Time saved, strain, and who pockets the difference
“It saves me time” is the most common sentence about AI at work and the least useful: it holds three. The first has a mathematical ceiling, the second can move the other way, and the third is not yours.
Press a developer on what changed since they started working with an assistant and the sentence comes apart. The same work takes fewer hours. Those hours no longer feel alike: lighter, or heavier. And more is expected of them per day than before. The three arrive together, so they sound like one; they are not.
None of what follows is new, and none of it is about AI. The oldest piece is an 1865 book about coal. What is new is only this: the three now land on the same person, at the same time.
Only one share of your work goes through the assistant. The rest does not move, and it is what sets the limit. A 1967 rule says it in one line: speeding up a fraction of a task can never bring the total below what the untouched fraction weighs. A model twice as fast next year will not shift that wall: it only approaches the same asymptote sooner.
// The 1967 rule: the accelerated share shrinks, the rest does not move.
const relativeTime = (share: number, speed: number) =>
1 - share + share / speed;
// Review is a tax on the gain, not on the work: it takes back a fraction of
// what was saved. At review = 1 the day returns to exactly its former length,
// never longer.
const effectiveTime = (share: number, speed: number, review: number) => {
const t = relativeTime(share, speed);
return t + review * (1 - t);
};The review term is the point of the model. Without it you draw the day you would have if nothing ever needed checking: a curve that flatters and lies. With it, the gap between the two traces is the bill: what verification takes back from what speed gave.
Four settings, handed over one at a time. Each redraws the trace below: the pale line is the 1967 rule alone, the accented line takes the review cost off it, and the gap between them is the bill.
- 01
the share that goes through the assistant
Only one fraction of your work passes through the tool. The rest does not move, and it, not speed, sets the ceiling. Push this slider and watch the dashed line lift; it is the only control that moves it.
1967. The rule is published for parallel computers: speeding up a fraction of a task can never bring the total below the weight of the fraction left by hand.
- 02
the speed of the assistant
Now push speed to the end. The dot rises, flattens, then nearly stops: the whole right-hand half of the plot is worth almost nothing. A model twice as fast next year will not pass the ceiling: it will reach it sooner.
The consequence is arithmetic, not technological. No generation of model has ever lifted it, and none will.
- 03
what review takes back
What remains is what the assistant does not take: judging, checking, deciding. It is a tax on the gain and not on the work: at 100 % the day returns to exactly its former length, never longer.
This is the term the original law never had to carry: a parallel machine does not proofread what it has just produced.
- 04
the share you make visible
The last setting describes an organisation rather than a machine. The fraction of the gain you show becomes the new normal; the fraction you keep never existed as far as anyone else is concerned.
1865. A book about coal names the mechanism: making a resource more efficient does not reduce its consumption, it raises it.
A shorter day can be a harder day. What remains is what the assistant does not take: judging, reviewing, deciding, and that material is dense. The model therefore separates two quantities the original sentence merged, hours and load, and shows them side by side. One sometimes falls while the other rises.
Past roughly ten dense hours the comparison is dropped rather than shown: a day without the assistant would not be a longer day, it would be a day that does not exist. Comparing a load against a fiction would be dishonest, so the simulator says so instead of drawing a figure.
The share of the gain you make visible becomes the new normal; the share you keep never existed as far as anyone else is concerned. It is the only parameter in the model that describes an organisation rather than a machine, and it is the one that decides who leaves with the hours. The 1865 book had already named the mechanism: making a resource more efficient does not reduce its consumption, it raises it.
- No storage, no analytics, no account. The six settings live in the address: the page link is the version you just built, and sharing it passes on the whole assumption.
- No figure is put forward without the control that produces it being on screen. A result you cannot contradict is no better than an opinion.
- The formulas are written in LaTeX and rendered at authoring time, never in the reader’s browser. A test fails if you forget to regenerate: the demonstration cannot drift from the text without the build noticing.
And one caveat, said once rather than implied throughout: none of this touches the workload you are given, expectations left deliberately vague, or a condition nobody has treated. Those are the three that recur most often in burnout, and this model measures none of them. It separates three claims; it treats nothing.