
Recent Posts
Archives
Categories
Meta
Author Archives: slehar
The InverseOptics 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 threedimensional model of the configuration of objects and surfaces in the external world that is most likely … Continue reading
Posted in Uncategorized
9 Comments
Let There Be Light!
Continuing from Chapter 5: RayTracing Algorithms Raytracing 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
Posted in Uncategorized
Leave a comment
RayTracing 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 raytracing applications that perform a very similar computational function. Figure 1 shows an example of a raytraced … Continue reading
Posted in Uncategorized
Leave a comment
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
Posted in Uncategorized
Leave a comment
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
Posted in Uncategorized
10 Comments
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
Posted in Uncategorized
1 Comment
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
Posted in Uncategorized
3 Comments
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
Posted in Uncategorized
Tagged Clifford Algebra, Geometric Algebra, stereographic projection
13 Comments
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
Posted in Uncategorized
3 Comments
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
Posted in Uncategorized
98 Comments