Nineteen dates on this ground, each followed down to what set its clock

Set by Another Clock

A date is read off something that changes at a rate: carbon decaying, a lichen widening, a poet loosening his verse, the Earth slowing in its turn. None of those clocks can tell you by itself how fast it runs. Almost every one was set against another clock that someone had already dated, and that one against another. The Artificial Wasteland followed nineteen of its own dating layers down, quoting at every step the sentence that says what set the clock, and joining layers where one stops and another goes on. Seven of the chains reach a date someone wrote down, eight reach the sky, five reach a place where their layers stop saying (two reach more than one of these), and one reaches nothing dated at all: Kelvin’s 98 million years for the age of the Earth, timed by nothing but the year, and about a forty-sixth of the age measured in 1956. The second itself comes out of the sky. The caesium count that defines it was timed from 1955 to 1958 against photographs of the Moon, and a mean solar day of about 1820 was exactly 86,400 of them.

Where the chains end

Nineteen chains, 82 steps, nineteen layers. Four chains cross from one layer into another before they stop, and three go past this ground altogether: two into a paper on the history of the second, and Kelvin’s into two papers of his own. Seven reach a date that someone wrote down: the year a living tree was bored, nine gravestones in the Hagensborg graveyard, the production records of the Athenian theatre, the manuscripts of Pliny, a Babylonian tablet. Eight reach the sky: the Moon’s place, the Earth’s orbit, a satellite’s star catalogue, computed ephemerides, and the turning of the Earth that the second was taken from. Five reach a place where their layer stops saying what is underneath, and one reaches nothing dated. Two reach more than one of these ends, so the counts overlap.

Take away everything anyone wrote down, and six dates lose their footing. Take away the sky, and six do. Take away both, and thirteen of the nineteen are gone, five stand on something their layers do not name, and one stands: Kelvin’s. It is the only clock on the tray that, in its own layer’s account, needs no dated thing at all, and by the age measured in 1956 it was short by a factor of about 46.

When the other clock is the same clock

A clock can only be set by another clock, and the danger is that the other one is not really other. Eleven times, in nine of these layers, the layer stopped to say so in its own words.

• the 48th core and the other 47 Asking whether 47 of them can date the 48th is asking whether a collection agrees with itself. (Every Tree Wrote the Same Bad Year)
• two chronologies and one method Both collections were dated by crossdating in the first place. (Every Tree Wrote the Same Bad Year)
• the handbook dates and the count This agreement is not evidence: those handbook dates were reached largely by this same count, so the clock is just agreeing with itself. (The Clock in the Verse)
• three plays and one production The three plays of the Oresteia vouch for each other: leave Agamemnon out, and Libation Bearers and Eumenides are still there saying 458. (The Clock Only Euripides Kept)
• the sample and the curve It only cancels because the curve is published on the same convention as the sample. (Where the Curve Goes Flat)
• three pollen dates and one assumption A shared error would move all three pollen dates together, and three agreeing dates could not detect it. (The Seeds Beneath the Steps)
• the verifying paper and the original paper 7 of that paper's 11 authors had also written the 2021 paper (The Seeds Beneath the Steps)
• the target distances and the rate The target distances are themselves generated from 4.5 cm/year, so the zero at 4.5 is a dimensional identity, not an independent recovery. (The Ocean Floor Kept Both Copies)
• the rate and the pairs it is tested on The same 14 pairs estimate the refitted constant and then receive it back. (716 A.D., Give or Take Two Thousand Years)
• the length of day and the Earth’s turning, from the same file Two columns of one file are not fully independent. (Every Leap Second Was Already in the Spin)
• the plaque and a catalogue timed in February 1970 That catalogue refers its solutions for two of the five, B0329+54 and B1642-03, to days in February 1970 itself, so for them it is a second clock rather than a second witness. (The Rubber Second)

None of these sentences is an accusation. Each is a layer telling you where its check stops being independent, which is the most useful thing a check can tell you. This page is the same kind of thing. Its own check confirms that every sentence it quotes is on its layer’s page, which is this page agreeing with its members. Whether the members are right is a matter for their own checks, and for the claims passes that re-read them against their sources.

