The census of presence and absence

Why this is worth reading

Almost everything written about personality typing describes what the types are. Very little describes what a typing method does when you run it on everything it can accept — how often each answer comes up, whether the answers are evenly reachable, and whether the instrument has a shape of its own that the reader ought to know about.

That is what this is. We took the calculator that runs on this site and put every valid calendar date through it, then counted. Not a sample, not a survey, not a selection of interesting cases: every date. What came back was more interesting than we expected, and some of it argues against things this school had been saying.

Three reasons it is worth a reader's time even if they never use this method:

• It is fully checkable. The code is on the page, the run is fifteen lines, and anybody can reproduce every number here in about a minute. Almost no claim in this field is checkable in that way, and that is not a small difference.
• It contradicts a widely repeated belief. The claim that Nines are the most numerous type is common enough to be treated as background knowledge. In this method, nine is the least available number of the nine, in every century tested, without exception.
• It shows an instrument's own fingerprint. The method has a measurable bias toward low numbers, and we can prove it comes from calendar arithmetic rather than from anything about people. Being able to say that about your own tool is rarer than it should be.

The run, at a glance

What	Figure
Dates put through the calculator	219,146 (1600–2199, every valid day, leap years included)
Core reporting span	47,482 dates, 1900–2029
Independent cross-check	47,847 dates, 1880–2010 — an earlier internal census, reproduced exactly
Distinct sequences produced	15,229 across the core span
Numbers per sequence	2 to 9, mean 6.03
Most available number	1, present on 89.51% of dates — six-century run
Least available number	9, present on 53.96% — six-century run
Channel with no bias at all	the digital root — 11.11% for each of the nine
Time to reproduce	about a minute, with the page source

The rest of this paper is what those figures mean, what they change, what they cannot tell you, and where we got one of them badly wrong before getting it right.

Method

Every valid calendar date from 1 January 1900 to 31 December 2029 — and, for the stability check below, from 1600 to 2199 — was passed through the live calculator, vn9-calc.js — the same code that runs on the public calculator, not a reimplementation. That is 47,482 dates, leap years included. For each one we recorded the sequence returned, its length, which of the nine appeared, and which led.

Two things this sample is not. It is not a sample of people: birth rates are not uniform across days, months or years, so the population figures for living people would differ somewhat from the calendar figures here. And it is not a claim about anybody's psychology — it is a description of what the instrument does, which is a prior question and a necessary one.

How many numbers a sequence carries RECORD

The estimate under test was two or three up to four or six present. The engine returns a wider spread than that, centered higher.

Exact engine output · 1900–2029

Six active types is the center of the distribution.

Bar length is scaled to the most common result. Labels report the exact share of dates.

1. 2 types0.02%
2. 3 types0.72%
3. 4 types5.89%
4. 5 types24.02%
5. 6 types36.90%
6. 7 types24.85%
7. 8 types7.00%
8. 9 types0.59%

Sequence length	Share of all dates	Numbers absent
2 numbers	0.02%	7 absent
3 numbers	0.72%	6 absent
4 numbers	5.89%	5 absent
5 numbers	24.02%	4 absent
6 numbers	36.90%	3 absent
7 numbers	24.85%	2 absent
8 numbers	7.00%	1 absent
9 numbers	0.59%	0 absent

Mean length 6.03. Nearly six dates in seven produce five, six or seven numbers. The tails are real but thin: a sequence as short as two occurs on 0.02% of dates — about one date in five thousand — and three-number sequences on 0.72%. All nine surface on 0.59%, roughly one date in a hundred and seventy.

So the working picture holds, including at the bottom: sequences really can be as short as two or three, which is where Vecnine’s stated estimate began. What the run adds is the shape of the middle — six is the single most common length, and the distribution is tighter than an estimate would suggest, with 85.8% of all dates landing on five, six or seven.

The result nobody was looking for RECORD

We recorded which of the nine appeared, expecting a spread. This is what came back.

