What This Visualization Shows

This data visualization displays "A plot of algebra space; the related algebras that come out of simple seed algebras. It likes to hug the walls. [OC]" and provides a clear visual representation of the underlying data patterns and trends. The visualization focuses on First things first, don't take this post too seriously. At the end of the day I'm just messing around, and sharing... to reddit. Oh god.

I thought it would be fun to make AI try to "solve" a hard problem, and I choose 3x3 matrix multiplication. I have no idea what it's doing. I am not a mathematician. I am watching it go brrrr

Quick note: I use use many AI across many instances and architectures, and I am the human in the loop orchestrator, but I will refer to this as "the AI" since LLMs are doing the heavy lifting, and I'm just going along for the ride like a messenger boy.

This is the best I can articulate what it is (or what *it thinks* it is) doing:

* I started by getting it to build the ADE (algebra discovery engine), designed to generate novel algebras. * It ran that and looked for known algebras to pop out as benchmarks. Things like the Cayley-Dickson tower were apparently produced unprompted, and many quaternion and octonions-like things. * After that we scanned the algebra space using gradient descent methods with random seeds. * Every result is logged to a database, and "isomorphisms" are checked to make sure they aren't the same algebra in disguise. * Then it seeded algebra multiplication, the M(3, R). One interesting algebra M(3, R) has an associator defect of 1.0, which I am told is weird. * At this point it's doing alot test of the most novel algebras. Mostly null results, but some new leads. About 10 hours of computation on a Ryzen 9 5900X yields about 700 "novel" algebra, and about 30 M(3, R) flavour ones. * We also have a system where novel results are backfed as seeds for the next round of exploration

So yeah, that's what I've been up to this week. I don't really know what it's doing, I wanted to share the pretty data, and it's fun as hell 😈, which allows us to understand complex relationships and insights within the data through visual storytelling.

Deep Dive into the Topic

This data visualization represents a sophisticated analysis of complex information patterns that provide valuable insights into underlying trends and relationships. Data visualization serves as a bridge between raw numerical data and human understanding, transforming abstract statistics into comprehensible visual narratives.

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Data Analysis and Insights

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Significance and Applications

This data visualization has important implications for understanding trends and patterns that affect decision-making across multiple sectors. The insights derived from this analysis can inform policy development, business strategy, resource allocation, and operational improvements.

For analysts, researchers, and decision-makers, this type of data visualization provides essential insights for strategic planning and performance optimization. Whether addressing operational challenges, market analysis, or policy development, understanding data patterns helps create more effective strategies and solutions.

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