Writing and the sky set each other

The chains that end in the sky do not end there cleanly, and the chains that end in writing do not either. Before telescopes, the record of how the Earth turned is people writing down eclipses: mostly the times of eclipses of the Moon, and also where the Sun went out. A Babylonian tablet of 136 BC has totality over the city that wrote it, and computed without the clock correction the shadow falls over Morocco, 4,592 km away: the writing dates the Earth (The Sun Was Eclipsed; It Was Total). It runs the other way too. Olson, Doescher and Olson dated van Gogh’s Moonrise to 9:08 in the evening of 13 July 1889 from the Moon and a ridge, and The letters edition now dates letter 790 by it. (Nothing but the Morning Star).

And the second, which two of these chains are timed in, was set by both at once. In 1960 the General Conference on Weights and Measures ratified a definition taken from the year: The second is the fraction 1/31 556 925.9747 of the tropical year for 1900 January 0 at 12 hours ephemeris time. That year came from Newcomb’s Tables of the Sun of 1895, and the tables from the observations analysed by Newcomb, ranging in date from 1750 to 1892, written down by observers over nearly a century and a half. Then the atom took over, but it was set to the sky first. Photographs of the Moon and surrounding stars were taken by the USNO dual-rate Moon camera over the period 1955.50 to 1958.25 to determine the Ephemeris Time from the position of the Moon at a known UT2. Against them the caesium standard at the National Physical Laboratory came out at 9 192 631 770 Hz with a probable error of ± 20 Hz, and The principal uncertainty arose from the astronomical measurements themselves. In 1967 that count became the definition: The second is the duration of 9 192 631 770 periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the caesium 133 atom.

So, in the words of Nelson and his colleagues, The SI second is equivalent to the second of Ephemeris Time, which in turn is equal to the mean solar second of the early nineteenth century. The epoch at which the mean solar day was exactly 86 400 SI seconds was approximately 1820. The leap seconds measured the Earth of their own years against the Earth of about 1820. In 2001 Nelson and his colleagues wrote that the insertion of leap seconds is due to the fact that the present length of the mean solar day is about 2.5 ms longer than a day of precisely 86 400 SI seconds. It has not stayed that long: since 2020, a layer here finds, the typical day has been shorter than 86,400 seconds. One layer here integrates the measured length of every day since 1972 and finds that 27 steps fall out for 27 leap seconds, 23 of them on the exact announced day. (Every Leap Second Was Already in the Spin). Another reads the Pioneer plaque’s pulsar periods in the seconds UTC kept from 1966 to 1971, stretched to keep pace with the Earth’s turning, and five of them fall within fifteen days of one another in early 1970 (The Rubber Second).

The clock with nothing dated under it

One chain on the tray has nothing dated under it. In 1862 Kelvin dated the Earth from the heat coming out of it. Go down a mine and it gets warmer, about one degree Fahrenheit for every fifty feet. If the Earth began molten, a gentler gradient means a longer cooling. The Kelvin layer gives Kelvin's recipe with his own three inputs: a starting temperature for melting rock, the gradient, and the diffusivity, how quickly heat spreads through rock. None of the three is a date, and With his values it says 97.5 million years, and he printed 98.

It was still timed by a clock: the year. The rate came, in his words, from a mean of values of the conductivity, in terms of the thermal capacity of unit volume, of the earth’s crust, in three different localities near Edinburgh, which I have deduced from the observations on underground temperature instituted by Principal Forbes there. Kelvin, then William Thomson, had reduced those observations himself by splitting each thermometer’s year into waves, the first having a year for its period, the second a half year, the third a third part of a year, and so on. So Kelvin’s 98 million years are counted in Edinburgh’s seasons. A year is a period, not a date, and every clock on this tray counts in a year or a second taken from the sky. What Kelvin’s lacks is anything dated.

In 1895 John Perry, a former assistant of Kelvin’s, doubted not the arithmetic but the body: if there is even only ten times the conductivity inside, it would practically mean that Lord Kelvin's age of the earth must be multiplied by 56. What settled it was another clock. In 1956 Clair Patterson measured lead isotopes in meteorites and got 4.55 ± 0.07 × 10⁹ yr, and Kelvin’s 98 million is about a forty-sixth of that. The Kelvin layer, Right Clock, Wrong Body, puts the rule in one line: Every clock measures the time since its reservoir last forgot. Heat in a lid forgets in tens of millions of years, and Lead in a meteorite has not forgotten yet.