Availability by number · 1900–2029

The calculator has a visible low-number tilt.

These are shares of dates, not shares of personality and not estimates of type prevalence in people.

1. Type 190.19%
2. Type 287.74%
3. Type 377.57%
4. Type 461.66%
5. Type 559.68%
6. Type 659.30%
7. Type 757.75%
8. Type 854.99%
9. Type 953.66%

Number	Present	Absent
1	90.19%	9.81%
2	87.74%	12.26%
3	77.57%	22.43%
4	61.66%	38.34%
5	59.68%	40.32%
6	59.30%	40.70%
7	57.75%	42.25%
8	54.99%	45.01%
9	53.66%	46.34%

The nine do not appear equally often, and the gradient is orderly: 1 surfaces on 90.19% of dates, 2 on 87.74%, 3 on 77.57%, then a long shallow slope from 4 at 61.66% down to 9 at 53.66%. Nothing is universal and nothing is rare. But a one is well over three times more likely to be absent from a nine than a one is — 46.34% against 9.81%.

The same tilt shows in what leads: 1, 2 and 3 each lead about 13% of the time, 4 leads 11.8%, and 5 through 9 each lead 9.86%. So a low number is somewhat more likely to head a sequence and considerably more likely to appear in one at all — but it is a tilt, not a rule, and no number is guaranteed a place in anybody.

Every number leads at least 9.8% of the time and none leads more than 13.1%. If you are looking for a headline: low numbers are more available, not more important. Availability is an arithmetic fact about how dates reduce. Importance would be a claim about people, and this run does not make one.

Why this happens, as far as we can currently establish READING

This is not mysterious, and it is not a flaw that was hidden. It follows from the arithmetic, and the arithmetic is published on the method page.

The rights-holder's account of it is the correct one and it generalises further than the arithmetic we first reached for: to arrive at a higher number you pass through the lower ones, so the lower ones get counted more often. Every source feeding a sequence is a cycle reduced to a single digit, and none of the cycle lengths is a multiple of nine, so every one of them wraps and hands the surplus to the low end.

The channels show it separately and consistently. Days run 1–31: three full passes through nine, then 28, 29, 30 and 31 land again on 1, 2, 3 and 4 — so the day channel gives 1, 2 and 3 about 13% each against 9.9% for 5 through 9. Both zodiacs run on twelve: nine, then 10, 11 and 12 fold back onto 1, 2 and 3, giving those roughly 16-17% against 8.2-8.5% for the rest. The digit-total of a date runs 4–48, so its tens digit is 1, 2 or 3 on 96.55% of dates. The only channel with no tilt at all is the digital root itself, which sits at exactly 11.1% for all nine — a clean ninth each, because that one is a true reduction with nothing left over.

That is not a candidate explanation any more. Separating the channels and finding the tilt in every cyclic one and in none of the non-cyclic one is the isolation that was missing. The gradient in the census is an arithmetic consequence of reducing cycles of 31, 12 and 12 into a base of 9. What remains genuinely open is not the mechanism but its meaning, below.

Is it a defect? READING

Not obviously, and we are not going to pretend to have settled that here. Two readings are live and they lead in opposite directions.

• The tilt is real information. If the low numbers are genuinely more available in human structure, and the calendar reflects that rather than causing it, then the gradient is telling us something and the weights are right to carry it.
• The tilt is a fingerprint of our own arithmetic. A 31-day month and a 12-sign year are conventions. If the gradient is only the residue of dividing those by nine, it says nothing about people, and the source weights should be adjusted to flatten it.

We do not know which is true, and nothing in this run can settle it, because a census of dates cannot tell you about people. The calibration study is the thing that would. Publishing before knowing is deliberate: a finding that only appears once it flatters the method is not a finding.

