The Law of the Times

The Clock hangs the two report clocks on one axis: the 1975 type-I curve, digitized from the paper's hand-drawn Figure 8, and the modern NUFORC histogram, 64,627 US reports. A ghost overlay puts either on the other's scale; the landmarks of the law are flagged; a polar inset wraps the day around a clock face, where the report mass sits almost entirely on the dark side.

The Witness is the zero-parameter counter-model: the published awake fraction times the astronomy of darkness, scaled, nothing fitted. One toggle removes darkness and the correlation collapses from 0.88 to 0.00. A latitude dial moves the night; a daylight-visibility dial buys the daytime floor the strict model honestly lacks.

The Correction is the paper's manoeuvre run live: each hour divided by its witness fraction, for all four combinations of dataset and divisor, with Poisson whiskers on the counts and the night floor on a dial. At 2.0% it lands exactly on Figure 9's plotted peak; at 2.5%, on the stated ×14; the violet band shows what the same curve does across every plausible reading of the ink.

The File runs twelve cards: the law's verbatim wording and its borrowed name, the digitization's certificate, the uncited divisor, the ×14 quote, the night floor, the awake-versus-at-home word choice, the replication, the missing bump, July 4th, Hendry's IFO clock, the darkness variable, and what would count. Two verdicts hang below at equal size.

The station's review of The Invisible College records a detail: in January 1975, while writing that book, Vallée co-signed a technical statistics paper with Claude Poher of the French space agency. That paper houses the two most famous exhibits in the close-encounter literature: a report clock (peak about 9 p.m., dip at 1 a.m., bump at 3 a.m.), and the same clock after division by a "potential witnesses" curve: a 3 a.m. spire, and the sentence "witnesses are only in a position to observe one in fourteen close approaches". The book leans on it for the intuition that the phenomenon selects its audience; the literature later named the curve the law of the times. The law's data was never published as a table, only as a hand-drawn figure. This bench digitizes that figure pixel by pixel (the trace sums to 2,090 against the paper's stated 2,000, which is the digitization's certificate), reruns the famous division exactly, and then fits it with the two things it never had: error bars, and dials.

It is also the station's fifth statistics bench, after INST-37 Project Stargate (what a margin is worth against chance), INST-50 Special Report No. 14 (what a percentage is worth when the denominator moves), INST-60 The Nuclear Lure (what a correlation is worth against a base rate) and INST-68 The Wave Schedule (what a rhythm is worth against a null): this one asks what a division is worth against its own denominator. As ever, the answer is not presupposed. The evening law itself replicates verbatim in 64,627 modern reports, the same peak hour fifty years apart, and the bench draws it exactly; and the ×14 swings from ×5 to ×19 inside the divisor's last two percentage points, and the bench draws that too. Two verdicts hang at equal size in the file, and the dials are yours.

Everything on the bench is arithmetic on published records: the digitized 1975 figure, the federal time-use table, the public NUFORC file, and solar geometry. A script that ships with the site re-derives every displayed number before the build is allowed to pass, including the two numbers the 1975 paper itself printed: the Figure 9 peak and the ×14.

M(h) = awake(h) · [dark(h) + ε(1−dark(h))] · Nc(h) = N(h) / P(h) · envelope: P_night ∈ [1.6%, 3.0%] · whiskers: N ± 1.96√N

The 1975 record is a picture, so the bench treats digitization as evidence handling. The N and P curves were separated by connected components at 600 dpi, the axes auto-detected, the calibration checked against the printed ticks (N = 2.5 × the left axis, exactly). The trace sums to 2,090 against the stated ~2,000. Where the curve is legible, the bench trusts it; where it touches the axis, the bench refuses to read a single value and installs a dial instead.

The witness model earns the curve before questioning the correction. Awake × dark carries no fitted constants: two public tables and a product. It reproduces the modern clock at r = 0.88 and the 1975 curve at 0.83, and its one honest failure, a 20h peak against the data's 21h, is the solar-time/DST hour, printed rather than tuned away. Awake alone scores 0.00: the toggle that shows darkness, not wakefulness, carries the law.

The correction is reproduced before it is priced. The bench's division lands on the paper's own plotted peak at a night floor of 2.0% and on its stated ×14.3 at 2.5%: strong evidence for what the hand-drawn divisor's night value really was, and a validation that the arithmetic here is theirs. Only then does the bench sweep the floor, swap the divisor, and transplant it onto modern data, where the ×14 returns (×13.0) for the modern file too: proof the multiplier lives in the denominator.

The uncertainty that matters is not sampling. Poisson whiskers on the 3 a.m. cell span 4,835-6,965; the divisor envelope spans 3,933-7,375. The dominant error bar on the most famous number in close-encounter statistics is the width of a 1975 pen stroke near the axis, and no published critique we could find has ever said so: the bench says it with arithmetic instead of authority.

What survives every dial is worth stating: the evening law is real, stable and explained; the corrected peak lands in the small hours under every divisor, at ×3.6-×5.0 with checkable inputs; and the 3 a.m. bump, the ×14 and the 28,000 manifestations do not survive contact with error bars. Whether the surviving residue is a phenomenon that prefers empty hours or the arithmetic of dividing evenings by nights is the reading the bench leaves to you.

Two files, two divisors, a night floor, a latitude, a daylight term and one load-bearing toggle. Between them they manufacture and unmake the most famous multiplier in the literature, which is the exhibit.

