PYTHON · NUMPY

The wrongly known fraction

Forty nodes cover a field, six of them drifting. Which is the larger number?

Distinguish volume no sensor reaches from volume a sensor reaches and misreports, and show why the second is the more expensive of the two.

01Challenge

A grower tells you their field is well instrumented: forty nodes, full coverage, no gaps. Six of the nodes have not been calibrated since installation. Decide what fraction of that field the grower actually knows, and defend the number.

Predict firstForty nodes cover a field, six of them drifting. Which is the larger number?

02Model

A sensing system divides a volume into three parts, not two. There is the part some sensor reaches and reports correctly. There is the part no sensor reaches at all, which TR-2026-44 calls the unknown fraction. And there is a third part that gets left out of every account: the volume a sensor reaches and reports wrongly. A drifted sensor does not go quiet. It keeps reporting, on schedule, with the same number of decimal places it had on the day it was installed. Nothing downstream can tell the difference. So the unknown fraction is the honest part of the problem, because a gap announces itself as a gap. The wrongly known fraction is worse, because it is counted as coverage and acted on as fact. A field with forty nodes and six of them drifting is not a field with thirty-four nodes. It is a field with thirty-four nodes and six confident liars.

03Guided practice

Work in the units the system reports. A node covers some volume, so a drifted node covers that same volume wrongly. Compute all three fractions and notice that the number the dashboard shows is the sum of the first and third, which is exactly the quantity nobody should trust.

04Feedback

PASS WHEN You separated the three parts and found the gap between reported coverage and trustworthy coverage. That gap is the whole subject of this course.

If your run fails, check:

Check that resolved and wrongly_known use the same REACH_VOLUME. A drifted node does not cover less ground, it covers the same ground wrongly.
unknown is what is left after every node is counted, drifted or not. Subtract the full mesh, not just the good part.
reported is what a system with no calibration model would print: every node counted as good.

05Retrieve & space

A drifted sensor adds to the wrongly known fraction, not to the unknown fraction.
A gap announces itself. A drifted reading does not.
Reported coverage is trustworthy coverage plus wrongly known volume, which is why it is always the larger number.

06Mastery & project

State, in one sentence and without using the word accuracy, why six drifted nodes out of forty are more dangerous than six missing nodes out of forty.

Take any instrumented system you have access to, or the specification of one, and write the three fractions for it. Where you cannot compute a number, write what you would have to know to compute it. The list of missing knowledge is the deliverable.

GO FURTHER · THE LIVE PLAYGROUND

The instrument this builds on ↗ · Set a grain bin's sensors and read the fraction no probe reaches. This lesson adds the third band that instrument does not yet draw.

← Trusting the Mesh: When a Sensor Network Stops Telling the Truth How fast a sensor forgets →

PYTHON · NUMPY

The wrongly known fraction

Forty nodes over a field. Six are drifting. Compute what the dashboard claims and what the field actually supports.

You read

the arrays and values already in scope

You change

the code you write in each cell

Fixed

the dataset and the checks that grade you