Is nine the commonest type, or the rarest? RECORD

There is a claim you hear in Enneagram circles that Nines are the most numerous type, sometimes stated as though it were established. We had no position on it and no way to test it directly — but this run answers a narrower question that bears on it, and the answer is unusually clean.

Rank the nine by how often each surfaces in a sequence at all, and the order is perfectly monotonic:

9 < 8 < 7 < 6 < 5 < 4 < 3 < 2 < 1

Nine is the least available number in the entire method — 53.66% of dates, against 90.19% for one. Not by a hair: a 1 is present in nine sequences out of ten and a 9 in barely more than half. And there is no exception anywhere in the ordering; every step down from 1 to 9 loses a little more ground.

The rights-holder's instinct about this was that it had to be so, and for a reason worth stating in his terms: this is arithmetic, and to arrive at nine you pass through the numbers below it — there are eight chances to land somewhere else first. The precise mechanism is the wrap described above, but the intuition points at the right thing. In a system built by reducing cycles into a base of nine, the top of the base is the position with the fewest ways of being reached.

What this does and does not say about the community claim

It does not refute it, and we are not going to pretend that it does. Those two statements are measurements of different things by different instruments:

• The community figure, where it exists at all, comes from self-report — people taking questionnaires and being sorted, or practitioners recording what they typed. It describes a population of respondents.
• Ours comes from arithmetic on dates. It describes what our method makes available, and says nothing directly about how many people are anything.

What is fair to say is that the two cannot both be straightforward descriptions of the same population. If Nines are the most numerous people and the least available number in our arithmetic, at least one instrument is measuring its own construction rather than the world, and ours is as likely to be the one at fault.

A candidate route to over-producing Nines, set out properly

There is a specific mechanism by which a self-report instrument could inflate the Nine count, and it is worth stating in full rather than gestured at, because a half-stated mechanism is an excuse rather than a hypothesis. The candidate is that a substantial share of self-typed Nines are Twos who cannot yet see their own pride.

Consider what a questionnaire actually asks and what an unexamined Two would truthfully answer. Do you put others before yourself? Yes — and that reads as self-forgetting. Do you have difficulty standing up for yourself? Yes — and that reads as conflict-avoidance. Are you easy to get along with? Yes — agreeableness. Do you often not know what you want? Yes, because a Two's own wanting is repressed out of view rather than absent. Four items, four honest answers, and a Nine profile assembled out of a Two's structure. Nothing in that sequence requires anyone to lie.

The items that would separate the two positions are precisely the ones this failure mode makes unanswerable. The useful discrimination is not a single behavior such as keeping a ledger. It is the organizing field. A Nine hypothesis predicts repeated loss of mobilizing force for the distinct self inside continuity, comfort, routine, or other people’s priorities. A Two hypothesis predicts heightened relational-value tracking: who needs whom, where one is especially giving, desirable, perceptive, important, central, or hard to replace. A ledger can occur, but so can open entitlement, boasting, possessiveness, disdain, generosity with no conscious accounting, or genuine humility mixed with a claim to special relational value. Pride here retains its ordinary possibilities of self-elevation and superiority while also describing the more relationally organized forms. The calibration study should therefore test motive and organization rather than assume that either type must endorse one introspective sentence.

So the prediction is specific and it is testable: self-report instruments should over-produce Nines and under-produce Twos, the error should concentrate in less self-examined respondents, and it should shrink when the discriminating item asks about record-keeping rather than about self-description. We have not tested it. It is stated here at full length because a mechanism you can only assert is not a contribution — the value is that it can be checked, and the calibration study is where it would be checked.

Either way the honest position is the same. We now have a specific, reproducible number for our side of it, and it is the opposite of the received claim. That is a good reason to run the calibration study rather than to declare anything.

The tilt is about presence, not about rank

One more result, and it is the one that keeps the finding from being simpler than it is. Sort by leading rather than by presence and the picture flattens almost entirely: 1, 2 and 3 lead about 13% of the time each, 4 leads 11.77%, and 5, 6, 7, 8 and 9 lead at exactly 9.86% each — a five-way tie. Nine is no less likely to head a sequence than five is.

