The Immutable Past · What Is
What Is an Ancestor
An ancestor is ordinarily described as someone you can trace, and the tracing is thought to run out where the documents do. Derived from the foundation, the word turns out to name somebody exactly as settled as your own mother and, for the overwhelming majority of them, permanently unreadable — and those are two separate facts, which is the distinction the family tree has no room for.
The number the diagram asks for and cannot have
1,073,741,824
Ancestor positions thirty generations back, on a chart that only branches. The world did not hold a billion living people until about 1800.
A pedigree doubles: two parents, four grandparents, eight. Thirty doublings is 230, and thirty generations is somewhere between seven and nine centuries. The positions cannot be filled by that many separate people, so the lines have to fold back on themselves, the same individuals occupying many positions at once. The ordinary picture has the tree thinning as it climbs into the past. The arithmetic says the reverse: the demand explodes while the supply contracts into a shared and largely unnamed set. The chart is not a tree, and it was not a tree at any point in anybody’s family.
Contents
- The tree, stated fairly
- Three cases the tree cannot hold
- What the word is the name of
- The assignment does not thin
- What a search for ancestry is actually doing
- Three ways a record fails, one of which is not a failure
- What is left of the word
- What it costs
- An ordinary Tuesday
Everyone knows what an ancestor is, and the picture is a reasonable one. There is a diagram: you at the bottom, two lines up to your parents, four to your grandparents, doubling as it climbs. And there is a practice that fills the diagram in — a name in a parish register, a line in a census, a ship’s manifest, a headstone somebody photographed, a tube of saliva that comes back a few weeks later with percentages attached to countries. Neither the diagram nor the practice is silly. Millions of people find both of them moving, and they are right to.
But the two agree about something they have not examined, and it is the thing worth examining. They agree that an ancestor is somebody you can get to. Where the getting-to stops, the ancestors stop being people. They turn into a category: the old country, peasants, a haplogroup, a founder population, a shaded region on a map. The chart goes grey at the top. And almost nobody notices the moment at which a statement about the limits of a parish clerk turned into a statement about the limits of what was real.
So it is worth asking what the word is the name of. Not how to research one, and not what it feels like to stand where one stood. What an ancestor is.
Three cases the tree cannot hold
The fastest way to find the seam in a picture is to put ordinary cases against it. Three are enough, and none of them is exotic.
Case one · the arithmetic
Count the positions. Two parents, four grandparents, eight, sixteen. Thirty generations back — call it eight centuries — the chart calls for 1,073,741,824 positions. Forty generations back it calls for a little over a trillion. The best available estimate of the number of people who have ever been born, across the whole species and the whole of its history, is around 117 billion. The chart, at forty generations, is asking for roughly ten times every human being who has ever lived, to fill the ancestry of one person. It is not a near miss on a hard estimate. It is off by an order of magnitude against a ceiling that cannot move. The chart is drawn wrong, and it is drawn wrong in a way that is invisible to anyone who only ever draws the first four rows.
Case two · the woman on one line
Somewhere back there is a woman whose entire surviving record is a name, a date and a parish. Ask an ordinary question about her. Was she frightened of dogs. The chart has no answer, which is fine and expected. Then watch what happens in the next half-second of ordinary thought: the question starts to feel improper, as though asking it were a mistake in kind rather than a question that cannot be answered from here. That small slide is the whole subject of this essay. Something turned an absence of documents into an absence of fact, and it did it without anybody deciding to.
Case three · the ones nobody wrote down
Go back far enough and it is not that a register burned or a courthouse flooded. There was no register. About the great majority of the people you descend from, no mark of any kind was ever made — not a name, not a tally, not a scratch on a post. The chart cannot distinguish this case from the case where there is nothing to know, and it offers the same grey shading for both.
That third case is the one this piece is about, and it needs separating from a neighbour before anything else happens. A record that exists and is kept from you is a completely different situation with a completely different account — the sealed envelope, the verdict already written, the result somebody else has already read. The essay in this series on suspense works that case at length and it is not this one. Here nothing was written. There is no envelope.
