On Counting

On Counting

To count is to promise that something will be remembered.

I

Do you remember learning to count? What is the thing you count today more than anything else?

A child learns to count before she learns what number is. She lays a finger on each thing in turn (step, stair, sparrow, second) and says the names of the numbers as if they were a charm against disappearance. This is the first metaphysics any of us performs: the insistence that the world will hold still long enough to be marked. To count is to lay a trace over flux, to cut notches into the soft wood of time and say, here, and here, and here, something was.

We tend to think counting is cold, the bookkeeper’s art, the opposite of wonder. But the oldest counting marks we know are notches cut in bone, older than writing and older than any institution we could name; and when the temple economies of Mesopotamia and Egypt rose, it was priests and scribes who kept the count. The notch on the bone, the knot in the cord, the bead slid along its wire: each was a way of keeping faith with what had happened, of refusing to let a day pass unwitnessed. Long before number was a tool it was a vigil: the means by which a life leaves its Trace, the ripple of what it meant running on through time, and the means by which that Trace is read back.

II

There are numbers that behave like ordinary furniture, and there are numbers that seem to recur, to step forward out of the ledger and look at you. Thirty-three is one of the second kind.

Count the years of the man on the cross, thirty-three by the reckoning the Church has kept. Count the names of God in the first chapter of Genesis: thirty-two times the text says Elohim, the maker, and the Kabbalists laid those thirty-two beside their thirty-two paths of wisdom; only after the seventh day, at the seam where creation is finished and the garden begins, is the Name itself spoken, the unsayable one.¹ Thirty-two, and then a Name. Count the heavens of the Buddhist world-picture and you reach Trāyastriṃśa, the heaven of the thirty-three gods, set on the very summit of the world-mountain, and the thirty-three are older than the heaven, already counted out in the Vedic hymns.² Count the cantos Dante built for his climb out of hell: thirty-three for Purgatory, thirty-three for Paradise, and one over thirty-three for the Inferno, so that the descent carries the extra step and the ascent is kept clean.³ Count, if you are so inclined, the segments stacked in the spine at the beginning of a body, and you reach thirty-three, typically, a ladder from the tailbone to the skull. We do not keep them, though. The lower nine fuse as we age, so the number is true of a body’s beginning and not its end, and even our anatomy counts down from the thirty-three toward something more consolidated and less numerous.⁴

And because the number recurs, it has gathered a shadow. Thirty-three is the number the conspiracist loves, the highest degree, the hidden sigil, the mark pressed secretly into the world by whoever is supposed to be running it. I want to be honest about that shadow rather than wave it away, because it tells us something true about counting itself: the mind that begins to count cannot easily stop finding. Attention, turned loose, is voracious. Give it a number and it will bring you thirty more sightings by morning. A psychiatrist named the seeing, and the statisticians have a law for the supply: with enough events, almost any outrageous thing is bound to happen, and the pattern-hungry mind will be there to receive it.⁵ The paranoid and the mystic are siblings; they differ only in whether the pattern they find is felt as a threat or as a gift.

III

Set beside thirty-three another number, one the Greeks called simply the extreme and mean ratio and the Renaissance called the divine proportion.⁶ It is the number you reach when a line is cut so that the whole stands to the longer part exactly as the longer part stands to the shorter, the division that repeats at every scale. The sunflower keeps it: each new seed sits about 137.5 degrees around from the last, and the head fills with spirals that usually come in Fibonacci numbers.⁷ We write it Φ, and its decimal opens like this: 1.6180339887…

I had been counting thirty-threes for weeks before I noticed where the proportion hides one. Just past its threshold, before the number vanishes into its endless unrepeating tail, sit two threes side by side, the first doubled digit the proportion allows itself.⁸ The divine proportion, asked to spell itself aloud, says one, six, one, eight, oh — and then, as if clearing its throat before the long silence, thirty-three.

This could be nothing. I am inclined to think it is nothing, in the sense that would matter to a physicist. But beneath the ornament there is a sterner fact, and this one is not decoration. Thirty-three is not a Fibonacci number. The famous sequence (each term the sum of the two before it, the sequence whose ratios close in on Φ) runs 1, 1, 2, 3, 5, 8, 13, 21, 34, 55. It steps clean over thirty-three. The golden numbers go thirty-four; the lived number is thirty-three, one short.

