...I saw a small iridescent sphere of almost unbearable brightness. At Þrst I thought it was spinning; then I realized that the movement was an illusion produced by the dizzying spectacles inside it. The Aleph was probably two or three centimeters in diameter, but universal space was contained inside it, with no diminution in size. Each thing (the glass surface of a mirror, let us say) was inÞnite things, because I could clearly see it from every point in the cosmos.       JORGE LUIS BORGES "The Aleph" 3

THE PHYSICAL ELEMENT

MILLENNIUM SPHERE

AS DETAILED IN THE ENGINEERING SPECIFICATIONS, the capsule itself will consist of a titanium sphere from 8 to 27 cubic feet, hermetically and permanently sealed with a single circular seal of minimum length, compatible with the objects to be deposited in it. The sphere diameter would therefore vary between 30 and 45 inches, depending on its capacity. For esthetic and cost reasons we recommend the smaller sphere.
      We have chosen titanium as the best material fulÞlling the speciÞcations, but to us, the millennium has come too quickly. For to pay it homage, neither gold, bronze nor platinum, stone nor marble, not even titanium (the bronze of the modern age), but metallic glasses, "translucent like opal, iridescent like butterfly wings," could adequately encapsulate the wonder of The Millennium Sphere.
      The capsule is the core of The Millennium Sphere. The Millennium Sphere would extend around the core to a diameter of 10 to 12 feet. This surrounding sphere would be made up of titanium elements welded together, forming geometric patterns and anchored on the core sphere by means of radial titanium rods.
      We have chosen the Platonic solids - the four-sided tetrahedron, the six-sided cube, the eight-sided octahedron, the twelve-sided dodecahedron and the twenty-sided icosahedron - as the fundamental geometry of these patterns. Although instrinsically beautiful, these Þgures link us through Plato - one of the key Þgures in Western thought - to the most ancient intellectual tradition on the one hand, and to the most recent thinking on the other; they are applicable to the cellular structure of viruses, to engineering construction and to many other applications. The study of Platonic solids constituted the apex of Euclidean geometry. It also formed the basis of scientiÞc and philosophical speculation from the Greeks through the Renaissance and beyond. It is through their use, for instance, that Kepler determined the orbits of the planets - within a remarkable precision of 10% of present Þgures. They also served from Plato on, and probably before, to symbolize the ancient elements of Earth, Water, Air and Fire, and the quintessence identiÞed by some to Space.
      The fact that Platonic solids are Þve in number and represent the only way in which Euclidean space can be evenly divided into 4, 6, 8, 12 and 20 equal parts is highly signiÞcant. It is a reminder, as we watch the center point exploding - so to speak - in this multiplicity of equalities, that diversity springs out of unity in the outward thrust of creation; that literally, "the same was in the beginning." Therefore, the human task is, through personal and collective inner evolution, to return to unity, to recognize and realize the primordial unity in the diversity of creation, articulating and making practical the motto E pluribus unum, not only politically, but socially and spiritually.
      The little-known fact that the entire geometry of the Platonic solids results, like the natural musical scale, from the simple ratios of the Þrst three whole numbers - one, two and three - is of such elegance that it is a perpetual source of wonder and deserves to be better appreciated. As shown on the models, the ratios 1/1, 1/2, 1/3 and 2/3 give rise in turn to the octahedron, the icosohedron, the cube and tetrahedron and Þnally the dodecahedron. These numbers, and none others, are needed to account for the fundamental shapes from which all others are derived. Is it therefore as casually as it seems that, at the opening of the Timaeus, Plato has Socrates ask: "One, two, three, but where my dear Timaeus is the fourth?" And that in the Republic he qualiÞes arithmetics as "the little matter of distinguishing one, two and three?"
      SigniÞcant also in this context is that, starting with the geometric point as origin, the Platonic solids constitute Þve steps towards the complete sphere which, becoming the seventh step, links them as in a musical scale in an octave progression. Their imbrications give rise to geometric Þgures of great beauty. Triangles, squares, pentagons, hexagons, ogives, mandorlas and stars to be found in the entire tradition of sacred geometry spill out as of a kaleidoscope of forms, a matrix or generatrix of abundance from which the whole architecture of the Cathedral springs. It is a visual Bach fugue of incredible resonance - our Visual Offering to a rising Millennium.
       Furthermore, a simple rotation of each Platonic solid traces the exponential growth spiral of its own development. The concept of evolution, so clearly apparent in the spiral and one of the great achievements of human thought in biology, Þnds therefore its natural expression in the geometry of The Millennium Sphere.
      The accounts of these remarkable relationships and their ensuing constructions will form part of a publication that will trace the history of the whole project, the philosophy and mathematics that inspired it, and the artistic considerations that informed it.
      As briefly mentioned earlier, the symbolism in terms of the ancient elements of Earth, Water, Air, Fire and Space, as well as in terms of the cosmos, is a powerful feature uniting ancient knowledge to present knowledge, to the architectural setting of its location and to perennial philosophy, strongly binding through multiple links The Millennium Sphere and its capsule core to the cultural memories of our civilization.
      The Millennium Sphere, shimmering in the penumbra of the nave, hanging from three braided cables reminiscent of the three qualities of nature of Hindu philosophy, or the Trinity of Christian theology, or the helix of the dna molecule, is also symbolic of the Clew of thread Ariadne gave Theseus to extricate himself from the labyrinth. That is indeed why we chose the labyrinth as a marker for The Millennium Sphere, in the middle of the nave. And this in turn links us, through the tradition of the labyrinth, to the great cathedrals of Northern Europe, and to Daedalus and the mythical beginnings of architecture.
      To ensure a greater probability of remembrance of The Millennium Sphere and of its capsule-core over the course of the millennium, we are planning not one but three of them, each to be placed in a different location within one of the traditional elements.
      The "main" one - The Millennium Sphere as described above and itscore-capsule - would be hanging in air in the nave over the center of the labyrinth. (A subsequent section addresses the labyrinth design.) A second sphere, made up of the capsule but without the superstructure of The Millennium Sphere and simply having the patterns of the Platonic sphere engraved on it, would be buried in earth, deep to the bedrock in the cathedral garden. Its site would be marked by a garden labyrinth basically following the same pattern as the one inside the nave.
      A third would be placed in the crypt of the cathedral under a slab of granite or other igneous rock, symbolizing Þre. The design of this sphere would be similar to the one placed in the garden and the slab would bear an engraved image of the labyrinth.
      Records of these emplacements, like all records pertaining to the capsule, would be kept securely in tight boxes in at least three locations: one under the central medallion of the nave labyrinth to be opened every Þfty years, a second in the archives of the cathedral, and a third in the archives of the Cooper Union or of the institution which may succeed it.