Second edition · 2026

Motion:The Fourth Spatial Dimension

4D Geometry does not need to represent an abstract, unreachable space still taught about today. It is simply the geometric trace of 3D forms as they move through spacetime.

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Paperback & Kindle · ISBN 979-8-1953-2627-2

The claim

We do not need to discover a fourth spatial dimension. It is the ever-moving world we already live in.

The thesis

Not time alone.
Not an unreachable space.

What if the fourth dimension isn’t simply time, or some extra direction at right angles to length, width, and height — but something we experience in every moment?

Stuart Hood reads Charles Hinton’s tesseract against Minkowski and Einstein: the new “four-dimensional edges” of 4D polytopes do not demand a hidden fourth perpendicular axis as still commonly taught about today. Instead, they describe a spacetime axis of motion traveled by three-dimensional forms as they move.

From there the book climbs: force as a fifth spatial capacity, enabling 5D geometry to describe the intricacies of the physical universe. Then a step into consciousness, where possibility is a 6D world of alternate realities, and finally into speculation of intelligence as a 7D system.

Existential Capactities as Geometric Dimensions

03Form

The still object — length, width, height. The cube before it moves.

04Motion

The spatial history of that object through spacetime. The tesseract as the trace of a cube's motion.

05Force

Motion affected. Energy and matter itself as the fifth capacity — a push that changes the path.

06Possibility

A constellation of states beyond the single worldline.

07Intelligence

Selection among those states. The intricacies and algorithms of reason, choice and will being developed artificially today.

Inside the book

01 A Dynamic Visualization Ch. 1
02 The Mathematics of Motion Ch. 2
03 Laws of Motion Ch. 3
04 Time Ch. 4
05 The Fifth Dimension: Force, A Matter Manifest Ch. 5
06 The Sixth Dimension: Possibility, Beyond Space Ch. 6
07 The Seventh Dimension: Intelligence Ch. 7

Research

The paper behind the book.

The geometric argument is also available as an independent research paper on SSRN — a tighter statement of the claim that four-dimensional figures are motion-histories of three-dimensional forms.

Four-Dimensional Geometry as the Motion History of Three-Dimensional Forms

Read the SSRN paper

A visual introduction

4D geometry as spacetime maps of motion.

Author

Stuart Hood

Stuart Hood is an independent researcher and writer in British Columbia. A lifelong student of mathematics, geometry, and the philosophy of science, he has worked with form in the places it actually shows up — programming, design, and the skilled trades.

MOTION began as a private astonishment: that the standard story of the fourth dimension still asks us to imagine an axis we can never enter, while the moving world is already drawing that figure in front of us. The book is the public version of that thought.

Second edition