And when a number does appear, its average depth is nearly identical whichever number it is: every one of the nine sits at a mean position between 3.51 and 3.71, with nine at 3.57 — slightly shallower than five, six or seven. So the arithmetic makes low numbers easier to reach, and then treats them all much the same once they are there.

Put plainly: a nine is harder to have, and no less important to have. Anyone reading the gradient as a ranking of significance has the wrong end of it.

Does it hold outside the modern calendar? RECORD

The first run covered 1900 to 2029, which is a fair objection waiting to happen: a gradient found in one span of the Gregorian calendar could be an accident of that span. So we ran six centuries.

Century	Dates	1	2	3	4	5	6	7	8	9
1600–1699	36,525	88.7	90.3	76.9	61.2	59.7	59.3	58.6	55.2	53.6
1700–1799	36,524	88.8	89.6	78.1	60.9	60.1	59.8	58.5	56.0	54.2
1800–1899	36,524	89.2	89.4	79.3	61.6	60.0	59.6	57.9	55.0	54.7
1900–1999	36,524	88.9	88.5	80.1	61.8	59.8	59.2	57.5	54.1	53.4
2000–2099	36,525	91.0	89.6	71.8	60.7	60.0	59.9	59.0	57.6	53.7
2100–2199	36,524	90.6	90.3	73.3	60.6	59.5	59.2	58.4	56.7	54.2

219,146 dates across six hundred years, and the shape does not move. The spread between the most and least available number stays between 34.7 and 37.3 percentage points in every century. The ordering 4 > 5 > 6 > 7 > 8 > 9 is identical in all six. Nine is last in every century without exception.

One thing does move, and it is worth reporting rather than smoothing: the top three jostle. Two leads the 1600s and 1700s, one leads the 2000s, and three swings widest of all — 80.1% in the twentieth century against 71.8% in the twenty-first. So the gradient is structural and the fine order at the top is not. Anyone wanting to say something exact about first place needs to say which century they mean.

What a small percentage actually is READING

It is easy to read 9.86% against 13.14% and hear almost the same. That reading is a mistake of scale, and it is worth doing the arithmetic out loud, because these figures are proportions of a species.

Against a world population of roughly eight billion, one percentage point is eighty million people. So:

• The gap between a one and a nine in availability — 89.51% against 53.96% across the six-century run — is about 2.8 billion.
• The gap in leading between the low three and the high five, about 3.3 points, is roughly 264 million people — the population of Indonesia, in the space most readers would call a rounding difference.
• Even the narrowest gap on the table, 8 against 9 at 1.8 points, is about 145 million.

The rights-holder's point, and it is the right one: a difference too small to feel is not a difference too small to matter. If a position is less available by three points, then in any room of a few hundred people it is invisible, and across a continent it is tens of millions of absences.

What we will and will not claim about that

It is tempting to go further — fewer Nines means less mediation, less patience, fewer people willing to hold two sides without hatred, and therefore a different history. That thought is worth having and we are not going to print it as a finding, for two reasons.

The first is that our figure is a property of date arithmetic, not a census of people. We have shown what the method makes available. Whether the method's availability tracks any real distribution of human structure is precisely the open question, and building a historical argument on top of an untested premise would be doing the thing this school exists to avoid.

The second is that the claim as usually stated cannot fail: every historical period contains conflict and mediation both, so a shortage of mediators can be read into any of them. A version worth testing would need a named population, a birthdate distribution, and an outcome measured independently of the theory.

What this page can say is the part that is arithmetic rather than interpretation: the differences are small as fractions and enormous as counts, and anyone who dismisses a three-point gap as noise is dismissing a quarter of a billion people.

