewriting systems. Remember that a stochastic stochastic C-set rewriting system consists of three parts…| Azimuth
We’ve been hard at work here in Edinburgh. Kris Brown has created Julia code to implement the ‘stochastic C-set rewriting systems’ I described last time. I want to start explainin…| Azimuth
Since May 1st, Kris Brown, Nathaniel Osgood, Xiaoyan Li, William Waites and I have been meeting daily in James Clerk Maxwell’s childhood home in Edinburgh. We’re hard at work on our pro…| Azimuth
Last time I presented a class of agent-based models where agents hop around a graph in a stochastic way. Each vertex of the graph is some ‘state’ agents can be in, and each edge is call…| Azimuth
Last time I presented a simple, limited class of agent-based models where each agent independently hops around a graph. I wrote: Today the probability for an agent to hop from one vertex of the gra…| Azimuth
Today I’d like to start explaining an approach to stochastic time evolution for ‘state charts’, a common approach to agent based models. This is ultimately supposed to interact we…| Azimuth
I’ve spent the last few weeks drawing pictures of tuning systems, since I realized this is a good way to show off their mathematical beauty. Now I’ll start deploying them! I’ve al…| Azimuth
guest post by David Spivak The problem The idea that’s haunted me, and motivated me, for the past seven years or so came to me while reading a book called The Moment of Complexity: our Emerging Net…| Azimuth
