PARDESCO
Ana & Kata: A Journey Through Higher Dimensions (e-book)
- Pages
- 395 (6 × 9 inch PDF)
- Chapters
- 32, in six parts
- Illustrations
- 38 full-page colour plates and 34 diagrams
- Companion
- 31 'Try it' exercises in the free viewer at 4d.pardesco.com
- Free sample
- Part I, 85 pages
- Delivery
- One PDF (about 12 MB), emailed right after purchase
$12.99
Instant PDF download by email · 395 pages · free Part I sampler below.
Instant delivery · non-refundable once delivered
A guide to the fourth dimension, for anyone curious
A cube has six square faces. A tesseract, its four-dimensional cousin, has eight cubic cells. Nobody can see one, but mathematicians have drawn, sliced and rotated them for 170 years. This book shows how, and follows the idea of higher dimensions through mathematics, physics, art, stories and philosophy.
The title comes from Charles Howard Hinton, who named the two directions of the fourth dimension ana and kata, the way we say up and down.
Read Part I free: the introduction, the reading guide and chapters 1 to 5 (85-page PDF).
Six parts, 32 chapters
- Learning to See: Flatland's Square and the Sphere; counting up from point to tesseract; shadows and slices; why a left glove can't be turned into a right one; what life in four dimensions would be like
- The Invention of Higher Space: the old arguments that there is no fourth dimension; quaternions; Riemann's 1854 lecture; Schläfli's six regular polychora; the 120-cell and 600-cell; Hinton's cubes
- Strange Spaces: the shape of the universe; inside-out worlds and the Klein bottle; why four dimensions is the odd one out; the paradoxes of high dimensions; fractal dimensions; infinitely many directions; data as space
- Time and Hidden Dimensions: when time is (and isn't) a fourth dimension; time travel and its paradoxes; why we have three; hidden dimensions in physics; the holographic universe
- Ghosts, Art, and Stories: the Victorian séance-room fourth dimension; Cubism and Dalí; the tesseract in fiction
- Mind and Meaning: whether a brain can learn to see in 4D; the high-dimensional brain; the speculative frontier; where the 600-cell lives
Pictures you can trust
The 38 full-page plates and the polytope diagrams were rendered with the 4D Polytope Engine, our Blender add-on, from the real four-dimensional coordinates. Each plate is an exact symmetric view, and its caption names the shape. Thirty-one "Try it" boxes send you to the free viewer at 4d.pardesco.com to turn the same shapes yourself.
Honest about the evidence
Every factual claim falls into one of three tiers: established, contested or speculative. The wording tells you which one you are reading. Popular myths about the fourth dimension are named and corrected in the text, speculative ideas are labelled as speculation, and the book makes no health or wellness claims. It uses the same standard as our Essence of Sacred Geometry e-book.
Common Questions
The fourth dimension and higher dimensions for a general reader: how mathematicians picture shapes they cannot see, where the idea came from, how physics uses (and does not use) extra dimensions, and what the idea has done in art, stories and philosophy. No maths beyond school level is assumed.
395 pages in 32 chapters and six parts, with 38 full-page colour plates of four-dimensional polytopes and 34 diagrams. Thirty-one "Try it" boxes send you to the free 4D viewer at 4d.pardesco.com to rotate the shapes yourself.
Yes. Part I (the introduction, the reading guide and chapters 1 to 5, 85 pages) is a free PDF download.
Every factual claim is sorted into one of three tiers, established, contested or speculative, and the wording tells you which you are reading. Popular myths are corrected in the text, and the book makes no health or wellness claims.
Every polytope image is rendered in Blender with the 4D Polytope Engine, our add-on: each shape is rotated in four dimensions and projected into 3D. Nothing is drawn by hand or generated by an AI image model.
A PDF (6 × 9 inch pages, about 12 MB) that reads on any phone, tablet or computer. A secure download link is emailed right after purchase and stays valid for 72 hours; if it expires, email us and we will send a fresh one.
Digital download only · No physical items shipped · PDF delivered by email immediately after purchase