What the word is the name of
The foundation is spare about this, and its vocabulary is locked, so it is worth using exactly. An act is a process. An artifact is a mark. Some acts generate a mark and some do not, and an act that leaves no mark enters no ledger. History, in the locked sense of that word, is the artifacts — present, surrounding you, revisable. The Past is something else entirely: one settled totality, complete, and it does not exist, because to exist is to vary (P3) and what cannot change does not vary (P0).
Put an ancestor against that and she comes apart into two things that ordinary usage keeps welded together. The entry in the register is here, in the present, on a shelf, readable and revisable. The woman is not here. She is also not somewhere else, waiting, because somewhere else is a claim about a place and the axiom is not one: the past being immutable is a consistency constraint on the record set, not a statement about a location where things are kept.
Which means the sentence people say at gravesides — she is back there — has no referent of the kind it needs. Not because she is gone in the sad sense. Because the destination in that sentence is a node, and a node is not a place that holds contents.
The assignment does not thin
Now the result this piece is built on, in its precise form. The axiom says the records admit exactly one consistent assignment (P0). The Past contains one settled totality, not one branch, with nothing left unrealized (P1). From those two: there is exactly one past — one totality, not several disconnected ones (R1).
That result has been read in this series six times, and every one of those readings put it to work on questions where several people were doing the reading and were obliged to agree. Read it instead where nobody is reading at all. The word carrying the weight in exactly one consistent assignment is consistent. It is not documented, and it is not read. The result is a statement about a totality, and a totality is not indexed to whichever of its marks happened to survive into somebody’s attic.
So: there is exactly one answer to whether that woman was frightened of dogs. And nothing here carries it, and nothing here ever will. Both of those are true at the same time, and neither one softens the other, and the combination is not a paradox. It is two quantities that the ordinary picture has collapsed into one dial.
An unrecorded life is not less determinate than a recorded one. It is exactly as determinate, and it is unreadable. Settled and readable are separate quantities.
The foundation already contains this from one side. It holds that the Past is inaccessible, and that the abundance of present records makes it appear otherwise (R9). You never had access to your mother either — not to the afternoon, not to the act. What you had was an unusually dense shelf of marks, and the density did the work of making the inaccessible feel reachable.
This piece needs the same observation pointed the other way, and the foundation does not derive that direction, so it goes in a box rather than into the argument as doctrine.
Marked construction 01 — consequence, not doctrine
The density of present marks about a region of the settled totality is a fact about the marks. It carries no information about how determinate that region is. A dense shelf makes the inaccessible look reachable; a thin shelf makes the settled look unsettled; these are the same error read at two densities.
The inaccessibility result in the foundation is stated in one direction only, for the dense case. The reverse reading is what the argument above uses, and a mirror is not an argument — the foundation says so itself about a different pair. Two things would close it. Either a derivation from the axiom and the inaccessibility result taken together, showing that mark-density is silent about determinacy. Or a demonstration that this is not a new claim at all — that it is the one-past result read at the totality rather than at the record set, in which case the construction dissolves and the argument stands on the result exactly as written. My own view is that the second is more likely correct. Until one of them is done, this is a consequence and is marked as one, and no sentence downstream of it is offered as doctrine.
What a search for ancestry is actually doing
Not making contact. That has to be said plainly, and then said carefully so that it does not read as contempt for a practice that people love.
A test result is an artifact, made this year, in a laboratory, out of present material. The ancestry it reports is a description assembled now by comparing that present material against present reference panels. By the foundation’s terms a named condition is an idea (P7), and a description of this kind is a term in the denominator of the Reality Equation (P4) rather than a piece of the numerator. What the host meets is the quotient (R8). The report is real, the laboratory work is real, and the percentage is a reading rather than a retrieval.
There is a second fact worth having here, because it is the genetic case of the same structure. In a model of a randomly-mating biparental population, there exist individuals who are genealogical ancestors of every single person now alive and genetic ancestors of none of them — the modellers call them ghost ancestors. A person can be in your line with certainty and have contributed not one base pair to you. Which means the material record thins independently of the documentary record, and both of them thin independently of what is settled. Two shelves, both uneven, neither of them the thing itself.
