What Is Perfection

Flawless. That is perfection as most people carry it, and it is not a foolish picture; it is the picture that gets the bridge inspected and the second draft written. Somewhere at the top of the scale there is a state in which nothing more could be added, corrected or improved, and every actual thing sits some distance below it. Good is nearer than bad, better is nearer than good, and perfect is the end of the line, which nothing quite reaches. The whole vocabulary is a vocabulary of height and distance. You aim for it. You fall short of it. You get closer. Nothing is perfect, we say, and we mean it as a fact about the world’s limits, the way it is a fact that nothing outruns light. I have used the picture my whole working life, and in June I published two essays that leaned on it. It is, I will argue, wrong about what perfection is, and wrong in a way three ordinary cases show before any foundation is consulted.

What the ordinary picture commits you to

State it strongly, because the weak form is not what anybody believes.

The picture makes three commitments. First, that perfection is a state of a thing — a property an artifact has or lacks, the way it has or lacks a crack. Second, that it is the limit of improvement: the place a sequence of better attempts is heading, defined by that sequence, reached or not reached by adding correction. Third, that perfect is a grade — the top rung of the same ladder that good and better are on, so that to call a thing perfect is to say it scored above a thing you would call excellent.

Three ordinary situations do not fit inside those commitments, and each one breaks a different commitment.

So perfection is not a state a thing reaches, not the limit an improving sequence defines, and not a grade on the scale of good. Something else is doing the work.

What the foundation says instead

I work from a small set of numbered primitives and results derived from them. The one doing the work today is the least-exercised primitive in the document, and this is the word it was made for.

P10, exemplarity: every condition has an exemplar — a complete and exact form against which any artifact can be measured.

One guard before that is allowed to run, the same guard the piece on copies put up, because the pull past it is stronger on this word than on any other. P10 hands over a measuring relation. It does not hand over a metaphysics of forms. Whether conditions are abstract objects — whether the exemplar is somewhere, is made of anything, is a thing in the sense a table is a thing — is an open problem in the foundation, Part VIII item eleven, and it stays open here. What P10 licenses is that an artifact has something to be measured against that its maker did not author, and that the something is complete and exact. That is all this piece uses. A reader who feels the pull toward a realm of forms should know that I feel it too, and that the primitives stop short of it on purpose.

Two more pieces of machinery. The locked definition of an artifact: an imperfect historical mark made in relation to an exemplar. Read the second word again, because it is about to do a great deal. And R10: every artifact is a miss — derived from P4, the Reality Equation, because the denominator through which each mark is made is not the maker’s to command, and so the mark never lands exactly.

Now put the ordinary word next to the primitive.

Case two comes out at once. Complete and exact is what perfect storm and perfect stranger were saying all along: the whole form of the condition, present in one instance, with nothing left out. The grade sense is the derivative one, and I come back below to what it is a derivative of.

Case one needs one more primitive. P8: a condition is prior to what it conditions. The exemplar is the form of the condition, so it is prior to every artifact made in relation to it, including the first one. The perfect circle was not extrapolated from the drawings; it is what the drawings were read against, and P7 says when that reading becomes possible: naming makes the relationship conscious. A child who has the word circle has a condition that can be read against, and the wobble becomes a wobble. Before the naming, the crayon marks are marks. The exemplar is not the far end of the sequence. It is what makes the sequence a sequence.

A mark and a form

Here is the move the ordinary picture cannot make. An artifact is a mark. An exemplar is the complete and exact form of a condition. Those are two kinds of thing, and R10 says the first is at some distance from the second — not sometimes, not so far, but by construction, because the denominator through which each mark is made is not the maker’s to command. The gap between a drawn circle and the circle is not a distance that a better compass shrinks toward zero. It is the difference between a mark and what the mark is read against, and it survives every improvement in the mark, because the improvement is another mark.

This is where I correct myself in public. In June I published two essays, Why Perfection Would End Reality and It Is All So Imperfect, that ran the hypothetical: suppose the perfect circle were placed in the record — then the idea would be satisfied, would stop having people, and Reality would end. Those pieces predate the foundation and are read now as report rather than doctrine, but I wrote them and I should say what has changed. Two things. First, the primitives no longer let me write that an idea “wants” its mark; P9 is precise that a condition conditions and does not intend, so the engine of that argument — a condition being satisfied — is not a sentence the foundation can hold. Second, and more simply, the hypothetical has no antecedent. R10 does not say a perfect artifact would be catastrophic. It says the phrase names nothing. A mark that is not a miss is not a rare mark; it is not a mark. The June argument treated as a door what the foundation now says is a wall. And the June pieces made the shortfall load-bearing for the whole movement of Reality — imperfection is the engine, I wrote. The foundation grounds the movement elsewhere, in P3, to exist is to vary, and leaves the shortfall as a fact about marks. It is not the engine. It is what the word artifact means.

