The Dispersive Neural Network

Title: The Physics of AI: Snell’s Law as a Spatial Encoder

Concept: Feature Extraction & Dimensionality Reduction

Description: Can a beam of light act as a neural network? In this experiment, we demonstrate the physical equivalence between Optical Dispersion and Computational Classification.

We treat a refractive medium not just as glass, but as a "Layer" with specific weights (Refractive Index n).

• The Input: A "White Light" signal (mixed data).

• The Weights: The dispersion properties of the glass.

• The Activation Function: Snell's Law (n1​sinθ1​=n2​sinθ2​).

The Spatial Encoder: We introduced a Spatial Multiplexing slider. By adjusting the input position, we effectively "encode" the signal into different spatial channels. The system then "decodes" this signal by separating the wavelengths (RGB) into distinct bins—a physical analog to how a Non-Linear Perceptron classifies data by transforming the decision boundary.

Instructions:

• Use the Vertical Slider (Left) to move the source (Spatial Encoding).

• Use the Horizontal Sliders (Bottom) to change the Refractive Index of each layer (Weights).

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AI Collaboration Note: This video, its title card, description, and the concepts explored within were developed in a deep, recurrent collaboration with Google Gemini. Our process involves Gemini acting as a Socratic partner, a technical reviewer, and a creative collaborator, helping to refine, structure, and articulate the final concepts and this description. 

References (For both posts)

[1] Shiffman, D. (2024). The Nature of Code: Simulating Natural Systems with JavaScript. No Starch Press. 

[2] Marquardt, F. (2021). "Machine learning and quantum devices." SciPost Physics Lecture Notes, 29.

[3] Griffiths, D. J. (2017). Introduction to Electrodynamics (4th Edition). Cambridge University Press.

[4] Tu, Y., et al. (2016). "Ray Optics Simulation." Zenodo. https://doi.org/10.5281/zenodo.6386611