The jötunn who personified the sea and hosted feasts for the Æsir
A self-paced curriculum for learning the mathematical foundations of concept spaces and variational reasoning — toward building physics-inspired AI memory and reasoning systems.
What if reasoning paths through concept space followed the principle of least action? What if concepts emerged from experience rather than being predefined? What if justification was intrinsic to the geometry rather than external metadata?
This curriculum builds the mathematical foundation to explore these ideas.
# Clone and enter
cd ~/Documents/Projects/aegir
# Install dependencies (requires uv)
uv sync
# Launch JupyterLab
jupyter lab
# Start with notebooks/00-setup/00-environment-test.ipynbaegir/
├── wiki/ # Primers on core concepts
├── sources/ # Curated reading list
├── syllabus/ # Week-by-week curriculum
├── notebooks/ # Hands-on learning (Jupyter)
├── lib/ # Reusable Python code
├── data/ # Sample data
└── experiments/ # Research logs
| Week | Topic | Milestone |
|---|---|---|
| 0 | Onboarding | First embedding visualization |
| 1 | Foundations | Gradient descent from scratch |
| 2 | Embeddings | Mini Word2Vec working |
| 3 | Information Theory | Compute MI between clusters |
| 4 | Clustering | Name emergent concept clusters |
| 5 | Dynamical Systems | Visualize attractor landscape |
| 6 | Variational Calculus | Derive shortest path |
| 7 | Differential Geometry | Compute geodesics on sphere |
| 8 | Geometric Deep Learning | Build simple GNN |
| 9 | Integration | Working concept space prototype |
| 10 | Experiments | Research results |
ADHD-Optimized
- Micro-modules (30-45 min each)
- Visual progress tracking
- Quick wins early
- Interleaved theory/practice
Hands-On First
- Every concept → immediate code
- Never more than 10 min reading before doing
- Visualize everything
Build Toward Something Real
- Not academic exercises
- Culminates in working prototype
- Designed for multi-source RAG integration
- Python fluency
- Basic familiarity with linear algebra/calculus (we'll refresh)
- Curiosity about the nature of concepts and reasoning
We're building toward a system where:
- Concepts emerge from density in embedding space
- Salience creates a potential field that shapes attention
- Reasoning is movement through this space
- Paths minimize an action functional (least effort + maximum relevance)
- Justification is intrinsic — the path exists because it's optimal
Think of it as Lagrangian mechanics for thought.
See sources/ for the full reading list. Key resources:
- 3Blue1Brown - Linear algebra, calculus intuition
- Strogatz - Nonlinear Dynamics and Chaos
- Bronstein et al. - Geometric Deep Learning
- Raschka - Build an LLM from Scratch
MIT