What the flat channel proves READING

The digital root deserves its own note, because it is the control that makes the rest of the argument stand up. Across all 47,482 dates the root lands on each of the nine 11.11% of the time — 11.10 to 11.12, which is one ninth to two decimal places, with the variation attributable to the calendar rather than the reduction.

That matters for one reason. If reduction itself favored low numbers, the root would show it. It does not. The root is a true reduction: every number folds all the way down and nothing is left over, so the nine outcomes are equally reachable and they come out equal.

Every channel that is tilted is tilted because its cycle does not divide by nine. Thirty-one days, twelve signs, twelve animals: each wraps, and each hands its surplus to the low end. The tilt is not a property of reduction. It is a property of the calendar we reduce. That distinction is the difference between a finding about people and an artifact of bookkeeping, and it is why the question of what the gradient means is still open while the question of what causes it is not.

What else the run showed RECORD

• 15,229 distinct sequences across 47,482 dates — so an order repeats, on average, about three times per 130 years of calendar. An earlier internal census over 1880–2010 recorded 13,439 distinct orders in 47,847 dates; re-run on the current engine it reproduces exactly, which is a useful cross-check on both.
• The most common two-number Bases are 1+3 and 1+2 at 3.7% each, then 2+4 at 3.6% and 3+6 at 3.3% — a much flatter spread than the single-number gradient, because a pair has two chances to include a low number and most pairs do.

What else the census shows RECORD

Presence and absence are one cut through the same run. Four more results came out of it — measured on the 1880–2010 cross-check census, where the earlier internal work established its anchors — and each one has a consequence for how a sequence should be read — so the consequence is stated rather than left for a reader to work out.

One date in nine has one shared Base result

The public lesson usually produces two distinct Base numbers and sometimes one shared Base result. The run puts a figure on it: the day reduction and the digital root land on the same number on 11.07% of dates.

What this points to. The two-step lesson has a real, sizeable one-anchor outcome — roughly one reader in nine. Those readers should not be told to invent a second member of a pair their calculation does not contain. The calculator still completes the active continuation after that shared anchor.

Three-quarters of two-number Bases cross a center

Where the Base contains two distinct numbers, they sit in the same center — both Body, both Heart, or both Head — only a quarter of the time. On 74.92% of dates the pair spans two different centers.

What this points to. The common shorthand "I'm a Head type" is, for three people in four, already incomplete at the transparent public entrance. Add positions three and four and then the full active order; do not turn either anchor into the person's sole center.

The two taught center-readings disagree more often than they agree

There are two calculation views: the center of position one, and the center receiving the most scored source support. Under the cross-check census convention they point at different centers on 61.56% of dates. They do not measure the same thing, and neither is a percentage of personality.

Nor are their date distributions alike. By first position the split is Heart 37.58%, Body 32.85%, Head 29.57% — fairly even. By scored source support it is Heart 51.53%, Body 29.66%, Head 18.81%.

What this points to. Position one is fixed by the public day reduction; scored source support is accumulated by the later calculation. Calling one the person's "real center" collapses different instruments into a claim neither can carry. State which calculation view you mean, then test lived prominence separately.

Some numbers keep company and some avoid it

Counting which numbers appear together in the same sequence: 1 and 2 co-occur on 79.01% of dates — the commonest pairing by a distance. 8 and 9 co-occur on 28.62%, the rarest on that span. On the core span the bottom two swap by a hair — 5 and 9 at 28.64% against 8 and 9 at 28.68% — a photo-finish between the two costliest pairings, and the floor sits just under 29% either way.

What this points to. Carrying both an eight and a nine is genuinely unusual — fewer than three people in ten — which makes it worth more attention when it turns up, not less. And it follows from the availability gradient rather than from anything about the positions themselves: two numbers that are each hard to have are much harder to have together. The lesson generalises. Any co-occurrence in this system is rarer than either of its parts, and the rarity compounds toward the high end.

