The Technology S-Curve: Why Progress Slows and Then Jumps

The technology S-curve plots what a change returns against the effort put into it, and the bottom axis is effort rather than years. Its right hand flattening says that more of the same at the same place returns less, and eventually nothing. An exact nought, worked out below, evidences that end. The flat beginning at the other end is evidenced nowhere here, and appears in the drawings as an outline.

One small habit that costs nothing carries everything else: the axis labels come before the line. A rising line that levels off says nothing at all on its own. The line becomes a statement only when somebody writes down which quantity runs along the bottom and which one climbs the side. Four shapes in these notes are drawn identically and mean four completely different things, and the only difference a reader can actually see is in those two labels.

The second habit is a rule about weight of evidence. A nought cannot be a rounding error and cannot be a matter of degree. A return that falls to exactly nothing is therefore stronger evidence than a return that merely falls. One such nought turns up below, and it is the only part of this shape that anything here evidences at all.

Everybody has seen this curve. What is actually along the bottom of it?

Ask the question the picture never answers. Something improves quickly for a long stretch and then stops improving. Why? The answer most readers reach for is that the thing is old, and that answer comes from a silent assumption about the drawing: that the bottom axis is a calendar.

The bottom axis is effort spent, not years passed. That is the whole correction, and every later sentence in this guide depends on it. The analyst puts effortWhatever is being spent on making something work better: money, engineers, machine time, attention. The word is loose because what gets counted differs from case to case, and no particular unit is assumed. along the bottom and the shape stops being a story about ageing. The shape becomes a statement about spending: a further unit of effort put into the same thing, at the same place, returns less than the last unit did.

Watch what that swap does to the same picture. Read as time, a flattening curve says a business is late. A claim about dates produces urgency. Read as effort, the identical curve says the next rupee at this place will do less than the last one. A claim about where money goes produces a question. One drawing, two axes, two different conversations in the room.

Richard N. Foster set the account out in Innovation: The Attacker's Advantage in 1986, and this guide borrows the frameA shape or a structure borrowed to organise thinking, rather than a picture drawn through points somebody measured. A frame can be useful and still carry no evidence of its own. from that work and takes no figure whatsoever out of it. Where an argument is read and where a quantity is read are two different places, and the two are kept apart throughout.

Here is the everyday version, and it is worth holding on to. A student revises for an examination. The first hour a day moves the marks a great deal. The second hour moves them a little less. By the fifth hour in one day the marks barely move at all, and nothing has aged: it is the same student, the same book and the same week. The return on the next hour ran out, not the calendar. Hours are along the bottom. Weeks are not.

Three other shapes in these notes look the same. How are they kept apart?

Telling the four treatments apart early decides whether they teach four things or one thing four times. Four rising and levelling shapes live in these notes. Drawn side by side with the labels rubbed out, nobody could tell which is which, and that is not a criticism of anybody's drawing. The sameness belongs to the shape itself.

One of them tallies the sellers a field carries as the years pass. Another tallies the buyers who have taken a thing up. A third follows a single product's own sales and its own earnings across a life. The technology S-curve plots how well a thing performs against the effort spent on improving it. Four drawings can be indistinguishable and still be about four unrelated things, and it takes the pair of labels to separate them. The other three all run on time, so the bottom axis sets the technology S-curve apart from them, and the side axis then tells those three apart from each other.

Notice what separates them and what does not. The separation is not the steepness, not the height and not how convincing the line looks. The separation is a population and a unit: sellers, buyers, one product's own sales, and effort. Three of those four count something that moves with the calendar. The technology S-curve counts something that moves only when somebody spends.

Each of the other three is worked in full elsewhere and none of them is touched again here. The pace at which something spreads belongs to Technology Adoption and Diffusion: What Sets the Pace. One product's own sales and its own earnings, first to last, belong to The Product Life Cycle: Launch to Withdrawal. Counting sellers in a field as the years pass is done in the material on the industry life cycle.

What does the shape itself actually claim, stretch by stretch?

Three stretches, one sentence each, and then a rule. At the flat beginning, a lot of effort buys very little: the thing is being made to work at all, and most of what goes in disappears into learning. Through the steep middle the hard part is behind and the easy gains are still in front, and each further unit of effort buys a great deal. At the flattening end, each further unit buys less than the one before it, and the line rises so slowly that the next unit may buy nothing measurable.

The two flat ends carry a working name in this guide. Each one is a shoulderEither end of a rising and levelling line, where the line runs nearly flat rather than climbing. A drawing of this sort has two of them, one at each end, and they are not the same thing as each other., and the interesting fact about the pair, once the evidence is looked for, is that they turn out to be evidenced completely differently in these notes. One of them arrives as a number. The other one arrives as nothing at all.

