Number as idea

One: the circle and the infinite

Tie a cord to the point and draw it taut. Call its length 1 — not one metre or one cubit, simply the unit, the measure against which all else will be spoken. Now swing it. The point it traces never leaves the centre's side, and yet it closes a perfect circle: an infinity of points, each in the identical relationship to the centre. Here is the first number and the first paradox together. The One is whole, without parts, and already it contains the infinite. Centuries later Pascal would describe nature as "an infinite sphere whose centre is everywhere and circumference nowhere."3 The circle is our first, disquieting hint that unity and the boundless are somehow the same thought.

The One is whole, and already it contains the infinite.

Two: the wound of the line

Now draw a line straight through the point and out past the circle on either side. With a stretched cord, with a straightedge, a line once begun runs without end in both directions. Something has happened that cannot be undone. Unity has been cut into a here and a there, a this and a that. The number two arrives heavy with everything that polarity will come to mean — self and other, light and dark, the ache of separation. The arithmologists did not celebrate the dyad; they mourned it a little. It is the first step away from home.1

Three: balance regained

Return now to balance. On the one circle, mark three points evenly and join them: an equilateral triangle, its corners just touching the circumference.5 Dwell there a moment. Three is the first figure that encloses a space, and the first that cannot be pushed out of true; the triad is gathered up and held inside the round whole that contains it. Three is the dyad reconciled — a third term that stands above the quarrel of opposites and holds them both in view. Of all numbers it is the nearest in spirit to the One: wholeness recovered on a higher plane.

Four: the square, and matter

Set four points on the same circle and close the square: the number four, and the signature of matter. The four directions, the four elements, the four-square solidity of the made world; the cross is its emblem. Set that square against the circle and you draw the oldest diagram of the human condition — Vitruvian man, the body reaching to touch both the squared earth and the round heaven, matter stretched toward the divine.9

This is the figure Leonardo drew for Luca Pacioli: the regular shapes nested in a single circle, each one touching the same circumference.10 Our small construction ends there too — circle, triangle and square gathered into the One that held them from the first. The point has unfolded into one, three and four, and folds back into the round whole it never really left.

And five? Five hides the golden cut inside the five-pointed star, and the Pythagoreans guarded it so closely that they made it their secret sign and swore never to set it down in writing — a number reserved, they felt, for those who sought union with the greater mind.1,7 That is too large a secret to unfold at the end of an essay; it deserves a page of its own, and will have one.

Why a builder begins here

None of this is decoration. To set out a building is to repeat the whole story in an afternoon: a point fixed, a unit chosen, a circle swung, an axis drawn, a square closed. The metaphysics and the method are the same gesture. Geometry, as Buhigas would say, is finally a way of seeing — and for us it is also a way of working, the reason the studio takes its name from an alignment.2 Every project still begins where this one did: with nothing, and then a point.