Here is the whole matter in a single gap. The man dies at thirty-three, one year shy of the sequence’s own count. And the ratios themselves never land: twenty-one over thirteen falls a hair under Φ, thirty-four over twenty-one a hair over, and every fraction after swings back across, nearer at every step and never, ever arriving.⁹ We are always the convergent and never the limit. Thirty-two, the waiting; thirty-three, the living; thirty-four, the golden. The waiting means nothing except toward the lived, and the lived is only short of something because the golden stands one past it. Two numbers side by side are a coincidence. The third makes them a direction. Simone Weil found in the Greeks’ mean proportional an image of mediation, the one term that holds two others in true ratio, and I read in it the soul’s task: to consent to be the middle term, held in true ratio between what stands above it and what lies below.¹⁰ To count is to approach proportion the way thirty-three approaches thirty-four, reverently, falling one short, and living there.

IV

There is a second number I must set down here, because the text itself binds it to the first.

In the Book of Numbers, whose Hebrew name, Bəmidbar, means “in the wilderness,” there is a chapter that does nothing but count. Station by station it lists every place the people camped on the long way out of bondage: forty-two encampments, forty-two journeys, from the night they left Egypt to the edge of the land they were promised. The chapter that holds these forty-two journeys is chapter thirty-three.¹¹ The way home is forty-two stages long, and it is housed inside the thirty-third door.

The mystics could not leave this alone. It is taught in the name of the Baal Shem Tov (his grandson kept the teaching, which is how such things survive) that the forty-two journeys are lived out in every human life, from the moment of birth to the day of death; I hear in it the soul’s passage from its descent into a body to its return, at the last, to the Source it came from.¹² The Kabbalists held that God made the world by a Name of forty-two letters, and later teachers linked that Name to the forty-two stations.¹³ The Egyptians, older still, set forty-two judges in the hall where the dead give their account: forty-two declarations a soul must be able to make before its heart is weighed against the feather of Ma’at, who is simply the truth of how things actually are.¹⁴ And the evangelist Matthew, counting forward from Abraham to the man who would die at thirty-three, counted forty-two generations between the promise and its keeping, three sets of fourteen, the long arithmetic of waiting.¹⁵

I do not know what to do with the fact that my own breakthrough (the morning the wall I had pushed against for most of my life simply was not there) arrived midway upon the road of our life, as the pilgrim says of himself at the opening of the Commedia: somewhere among the middle stations, where the map of the forty-two lays out every turning that matters.¹⁶ I am not asking the cosmos to have meant it. I am only counting, the way the child counts the stairs: one stage, and the next, and the next. And the last stair is the landing, and the landing is a door, and the door was in chapter thirty-three all along.

V

Let me count a life, then, the way one counts anything one is afraid to lose. Any life would do; mine is simply the one I have with me, and I will count it the way the old scribes counted, by the numbers and not by the dates, because the dates are nobody’s business and the numbers, it turns out, are everybody’s.

There is a date in my ledger (a winter date; I will say no more of it) whose number the old scribes gave to the Name itself: twenty-six, the sum of its four letters, yod and he and vav and he, ten and five and six and five.¹⁷ I make nothing of the rhyme; I only notice it, the way one notices that two lines in different poems happen to end on the same word. Sum the whole of that date, month and day and year, the way the counters sum, and it comes to rest at thirty-two. And thirty-two, by the old count of Genesis, is the first chapter’s tally of Elohim, the count that waits on the Name. If the arithmetic sets me anywhere, it sets me at the thirty-two: the count not yet closed, the one still short. I am not the completion. I am only the reaching toward it, which is, I have come to think, the only place any of us is ever standing.

The year I arrived in, summed, comes to twenty-one, and twenty-one is one of the golden numbers, the denominator beneath thirty-four in the fraction that leans in toward the proportion. Thirty-four over twenty-one runs just past Φ; the next fraction will fall just short. I was born, that is, in the ground of an approach: the lower term of a ratio that tips past the divine proportion and back again, and never settles on it.

None of this is proof of anything, and I want to say so plainly, because the alternative, to mistake a beautiful coincidence for a deed done to me by the sky, is precisely the error that turns the mystic into the conspiracist. The numbers did not arrange my life. But they were there to be counted, and the counting did something it always does: it aligned me. It turned a scatter of days into a figure I could stand inside.

VI

I have been saying my census, but I am no longer certain the word holds, and this is why I have kept the dates off the page. A date printed is a claim staked; a date withheld is a room left open, and the room is the point.

