4 TRICAP
2Using the vast, water-smoothed surface of the many-miles-long sandy beach, and walking along as she talks, Goldy keeps drawing pictures large enough for the bears to see. Goldy says to the bears, ‘‘Let’s try an experiment with our tetrahedron.’’
3 By pushing successively on the tetrahedron’s top vertex, Goldy keeps rolling the tetrahedron ahead of her across the beach. This succession of rollings makes a long, parallel-edged ribbon with a line zigzagging between its edges to produce a succession of adjacent triangles.
4 Goldy says to the bears, ‘‘We have discovered a triangularly subdivided ribbon-printing machine---a wave-printing machine.’’ And Daddy Bear says, ‘‘That is also the sand print patterning made by our four (A, B, C, D) bear’s feet when we are running. We can start our run with our right hind foot D elevated. We then lunge forwardly over the hinge line running between our two front feet C, D, as foot A goes forwardly and down while foot B is elevated. Because a bear’s foot is itself a triangle, Goldy makes a pattern of Big Sky Bear’s footprints as he walks or runs eastwardly along the beach. Goldy uses the successive triangles as the frames for the succession of illustrations of her conversation with the bears. She says the ribbon is like a scenario filmstrip with the successive triangular pictures overlapping instead of being vertically separated.
6 Using the vast, water-smoothed surface -of the many-miles-long sandy beach, and walking along as she talks, Goldy keeps drawing pictures large enough for the bears to see. The pictures illustrate each of her experimentally demonstrated explanations. She is recounting to the bears what humans have thus far learned regarding the principles employed by Scenario Universe to accomplish its eternal regeneration.
7 Goldy says to the bears, ‘‘Let’s try an experiment with our tetrahedron. Let’s see what happens if I use three of its four corners, A, B, C, representing you three bears, as the tetrahedron’s base on the sand---because you have been together for billions of years---and corner D, which is the newcomer me---Goldy---I put at the top of the tetrahedron. Now I am taking hold of my corner D at the top and am rolling it over around its bottom edge BC until corner D lies down in the sand, pointing in an easterly direction to my right, along the beach.’’ This rolling leaves the triangular print ABC in the sand westward, to Goldy’s left, where the tetrahedron had been sitting before that first rollover. Goldy now takes hold of corner A, which rose from the sand base to replace D at the tetrahedron’s top. She pushes the new top corner A again over and downwardly to her right around edge CD, which means farther eastwardly along the beach until/! hits the beach, as corner B rises to take the top corner place of the tetrahedron, leaving a second triangular print BCD in the sand with its edge BC congruent with BC of the first printed triangle ABC. She now pushes top corner B eastward, rolling it over and down around bottom edge DA, which brings corner C to the top and leaves a third successive triangular print CD A. She next rolls top corner C eastward over bottom edge BA to leave a fourth successive print DAB, making an altogether eastwardly developing ribbon of triangular prints. Goldy then pushes top corner D, then successively tops A, B, C, D again and again, as each rotates to the top to replace the one Goldy last rolled over and downward, eastwardly to her right. By pushing successively eastward the tetrahedron’s successively latest top vertex, Goldy keeps rolling the tetrahedron ahead of her along the beach. This succession of rollings makes a long parallel-edged ribbon with a line zigzagging between its edges to produce a succession of adjacent triangles. One of the ribbon’s edges reads successively AC, AC, AC, AC, while its other edge reads BD, BD, BD, BD. The succession of eastwardly occurring tops reads D,A,B, C, D, A, B, C, D, and so on.
8 Goldy says to the bears, ‘‘We have discovered a triangularly subdivided ribbon-printing machine---a wave-printing machine.’’ And Daddy Bear says, ‘‘That is also the sand print patterning made by our four (A, B, C, D) bear’s feet when we are running. We can start our run with our right hind foot D elevated. We then lunge forwardly over the hinge line running between our two front feet C, D, as foot A goes forwardly and down while foot B is elevated.’’
9 Because a bear’s foot is itself a triangle, Goldy makes a pattern of Big Sky Bear’s footprints as he walks or runs eastwardly along the beach. Goldy uses the successive triangles as the frames for the succession of illustrations of her conversation with the bears. She says the ribbon is like a scenario filmstrip with the successive triangular pictures overlapping instead of being vertically separated. ‘‘You may notice,’’ says Wee Bear, ‘‘That the starry pattern of the chair Cassiopeia left for me looks like the first three triangular frames of that scenario filmstrip.’’ ‘‘Yes,’’ Goldy replies, ‘‘and I see that if I print these triangular frames of the scenario strip of overlapping conceptual events on a heavy paper ribbon, the strip can be spooled onto a tetrahedron. This will make a tetrahedron book that can be progressively unrolled from a tetrahedron at one end and rerolled to form another tetrahedron at the other end of the strip, with the progressively exposed strip in between telling the picture story---the scenario---of ‘‘nonsimultaneous universe,’’ with both the four-dimensional tetrahedronal othernesses scrolls of tomorrow and yesterday as yet unrolled or already rolled back in, and therefore consciously and directionally identifiable but inscrutable. Because the tetrahedra are serving as four-dimensional scrolls, we will call our first such book The 4D Tetrascroll.