What perfect says when you say it

So what is happening when somebody calls a thing perfect — a perfect evening, the perfect word, a perfect cup? By the first construction they cannot be reporting that the artifact is the exemplar. P4 and R8 say what they are reporting. R = A / E, and the host experiences neither the actual nor the expectation but the quotient. A reading of a mark is a reading of the actual against a prediction, and the miss a reading can find is bounded by the resolution of the prediction: a departure smaller than the denominator can distinguish does not register. Perfect, as praise, is the name for a reading in which the miss did not register. The surprise came back with nothing to subtract, and the reader had nothing finer to read with.

Both pieces of evidence have machinery behind them. The expert is a host whose denominator resolves finer; the piece on taste called that capacity reading the shortfall, and it is the same capacity. Two readers, one mark, two resolutions, two verdicts, and the mark sits where it sat. The forty-year-old is the same reader later: R2 says records update expectation forward and never re-open, so twenty years of marks have narrowed E, and the same actual now reads smaller against it. The praise at twenty was accurate about the reader and silent about the thing. And R14 closes it: an idea is oriented and prejudiced in the same act, so a reader who calls a thing perfect has also just told you what they cannot see. That is not an insult to the reader. It is what the word contains.

It also says what the grade sense is a derivative of. Perfect as the top of good is the reading at which the reader runs out of subtraction. It is a fact about where a particular denominator stops, wearing the vocabulary of the form. The idioms kept the form; the compliment kept the stopping point; and the dictionary, which lists the compliment first, has the order backwards.

Figure 01

Three objects the ordinary word runs together

• The condition, as a point The category What it answers: which condition a mark serves — is it a circle?
  Its edge: the reader’s tolerance, host-side, a term in E.
  Its zero: none. A point has no inside for a mark to be nearer the middle of.
• The condition, as a form The exemplar What it answers: how far a mark falls from the whole — how far from the circle?
  Its edge: none. Complete and exact admits no tolerance.
  Its zero: the point of no miss — which no mark occupies. This is what perfect names.
• The attempt The mark What it is: an imperfect historical mark made in relation to an exemplar — imperfect by definition.
  What it carries: a size and a direction of miss.
  What it can be: near or far. Not the form.

The point and the form

Two days ago I argued that a category is a point on the circle and that a point has no inside — nothing is in a category, and the edge of one is the reader’s tolerance. That piece kept the exemplar out entirely, and a reader could fairly ask whether the exemplar is just the category drawn tight. It is not, and the difference is the difference between two questions. Is it a circle? asks which condition a mark serves, and it admits a tolerance: a host decides how much wobble the word will still carry, and that decision is host-side. How far from the circle? asks about the mark’s miss against the complete form, and it admits no tolerance, because the form is exact. The first question has an edge and no zero. The second has a zero and no edge — a zero no mark occupies. Perfection is the zero of the second question. It is not the first question asked strictly, and a category made stricter does not approach it; it only moves an edge.

And yesterday, writing about deadlines, I drew a line I need now: a promise fixes the measure, a deadline fixes the moment of measurement. Perfection is about the measure. It is the measure’s zero, and it says nothing about when a reading is taken. Perfectionism is the conversion of the one into the other.

The standard is not a variable, and this is the part the ordinary advice gets wrong from both sides. By P8 the exemplar belongs to the condition and is prior to the person; it cannot be raised or lowered by anyone, so lower your standards is advice to do a thing the primitives say cannot be done, and hold yourself to a higher standard is a description of nothing. What a person has is a resolution of reading and a rule about when to read. Both are theirs to revise — P5, the host occupies a position from which its response to a readable condition is revisable, and R13, the host is where that responsibility sits. The form is not theirs to revise. And R11 says what the perfectionist’s rule rules out: the evaluative question is fidelity, how near, and the rule admits only one answer to that question, which is the one no mark gives.

