The Educational Illustration Label: Why Every Output Carries It

The educational illustration label claims that a figure was computed to demonstrate a relationship and was not observed anywhere. The label says the number is arithmetic on invented inputs, and it says nothing at all about whether the arithmetic is right or the relationship worth demonstrating.

The phrase appears everywhere in this subject area. The label sits under the figures, it sits in the closing line of every reference block, and it sits beside every parameter set that anybody has named. Ten reading orders have carried the label and none of them stopped to say what it means. The meaning is worth stopping for.

The reason for stopping is not tidiness. A label that appears everywhere and is explained nowhere becomes furniture, and furniture gets read past. Worse, a label that is read past gets guessed at, and the guess almost everybody makes is the wrong one: that it is a hedge, a line of small print, a way of saying do not hold me to this. The label is the opposite of a hedge, and a reader who guesses wrong will treat every number in this subject area with less care than it deserves rather than more.

Start with something concrete. A cookery book gives a recipe for four people and says, at the foot of the recipe, that the timings were worked out on a domestic oven at a stated temperature rather than measured in a test kitchen. The line about the oven is not an apology. The line is the single most useful one in the recipe. Timings are arithmetic on a stated assumption, and the line says so. An oven that runs hot tells the cook precisely which part of the recipe to adjust, and it is clear that nobody stood over a stopwatch to produce those numbers. Take the sentence away and a reader would reasonably assume somebody had. The recipe has said more by naming where its numbers came from, not less.

Naming where a number came from is exactly what the educational illustration label does, worked out carefully and in the specific setting of a subject area whose every number is constructed. Everything below is about a sentence, not about a quantity. Every number named here was derived elsewhere and is pointed at rather than recomputed, an instance of the rule under discussion.

What does the educational illustration label claim?

The label makes two assertions and no more. The first is about the number itself: it was produced by calculation. The second is about the calculation: its starting values were chosen by an author rather than taken from anywhere. Put together, the label says that the figure is downstream of somebody sitting down and picking a few numbers, and that no part of the chain touches a measurement of anything.

An educational illustrationA figure computed to demonstrate a relationship rather than observed. It exists so that a mechanism can be shown working on numbers a reader can check. is therefore a claim about provenanceWhere a number came from: what was assumed, what was calculated, and by what route. It is a separate question from whether the number is correct. and about nothing else. Provenance is a question with a definite answer for every figure ever produced. Somebody either read the number off something, or they worked it out. The label answers that question, in public, before anybody has to ask.

A worked case shows how sharp the claim is. Consider the figure 0.559618, the second normal term in a closed form price on the standard process. The label attached to it says: nobody observed 0.559618 anywhere. The figure is what comes out when a starting value of Rs 100/-, a volatility of 20 per cent, a rate of 5 per cent and a horizon of one year, all invented, are pushed through a formula. The label pins the figure to a route rather than to a source, and the route is the only thing anybody could ever check.

Notice what the partition settles and what it leaves open. The partition settles that a figure is not an observation. A wrong calculation on invented inputs is still a calculation on invented inputs and still belongs in the second pile, so the partition does not settle that the arithmetic reaching a figure was carried out properly. The pile is defined by route, not by quality. The distinction between route and quality is the hinge of everything that follows.

What does the label not claim?

The silences are the harder half, and they are harder because the label sits in the visual position that small print usually occupies. Under a figure, in grey, in a smaller size. Everything a reader has ever seen in that position was there to reduce somebody's exposure, so the eye arrives expecting a hedge and finds a provenance statement instead.

Take the four silences one at a time. Each one is a real gap that somebody could fall into.

The label does not claim the arithmetic is right. An arithmetic errorA mistake in the working: a wrong sign, a term dropped, a value carried into the next line incorrectly. It is a fault in the calculation, not in where the calculation started. in a labelled figure is still an arithmetic error and the label neither hides it nor forgives it. If the closed form price of the at-the-money contract on the standard process is written as Rs 10.45/- and somebody has in fact fumbled the working and should have arrived somewhere else, the label has not made the result any less wrong. The label has named where to look for the mistake, and the place to look is the working.

The label does not claim the relationship being demonstrated is worth demonstrating. A demonstration could compute something perfectly and be teaching a relationship that nobody needs, and the label would sit under it looking exactly the same as it does under something useful. Judging the worth of a demonstration is a reader's job and an author's responsibility, and no sentence at the foot of a figure discharges either.

The label does not claim the inputs were well chosen. The four numbers underneath this whole subject area, a starting value of Rs 100/-, a drift of 8 per cent, a volatility of 20 per cent and a rate of 5 per cent, were picked because they make results land on figures a reader can verify in their head. Half the variance rate comes to 0.02 exactly, the drift less that correction comes to 0.06 exactly, and volatility times the square root of the horizon comes to 0.20 exactly. The four are convenient choices, openly convenient, and the label says nothing about whether convenience was the right criterion. The label says only that they were choices.

