Category Archives: Uncategorized

The Inverse-Optics Problem

Continuing from Chapter 6: Let There Be Light! Visual perception is a constructive, or generative function that interprets the visual stimulus by constructing a three-dimensional model of the configuration of objects and surfaces in the external world that is most likely … Continue reading

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Let There Be Light!

Continuing from Chapter 5: Ray-Tracing Algorithms Ray-tracing algorithms highlight the vital importance of lighting to the interpretation of a scene, whether it be the stark bright light of the sun, the more diffuse glow of the blue sky, indirect light … Continue reading

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Ray-Tracing Algorithms

Continuing from Chapter 4: The Language of the Mind The computational function performed by mental imagery can be better understood by comparison with computer ray-tracing applications that perform a very similar computational function. Figure 1 shows an example of a ray-traced … Continue reading

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The Language Of The Mind

Continuing from Chapter 3: Amodal Perception Images are the primary language of the mind. We think and imagine in terms of scenes and views of objects and events that we conjure into existence and examine from different angles, testing in our … Continue reading

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Amodal Perception

Continuing from Chapter 2: The Schema As A Mental Image Amodal perception was first discovered as a property of perception, where it occurs so unconsciously and effortlessly that we tend not to notice it at all. For example if we … Continue reading

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The Schema As A Mental Image

Continuing from: Chapter 1: The Perceptual Origins of Mathematics The schema, it seems, is a kind of mental image. But what is mental imagery? There has been considerable debate in the literature over whether mental images even exist as actual … Continue reading

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The Perceptual Origins of Mathematics

Mathematics is a strange and wonderful mystery, that grows more strange and wonderful the more we learn about it. Our first introduction to mathematics in school is through arithmetic,  a pragmatic system of accounting and quantification,  first developed for applications … Continue reading

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Geometric Algebra: Conformal Geometry

This is the third and final chapter in my Visual Introduction to Clifford Algebra, following on from Chapter 2 on Projective Geometry in Geometric Algebra. In Chapter 2 we showed how the perspective projection provides a wonderful means for projecting an … Continue reading

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Geometric Algebra: Projective Geometry

The first chapter in this series, Clifford Algebra: A Visual Introduction, presented a brief history of the incremental discovery of algebra, culminating in the discovery of Clifford Algebra, the algebra that subsumes them all, because Clifford Algebra is not just another … Continue reading

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Clifford Algebra: A visual introduction

Clifford Algebra, a.k.a. Geometric Algebra, is a most extraordinary synergistic confluence of a diverse range of specialized mathematical fields, each with its own methods and formalisms, all of which find a single unified formalism under Clifford Algebra. It is a unifying … Continue reading

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