And then the far end, which is the part people find hardest. Immutable, therefore cannot change; cannot change, therefore cannot perceive; cannot perceive, therefore cannot recognise or stand in relation (R6). The Past does not watch, does not know, and is not proud. They would be proud of you and the ancestors are watching are frame-language, and the foundation permits frame-language when it is marked as such, which is what this sentence is doing. People say these things at gravesides and they are doing something real when they say them. What they are not doing is addressing somebody.
This runs close to another piece in the series and the difference matters. The essay on a witness asks what a witness is, and answers that a witness is a mark an act left in a host rather than a party to a relation with the act. This one is not asking about the perceiver at all. It asks what the assignment is where there was no perceiver and no mark — a question about the record, and one that has an answer even when the shelf is empty.
Figure 01
What the chart asks for, and what there was
| Generations back | Roughly | Positions the chart asks for | Against |
|---|---|---|---|
| 10 | 250–300 years | 1,024 | Comfortable. This is the range in which the tree picture works, and it is the only range most people ever draw. |
| 20 | 500–600 years | 1,048,576 | A million positions. Already larger than most of the populations those positions would have to be drawn from. |
| 30 | 750–900 years | 1,073,741,824 | More positions than there were living people anywhere on earth at the time, by a wide margin. The world reached one billion living people only around 1800. |
| 40 | 1,000–1,200 years | 1,099,511,627,776 | Roughly ten times the estimated number of humans ever born, for one person’s ancestry alone. |
Marked construction 02 — consequence, resting on a reported fact
Because the positions outrun the people, the set of somebody’s ancestors is not recoverable by any naming available from here, and not merely undocumented. A family tree is a naming, and it is finite.
The foundation gives the naming half directly: conditions are nameable without limit while the named conditions at any moment are finite (S1), and naming makes a relation conscious rather than creating it (P7). The step this adds is the arithmetic one, and the arithmetic is not in the primitives — it comes from outside, from the doubling and from two population estimates. So the claim is a consequence resting on a reported fact, not a derivation. It matters because it blocks the obvious rescue of the tree picture, which is that the chart is right in principle and merely incomplete in practice. It is not incomplete. It is the wrong shape.
Three ways a record fails, one of which is not a failure
With the two quantities separated, a sort becomes available that ordinary language cannot make, because ordinary language has one word for all three of these and the word is lost.
Figure 02
The sort the word “lost” cannot make
- One · lost A mark was made and the mark is gone. The register burned. The letters were thrown out. Something happened, and what it happened to was an artifact, in the present, where things happen. A real failure. Sometimes repairable from other marks.
- Two · withheld A mark exists and you cannot read it. Sealed, paywalled, in a language you do not have, in a building you cannot enter. The mark is intact and the reading is blocked. A real failure, and not this essay’s case. The piece on suspense owns it.
- Three · never made No mark was made. Nothing failed. An act that leaves no mark enters no ledger. There was never an artifact here to burn, to seal, or to misplace. Not a loss. The word has no referent in this column.
That correction is small and it changes the feel of the whole subject. The woman with one line in a parish register is not a faded version of a person. The tens of thousands behind her with no line at all are not fainter still. There is no gradient running up the chart on their side at all. There is a gradient of documentation running up the chart, and that gradient is a fact about clerks, wars, paper, climate and literacy — about what happened to artifacts in the present. It reports on the shelf. It does not report on them.
What is left of the word
Strip the tracing out and see what survives. An ancestor is a person whose acts are over; who is in the one settled totality, entirely and without remainder; about whom some number of present marks exist, that number running from a full shelf down to zero; and to whom no living person stands in any relation, the far end having been removed by the result above rather than merely put out of reach.
Every clause of that is identical for the ones with portraits and the ones with nothing. Which is the finding, and it is worth saying in the plainest available words: documentation confers no degree of being an ancestor. The chart is not a partial inventory of a set that thins as it climbs. It is a naming, done here, in the present, out of present material — exactly as real as any naming and exactly as non-constitutive.