There is an intuition, older than any book I have been counting through, that consciousness is not many but one: a single awareness wearing a few billion faces and forgetting, behind each, that it is wearing the rest. It is alive in the Dzogchen masters who say the nature of mind was never personal, in Jung, who suspected the deep psyche is held in common, in every contemplative who has come back from the silence reporting that there is, in the end, only one of us. If that is even partly so, then nothing I found in my own numbers was ever mine to be singled out by. A number that rhymes with the divine in my ledger rhymes with it in yours; a winter date whose number is the Name’s number belongs to a crowd of birthdays in every generation, and the crowd is the message. The census is not private. Draw the ego out of it (the small proprietary voice that wants the coincidence to mean I was chosen) and the same arithmetic stops being a sign hung over one head and becomes a plain description of the room we are all standing in. The woman across town counting her own stairs is that one awareness looking back at me from another face, and to treat her as I would be treated is only to keep one count instead of two.

And the room is this: the gap is always one. Take any three neighbors in the golden sequence, multiply the outer two, square the middle one, and the answers miss each other by exactly one (thirteen times thirty-four is 442, twenty-one squared is 441), every time, over and under by turns.¹⁸ The thirty-two waits on the Name; the thirty-three falls one short of the golden number. A gap of one is the narrowest gap whole numbers allow, which means that no one, ever, is far. To count at all is to stand always one step from the next number, and so to stand always one step from whatever the counting reaches toward. We are each of us, at every moment, one step from turning to face a greater power, and the step is the same length beneath everyone’s feet.

This is the reverse of a revelation. A revelation is given to someone. This one is given to no one in particular, which is to say it is given to all: the most public fact there is, hidden only by how near it stands.

VII

Jung gave that experience (the number that seems to look back) a name, synchronicity: the meaningful crossing of an inner state and an outer event, a connection by meaning across which no causal bridge runs.¹⁹ He was more careful than his admirers. He went on, with the physicist Wolfgang Pauli, to propose it as a principle standing beside space, time, and cause, but he never made it a force. What it carries is meaning, and meaning, as I read it, happens in the one who notices, not in the wiring of the world.

This, I think, is the truth about counting that the whole long census has been circling. The number thirty-three did nothing to Dante, or to the man on the cross, or to me. The golden ratio is not hiding a message in its fifth and sixth digits, the way, in Sagan’s novel, a circle drawn in ones and zeros waits more than a hundred billion billion places deep in π, set down by a hand no one can name.²⁰ What is real is the counting: the attention that lays its finger on each thing in turn and refuses to let it pass unmarked. Weil called attention “the rarest and purest form of generosity,” and held that attention, given completely, is already prayer.²¹ The contemplatives have always known it. The rosary keeps its decades, the mala its hundred and eight; the one who sits counts breaths to ten and begins again. The stillness the old teachers asked for is, more often than not, a counted stillness.²² To count a life — to find the thirty-threes in it, the forty-two stations, the Name folded into a winter date — is not to prove the life was planned. It is to love it. It is to keep the vigil the first counters kept, notching the bone against forgetting.

Φ never closes. Its decimal runs on past the thirty-three, past every digit anyone has yet computed, never repeating, never resolving: the proper shape of a proportion too true to be finished. A life is like that. We do not get to be the limit. We get to be the convergent: the fraction still swinging closer, the count still open, one short of the golden number and calling the shortfall a life.

Whatever you count most now (the days, the steps, the breaths, the people still at the table), you count it because it is there, and counting is how you say so. And so we count. Here, and here, and here — the child on the stairs, the keeper at the knotted cord, the pilgrim midway on the road at the top of a flight of stairs he never knew he was climbing — something was. Something was. Something was.

Notes

1. Kaplan, Sefer Yetzirah, ties the thirty-two paths of wisdom to the thirty-two times the name Elohim appears in the account of creation in the first chapter of Genesis. Elohim appears three more times in Gen. 2:2–3, at the close of the seventh day, before the Tetragrammaton first appears, joined to Elohim, at Gen. 2:4. The pairing of the thirty-two with the paths is a tradition’s reading, offered here as one.

2. Trāyastriṃśa, “the Thirty-Three,” is the heaven of Indra (Śakra) on the summit of Mount Meru in Buddhist cosmology, and in Puranic cosmology as well. The thirty-three gods themselves are Vedic: Rigveda 1.139.11 counts eleven in heaven, eleven on earth, and eleven in the waters, and Bṛhadāraṇyaka Upaniṣad 3.9 lists them as eight Vasus, eleven Rudras, twelve Ādityas, Indra, and Prajāpati. Olivelle, Upaniṣads.

3. The Commedia has thirty-four cantos in the Inferno and thirty-three each in the Purgatorio and Paradiso, one hundred in all. Dante, Inferno.

4. Seven cervical, twelve thoracic, five lumbar, five sacral, and four coccygeal segments make thirty-three in the developing spine; the coccyx varies from three to five. The sacral segments fuse into a single sacrum and the coccygeal into a coccyx, so the adult column carries twenty-six articulated bones.