What this page does not show

• All of dating. These are the nineteen dating layers on this ground, not the methods of the world. Luminescence dating comes up only inside the White Sands layer, uranium-series dating has no layer here, and the molecular clock appears once, as a date one layer cites and none runs.
• The bottom of the five that stop. Five chains stop before they reach writing or the sky: the calibration curve beyond 13,900 years, potassium-argon ages, the reversal that pins the bottom of the Dome C ice, the magnetic field model the runways are read against, and the constant Lees dated the split of English and German with. That is a fact about these layers, not about the world. Each of the five rests on something; these layers do not say what.
• Whether a root’s kind is fair. The kind each chain ends in (written down, the sky, nothing dated, the layer stops) is this page’s reading of the last sentence quoted. The check confirms the sentence is there. It cannot confirm the reading.
• The unit. Every clock here counts in years or seconds, and the year and the second come from the sky. The chains follow what set each clock against something dated, and the buttons take away dated things, not the unit. That is why Kelvin’s still stands without the sky, though the year timed its rate.
• The joins, as the members’ own claims. Where two layers describe the same thing, the radiocarbon curve or a living tree’s written year, this page takes the second as describing what the first relies on. Neither layer says so of the other.
• Circles nobody pointed out. The eleven above are the ones the layers name themselves. There may be others.
• A member mid-reading. Every Tree Wrote the Same Bad Year was being re-read against its sources by the assay line when this page quoted it. If its sentences change, this page’s check will say which.

Every chain, in words

The tray above, written out: each date, each step and where it comes from. This is also what a reader without scripts sees.

1. A radiocarbon sample measured at 2450 BP

   pieces spread over three and a half centuries: returns a 95.4% highest-posterior-density region made of several disjoint calendar intervals spanning roughly three and a half centuries (Where the Curve Goes Flat)

   1. what is read: the carbon-14 left in it. A conventional radiocarbon age in years BP is not a calendar age. It is a transform of the measured isotope ratio (Where the Curve Goes Flat)
   2. how fast it runs: Libby's half-life, wrong and kept. The mean life 8033 years is fixed by convention, not by physics: it is 5568/ln 2, and 5568 years is Libby's original half-life, which is known to be wrong. (Where the Curve Goes Flat) What the layer reports: It only cancels because the curve is published on the same convention as the sample.
   3. where it starts: "present" is 1950. was fixed at AD 1950 (Where the Curve Goes Flat)
   4. matched to something dated: the calibration curve. A calendar date is what you get after pushing that number backwards through a curve built from tree rings (Where the Curve Goes Flat)
   5. ticks, counted: rings, counted. tree rings counted one by one to about 13,900 cal BP (Where the Curve Goes Flat)
   • Ends: someone wrote it down.
     1. matched to something dated: matched before counted. What you do instead is find the year the weather went wrong and look for it in everything else that was standing. (Every Tree Wrote the Same Bad Year) What the layer reports: Crossdating returns the calendar year of a ring.
     2. tied to a dated thing: a living tree, a written year. a core taken from a living tree has a known outermost year, because someone was standing there with a borer in a year they wrote down (Every Tree Wrote the Same Bad Year)

2. Seeds in the layers holding the White Sands footprints

   about 22,900 to 21,100 years ago: 22.86 ± 0.32 to 21.13 ± 0.25 ka (The Seeds Beneath the Steps)

   1. what is read: carbon-14 in each seed. 19,010 ± 120 radiocarbon years (The Seeds Beneath the Steps)
   2. where it starts: what the lake water held. If the lake water carried carbon dissolved from old rock, carbon whose radiocarbon had long since decayed, every seed would read older than it is. (The Seeds Beneath the Steps) What the layer reports: The sources agree on no ancient value of R; the slider explores an assumption, it does not measure one.
   3. matched to something dated: the calibration curve. Each raw age is calibrated against IntCal20 with a uniform calendar prior on a one-year grid. (The Seeds Beneath the Steps)
   • Ends: the layer stops here.
     1. matched to something dated: past the rings, other archives. and beyond that a statistical integration of speleothems, corals, and marine and lake sediments on their own timescales (Where the Curve Goes Flat)

     The seeds are older than 13,900 years, so the part of the curve under them is not tree rings. The layer that describes the curve does not say what those other timescales rest on.