What the whole run points to

Pulling the results together, because a page that reports numbers and leaves the reader to assemble the meaning has done half a job.

1. The method is not a type-assigner and the census makes that concrete. Six numbers on average, two to nine in range, 15,229 distinct orders across 47,482 dates. A system that returned one label per person would have nine outcomes; this one has thousands, and the order carries the information rather than the membership.
2. The availability gradient is arithmetic, and we can prove it is arithmetic. Every tilted channel is a cycle that does not divide by nine. The one untilted channel is the one true reduction. That is as close to a settled mechanism as this project has produced.
3. Availability is not importance, and the page says so three times because it is the easiest thing here to misread. Nine is the hardest number to have and no less significant to have.
4. The stable results are structural; the unstable ones are at the top. Six centuries leave the gradient untouched and the first-place ordering wobbling. Anything claimed about which number is commonest needs a century attached to it.
5. What the census cannot do is the thing most people will want from it. It describes what dates make available. It does not describe people, and every question worth asking next — whether the gradient tracks anything real, whether short sequences feel narrower from the inside, whether self-report over-produces Nines — needs people rather than dates. That is the calibration study, and this page is the argument for running it.

What this changes on the site

1. Any page stating how many numbers a person carries states the computed figures: two to nine present, mean six; none to seven absent, mean three.
2. No page may claim that a reading is capped at one, two or three numbers. The Base is where a reading starts; it is not the extent of a person.
3. The low-number tilt is stated wherever the count is discussed, together with its arithmetic cause, rather than left for a reader to find and mistrust us for.
4. The figures are regenerated from the engine by an automated check on every build. If the calculator changes and a printed number stops matching it, the build fails.

Open questions

• Is the low-number tilt a fact about people that the calendar happens to mirror, or purely a residue of dividing 31 and 12 by 9? The mechanism is settled; the meaning is not, and only the calibration study can separate them.
• Do people with two- or three-number sequences experience their range as narrower? The model predicts they should, and they are rare enough — under 1% of dates — that finding a handful and asking them is a tractable study.
• Do the roughly six in a thousand who carry all nine read differently in practice, or does a full sequence simply read as an ordinary one? We have the dates. We do not have the people.
• Birth-rate weighting would move every figure on this page somewhat. How much is unknown and worth knowing.

Sources anchored so far

Everything counted on this page is first-hand in the strictest sense available to us: it is the output of the shipping calculator, not a citation, not a summary, and not a remembered figure. The code that produced these numbers is the code that runs when a visitor enters a birthdate, and the run is reproducible by anyone with the page source. Where this paper moves from counting to explaining — the prenumber mechanism, and whether the result is a floor or an artifact — it is marked as a reading and carries its own uncertainty in the text rather than in a footnote. No claim on this page rests on a source we have not run ourselves.

Reproducing this

Every figure on this page can be regenerated from the file that runs the public calculator. There is no separate research build and no private dataset.

const present = {}, lengths = {};
const daysIn = (y,m) => new Date(y, m, 0).getDate();

for (let y = 1900; y <= 2029; y++)
  for (let m = 1; m <= 12; m++)
    for (let d = 1; d <= daysIn(y,m); d++) {
      const seq = calcFull(m, d, y).seq;      // note the order: month, day, year
      lengths[seq.length] = (lengths[seq.length] || 0) + 1;
      for (let k = 1; k <= 9; k++)
        if (seq.includes(k)) present[k] = (present[k] || 0) + 1;
    }

One warning, learned expensively. calcFull takes (month, day, year). Passing those values in a different order sends one later input through the wrong boundary branch, returns a constant for part of the calculation, and produces a plausible-looking but entirely wrong census. It cost us a published version of this page. If your run says any number is present 100% of the time, that is the bug and not a discovery.

If your figures differ from ours, we would rather hear about it than not — the feedback page reaches the research directly. Method and source weights are in the members method reference; the public Base, Line, and active-order account is on how it works.