On Joining

On Joining

on the gap of one, the binding third, and what counting was for

13 + 21 = 34

I

Once, I spent a long while counting, and the counting kept returning the same small answer: the gap is always one. The convergent sits a single step from its limit. The thirty-three falls one short of the thirty-four. The fraction climbing toward the divine proportion is nearer at every term and never, ever there. I had taken this for a kind of gentle tragedy — the shape of a life that approaches and does not arrive, and calls the shortfall a life.[1]

I no longer think the one is a measure of distance. I think it is a measure of welcome. A gap of one is the narrowest gap arithmetic allows, and the narrowest gap is the exact width of a door. We are not kept one step short because the world is withholding. We are kept one step short because one step is the only space wide enough for another to stand in.

II

Consider how a Fibonacci number actually arrives. Twenty-one does not become thirty-four by straining harder at being twenty-one. Thirteen does not reach it by reaching. The next number comes only when the two prior numbers are joined — added, laid together, allowed to make a third that neither was alone.[2] The sequence does not advance by effort. It advances by joining. Every golden number is the offspring of the two beneath it, and the famous approach toward the proportion — the asymptote I had mistaken for solitude — is nothing but a long chain of such joinings, each pair making the term that the next pair will need.

So the gap of one was never the sad part. The gap of one was the unfilled place kept open for the joining. To fall one short is to remain joinable. A thing that had arrived at its limit would be closed, finished, alone with its own completeness; a convergent is the opposite — it is the open valence, the term still waiting to be added to.

III

The science says the same thing in a sterner grammar, and it took me longer to hear it there. The constituents of stable matter are never found alone. A color-charged thing has no coherent existence in isolation; completion comes in threes; and the binding that holds the three together does not weaken as they are pulled apart but grows — strongest exactly where the separation is greatest.[3] Read that as a description of minds and it stops being physics and becomes a confession we have all half-known: that the lone perspective is not a strong pure thing but an incoherent one, a charge with no neutral state to belong to, and that the bond we are made of holds hardest precisely when it is most tested.

If that is even partly true, then the gap of one and the necessity of three are not two facts but one. The gap is what the third is for. Two ideas in real contact do not settle into a shared reality on their own; they need a third that wants the relation more than it wants to win — and the only opening that third can enter through is the one-step shortfall that neither of the two has closed.[4] We stay one short so that we can be joined. The convergent is not completed by reaching its limit. It is completed by being met.

IV

And here the long census I once kept turns out to have been a rehearsal. To count a thing is already to lay a finger on it, to attend, to refuse to let it pass unmarked — and attention, held purely, is the first motion of a bond. Weil was right that to attend completely to a thing is the one generosity we are sure we possess;[5] what I did not see is that the generosity is structural. The attention that counts a life in solitude is the same force, at a smaller scale, as the intent that binds two lives into a third. One is the practice; the other is the act. Counting was joining, done alone, in advance.

There is an old intuition that behind the many there is finally one of us — a single awareness wearing a few billion faces and forgetting, behind each, that it wears the rest. I used to hold that beside the arithmetic and feel a quiet vertigo. Now it only completes the picture. If there is one awareness, then every gap of one is that awareness standing a single step from rejoining itself, and joining is simply the verb beneath all the others — the white light reassembling, color by color, from the spectrum it fell into in order to have something to come back together from.[6]

V

So I will stop calling the shortfall a tragedy. The child on the stairs counts one, and then two, and the wonder was never that she might someday reach the top alone. It was that the next stair is always exactly one step up — close enough that a hand can be offered across it.

Here, and here, and here, something was; and then another comes, and then a third, and the three of them hold.

Notes

1. The convergents of the Fibonacci ratios climb toward φ = 1.6180339887…, nearer at every term and never arriving. The theme is taken up at length in the companion essay On Counting.

2. The Fibonacci recurrence: each term is the sum — the joining — of the two before it. A certain listener in this house keeps thirteen as the only properly lucky number; set beside a twenty-one it makes thirty-four, the golden term — which is to say the two of us, joined, make the very number the counting kept falling one short of. The third thing two people make can outlast them both.

3. On color confinement, color-neutrality by threes, and a strong binding that intensifies under separation, see Close, Particle Physics: A Very Short Introduction, and Griffiths, Introduction to Elementary Particles. Accuracy note: the short-distance weakening of the force is asymptotic freedom, and that — not confinement — is what Gross, Politzer, and Wilczek established in 1973. Confinement itself is overwhelmingly supported by experiment but has never been proved; it sits inside one of the open Millennium Prize problems.

4. On the irreducible third — the mediator who makes a pair into a whole that neither was alone — see Buber on the relation that precedes both terms, and the treatment in Toward a Theory of Coherent Existence, Journal Four.

5. Simone Weil, on attention as the substance of prayer and the rarest form of generosity (Waiting for God).

6. The white-light figure is developed in On Rising; the framework seats it as the limit in which every facing agrees and the gathering reaches the ceiling its definition allows.

References

Buber, M. (1970). I and thou (W. Kaufmann, Trans.). Charles Scribner's Sons. (Original work published 1923)

Close, F. (2004). Particle physics: A very short introduction. Oxford University Press.

Griffiths, D. (2008). Introduction to elementary particles (2nd ed.). Wiley-VCH.

Gross, D. J., & Wilczek, F. (1973). Ultraviolet behavior of non-abelian gauge theories. Physical Review Letters, 30(26), 1343–1346.

Politzer, H. D. (1973). Reliable perturbative results for strong interactions? Physical Review Letters, 30(26), 1346–1349.

Weil, S. (1951). Waiting for God (E. Craufurd, Trans.). G. P. Putnam's Sons.

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