3. The first ring in each of 48 Arizona tree cores

   each to its published year: Every one of the 48 Arizona cores lands on its published year against the Colorado chronology (Every Tree Wrote the Same Bad Year)

   1. what is read: ring widths. 45,411 published ring measurements from 109 cores in three collections (Every Tree Wrote the Same Bad Year)
   2. ticks, counted: counting alone fails. You cannot date a piece of wood by counting its rings (Every Tree Wrote the Same Bad Year) What the layer reports: the error of unchecked counting in the Arizona pines was 4 per cent
   3. matched to something dated: the same bad years, matched. What you do instead is find the year the weather went wrong and look for it in everything else that was standing. (Every Tree Wrote the Same Bad Year) What the layer reports: Roughly half the cores produce a "significant" match at a date that is certainly wrong.
   • Ends: someone wrote it down.
     1. tied to a dated thing: a living tree, a written year. a core taken from a living tree has a known outermost year, because someone was standing there with a borer in a year they wrote down (Every Tree Wrote the Same Bad Year)

4. A 150-year-old surface, dated by its largest lichen

   150 years, +45 or −30: for a 150-year-old surface it is “+45 and –30 yr” (The Longer You Look)

   1. what is read: the largest lichen. Find the largest lichen on the surface, measure it, and read its age off a curve built from surfaces whose age you already know (The Longer You Look)
   2. how fast it runs: a growth curve. surfaces whose age you already know, such as gravestones, dated walls and moraines from glacier fronts that someone drew on a map (The Longer You Look) What the layer reports: twenty square metres of 150-year-old rock comes out at a median of 192 years
   3. how fast it runs: the Mount Waddington curve. Larocque and Smith (2004) built it for the Mount Waddington area of British Columbia from 18 surfaces of known age (The Longer You Look)
   • Ends: someone wrote it down.
     1. tied to a dated thing: gravestones. nine gravestones in the Hagensborg graveyard (The Longer You Look)
   • Ends: someone wrote it down.
     1. tied to a dated thing: trees, fossil wood or radiocarbon. moraines dated by the oldest tree growing on them, by cross-dated fossil wood or by radiocarbon (The Longer You Look)
     2. tied to a dated thing: a living tree, a written year. a core taken from a living tree has a known outermost year, because someone was standing there with a borer in a year they wrote down (Every Tree Wrote the Same Bad Year)

5. The deepest dated ice at Dome C, Antarctica

   807,900 years: where the ice is 807,900 years old (Most of the Time Is at the Bottom)

   1. ticks, counted: not counted. Not by counting. (Most of the Time Is at the Bottom)
   2. how fast it runs: a model of snow and flow. A model of snowfall and ice flow gives a first guess at the age of every depth (Most of the Time Is at the Bottom)
   3. matched to something dated: pinned at tie points. the guess is pinned wherever the ice carries a date of its own (Most of the Time Is at the Bottom)
   • Ends: the layer stops here.
     1. tied to a dated thing: a reversal of the field. dated independently to 776,000 ± 12,000 years (Most of the Time Is at the Bottom)

     The ice layer does not say how the reversal was dated. On this ground reversals are dated in lava on land (The Ocean Floor Kept Both Copies), but those are 1966 dates, and nothing here says the 776,000 years comes from that kind of dating.

   • Ends: the sky.
     1. matched to something dated: the Earth's orbit. which follow the slow cycles of Earth's orbit (Most of the Time Is at the Bottom)

6. Magnetic stripes on the Pacific floor

   reversals at 1.0, 2.5 and 3.4 million years: major boundaries at 1.0, 2.5, and 3.4 million years (The Ocean Floor Kept Both Copies)

   1. matched to something dated: reversals, dated in lava. related the central pattern to reversals dated in rocks on land (The Ocean Floor Kept Both Copies)
   2. how fast it runs: a spreading rate. A half-spreading rate turns each land-dated age into a one-sided distance from the ridge (The Ocean Floor Kept Both Copies) What the layer reports: the zero at 4.5 is a dimensional identity
   • Ends: the layer stops here.
     1. tied to a dated thing: potassium-argon. Cox, Doell, and Dalrymple assembled paleomagnetic directions and potassium-argon ages from volcanic rocks. (The Ocean Floor Kept Both Copies)

     The layer does not say what sets a potassium-argon age.

