The sphere stands with its bottommost point resting exactly on the origin, and the six full axes — bearing the ordinals D₅ through D₁₀ of the dimensions they await — pass through that point. Their positive halves rise into the sphere’s interior at one and the same opening — forty-five degrees from the vertical, since a chord from the bottom point to the equator subtends, by the inscribed angle, exactly half of ninety — and they are turned evenly about the vertical at sixty degrees apiece. Every positive axis therefore terminates on the same latitude line, the equator, drawn in gold: the six tips stand evenly distributed around that circle as a regular hexagon, and the six chords are all equal, each the radius times √2. The negative halves mirror below the origin into the second container, forming the downward cone of the figure: a bow tie made whole in three dimensions, two cones meeting at the tangent point of the two spheres. The frame stands ready to be given its meanings.
Within the container a second sphere now stands, grey and solid, four-fifths the size of the first, its bottommost point resting on the very same origin. The animation shrinks it uniformly to a very small sphere — and throughout the shrinking its bottom point never leaves the origin: the center descends exactly as the radius falls, so the whole family of spheres it passes through are tangent to one another, and to the container, at the single shared point. One consequence follows from the inscribed-angle law already at work in the figure: since a ray from the tangent point at forty-five degrees cuts any sphere tangent there at that sphere’s own equator, the six axes cross the shrinking sphere always upon its equator — a hexagon whose side is its current radius, sliding down the six chords as the sphere descends toward the origin.
The axes are now given their meanings: the six compact dimensions of string theory, the coordinates numbered here X⁵ through X¹⁰ — the fifth through the tenth, standing beyond the three of space and the fourth that time, on this account, is. The shrinking of the grey sphere is compactification drawn as an act — a space contracting below sight while never leaving the point it touches — until what remains at the middle is the particle. When the sphere reaches its smallest, the tour begins: each axis is lit in its own color, its ordinal receiving its coordinate — D₅ becoming X⁵ — and annotated with what that direction does to the particle at the center — the quantized momentum of the small circle, the winding of the string and its T-duality, the shape that writes the couplings, the sizes that set the forces, the holes that count the generations, and the twist of holonomy that spares exactly the right supersymmetry.
One honesty the figure owes the theory: in string theory the six are not six separate straight lines but one small curled space — a Calabi–Yau shape of three complex pairs — attached perpendicular to large space at every point. The six axes display its six real directions separately for the graph’s sake, and the six annotations distribute among them, one strand apiece, properties that in truth belong to the shape as a whole. So read, the figure joins the corpus’s dimensional account: the compact dimensions are the perpendicular made permanent — directions standing at right angles to the whole of visible space, too small to travel, large enough to legislate.
A second containing sphere now hangs directly opposite the first, anchored at the very same origin: its topmost point is the tangent point, and it covers the lower halves of the axes exactly as the upper sphere covers theirs — by the same inscribed-angle law the six negative rays terminate upon its equator, a second regular hexagon mirroring the first. At the end of the series the reading pauses for a hand: a click, and the particle closes from its smallness to a point. From that same point Metatron’s Cube then opens — thirteen circles and the seventy-eight lines joining all their centers — lying flat and horizontal, dropping as it expands. Its proportions are bound to the frame: because the axes open at forty-five degrees, the six lower rays pass through a horizontal ring whose radius equals the depth, and since the six outer circles’ centers stand at four-fifths of the figure’s radius, holding the plane at a depth of four-fifths keeps every outer center riding its own axis at every instant of the growth — until the centers dock precisely upon the six tips of the lower equator, and the Cube comes to rest in the lower sphere’s equatorial plane: the figure in which the outlines of the regular solids are traditionally read, unfolded where the particle vanished and carried down by the dimensions themselves. Above, the six compact dimensions; below, flat within their mirrored ring, the opened form.
The diagram now reads in full. The containing sphere and the shrinking sphere are the three dimensions of space — and the small positive triad standing on the tangent plane between the two containers is their legend: x, y, and z, the familiar three, drawn once in a single octant, never passing below the plane, referring the eye to the upper sphere it explains. The fourth dimension is not drawn as a line at all: it is the time of the animation itself — the duration through which the figure moves is the axis on which it moves, exactly as the dimensional account holds. The six axes are therefore the fifth through the tenth, the compact six, and the tour shows how each affects the particle. The sequence is the argument entire: space compactifies to the particle; the particle, read through its six hidden dimensions, closes to a point; and from that point the full dimensional space, represented by the material cube, unfolds from within, flat upon the mirrored ring below. What implodes above unfolds beneath — the point is not an end but a hinge.