5/18/2025 at 10:09:10 PM
Clearly a labor of love. Props to youI suppose if one is teaching or evangelizing constructor theory, this could be sort of like an interactive textbook
Needless to say, constructor theory hasn't really earned a stable foothold in mainstream physics, and there's a lot of hype in this space, but that's not a criticism of this particular project, just good to know for anyone not familiar
The quantum gravity + graviton tasks stuff especially. without a falsifiable physical model backing it, this can feel like mathematized cosplay. But that has more to do with constructor theory vs this project
Would love to see someone do a pluggable backend so you could test different "task ontologies" against each other.
Mainly I came here to say that categories can likely be used to great effect here a la Geroch
For instance you can start by modeling tasks as morphisms between substrate states (objects), and then enforce composition explicitly. define constructors as functors that map tasks and substrates while preserving structure.
for quantum or irreversible effects, use monads to encapsulate branching and decoherence. Then one could represent task sequences as categorical diagrams and check for commutativity. Or embed substrates via Yoneda to expose behavior in terms of available tasks
by canvascritic
5/19/2025 at 9:40:54 AM
https://arxiv.org/abs/2401.05364>In this work, we show how to formulate fundamental notions of constructor theory within the canvas of process theory. Specifically, we exploit the functorial interplay between the symmetric monoidal structure of the category of sets and relations, where the abstract tasks live, and that of symmetric monoidal categories from physics, where concrete processes can be found to implement said tasks.
by Xmd5a
5/18/2025 at 11:17:53 PM
This is very helpful and insightful. Thank you!by SandroG