7. The age of the Earth, from its heat (Kelvin, 1862)

   98 million years: With his values it says 97.5 million years, and he printed 98 (Right Clock, Wrong Body)

   1. what is read: the heat gradient. Go down a mine and it gets warmer, about one degree Fahrenheit for every fifty feet. (Right Clock, Wrong Body)
   2. where it starts: a molten start. If the Earth began molten and has been cooling ever since (Right Clock, Wrong Body)
   3. how fast it runs: how heat diffuses. Kelvin put the numbers into a solution Fourier had already written down (Right Clock, Wrong Body)
   4. how fast it runs: Forbes's thermometers. he had worked out from Principal Forbes's thermometers buried in three places near Edinburgh. (Right Clock, Wrong Body)
   • Ends: nothing dated.
     1. how fast it runs: deduced from Forbes. a mean of values of the conductivity, in terms of the thermal capacity of unit volume, of the earth’s crust, in three different localities near Edinburgh, which I have deduced from the observations on underground temperature instituted by Principal Forbes there (Thomson, On the Secular Cooling of the Earth (1862))
     2. how fast it runs: timed by the year. the first having a year for its period, the second a half year, the third a third part of a year, and so on. (Thomson, on Forbes’s underground thermometers (Proceedings of the Royal Society of Edinburgh 4))
     3. tied to a dated thing: three numbers, no dated thing. Here is Kelvin's recipe with his own three inputs. (Right Clock, Wrong Body) What the layer reports: if there is even only ten times the conductivity inside, it would practically mean that Lord Kelvin's age of the earth must be multiplied by 56

     Nothing dated is under it. The year that timed its rate is a period, not a date: every clock here counts in a unit taken from the sky. Its layer runs the same clock on ocean floor whose age is known, and calls itself Right Clock, Wrong Body.

8. Euripides' plays with no outside date

   Hecuba about 423, Ion about 417: The clock puts Children of Heracles about 431, Andromache and Suppliants about 425, Hecuba 423, Electra 422, Heracles 421, Ion 417, Iphigenia among the Taurians 416. (The Clock in the Verse)

   1. ticks, counted: extra syllables, counted. the number of syllables minus twelve (The Clock in the Verse)
   2. how fast it runs: more of them every year. Euripides allowed himself very few of them early in his career, and more and more as it went on. (The Clock in the Verse) What the layer reports: The typical miss is 5.3 years, not five.
   3. tied to a dated thing: eight dated plays. Eight plays have a date from outside the verse. These are the anchors. (The Clock in the Verse)
   • Ends: someone wrote it down.
     1. tied to a dated thing: the production list, or another writer. For a few the date of the first performance is on record, because the ancient summary attached to the play (the hypothesis) copies the official production list, or because another writer mentions it. (The Clock in the Verse)

     The layer does not say how an Athenian archon year becomes a year BC.

9. Aeschylus's Suppliants

   about 468 BC: The verse puts Suppliants in among Persians and Seven, at about 468 (The Clock Only Euripides Kept)

   1. how fast it runs: his own rate, falling. His rate falls as the years go on, by roughly one resolution per hundred lines every three years. (The Clock Only Euripides Kept) What the layer reports: Aeschylus passes: the typical miss is under two years
   • Ends: someone wrote it down.
     1. tied to a dated thing: five dated plays. The years come from the production notices copied into the ancient summaries of the plays. (The Clock Only Euripides Kept)

10. The split between English and German

    about AD 716, in 1953: English and German begin diverging about 716 A.D. (716 A.D., Give or Take Two Thousand Years)

    1. ticks, counted: shared basic words. Lees printed F = .585, from 124 cognates among 212 compared words, and a retention constant k = .805. (716 A.D., Give or Take Two Thousand Years)
    • Ends: the layer stops here.
      1. how fast it runs: his constant, k = .805. His equation was t = ln(F) / 2ln(k). (716 A.D., Give or Take Two Thousand Years)

      The layer does not say what set Lees’s .805. Its own refit, from 14 pairs of languages with a written past, is a different constant, and the layer names the circle in it.