And the label does not claim that anybody requires it. There is no authority behind it. No regulator anywhere has written it down and no standard body publishes it. The label is a sentence this subject area writes because its figures would be unreadable without it, not a sentence anybody made it write.

What separates an invented input from a computed consequence?

The partition above does no work until a figure can be sorted into it on sight. The test is short: what would have to change for the number to change? If the answer is that somebody would have to make a different decision, it is an invented inputA starting value chosen to make a demonstration work. Nothing determines it except an author deciding, which is why it can only be declared and never derived.. If the answer is that some other number would have to change first, it is a computed consequenceA figure following from invented inputs by arithmetic. Change an input and it moves; change nothing and it cannot move at all..

Run the test on the volatility of 20 per cent. Only somebody deciding to write a different number would make it something else. Nothing else in this subject area determines it, no calculation reaches it, and no argument forces it. The volatility is an input. Now run the test on the median of the distribution at the horizon, Rs 106.18/-. A different starting value, a different drift, a different volatility or a different horizon would make the median something else. The median cannot move on its own. The median is a consequence.

The test also catches the cases people find slippery. The realised quadratic variation of the logarithm along the locked path at its twelve step partition is 0.040300 rather than 0.040000, and that excess of exactly 0.000300 unsettles readers who expected the round number. But the test is not about roundness. The realised figure moves only if the driving values or the parameters move, so it is a consequence, and the fact that it is not round is a fact about the arithmetic rather than a sign of sloppiness. Anybody quoting 0.040000 as the twelve step reading would be reporting the limit and calling it the measurement.

An observationA figure taken from somewhere outside this subject area, such as a reading, a quote or a record. This subject area contains none of them anywhere. would fail both halves of the test. An observation changes when the thing being observed changes, and the thing being observed sits outside this subject area entirely. Observation is the category this subject area does not use, and the label is how a reader can tell.

Sorting a figure takes one question and the question never has two answers, so the label can be attached honestly to every number in this subject area without anybody having to make a judgement call.

Why does every figure in this subject area carry the label?

Because every figure in this subject area needs it. The claim sounds like a slogan until the counting is done. This whole subject area, ten reading orders and ninety four guides, rests on a listable set of chosen numbers, and every other figure anybody has ever quoted from it is arithmetic on that set.

Here is the complete list. Counting an input as one decision an author made brings the total to thirteen, with a parameter set named as a group counting once. Counting individual numbers instead gives a larger total, but not a longer list. The grouping changes the count and never the content.

Everything else came out of those. The mean at the horizon of Rs 108.33/- and the median of Rs 106.18/-, and the gap of Rs 2.15/- between them which is the half variance correction made visible. The discount factor of 0.951229. The intermediate quantities of 0.350000 and 0.150000 and the price of Rs 10.45/-. The three fitted volatilities of 19.82, 20.70 and 20.44 per cent that identical data returns under three different loss functions. The two jump parameter sets that agree exactly on a total variance of 0.046250 and differ by a factor of four on excess kurtosis, 0.106647 against 0.026662. Every one of them is arithmetic on the thirteen.

The label is therefore not a policy applied to the figures; it is a description of them that happens to be true of every single one. There was never an occasion where somebody had to decide whether the label applied. No figure ever came from anywhere else.

What would be true if the label were absent?

Strip the label off and nothing about the numbers changes. Rs 106.18/- is still Rs 106.18/-. Removing the label changes what a reader is entitled to conclude, and the change is large.

A reader who finds a figure with no statement of where it came from will assume it was observed. The assumption is not carelessness on their part; it is the ordinary reading. Numbers in print, presented without qualification, are taken as reports. A temperature in a weather column is a reading. A population in an atlas is a count. A price in a table is a quote. The default is that somebody went and looked, and the default holds because it is right almost everywhere.

So an unlabelled Rs 10.45/- reads as a price somebody saw. An unlabelled 20 per cent reads as a volatility somebody measured. An unlabelled set of five quoted volatilities at 24.0, 22.0, 20.0, 19.0 and 18.5 per cent reads as a curve somebody pulled off a screen, and once it reads that way, everything downstream of it inherits the same standing. The fitted 19.82 per cent stops being an illustration of what a squared price loss does to five invented numbers and becomes, in the reader's head, a finding about something.

Without the label this subject area would be making claims about the world, and it has no basis for a single one of them and never intended to make any. The sharp version runs like this. Ninety four guides asserting how something behaves, resting on four numbers somebody chose over a coffee because they made the arithmetic land neatly, presented as though they had been gathered. There is a word for that and it is not a flattering one.

The label is what stops the inheritance at the top. The label says: the chain starts here, with a decision, and everything below it is a demonstration of a mechanism rather than a report about anything. ReproducibilityWhether a reader can recompute a figure from what was published alongside it. It is the only kind of checking available when a number was constructed rather than observed. replaces sourcing as the check available on the figure, and reproducibility can only replace sourcing if the reader has been told which of the two applies.

Where does the label have to appear?