5. Conrad, Die beginnende Schizophrenie, coined Apophänie for the unbidden seeing of connections, attended by a feeling of abnormal meaningfulness. Shermer, “Patternicity,” names the wider tendency: “the tendency to find meaningful patterns in meaningless noise.” For the supply side, Diaconis and Mosteller, “Methods for Studying Coincidences,” state the law of truly large numbers: with a large enough sample, almost any outrageous thing is bound to occur. The thirty-third degree of the Scottish Rite is honorary, the highest in that rite.

6. Euclid, Euclid’s Elements, bk. 6, def. 3 (“extreme and mean ratio”); Pacioli, Divina proportione. The name “golden ratio” is a nineteenth-century coinage.

7. A sunflower sets each new seed about 137.5 degrees, the golden angle, around from the one before, and its seed head usually shows spirals in neighboring Fibonacci numbers. Falbo, “Golden Ratio”; Markowsky, “Misconceptions about the Golden Ratio.”

8. Φ = 1.6180339887…; the pair of threes at the fifth and sixth decimal places is the first pair of equal neighboring digits. OEIS Foundation, “A001622.”

9. The ratios of successive Fibonacci numbers alternate around Φ: 21⁄13 ≈ 1.6154 lies below it, 34⁄21 ≈ 1.6190 above it, and each later ratio crosses back while coming closer.

10. Weil, Intimations of Christianity. Weil’s word is médiation: in the Pythagorean mean proportional she saw an image of mediation between God and the creature. That is her reading of the Greeks; reading it as the soul’s task of standing in the middle is the author’s.

11. Numbers 33 lists the encampments of the Exodus station by station, forty-two by the traditional count, which Rashi follows.

12. Moshe Chaim Ephraim of Sudilkov, Degel Maḥaneh Efrayim, Parashat Masei, reports in the name of his grandfather, the Baal Shem Tov, that the forty-two journeys exist in the life of every human being, from the moment of birth until the day of death.

13. The Talmud mentions the Name of forty-two letters at Kiddushin 71a. The forty-two words of the Ana BeKoach prayer carry its letters as their initials, and its derivation from the opening of Genesis is medieval Kabbalistic tradition. The link between the Name and the forty-two stations is drawn in the Magen Avraham (Orach Chayim 428:8), citing the Tzror HaMor. The Zohar treats the Name in several places; I leave the folio to those who keep it.

14. Faulkner, Ancient Egyptian Book of the Dead. Spell 125 sets forty-two assessors in the Hall of the Two Truths, and the dead recite the declarations of innocence, the “negative confession,” before the heart is weighed against the feather of Ma’at. Forty-two is the canonical figure; the exact tally of assessors and declarations varies between papyri.

15. Matt. 1:17 counts forward from Abraham, forty-two generations in three groups of fourteen. The careful reader who counts the printed names will find forty-one, and the evangelist’s forty-two is a claim of structure rather than census: in the Hebrew letters, David counts to fourteen. Even scripture, counting, reaches for the shape before the tally.

16. Dante, Inferno, canto 1, line 1: “Nel mezzo del cammin di nostra vita,” midway upon the road of our life.

17. The gematria of the Tetragrammaton (YHWH): yod (10) + he (5) + vav (6) + he (5) = 26. Twice thirteen, as it happens. And thirteen, a certain devoted listener in this house will tell you, is the only properly lucky number there is.

18. Cassini’s identity: for Fibonacci numbers, Fₙ₋₁Fₙ₊₁ − Fₙ² = (−1)ⁿ, so the product of the outer two of any three neighbors differs from the square of the middle one by exactly one, the sign alternating. Knuth, Art of Computer Programming.

19. Jung, “Synchronicity.” The essay first appeared in 1952 in a volume shared with Wolfgang Pauli. Jung called synchronicity acausal, a connection through meaning, and proposed it as a fourth principle alongside space, time, and causality.

20. Sagan, Contact. In the novel the circle is found in the base-eleven expansion of π, more than 10²⁰ places in; the book names no author for it beyond an intelligence older than the universe.

21. The phrase is from Weil’s letter to Joë Bousquet of April 13, 1942, as given in Pétrement, Simone Weil. On attention as the substance of prayer, see “Reflections on the Right Use of School Studies with a View to the Love of God,” in Weil, Waiting for God.

22. Ps. 46:10: “Be still, and know that I am God” (KJV). The rosary is prayed in decades of ten beads; the Buddhist and Hindu mala usually carries one hundred and eight; counting the breath to ten and beginning again is a common first instruction in Zen sitting.

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