Now the rule, stated before any drawing of the shape appears rather than after it. Neither axis of this shape carries a number, so no position on the line can be read as a diagnosis. The rule is not modesty. The reason is what happens next in a real room: the moment a business is marked at a point on a drawn line, the drawing has supplied a conclusion nobody measured, and from then on the conclusion travels on its own without the drawing and without anybody remembering how it was reached.

Do these notes have any evidence for the flattening at the right hand end?

The evidence exists, and it arrives as arithmetic rather than as a picture. Throughput: The Rate the System Actually Produces works a single stationery works in full, and everything below is quoted from there rather than rebuilt here.

The works belongs to Anjani Stationers Private Limited, invented for teaching and trading nowhere. The works turns out hard-bound registers through three stages taken in order. The first stage cuts at 150 registers an hour, the second prints at 125, the third binds at 100. The slowest of the three governs all of it, so the whole line turns out 100 an hour. Set that rate against 4,000 line-hoursA unit that pairs one line with one hour of the time it was open. Sixteen of them is what two lines standing ready through an eight hour shift come to, and they count time offered rather than goods finished., which is what two lines running eight hours over 250 working days come to, and the year's rated capacityThe most a works could turn out in a year, taken as its own hourly rate carried through every hour it treats as open. Read it as an upper limit nobody expects to touch, and read how it gets assembled where it is taught in full. is 4,00,000 registers. Paper in against registers out gives a yield of 70.42 per cent.

The throughput treatment then works two changes, both of them in the conditional, as demonstrations of what would follow rather than as anything that took place. Binding is the stage currently governing everything, and the first change lands there. The result is put this way.

Cutting and printing can both keep pace with that, the line-hours are untouched, and in that working the year's ceiling then reads 5,00,000 registers instead of 4,00,000. The gain is 1,00,000 registers of yearly ability, bought at one stage and nowhere else. Now the question worth asking: what would a second change of the same kind, at the same stage, be worth? The same working answers it, and the answer is the right hand end of the shape arriving as a number. Binding at 125 an hour would no longer be alone in setting the pace: printing sits at 125 too, and the pair of them would hold the ceiling jointly.

The second change of the same kind at the same place returns exactly nothing rather than merely less. That is what a flattening curve says when a number finally comes out of it, and the number here is a nought.

Which part of that is evidenced, and which part is not?

The pair is worth taking apart slowly. The fall in return is published: 1,00,000 registers of yearly ability, then nothing, both worked in these notes, both checkable by anybody who opens them. The fall is movement up the side of the shape, and it is real.

The effort that would buy either change is published nowhere. Neither change is priced, in money, in hours, in machine time or in anything else, anywhere in these notes. The vertical movement is published and the horizontal axis is published for nothing at all.

Follow that through to the drawing. The missing axis has a consequence rather than merely being awkward. Two heights are known and the distance between them along the bottom is not. So the two marks can be placed in order but they cannot be placed in proportion, and a smooth line drawn between them would be manufacturing the distance. The line would look like a finding. The line would be a guess with a ruler held against it.

The cheerful half deserves saying plainly too. A return that falls to exactly nothing carries more weight than most carefully measured curves ever produce. A nought cannot be rounding, cannot be within the error, and cannot be argued down to a smaller number by somebody who wants a different answer. The one thing these notes evidence about this shape happens to be the one thing that is hardest to wriggle out of.

And the flat beginning at the other end?

The flat beginning is evidencedBacked by something somebody actually measured and wrote down, as opposed to drawn because the shape is expected to go that way. A stretch of a drawing can be perfectly reasonable and still be evidenced by nothing. nowhere in these notes, and saying so straight is worth more than filling it in. Now earn that sentence rather than leaving it as a shrug.

Three things would have to exist before anybody could evidence the flat beginning of this shape. The first is what was spent on improving one particular thing, period by period. The second is what each period's spending returned, printed beside it. The third is that both of those cover the same thing, and the pairs then line up. All three together are the disclosure. Nothing less produces a single point on the bottom axis.

