Concentric

Notebook

26 August 2026

The rule that keeps this from being astrology

Four points always look like they have a shape. That is true of noise too.

Plot four numbers in a row and your eye will find a shape in them. A cliff, a taper, a plateau, a dip in the middle. It will do this whether or not one is there, and it will do it confidently.

That reflex is the entire business model of several personality products, and it is the thing this instrument has to defend against hardest, because it produces exactly four numbers per trait and then draws them as a line.

What the site does about it

Every profile is resampled a few thousand times within its own uncertainty, and the shape is classified each time. A name is printed only if the same name comes back at least 60% of the time.

Below that, the page shows the four points with their error bands and says the pattern is not distinguishable from noise. No label. Not a hedged label — no label.

That threshold is calibrated rather than chosen: at 60% the rate of wrongly-named shapes sits inside the target. It could move if the data says so. It cannot move because a page looked empty.

What the calibration also found

Two things worth admitting, since both limit what the shape names are worth.

A clean straight ramp gets confidently called a cliff about 30% of the time at realistic noise levels. The reason is structural: the cliff test looks at the largest of three gaps, and the maximum of three noisy numbers is biased upward. And the bootstrap cannot rescue it, because it resamples around the observed curve — once noise has bent a ramp into a step, resampling faithfully confirms the step.

And the whole module is underpowered for individual feedback. At realistic noise it reaches about 50% power for a total change of two points on a seven-point scale, and does not approach the conventional 80% until the change is nearly three points — half the scale. Changes smaller than about two points are mostly invisible.

Why publish that

Because it decides what a reader should do with their own result, and because it might be the finding.

If real gradients turn out to be subtle, this instrument will mostly say nothing, and a respondent will see two or three of their ten traits labelled and the rest reported as unresolvable. That is the correct behaviour. It is also, if it holds up, an answer to the research question rather than a failure to answer it — and the temptation will be to loosen the thresholds until the page speaks.

The thresholds do not move. If the module has little to say, the module says little, publicly, and that is the result.