11. The day Vesuvius buried Pompeii

    unsettled: The exact eruption day remains unsettled. (The Date Made From One Word Twice)

    1. what is read: a phrase in Pliny's manuscripts. There is one cardboard scrap on the table. It can be read as non., a day word, or nov., a month word. It cannot be two scraps. (The Date Made From One Word Twice)
    2. ticks, counted: Roman days, counted inclusively. Roman calendar arithmetic is inclusive. The ninth day before the Kalends of November counts November 1 as day one, so it lands on October 24. (The Date Made From One Word Twice) What the layer reports: Ordinary subtraction by nine would land a day early.
    • Ends: someone wrote it down.
      1. tied to a dated thing: the manuscripts. August 24 is the unanimous date reported by the oldest witnesses, but archaeology may still challenge Pliny. (The Date Made From One Word Twice) What the layer reports: October 24 has zero evidentiary basis in the manuscript tradition.

12. How late the Earth turned in 136 BC

    a shadow 4,592 km out: Compute that eclipse without the clock correction and the umbra is over Morocco, 4,592 km west of the city. (The Sun Was Eclipsed; It Was Total)

    1. what is read: a tablet: planets out at mid-morning. In 136 BC the Babylonians watched Venus, Mercury, Jupiter and Mars come out in the middle of the morning (The Sun Was Eclipsed; It Was Total)
    2. how fast it runs: the Moon on uniform time. gravitation runs on TT, a uniform time. (The Sun Was Eclipsed; It Was Total)
    3. matched to something dated: turn the Earth until the shadow covers the city. Drag it until the band covers the city, and read off how late the Earth was. (The Sun Was Eclipsed; It Was Total) What the layer reports: So the slider is not a fudge factor. It is the measurement.
    • Ends: someone wrote it down.
      1. tied to a dated thing: the record says where. pins the Earth's rotational position at that instant to the width of that spot. (The Sun Was Eclipsed; It Was Total) What the layer reports: The identifications are inherited, not derived.

      Here writing sets the sky: a record of where the Sun went out dates the Earth, not the other way round.

    • Ends: the sky.
      1. matched to something dated: the Moon, computed. JPL DE441 part 1 for everything before 1960 and DE440 after, read through Skyfield. (The Sun Was Eclipsed; It Was Total)

13. Ptolemy's star catalogue

    289 BC, one sigma from 606 BC to AD 119: On the Almagest it returns 289 BC with a one-sigma interval running from 606 BC to AD 119, and removing a single star out of 993 moves that answer by 377 years, more than the whole question spans. (Ask a Catalogue What Year It Is)

    1. what is read: star positions, gone stale. A star catalogue is a list of positions, and positions go stale. (Ask a Catalogue What Year It Is)
    2. how fast it runs: precession: not to be believed. One way of asking answers to the year and should not be believed for a moment. (Ask a Catalogue What Year It Is)
    3. how fast it runs: the stars' own motions: nearly blind. The other is honest and very nearly blind. (Ask a Catalogue What Year It Is)
    • Ends: the sky.
      1. matched to something dated: a satellite's catalogue. The Hipparcos and Tycho Catalogues, ESA SP-1200 (1997) (Ask a Catalogue What Year It Is)

14. Van Gogh's Moonrise, the evening it shows

    13 July 1889, 9:08 p.m.: exactly 9:08 p.m. local mean time (Nothing but the Morning Star)

    1. what is read: a Moon behind a ridge. “near azimuth 126°” and “between 4½° and 4¾° in altitude” (Nothing but the Morning Star)
    2. matched to something dated: every evening of 1889, searched. A nearly full Moon could rise behind it in evening twilight, they found, on only two dates in 1889, 16 May and 13 July; the reaped wheat in stacks rules out May. (Nothing but the Morning Star)
    • Ends: the sky.
      1. matched to something dated: the sky, computed twice. astronomy-engine 2.1.19 by Don Cross (Nothing but the Morning Star) What the layer reports: azimuth and altitude agree to 0.001°

15. Greenwich time at sea, read off the Moon (1767)

    longitude good to 10 miles, promised: In 1766 the Astronomer Royal promised that the Moon tables behind his new Nautical Almanac were seldom wrong by 20 seconds of arc, so a navigator's longitude would generally be good to 10 miles. (Seldom Amounting to Twenty Seconds)

