Geometric Algebra for Data Science: A Manifesto
Welcome to the Geometric Learning Series
If you work in Data Science, Econometrics, or Machine Learning, you speak a specific mathematical language: Linear Algebra. You think in scalars, vectors, matrices and tensors. You optimize dot products, wrestle with determinants, and struggle to visualize high-dimensional spaces.
But if we are honest, standard Linear Algebra has deep cracks in its foundation when applied to modern data problems.
We rely on “hacks” and simplifications that obscure the true structure of our data:
The Scalar Trap: Why do we treat a feature like “Square Footage” as a scalar number, when semantically it is a distinct direction in space?
The “Black Box” of Econometrics: We run Cointegration tests and PCA, but do we understand the geometry of what those tests are actually measuring?
The Rotation Problem: Why is rotating a neural network embedding so difficult, requiring expensive orthogonalization constraints?
The Blind Spot: Why does “Correlation” only measure if variables move in a line, completely missing circular (lead-lag) relationships?
We believe the answer lies in a mathematical framework that has been waiting in the wings for decades: Geometric Algebra (GA).
The Mission
We are embarking on an open-ended project to rebuild the Data Science stack from first principles.
We are not just writing a few tutorials. We are going to revisit every major concept—from simple Linear Regression to Deep Graph Neural Networks—and ask a simple question:
“What does this look like if we treat Data as Geometry?”
We will discover that:
Probability is actually Volume.
Correlation is actually just the shadow of a Bivector.
Neural Networks are actually Coordinate Transformers.
Economic Stationarity is actually Subspace Stability.
The Philosophy: “Pragmatic GA”
Geometric Algebra is often sold as a “Theory of Everything” for physics. It is usually taught with abstract axioms, dense notation and software libraries that don’t integrate with modern tools.
We are taking a different path.
We are GA Pragmatists:
No Custom Libraries: We will not ask you to install slow, object-oriented GA libraries. We will use standard NumPy and PyTorch.
Intuition First: We focus on the geometric intuition and the code, not just the proofs.
Real-World Application: We bridge the gap between abstract math and real-world implementation in high-dimensional vector spaces.
The Roadmap
Because this field is vast, we will explore it through five parallel tracks. We will interweave these topics, building a comprehensive guide to Geometric Data Science.
🔹 Track 1: Foundations
Redefining the atomic units of computation.
We start by escaping the “Scalar Trap.” We will redefine vectors, introduce the Wedge Product (the missing operator for Area) and the Geometric Product (the master algorithm that unifies geometry).
🔹 Track 2: Geometric Statistics
Redefining descriptive statistics.
We show that statistical moments are geometric shapes. We will re-derive Linear Regression as a geometric projection and reveal how Geometric Covariance captures relationships that standard correlation misses.
🔹 Track 3: Geometric Econometrics
Analyzing how geometric objects move and evolve over time.
A deep dive into Time Series. We will show how Cointegration, Impulse Responses and Dynamic Models are best understood as rotations in phase space, offering new ways to detect “Lead-Lag” relationships in markets.
🔹 Track 4: Classical Machine Learning
Visualizing algorithms as geometric operations.
We will look at classic algorithms like SVMs, Clustering and Feature Selection through a geometric lens, using “Information Volume” to detect multicollinearity.
🔹 Track 5: Deep Geometric Learning
Building networks that preserve symmetry and structure.
The cutting edge. We will build Rotor Layers (that rotate without stretching), Geometric Attention mechanisms (that attend to orientation), and loss functions that optimize manifolds directly.
Join Us
Whether you are an Econometrician trying to visualize VECM models or a Deep Learning practitioners building the next Transformer, this series is for you.
We are about to give you a new set of eyes for your data.
Next Up: We start at the very beginning.
Post 1: The Great Embedding — Escaping the Scalar Trap.