Now, to the craft. I have a many-coloured glass sphere made by a master glassblower. By design it is an ornament, in reality a superfluous object. Speckles of English red and sun-yellow, a translucent sphere – no, this is not a superfluous ornament after all, but a fragile scale model of our world. By virtue of his craft the glassblower can do what even the great mystics cannot: bend space. Mathematics and geometry, arm in arm with theoretical physics, strain to bend space, while the glassblower does it day after day. He mixes elements: he turns solids to liquid, adds air, gives it form, and the malleable matter sets solid once more. A veritable heir of the alchemists, but who knows, perhaps a genuine alchemist?
Now, to geometry. Two points are enough to mark out a line. This in itself is a magical act, for in this way what had not been before came to be. How the point, which has no extension, can nevertheless mark or define anything at all, how from one there are at once two points, and how together they can bring forth the line, an object that has one dimension yet cannot be grasped, remains a mystery.
If this line fixed by two points, or more precisely this segment, is broken once, nothing happens yet, but break it once more and join its starting point to its end point, and a new wonder comes forth, the triangle. Just as the line divides the plane into two halves, or, if you like, halves the universe, parting into two semicircles the great sphere of existence projected onto the plane, so the triangle folded from that line is bound by the same fact. The halved circle of existence is 360 / 2 = 180°, and the sum of a triangle's angles cannot be more than 180° either. Shall we resign ourselves to this geometric law, or shall we attempt the impossible?
Now, to the experiment. Take the next step! If you break your segment not twice but three times, at right angles, in equal divisions and in the same direction, you get a square. You need only double it, then turn one of the two by 45° about their centre, and there before you is an octagon, which is only a few steps from the circle. If you repeat the rotation over and over in tiny steps, the vertices of the squares mark out an infinite number of points on a circular arc, which is to say you have succeeded in making a circle out of the square. If you do not follow this laborious method but, instead of breaking your original segment, gently bend it, the circle comes forth all the same. Take the circle and turn it about one of its diameters: the sphere has come forth. Here too something new was born: first the point, existing without dimension, gave birth to the straight line, then the one-dimensional line to the two-dimensional plane figure, and then the plane figure to the harmonious geometric solid. We leap freely from one dimension into another.
Now, to bending space. Take your pliable triangle and gently smooth it onto the surface of your sphere. Another enchantment: the spherical excess is the amount by which the angles of a spherical triangle exceed 180°. Once the strict triangle is bent into space, the rules become flexible. The inner space of the sphere and the outer space presuppose each other, are distinct from each other, and yet cannot exist without each other. The sphere has no flat surface, it cannot be grasped… And yet you can hold this sphere that represents the universe in the hollow of your hand, O man. Perhaps the world, too, is a sphere in God's hand – this is simply the fact of love. Besides the great sphere of the world, the Sun, too, is a sphere, a light in the heavens. On the Sun, too, you will find no flat surface, and yet, when the Sun Gate opens, you can walk through it into the light.
Triangle, square, circle or sphere – shapes chasing one another, mystical figures. All is material, and yet gates open, dimensions become passable, and what had not been before comes to be. The triangle, the square and the circle united are the great Hermetic seal, the great work of union, which locks the secrets away from the uninitiated. Whoever possesses the three plane figures – the triangle, the square and the circle – has gained power over space and time, loosing and binding, outside and inside, straight and curved. Nothing is missing any more.