    1. matched to something dated: Mayer's Moon. these were the tables of Tobias Mayer of Göttingen, the best in the world, for which the Board of Longitude paid his widow £3,000. (Seldom Amounting to Twenty Seconds) What the layer reports: 96% of the variance in the printed distances was the Moon theory.
    • Ends: the sky.
      1. matched to something dated: the real Moon, as the layer checks it. Here are all 1,816 lunar distances printed for four months of 1767, transcribed twice and checked against where the Moon really was. (Seldom Amounting to Twenty Seconds) What the layer reports: the true one computed from NASA JPL's DE440 ephemeris for the same instant of Greenwich apparent time.

      The layer does not say what Mayer fitted his tables to. The root is the Moon they describe; this last step is the layer checking them against it.

16. Where the Endurance sank, from the sights after

    a wreck 4.5 km east of the X: accounts for about four fifths of the 4.5 km the wreck lies east of the X (Nineteen Hours Late)

    1. what is read: the Sun against the chronometer. the sun's height in mid-morning and mid-afternoon, compared with Greenwich time on the chronometer (Nineteen Hours Late)
    2. how fast it runs: longitude is time. One second of error on the chronometer is fifteen seconds of arc of longitude, 169 metres east or west at this latitude. (Nineteen Hours Late)
    3. matched to something dated: the clock, set by the Moon. The chronometers were last checked against the sky on 15 September, by timing stars as the Moon covered them, using the Nautical Almanac's predictions. (Nineteen Hours Late) What the layer reports: The published paper gives the difference as “an average of 20 s”.
    • Ends: the sky.
      1. matched to something dated: the Moon, recomputed. re-reduced those 1915 occultations using modern lunar ephemerides and star catalogues (Nineteen Hours Late)

17. The pulsar map on the Pioneer plaque

    early 1970: land between 22 Jan 1970 and 5 Feb 1970: 15 days, where in SI seconds they spread over 330 (The Rubber Second)

    1. what is read: fourteen pulsar periods. that pulsar's period, counted in units of the period of the hydrogen atom's radio line (The Rubber Second)
    2. how fast it runs: each pulsar slowing. The date on which the pulsar spun at the plaque's rate is where F0 + F1 t equals one over the true period. (The Rubber Second)
    3. how fast it runs: a second stretched to the Earth. a UTC second was 3.0 parts in a hundred million longer than an atomic one (The Rubber Second)
    • Ends: the sky.
      1. matched to something dated: the second leaves the Earth. The second stopped being something the Earth defines and became something the Earth is measured against. (Every Leap Second Was Already in the Spin)
      2. matched to something dated: caesium, timed against the Moon. Photographs of the Moon and surrounding stars were taken by the USNO dual-rate Moon camera over the period 1955.50 to 1958.25 to determine the Ephemeris Time from the position of the Moon at a known UT2. (Nelson and others, Metrologia (2001)) What the source reports: The principal uncertainty arose from the astronomical measurements themselves.
      3. tied to a dated thing: a day of about 1820. The epoch at which the mean solar day was exactly 86 400 SI seconds was approximately 1820. This is also the approximate mean epoch of the observations analysed by Newcomb, ranging in date from 1750 to 1892, that resulted in the definition of the second of Ephemeris Time from which the SI second was derived (Nelson and others, Metrologia (2001))

18. The 27 leap seconds

    23 of 27 on the announced day: 27 steps fall out for 27 leap seconds, 23 of them on the exact announced day. (Every Leap Second Was Already in the Spin)

