Journey 4 of 10 · 11 steps
The Plane Rises
Every flat figure is a view of a solid
Tilt your head off the page. Each sacred figure turns out to be a slice or a shadow of a shape in space, and it grows out of the plane before your eyes.
In the app each step moves: figures draw themselves, rise from the page, turn and slice, and the narration can be read aloud. Here they are held still, one picture each.
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Step 1 · The Monad
The circle and the sphere
A circle is what a sphere leaves on a plane that passes through its middle. Turn off the page and the sphere rises around its own equator.
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Step 2 · Vesica Piscis
Two spheres
The two circles of the vesica are equators of two spheres, each passing through the other’s centre. In space their overlap is a lens, and they meet in a ring.
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Step 3 · Seed of Life
Halfway
Stop halfway and you can see both at once: the flat Seed of Life lying inside thirteen spheres, twelve gathered around one.
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Step 4 · Flower of Life
The Flower is a packing
The Flower of Life is one layer of the densest way to stack oranges. Kepler guessed it was the densest in 1611. It took until 1998 to prove.
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Step 5 · Torus Yantra
The torus
Circles that all pass through one centre are the equators of spheres that all touch it. Together they carve a horn torus, the shape with no hole left in its middle.
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Step 6 · Hexagram
A shadow, not a slice
Some figures are shadows. The six-pointed star is the silhouette of two interlocked tetrahedra, the star tetrahedron, seen straight down one axis.
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Step 7 · Golden Spiral
A shell
Give each quarter-turn of the spiral a body that grows by φ and it becomes a shell. The flat spiral is its exact middle slice.
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Step 8 · Chladni Figure
A singing cube
A Chladni plate is one face of a vibrating cube. Every face carries its own sand figure, and they meet along the edges.
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Step 9 · Sri Yantra
The mountain in the yantra
The Sri Yantra is also a view from above. Raise each ring of triangles into a terrace and it becomes Maha Meru, the cosmic mountain, with the bindu at its summit.
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Step 10 · Metatron’s Cube
Metatron in space
Lift the thirteen centres into the sphere packing and the 78 lines follow them. The flat figure was always a view of this. Try any figure in Explore
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Step 11 · Tree of Life
The Tree stands up
The Tree of Life fixes where each sefirah stands across the page but not how deep. Stand it up with the outer pillars set back and its three triads become perfect equilateral triangles, while face on it is still the flat Tree.