“Coincidence and Randomness, The Architecture of Pattern”. A new essay has been added to SUPPLEMENTS.

“We live within a vast ‘ocean’ of randomness, navigating our way by the ‘islands’ of order we discover—and sometimes create—within it.”

Cultivating Perceptual Reasoning Through Altair Designs

As a response to a reader’s question, please see a short article, GO TO THE SUPPLEMENTS PAGE, about Altair as a means to cultivate perceptual and adaptive reasoning. My involvement with what later became known as Altair Designs began in 1968, while working in London with Dr. Ensor Holiday. The initial impulse arose from a […]

From Sunflowers to God’s Divine Architecture of Life.

In response to questions from readers of the “Visual Thinking, Seeing Through Time” book series (ebook and print formats) I’ve added a SUPPLEMENTS page to this website. This is the first! “From Sunflowers to God’s Divine Architecture of Life.” This supplement relates to Book 1, Chapter 5, Ancient Egypt. It also covers Book 2, Chapter […]

Explore Visual Thinking Through Time

Overview Visual Thinking, Seeing Through Time is a five-book series. It explores the development of visual logic from archaic humans through early civilizations. It continues into the age of artificial intelligence. The series examines how visual‑cognitive structures shape human reasoning across the arts. These structures affect architecture and geometry. This reveals deep connections between perception, culture, […]

Launch of ‘Visual Thinking’: Five Books on Art and Geometry

“Visual Thinking, Seeing Through Time” is a five-book odyssey through the human experience in Architecture, the Arts, and Geometry from the dawn of consciousness to the frontiers of artificial intelligence.

Altair Designs and Jules Bourgoin. Bridges MathArt 2025.

Jules Bourgoin was a master of Early Islamic visual logic.

Presentations & Workshops

PRESENTATIONS WORKSHOPS

FIRE ALTARS OF THE VEDAS – A LOGICAL PUZZLE FROM ANCIENT INDIA

“3D Thinking” Pages 67 to 72: Vedic Fire Altars present a logical puzzle for those building them. Firstly, the surface area has to be in direct proportion to the height of the individual whose task it is to construct the altar. Secondly, there is to be a precise alignment of the altar with the four […]

PATTERNS OF PERCEPTION

“3D Thinking” Pages 22, 292: Patterns of Perception follow a methodology that has been applied through time from antiquity to the present. The first books to appear that feature “perceptual lattices” are books on designs developed during the early Islamic period – in the middle-east, north Africa, and in Moorish Spain. References are Jules Bourgoin […]

Altair Design – Page Update

Have updated the Altair design page with a new animation that shows the logic of how the designs are generated plus how the designs themselves can be perceived – with imagination, with logic, with creativity.