Good enough is the other side of the same coin, and it is not what it is accused of being. It does not lower the exemplar; nothing does. It is a decision about the act: that the correction stops here and the mark is read as it stands, miss and all. The locked vocabulary has a name for that and a name for its counterfeit, and the piece on taste already separated them. Shipping is letting the reading be taken. Settling is ceasing to correct. Both say good enough on the day, in the same voice, and they are told apart by the next mark — whether it is aimed nearer. Approximation is correct phase with insufficient magnitude, and it is not a sin. Settling is the only one.

The form is prior to the first attempt and it is not reached by the best one. Complete, exact, and nobody’s.

What this costs

It costs the summit. There is no state your work can reach that the word perfect names, and there was not one for anybody: not for the sword, not for the proof, not for the remaster. Each mark in the record is a miss and the best ones are near. If you were working toward the day the miss would be gone, that day is not late. It is not a day.

It costs the standard as a possession. You do not have standards, high or low; in the sense P8 gives, the condition has you — it is prior, and you are where it became readable and got marked. What you have is a resolution and a rule about when to read, and both are yours. The form is not.

It costs the compliment. Perfect, said of your work, is a report on the speaker’s denominator. It is a real report and worth having, and it is not what the ordinary picture took it for. A compliment from a fine resolution is worth more than one from a coarse resolution, and the word is identical in both mouths, which is why it tells you so little on its own.

And it costs the consolation of nothing is perfect, which is the one people lean on. Read as the ordinary picture reads it — we all fall short, so do not mind — it is a soothing sentence. Read as the second construction reads it, it is a definition, and a definition is not a comfort. It does not say your miss is small or forgivable. It says the miss has a size and a direction, and that the honest question is what they are — which is a harder question than whether the thing is perfect, because whether the thing is perfect was not in doubt.

R14 once more: an idea is oriented and prejudiced in the same act, and so is this one. It is kind to the person who ships, and unkind to the person whose refusal to ship is the last thing standing between the work and a coarse reading — the one who is right that the mark is not ready and is being told, here, that ready was not going to mean what they meant by it. It suits a temperament. Worth noticing before deciding it is merely correct.

Where this is unfinished

Three edges, stated so someone can hold me to them.

The first is the wall the live index said this piece would hit, and it did. I have used exemplar throughout as the complete and exact form of a condition against which any artifact can be measured, and I have not said what an exemplar is beyond that, because the foundation has not. Whether conditions are abstract objects is Part VIII item eleven, open, and a piece on perfection is the single strongest temptation in the series to close it in passing — each sentence about the form points at the form. What closing it would take is a published answer to the abstract-objects question, or an amendment giving the exemplar a standing of its own in the locked vocabulary. Until one of those exists, the measuring relation is the whole of what this piece uses, and a reader who finds it thin has found the edge of the foundation and not a place I declined to look.

The second is scale. The artifact algebra gives a miss a direction and a size, and the piece on copies already recorded that the foundation supplies no unit in which the size is stated. So how far from perfect is an order — nearer, farther — and not a number, and I have read it as an order throughout. That reading is mine. It stands beside the question the piece on age recorded, whether the record carries a magnitude or only an ordering, and I have not tried to settle either.

The third is the machine. A model can be trained on marks and can return the word perfect about a new one. Whether it is reading through those marks to the exemplar or reading against the marks themselves is the distinction the piece on copies drew between two operations, and it is not settled by watching the output. And whether anything on the other side of its reading is surprise — whether its threshold is a denominator in the sense P4 gives — is Part VIII item nine, which the foundation’s own table says to state and not resolve in passing. So: a machine has a threshold, and on the present definition of a host the third construction does not apply to it, and that is where this piece stops.

On a Tuesday

1. When you say perfect, add whose resolution. Perfect to me, at this distance. It is accurate, and the appended clause is the whole content. Said of your own work, it tells you what you cannot yet see, which is the useful part.
2. Find the measure and the moment separately. What is this mark measured against, and when will it be read? If your rule for the moment is when the miss is gone, you have written a rule for never. Write a different moment. The measure will not have moved.
3. Read the miss instead of grading the mark. Which way is it off, and by how much can you tell? That is the evaluation; it completes, and it updates the next mark. Not perfect completes nothing, because it was not in question.
4. On the day you say good enough, check which way the next mark is aimed. Same words, two directions. Only the next mark tells you which one you meant.