The test for placement is the same one that applies to a unit. Nobody writes a length as 4 and leaves the reader to work out whether it was metres or feet, and nobody puts the unit once at the front of a document and considers the rest covered. The unit travels with the number because the number is meaningless without it.

Provenance travels the same way, and for the same reason. A figure that gets quoted, copied into a note, read aloud or lifted into a summary arrives at its destination carrying whatever was attached to it and nothing else. A label that lives only in a preface has already been left behind by the time the figure is doing any work.

So the rule is simply stated: wherever a number appears in a form somebody could carry away, the statement of where it came from appears with it. In practice that means every figure and its caption, every table of quantities, every worked step in the running text, every quiz whose answer is a number, every parameter set named anywhere, every simulation wherever one appears, and the closing note of every reference block.

Asked the other way, the question gets shorter still. Is there anything here that carries a number and does not need the label? The branch exists in principle and is empty in practice. Every guide in this subject area carries a figure, and no figure anywhere was observed. The decision has one branch that is ever taken, so the label is on everything rather than on a selection.

What does the label not excuse?

The label is not a licence. Four things sit outside its reach entirely, and it is worth naming them one at a time because each has a different flavour of wrongness and the label is equally useless against all four.

An arithmetic error. Somebody drops a term, carries a sign the wrong way, or divides where they should multiply. The number that comes out is not a demonstration of anything; it is a demonstration of a mistake. The label announces that this figure came from working, and the working is broken, so the label has done nothing except point directly at the fault.

A wrong relationship. The arithmetic is flawless and the thing it is showing is not true. A demonstration might claim that the size of a discretisation error falls smoothly as the partition refines, and compute every step correctly, and still be wrong. Along the locked path the signed error runs positive three times, then negative twice, then positive again, crossing zero between three steps and four and once more between six and twelve. Correct arithmetic in the service of a false claim is still a false claim.

A misleading arrangement. Every individual figure is right, every calculation checks out, and the way they have been ordered or drawn tells a story the figures do not support. Drawing a coarse-partition sequence as a smooth approach when the numbers oscillate is exactly this. Nothing in the table is false and the picture is.

And a number chosen to make a point come out. A chosen number is the fault the label is most often reached for and the one it covers least. If an author picks an input because it delivers a tidy conclusion and then labels the output as an illustration, they have not illustrated anything; they have arranged a result and attached a sentence that describes a different activity. An illustration demonstrates a mechanism on stated inputs. Working backwards from a desired answer to the inputs that produce it is a separate act, and calling it an illustration does not convert it into one.

A disclaimerA statement that lowers a standard or limits what somebody can be held to. The label is not one, which is why none of these four is covered by it. would arguably cover some of these, and the overlap is precisely why the confusion matters. The label is not a disclaimer, so it does not lower any standard, so there is nothing for these four to shelter under.

Does the label lower the standard a figure must meet, or raise it?

How does a reader use the label when a number lands in front of them?

All of the above is a way of thinking, and a way of thinking is worth having only if it changes what somebody does on a Tuesday afternoon. Here is what it changes, for the three kinds of person who will meet a figure from this subject area.

A student working through the material uses the label as an instruction about method. The label tells them that checking the figure means recomputing it, not looking it up. So when the median at the horizon is given as Rs 106.18/-, the response is not to wonder which market that came from, but to take the starting value, the drift, the volatility and the horizon off the list of thirteen and get Rs 106.18/- back. If it does not come back, one of two things is wrong and both are close at hand: either the working shown is faulty, or the reader has misread it. Nothing external can be blamed and nothing external needs to be consulted.

Somebody reviewing a body of work uses the label as a sorting instruction. Chosen and derived numbers attract completely different questions, so a reviewer's first pass over any set of numbers separates the two. A chosen number attracts: why this value, was the choice disclosed, and does the conclusion survive a different choice. A derived number attracts: does it recompute, and is every intermediate step visible. Mixing the two wastes a review. Asking a derived number to justify its value is asking the wrong question of it, and asking a chosen number to recompute is asking an impossible one.

And somebody writing uses the label as a discipline rather than a formality. Attaching it commits them to the claim that the figure is reproducible from what the reader was given, and so commits them to publishing enough for that to be true. The commitment is why this subject area carries the thirteen inputs as a printed list rather than mentioning them in passing, and why the locked path is published as twelve values rather than drawn from a generator. A path sampled fresh each time cannot be recomputed by a reader, so labelling it would be attaching a claim that could not be honoured.

The label converts every figure here from something to be believed into something to be checked, and the only work it asks of a reader is to accept that invitation. Take the fitted volatilities of 19.82, 20.70 and 20.44 per cent. Three answers, from identical data, differing only by the loss chosen. A reader treating those as observations would be baffled and would look for the mistake. A reader treating them as constructed knows immediately where to look. The three losses are the place, and nothing about the data chose those three numbers because the loss function did.

The standard process, the thirteen inputs behind it and the five quoted volatilities are invented.
Educational material. Not advice on any investment, tax, budget or market position.