A person has two work records. The first runs from 09:00 to 10:00. The second runs from 09:30 to 10:30.
Add the durations and you get two hours. Combine the time they cover and you get ninety minutes. Both calculations are straightforward. They answer different questions.
The mistake begins when a report adds the rows, calls the result time worked and forgets to mention the shared half-hour. A perfectly accurate sum has become a misleading claim.
That is the interval fallacy: treating a collection of durations as though every recorded minute occupies a separate minute on the clock.
The half-hour did not come from nowhere
Draw the two records on the same timeline:
| Record | Start | End | Recorded duration |
|---|---|---|---|
| A | 09:00 | 10:00 | 60 minutes |
| B | 09:30 | 10:30 | 60 minutes |
Between 09:30 and 10:00, both records cover the same time. The separate durations total 120 minutes. Their combined coverage runs from 09:00 to 10:30: 90 minutes. Subtract that coverage from the sum and the overlap excess is 30 minutes.
The relevant operation is the union of intervals. Combine the admitted spans and count each covered second once. With more than two records, calculate the union across the whole set. Adding every pairwise overlap is not a substitute: three records covering the same period can make that shortcut subtract too much.
The original records still matter. Combining their clock coverage does not mean deleting them or pretending that the two activities were the same activity.
An overlap is evidence, not a verdict
A database query can run while its operator answers a message. A meeting can overlap a recorded approval. Two systems can describe the same work. A person can report time that also appears in a system record.
Those possibilities have different meanings. A shared timestamp cannot tell you which one occurred.
It would be convenient to label every non-overlapping minute “deep work” and every overlapping minute “distraction.” It would also be wrong. A single uninterrupted record does not prove concentration. An overlap does not prove poor performance. Neither tells you what the work was worth.
Investigate the source before judging the person. What starts the clock? What stops it? Does the record describe a process step, a reported work interval or screen coverage? A process can remain open while nobody is working on it. An application can remain visible while its user is elsewhere.
Keep one authority for the calculation
Ghost Observatory’s Engine calculates the published results. The Reader presents them. A chart should not quietly invent a second answer from whatever rows happen to be visible.
For recorded work time, the documented calculation combines a person’s admitted work intervals within the relevant day and reporting window. It preserves distinctions between system-recorded, self-reported and unclassified work. Screen observations remain separate from the pooled work total.
This matters when sources overlap. Their individual totals can each be correct without being safe to add together. The combined quantity answers how much clock time the admitted work records cover. It does not establish productivity, effort or every minute actually worked.
A duration with no admissible position on the clock needs separate treatment. Five reported minutes cannot be inserted into a convenient gap merely to complete the picture. Missing information is a limit on the result, not permission to improvise.
Ask a better question of the total
Before rewarding a large number, ask what it counts. Separate recorded duration, combined clock coverage, overlap and the value of the outcome. Compare like with like, using the same person, period and evidence basis.
The point is not to make everybody’s hours smaller. It is to stop a report from saying something its records cannot support.
One hour plus one hour is still two hours. Two overlapping one-hour records do not necessarily describe two hours of a person’s day.