One line in 5 has nobody under it

600 charts, 40 lines each, against all 3,114 settlements of the pinned public-domain gazetteer this product ships. A line counts as quiet when no settlement lies within 80 km of it: the innermost band, the only one this engine allows to say a line is over a place, and the one figure in that scheme that is ours rather than borrowed from the literature.

The charts are synthetic instants rather than real birth data, because the question is about where the forty lines fall and that is set entirely by the moment. They are spaced by intervals like 9d 5h 07m rather than by whole days on purpose: a sidereal day is 23h 56m, so stepping a whole number of days would hold the sky nearly fixed and sample almost the same longitudes forever, a corpus of one dressed up as a corpus of hundreds.

Everything below is computed from that record at build time. Nothing on this page is a figure somebody typed.

Each row asks the same question at a different radius: what share of lines have nothing at all inside this distance? The answer falls by a factor of about 28 between the innermost published orb and the outermost.

That last row is the commercially interesting one. A tool reading at 805 km, the widest orb anyone in the literature publishes, can offer you somewhere 99.3% of the time. It is not finding more than a stricter tool does. It is counting further away as near. Both tools are looking at the same sky and the same cities; the only difference is the radius at which one of them stops calling a city “yours”.

The bands are cumulative, not rings: the 320 km row counts lines with nothing inside 320 km at all, which is why the numbers fall as the radius grows. That is the form that answers the reader's actual question. Would a tool with a wider orb have found me something?

0.7% of chart-lines, 175 of 24,000, have no settlement within 805 km along their entire length. Not a small town, not a distant one: nothing in the gazetteer, anywhere on the curve, at the widest radius any practitioner has published.

Those are rare per line and common per person, because a chart has forty of them: 22.5% of charts have at least one. Roughly one reader in 4 has a line that runs the whole way round the Earth without passing near anybody.

The corpus above is synthetic, so here are the same facts on the three published charts this site shows complete readings for. Every row is reproducible: open the reading, open the line page, measure.

Frida Kahlo's Sun and Jupiter Ascendant lines are the striking pair. They are lines a tool would ordinarily be delighted to talk about, and on her chart they cross open Pacific for their entire usable length. The last row is the opposite kind of case: Einstein's Pluto Descendant line misses Majuro by 90.5 km, just outside the 80 km band, and reported as quiet rather than rounded in, because a threshold that bends for a near miss is not a threshold.

Across all three charts: Einstein 4, Kahlo 9, Hendrix 7 quiet lines of 40 each. That is 20 of 120, on a corpus far too small to carry a page, and it lands inside this study's interval of 19–19.8%.

The rest of this site quotes 21 of 120, or 18%, and the extra line is not a discrepancy but a different question. This study asks whether anything is there. The product asks whether there is anywhere it can name. Jimi Hendrix's Mercury Imum Coeli line passes 1 km from Mandalay, Myanmar with 9 settlements inside the band, and every one of them is in Myanmar, which sits on the US State Department's Level 4 list. A reading withholds those, so the line is geometrically busy and has nothing to offer. It is one line in 120, and it accounts for the whole difference between the two counts.

Nobody has a mean chart. The average is 19.4% of forty lines, but the middle eighty per cent of charts fall between 12.5% and 27.5%, and the full corpus runs from 5% to 45%, that top figure being 18 lines of 40 landing nowhere anybody lives.

The three published charts show the same spread in miniature: Albert Einstein 4, Frida Kahlo 9, Jimi Hendrix 7. Same method, same gazetteer, more than double the quiet lines on one chart as on another.

The interval is computed across charts rather than across lines because the chart is the unit that was sampled. The expected reason, that forty lines of one chart share one sky and so are not forty independent observations, was checked and is not true here: the observed spread between charts is 5.4 points against a binomial expectation of 6.3 for forty independent lines. Correcting for clustering that is not there would have made this interval narrower, not wider.

The study is always computed four ways rather than once, over corpora starting decades apart with unrelated step intervals. The headline moves by 1 percentage point across all four, which is what entitles it to be stated as a single number.

The planet does not matter. The whole spread across the ten bodies is 0.9 percentage points, from sun at 20% to pluto at 19.1%, which is about the same as the 1-point wobble the headline itself shows between corpora. There is no effect here to report, and reporting the null is the point: silence is a fact about where the oceans and the empty quarters are, not a fact about the body. No rival method computes it away.

The angle matters slightly, and the effect survives checking. Meridian lines are quiet 20.2% of the time against 18.6% for horizon lines, a gap of 1.6 points. A meridian line is one north-south sweep through a single longitude, so it gets fewer chances to pass near anybody than a curve crossing many latitudes does. The gap comes out +1.7, +1.1, +2.2, +1.3 points in the four corpora, the same sign every time, which is the whole reason it is stated here and the finding below is not.

The first corpus computed here showed Ascendant lines quiet 21.5% of the time against 16% for Descendant lines. A 5.5-point gap, larger than the angle-class effect above, with a story ready to explain it and a standard error that made it look decisive. It is noise.

The gap changes sign. What produced it was sampling a single corpus and then trusting a standard error computed as though the lines in it were independent draws from the sky. They are not, and the size of that mistake is measurable rather than a matter of opinion: the naive standard error for this gap is 1.4 points, while its actual spread across the four corpora is 3.4, about 2.4 times larger. A corpus of instants stepped at a fixed interval is not a random sample of skies, so a statistic that keys on where lines fall inherits structure from the step. No mechanism beyond that is claimed here, and none is needed: the comparison is the reason the fix is four corpora with unrelated steps rather than a better formula applied to one.

It is on this page rather than deleted from history because it is the most useful thing the study can show about how to weigh the rest of it. The four corpora exist so that this class of finding dies here instead of on your screen. Everything above passed that test; this did not.

Two further limits worth stating. The gazetteer holds settlements of about 100,000 people or a national capital, so “nothing is near this line” means no settlement of that size. A line over a village of four thousand reads as quiet here. And the corpus is synthetic instants, uniform in time, whereas real birth data is not: it clusters in populated longitudes and recent decades, so a population of real charts would not be expected to match this exactly.