Three things drop out along with the gradient. The idea that a family tree is an inventory rather than a construction. The idea that a person becomes more of an ancestor as evidence accumulates. And the quiet assumption underneath the grey shading at the top of the chart, which is that the limit of the archive is the limit of the fact.
What it costs
The result is not a comfort and should not be dressed as one. It costs four things, and they are worth stating without softening, because a claim that only ever arrives as reassurance is not doing any work.
You will not meet them. Not in the ordinary sense and not in the consoling sense. The result on the far end removes the relation and not merely the route to it, and no amount of research, ritual or feeling supplies a second end to a relation that has one.
“They live on in you” is false as stated. What exists is you, varying, and a set of marks in the present (P3). Something true sits very near that sentence — the marks are real, they are all around you, and you are reading them constantly — but the sentence as people say it claims persistence for the person, and the foundation does not supply it.
The past does not keep them safe. That comfort is a claim about a place with contents, and the axiom is a constraint on the record set. The sentence sounds metaphysical and is architectural, and the architecture it describes is not there.
The reaching has no completion condition. The foundation splits any backward-facing feeling into two jobs. One is an evaluation, aimed at a present artifact read against what it is a mark of; it has a completion condition, it can succeed, and it returns something usable. The other is a reaching, aimed at the settled thing itself; it has no completion condition, not because you have not tried hard enough but because what would complete it is not the kind of thing that can be reached. In genealogy the two are wound together so tightly that they look like one activity, which is why the research can go on for decades and never once discharge the feeling that started it. The research was answering the other question the whole time.
And one refusal, stated once and kept: nothing here says that the forgotten are counted somewhere, that it evens out across the whole of the record, or that anybody is owed remembrance. The foundation does hold a position about totals, and that position is not a consolation and is not available to anybody on this side of it. This essay does not reach for it.
If you came to this from a grave
If you are reading this a few weeks after a funeral, or a few years after one that has not settled, the argument above is not the right tool and it is better to say so here than at the end. Nothing in it says the feeling is a mistake. The claim is narrower and colder than that: the part of the feeling aimed at reaching the person has nothing at the far end to land on, and the part aimed at reading what they left can succeed and is worth doing. Knowing which part is which does not stop either of them, and there is no schedule on which it is supposed to. What a metaphysics can do is take the shame off a mechanism — the reaching not landing is not a failure of love, of effort, or of research, it is what happens to a well-built mechanism aimed at something that does not have the shape it is aimed at. What a metaphysics cannot do is treat a mind that is grinding. If that is what is happening, this essay is not the thing to reach for. A person is.
An ordinary Tuesday
- Read the marks as marks. The photograph is not her. It is an artifact, made at a particular moment in relation to something, and reading it against what it is a mark of is a job with an end — it terminates, and it returns something. Asking what it is evidence of is answerable. Asking it to produce her is the other job, and that one does not close.
- Stop grading ancestors by paperwork. If the family story runs out in 1830, that is a fact about a parish clerk and a fire, and it is not a fact about the hundreds of people on the other side of 1830. They are not dimmer. The shelf is dimmer.
- You are the one with no record, for somebody. This is not an argument for building a legacy. Every artifact is a miss (R10), the evaluative question about anything you make is its fidelity rather than its success (R11), and whether anything you make is ever read is not yours to command. Records are add-only, and a new mark made now stands beside the old ones rather than editing them (R2). So the available move is small and it is genuinely available: make the mark accurately. That is the whole of it, and it can be done this afternoon.
The shelf is uneven. The totality is not. What people mean by an ancestor going dim at the top of the chart is a report on the shelf.
Held open
- Does the foundation have any expression for the unevenness of the shelf?
- The argument above needs mark-density to be silent about determinacy, and the foundation states the relation in one direction only. What would close it: a derivation from the axiom and the inaccessibility result together; or a demonstration that the claim reduces to the one-past result read at the totality rather than at the record set, in which case there is nothing new here and the construction can be struck. Marked construction 01 states both and nothing downstream is offered as doctrine.
- Why a given condition is legible to one host and not another.
- The foundation records this as unresolved. It is named here and deliberately not used: nothing in this essay turns on which conditions a host can read, only on whether a mark was made at all. Not approached.