• The file. The 1975 vetted catalogue (n ≈ 2,000, digitized) or the modern NUFORC scrape (64,627, recomputed). They agree on the evening; they part company at 3 a.m.
• The scale. Share-of-day makes the two files directly comparable; raw counts show what each actually holds.
• The darkness toggle. The single most consequential control on the bench: r = 0.88 with it, 0.00 without it. The 1975 paper never modelled the variable it flips.
• Latitude and daylight visibility. The darkness term's geometry, and the fraction of visibility a luminous stimulus keeps in daytime. The daylight dial buys the daytime floor; the peak is never for sale.
• The divisor. The published awake table, or the 1975 hand-drawn "not at home" curve. At 3 a.m. they differ by a factor of 2.5, and the famous ×14 inherits all of it.
• The night floor. The divisor's value where the pen touches the axis, swept 1.6-3.0%: the ×14 runs ×18.7 to ×12.7 across it, with the paper's own two anchors (the plotted peak, the stated ratio) at 2.0 and 2.5.

Six claims that orbit the law of the times, from the 1975 paper's own sentences to the exposure counter-model, with where each lands against the arithmetic.

1. Start on the clock, modern file. The peak is 21h, 14.9% of the day. Toggle the ghost: the 1975 curve peaks at the same hour. Fifty years, same clock.
2. Switch to the 1975 file and find 3 a.m. The bump: 118 cases against 232 at the peak. This cell is where everything downstream begins.
3. Go to the witness. Turn darkness OFF. r = 0.00. Awake alone explains nothing. Turn it back on: r = 0.88, nothing fitted. That toggle is the whole argument.
4. Go to the correction: 1975 file, "not at home", floor 2.0%. The corrected curve spikes to 5,900 at 3 a.m., exactly the peak the paper plotted. You have just rerun 1975.
5. Drag the floor from 1.6 to 3.0. The multiplier runs ×18.7 to ×12.7 and the peak halves. Half a point of ink, half the conclusion.
6. Switch the divisor to awake. ×5.0. One word, two thirds of the multiplier gone.
7. Switch the file to NUFORC, divisor back to "not at home". ×13.0: the famous number returns on data that never produced it, because it lives in the denominator.
8. End on the file. Read The Law, then The Night Floor, then the IFO Clock, then both verdicts: what was claimed, where it stands, and who keeps the same hours.

The honest line between what is reported, what is measured, what is modelled on them, and what is a reading:

In one line: the 1975 curves are REPORTED, digitized from a hand-drawn figure with the trace validated against the paper's own stated total and the night cells refused as constants; the modern clock and the calendar are REPORTED from the public NUFORC file, recomputed twice with the rounding artifacts disclosed; the awake table is MEASURED federal survey data; the darkness term, the witness model and the correction with its whiskers and envelope are MODELLED arithmetic with every choice on a visible dial, re-derived by scripts/law-of-times-tune.mjs before the build passes; and whether the corrected curve's small-hours residue is a phenomenon is a READING the bench declines to make, hanging the signal and the mirror at exactly equal size. Switch the file, choose the divisor, drag the floor, and watch what a division is worth.

• Claude Poher and Jacques Vallée, "Basic Patterns in UFO Observations", AIAA Paper 75-42, 13th Aerospace Sciences Meeting, Pasadena, January 1975 (DOI 10.2514/6.1975-42; the paper is freely mirrored, including at jacquesvallee.net). Figures 7, 8 and 9, the law's verbatim wording (p. 7) and the "about 14 to 1" passage (p. 8). The phrase "law of the times" appears nowhere in the paper; it is in print by 1979.
• Alexander Szalai (ed.), "The Use of Time: Daily Activities of Urban and Suburban Populations in Twelve Countries" (Mouton, 1972): the only time-budget study in the paper's bibliography and the likely source of the "not at home" curve; stated as inference, since Figure 8 carries no inline citation.
• U.S. Bureau of Labor Statistics, American Time Use Survey, Table A-3, "Percent of the population engaging in selected activities by time of day", 2023 annual averages (bls.gov/tus; archived copy on the Wayback Machine): the sleeping-by-hour table behind the awake divisor.
• NUFORC report scrape, geocoded and time-standardized (github.com/planetsig/ufo-reports; mirrored at Zenodo record 1205624): 80,332 rows; hourly histograms and the calendar census recomputed twice, independently, for this bench. Underlying reports are self-submitted to the National UFO Reporting Center.
• Allan Hendry, "The UFO Handbook" (Doubleday, 1979): 1,307 cases, 88.6% identified. Quoted through Peter Rogerson's review in Magonia No. 2 (Winter 1979/80), the source of "It will come as no surprise that IFOs obey the ‘Law of Times’"; the book's own IFO figure was not available to this bench and no page number is invented for it.
• R. M. Medina, S. C. Brewer and S. M. Kirkpatrick, "An environmental analysis of public UAP sightings and sky view potential", Scientific Reports 13, 22213 (2023): 98,724 NUFORC reports, light pollution credibly negative at -7.7% per SD; the spatial version of the exposure reading, with the then-director of AARO as co-author.
• Solar geometry: declination by the standard cosine formula, civil darkness at solar elevation below -6°; the darkness term is computed from these alone, at local mean solar time.
• Jacques Vallée, "The Invisible College" (1975; Anomalist 2014), reviewed in this site's culture wing: the book the statistics paper was written alongside, and the reason this bench exists.