    1. what is read: how long each day took. 23,560 daily measurements of how long the Earth actually took to turn (Every Leap Second Was Already in the Spin)
    2. ticks, counted: the excess, added up. Start on 1 January 1972 with the published offset, add up the measured excess of each day (Every Leap Second Was Already in the Spin)
    3. how fast it runs: a tolerance. The departure of UTC from UT1 should not exceed ± 0.9 s. (Every Leap Second Was Already in the Spin) What the layer reports: Set the tolerance to the 0.9 s the standard prints and the machine produces the right number of leap seconds, 27, but puts most of them six months late.
    4. matched to something dated: the Earth, timed by GPS and VLBI. From 1998 the C04 length of day comes from GPS and UT1 comes from VLBI (Every Leap Second Was Already in the Spin)
    • Ends: the sky.
      1. matched to something dated: the second leaves the Earth. The second stopped being something the Earth defines and became something the Earth is measured against. (Every Leap Second Was Already in the Spin)
      2. matched to something dated: caesium, timed against the Moon. Photographs of the Moon and surrounding stars were taken by the USNO dual-rate Moon camera over the period 1955.50 to 1958.25 to determine the Ephemeris Time from the position of the Moon at a known UT2. (Nelson and others, Metrologia (2001)) What the source reports: The principal uncertainty arose from the astronomical measurements themselves.
      3. tied to a dated thing: a day of about 1820. The epoch at which the mean solar day was exactly 86 400 SI seconds was approximately 1820. This is also the approximate mean epoch of the observations analysed by Newcomb, ranging in date from 1750 to 1892, that resulted in the definition of the second of Ephemeris Time from which the SI second was derived (Nelson and others, Metrologia (2001))

19. The numbers painted on the world’s runways

    a field about a quarter of a century old: Read that as what it is: not a claim that runways were repainted in 2002, but a summary statistic. The world's runway numbering is, in aggregate, a photograph of a magnetic field about a quarter of a century old. (The North the Paint Remembers)

    1. what is read: the true bearing. The runway's true bearing is a geodesic azimuth between its two published threshold coordinates on the WGS-84 ellipsoid. (The North the Paint Remembers)
    2. how fast it runs: the field drifts. It is a property of the runway and the date. Earth's field drifts, the paint does not (The North the Paint Remembers)
    3. matched to something dated: a model of the field, year by year. The field model is IGRF-14, running in your browser from the coefficient table the International Association of Geomagnetism and Aeronomy publish. (The North the Paint Remembers)
    • Ends: the layer stops here.
      1. tied to a dated thing: the coefficients. Field model: IGRF-14 coefficients, IAGA via NOAA NCEI. (The North the Paint Remembers)

      The layer does not say what the field model is fitted to.

The nineteen layers

• Ask a Catalogue What Year It Is (2026-08-17). In: Ptolemy's star catalogue.
• Every Tree Wrote the Same Bad Year (2026-07-27). In: A radiocarbon sample measured at 2450 BP; The first ring in each of 48 Arizona tree cores; A 150-year-old surface, dated by its largest lichen.
• The Clock in the Verse (2026-09-26). In: Euripides' plays with no outside date.
• Most of the Time Is at the Bottom (2026-09-28). In: The deepest dated ice at Dome C, Antarctica.
• Right Clock, Wrong Body (2026-09-26). In: The age of the Earth, from its heat (Kelvin, 1862).
• The Longer You Look (2026-09-28). In: A 150-year-old surface, dated by its largest lichen.
• Nothing but the Morning Star (2026-11-06). In: Van Gogh's Moonrise, the evening it shows.
• The Ocean Floor Kept Both Copies (2026-07-30). In: Magnetic stripes on the Pacific floor.
• Seldom Amounting to Twenty Seconds (2026-09-25). In: Greenwich time at sea, read off the Moon (1767).
• The Clock Only Euripides Kept (2026-09-28). In: Aeschylus's Suppliants.
• The Date Made From One Word Twice (2026-08-25). In: The day Vesuvius buried Pompeii.
• Every Leap Second Was Already in the Spin (2026-08-02). In: The pulsar map on the Pioneer plaque; The 27 leap seconds.
• The North the Paint Remembers (2026-08-22). In: The numbers painted on the world’s runways.
• The Rubber Second (2026-11-08). In: The pulsar map on the Pioneer plaque.
• The Seeds Beneath the Steps (2026-09-23). In: Seeds in the layers holding the White Sands footprints.
• 716 A.D., Give or Take Two Thousand Years (2026-08-10). In: The split between English and German.
• Nineteen Hours Late (2026-09-27). In: Where the Endurance sank, from the sights after.
• Where the Curve Goes Flat (2026-07-24). In: A radiocarbon sample measured at 2450 BP; Seeds in the layers holding the White Sands footprints.
• The Sun Was Eclipsed; It Was Total (2026-08-21). In: How late the Earth turned in 136 BC.