Mathematics is not confined to textbooks—it lives invisibly in the fabric of perception and cognition. From the moment light enters the eye to the mind interpreting scenes, mathematical principles govern how we see and think. This hidden language reveals itself through luminance and illuminance, the geometry of refraction, and the brain’s probabilistic reasoning—all unified by elegant equations and statistical logic.
Luminance and Illuminance: Measuring Light as Mathematical Data
At the core of visual perception lies the quantification of light. The unit lux—lumens per square meter—translates luminous flux into measurable surface exposure. This conversion is not poetic; it is mathematical precision translating physics into data the brain interprets. Using lux, we transform abstract photons into meaningful signals: a dimly lit room registers lower lux values, dampening visual clarity and attention. Conversely, bright environments with high lux enhance focus, showing how mathematics turns light into actionable insight.
Mathematical modeling allows us to simulate real-world lighting conditions. By applying integrals over surfaces and angles, we predict visual clarity and guide design—whether in architecture or digital interfaces. Ted uses lux values dynamically, encoding how light intensity shapes perception, revealing vision not as mere sensation but as calibrated measurement.
Refraction and Geometry: Snell’s Law as the Optics of Thought
Light’s path bends at interfaces—a phenomenon described by Snell’s Law: n₁sin(θ₁) = n₂sin(θ₂). This equation bridges angles and media, enabling precise modeling of the eye’s optical system. The cornea, lens, and vitreous humour act as refractive media, focusing light onto the retina with geometric precision. But Snell’s law does more than explain vision—it empowers simulations where varying media distort or sharpen visual input, demonstrating how mathematical symmetry creates clarity or blur.
Ted’s visualizations illustrate how refractive paths shape perception, transforming abstract optics into interactive insight. By mapping light through layered media with Snell’s law, he reveals how the brain interprets retinal images—often corrected by neural “software” that compensates for optical imperfections.
Bayes’ Theorem: Updating Beliefs with Light and Uncertainty
Visual perception thrives on ambiguity—shadows, occlusions, partial views. The brain resolves this through Bayesian inference, formalized by P(A|B) = P(B|A)P(A)/P(B). Here, prior knowledge (A) blends with sensory evidence (B) to update beliefs—much like solving a visual puzzle with incomplete clues.
In everyday vision, this means your brain combines stored knowledge of objects with current light cues to “fill in” missing details. When fog obscures a face, Bayesian reasoning helps you recognize it anyway—using math to resolve uncertainty. Ted models this process interactively, showing how Bayesian updates turn noisy input into coherent understanding, from pixel data to confident perception.
Ted: A Modern Illustrator of Mathematical Cognition
Ted’s creative work encodes light intensity (lux), refraction (Snell’s law), and inference (Bayes) into dynamic, interactive models. Each math principle translates directly into perceptual experience: lux values shape visual clarity, Snell’s law simulates optical distortion, and Bayesian logic drives decision-making under uncertainty.
Through Ted’s lens, math ceases to be abstraction—it becomes the invisible structure guiding vision and thought. His work invites exploration: not just seeing light, but understanding the equations behind each detail.
Beyond Basics: Deeper Mathematical Threads in Visual Intelligence
Mathematical vision extends beyond basic optics and statistics. Topology explains how light propagates continuously across surfaces, preserving visual continuity—even when parts of a scene fade. This underpins how we perceive edges and motion without gaps.
Information theory further refines perception by quantifying noise. The brain compresses visual data using entropy principles, discarding redundancies while preserving key details—an elegant balance of compression and fidelity.
Perhaps most profound is the role of recursive math in adaptive learning. Neural networks and cognitive models use feedback loops and iterative updates—mathematical recursion—to improve visual recognition over time, mirroring how the mind learns from repeated exposure. These layers reveal vision as a dynamic, self-correcting system governed by deep mathematical order.
Explore the Hidden Structure—See Math in Action
Discover how Ted transforms abstract equations into living visuals at Psychedelic Colossal Spin—where math meets perception in real time.
| Section Luminance & Lux—Quantifying Light | Light measured in lux (lumens/m²) translates luminous flux to surface exposure, enabling measurable visual clarity. |
| Section Refraction & Snell’s Law—Geometry of Light Paths | Snell’s law (n₁sinθ₁ = n₂sinθ₂) mathematically models eye optics, simulating how media like cornea and lens focus light. |
| Section Bayes’ Theorem—Inference from Uncertainty | P(A|B) = P(B|A)P(A)/P(B) models how the brain updates beliefs using light evidence and prior knowledge. |
| Section Ted’s Model—Math as Perceptual Architect | Ted’s interactive design encodes lux, refraction, and Bayesian inference, revealing math as the hidden structure of vision. |
| Section Beyond Basics—Topology, Entropy, and Recursion | Topology ensures visual continuity; information theory reduces noise; recursion enables adaptive learning—deep layers of computational thought. |
“Math is not the language of science—it is science made visible, shaping how we see, think, and interpret the world.”