What's this all about?

This is Residuated, an aperiodic periodical exploring the mathematics of periodicity feeling around the edges of the under-appreciated geometry of modular arithmetic.

Launched in 2023 (after fermenting for many years) with the aim of sharing some amusingly absurdist and hopefully intriguing research. The ideas cut across a variety of disciples, bridging concepts from number theory, mathematical logic, computer science, information theory and the like to tangible mathematical entities; occasionally making contact with real world phenomena from chemistry and physics; and some light quantum stuff.

While these explorations invariably end with far more questions than answers, it's great fun none the less. And often leads to useful pedagogical insights for those of us chasing a deeper understanding. Occasionally, we may even shed new light on some very stubborn old conjectures.

The subject matter may seem a bit esoteric at times, but it should be mostly self-contained, and usually shouldn't require much beyond basic middle school mathematical knowledge to follow along. And a large dose of mathematical curiosity.

If these kinds of questions are interesting to you, you’re in the right place.

Are there more of us out there?

Do subscribe if you're into this kind of thing, and chime in on the discussions. It helps to know you're not shouting into a complete void. And it'll certainly light a fire under my ass to get more of this work cleaned up and published.

You'll be joining an extremely niche community of folks that share a peculiar combination of overlapping interests. To be honest, I can't imagine there are that many of us. But wouldn't it be cool to connect with a small group of other folks that geek out about obscure number systems, or the vagaries of mathematical physics?