Now walk what these notes actually publish about spending. One business names three things it spent Rs 24,40,000/- more on across two published years, being people, space and the binding operation it bought into, and all three of them do carry a price. Employee benefits rose Rs 6,00,000/-, the fixed part of other operating costs rose Rs 11,40,000/- on a second warehouse taken during the year, and depreciation and amortisation rose Rs 7,00,000/- on the assets bought. The three come to the Rs 24,40,000/- exactly. The notes that carry that split stamp it as an estimate rather than a disclosure. All three are priced and the three prices reconcile to the total exactly, and still nothing there puts a single point on the bottom axis. An estimated split of a standing cost across people, space and assets is not a measure of effort put into improving one particular thing, and no return is printed beside any of the three.

The silence is not a peculiarity of this one set of accounts. The silence is the ordinary condition, and it connects to a finding made elsewhere: from outside a business, a spend on something new and a spend on more of the same arrive as the same line. The disclosure this shape needs is therefore the disclosure almost nobody makes. The flat beginning of the curve is drawn everywhere and evidenced almost nowhere.

One honest course is left. The frame is drawn with one shoulder marked and the other left as an outline, and the drawing itself says which is which. That counts as something found rather than something missing, and the difference matters: a drawing that shows where its own evidence stops can be argued with, and the same drawing completed smoothly cannot, because there is nothing left in it to disagree about.

Why does progress jump rather than simply stopping?

The answer is already written in the same throughput working, and writing it again in weaker words would be a loss. Once binding runs at 125 an hour and printing also runs at 125, the two tie. The works cannot pass 125 an hour until both of them move: lifting binding again by itself leaves printing holding the line, and lifting printing by itself leaves binding holding it.

Read that as a statement about the shape and it becomes the jump. The next gain is available and it needs a different move, not more of the same move. A second curve is not a mystical event and it is not somebody's optimism. A second curve is a different place to spend. The flattening of the first curve is the signal to go and ask where that place is, rather than a signal that anything is over.

Notice the effect of the tie on the constraintWhichever step in a sequence is holding everything else back, so that the whole sequence can go no faster than it does. Which step that is can change once somebody improves one of them.. The constraint does not vanish when it is fixed. The constraint moves, and here it moves into a place where two stages hold it jointly. One of those two stages alone can no longer shift it. Which step is slowest has to be asked again after every change, and a capacity plan resting on the ranking somebody made a year ago spends at whichever stage used to be the trouble.

And now the boundary, stated in the same breath so that it reads as precision rather than as hedging. No period is named in which anybody makes that move, no pace is given at which anything happens, and nothing is read off any shape. The correction travels again as well: nothing was bought and nothing happened. Both changes are worked on paper.

So is the flattening a fact about the machine?

No, and this is where the whole reading order arrives at its own centre. Take the same kind of purchase, a lift of 25 registers an hour, and put it at two different stages. At binding it would be worth 1,00,000 registers of yearly ability. At printing it would be worth exactly nothing. The works would still make 100 an hour and still make 2,50,000 registers a year, and the cost of it would be worse than nothing: a faster press bought there joins the pile of charges that sit where they are whatever the works turns out, and the volume carrying that pile would not have shifted at all.

Nothing about the two machines accounts for the gap between those two answers. Same kind of change, same size, same building, same people, same year. An innovation's return is not a property of the innovation, it is a property of where the change lands.

Applied to the shape, that yields the payoff. The identical improvement sits at a different height depending on where it lands, and there is no such thing as a curve for a technology considered on its own. The flattening belongs to a position rather than to a machine, and any sentence valuing an improvement without naming where it lands is unfinished.

Here is the version anybody can picture. A household fits a second tap in a kitchen fed by one thin pipe. The tap is a good tap, the fitting is competent, the plumber did nothing wrong. The pipe was holding the water back and nobody touched the pipe, so the water arrives no faster. Nobody in that kitchen would blame the tap. Put the same thing on a printed proposal with a price quoted beside it and, somehow, the tap gets the blame.

What can a reader outside a business honestly do with any of this?

Not measure a curve, and it is worth being clear about that before offering anything else. A reader outside can ask two plain questions. Both are usually unanswerable from published material, and asking them anyway names what is missing.

One: where did the last change land? Not what it cost, and not how clever it was. Which part of the work did it touch, and was that part the one holding everything else back? Two: what did the next change at the same place return? The second question is the whole right hand end of this shape, asked in words that need no drawing at all.

Both questions are about position rather than about size, and neither one needs a curve to be drawn. Nobody published the effort figure and nobody is going to, and both questions survive that.

And when the answer is not disclosed, that is what gets written: that the business made changes, that the accounts name what was bought without pricing it separately, and that the return on either cannot be established from outside. The note reads as thin only against the alternative, a sentence that sounds firm and rests on nothing. Silence about the return is the ordinary situation rather than a special failing, and a note that says so is more useful than one that hides it.