The Wave Schedule

The Index lays out the Blue Book monthly file, 1947-1962 in Vallée's frame or 1947-1969 in full, on a log or linear scale, with the trend drawn as a dashed line whose window is a dial. Below it, the detrended lane Figure 3 lived in: a threshold dial defines what counts as a wave, violet dots mark the detections, and the intervals are labelled in months. The Mars toggle drops the eleven real opposition dates onto the axis.

The Spectrum draws the power of every period at once against a 95% null band you choose: shuffled months, or surrogates carrying the record's own month-to-month memory. The needles never move; only the band does. Markers stand at 12.0 months and at the Mars synodic period of 25.6.

The Schedule is the Skinner machine: the detected waves as a rhythm on one rail, and beneath them fixed-interval, variable-interval and Poisson schedules run at the same rate from fixed seeds. The gauge below computes the interval CV with its bootstrap CI against the three analytic anchors, and answers the caption's question with the only honest answer six waves permit.

The File runs twelve cards: what Figure 3 actually was, where this series comes from, the nine years whose bookkeeping disagrees with itself, Sputnik month, the 1952 summer, Skinner's box, Condon's own health warning, the surge outside the window, the Mars file, and the sentence that closes the loop. Two verdicts hang below at equal size.

The culture wing of this station has just taken in a review of Jacques Vallée's The Invisible College (1975), the book where the control-system hypothesis was first laid down. That review names the book's quantitative heart: Figure 3, a monthly index of UFO activity, 1947-1962, trend removed, captioned "Is this a schedule of reinforcement?", with the whole Skinnerian mechanism standing on it. The review also names it the argument's weakest link: a graph read by eye, built on a private catalogue with unpublished weights, never tested against any null. This instrument was built for that link. Vallée's index cannot be recomputed by anyone; the public record that carries the same waves, the Blue Book monthly file, can be recomputed by everyone. The bench turns the three load-bearing words, wave, period, schedule, into dials, and turns them in front of you.

It is also the station's fourth 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) and INST-60 The Nuclear Lure (what a correlation is worth against a base rate): this one asks what a rhythm is worth against a null hypothesis. As ever, the answer is not presupposed. At the strict dial inside Vallée's own window the five-year clock is real, 60 and 64 months, and the bench draws it exactly; extend the record to 1969 and the next wave arrives 93 months late and shatters it, 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 Condon monthly table, the desk-archive histograms, the programme sheets, and the real Mars dates. A script that ships with the site re-derives every displayed number before the build is allowed to pass, including the places where the record disagrees with itself.

resid = v − CMA_W(v) · wave: resid > θ·σ · CV = sd(Δt)/mean(Δt) · P_k vs 95% of AR(1) surrogates · p_Mars = P_shift(|Δ| ≥ |Δ_obs|)

The definition of a wave is a dial, because the literature never supplied one. A centered moving average removes the trend (window 7-49 months); a wave is a run of residual months above θ·σ merged within a separation dial. Every downstream number inherits these choices visibly. At 1.5σ the record holds six waves; at 2.0σ, three; at 1.0σ, eight.

The null hypothesis is a switch, because it decides the verdict. The same periodogram clears 32, 24 and 21.3 months against shuffled months and clears nothing beyond a year against AR(1) surrogates with the record's own φ = 0.59. The eye is a white-noise instrument; a bursty series manufactures two-year 'cycles' for free. Both bands are drawn from 400 seeded surrogates each.

The schedule question is answered at the sample size the record permits. Skinner's taxonomy separates schedules by interval statistics, and the laboratory needed thousands of trials per animal. The file supplies five intervals; the CV's bootstrap CI spans from near-clockwork to well past the variable schedule. That is not a failure of the bench. It is the finding: the caption's question was unanswerable from its own data in 1975, and it still is.

The Mars test uses circular shifts, not shuffles, because shuffling months would credit the test with destroying the very autocorrelation that produces false hits. The shifts preserve the series' structure and slide the opposition mask around the calendar: 2,000 of them price the observed +20.1 excess at p = 0.13, and dropping the single 1952 coincidence inverts the sign.

What this bench will not do is answer the book's question for you. A trainer permitted to mislead cannot be disproven by any dial, and the bench says so on the card that quotes the sentence. What it can do is separate the checkable from the unfalsifiable: the periodicity is a dial artifact, the unpredictability is what human reporting produces unaided, and the only rhythm the record proves is the year.

Two windows, two scales, three dials, one null switch. Between them they manufacture and unmake every pattern ever claimed in this series, which is the exhibit.

• The window. 1947-1962 is Vallée's frame, and the five-year clock lives only inside it. 1947-1969 is the out-of-sample test: one button, and the clock meets August 1965.
• The scale. Log compresses the 1952 monster so the early waves exist at all (Vallée's weighting did the same job for his index); linear shows why one month is an eighth of the whole file.
• The trend window. 7 to 49 months. Short windows swallow slow waves into the trend; long ones leave drift in the residual. The default 25 is stated, visible, and movable.
• The threshold and the separation. What counts as a wave, and when two crossings are one wave. The wave count runs from three to eight across honest settings, and every downstream statistic follows it.
• The null switch. White blesses the wave periods; red kills them. The single most consequential control on the bench, and in most published analyses it was never a control at all.
• Mars and labels. The real opposition dates on the axis, and the numbers on or off the charts for reading against screenshots.

Six claims that orbit the wave record, from the book's own caption to the psychosocial null, with where each lands against the arithmetic.

1. Start on the index at the defaults. Six violet dots, intervals 32, 28, 49, 15, 34. This is the pattern the book heard as a training schedule.
2. Turn the threshold to 2.0σ. Three waves: 1947, 1952, 1957, spaced 60 and 64 months. The five-year clock of the 1950s literature, really there, at this dial.
3. Now press 1947-1969. The fourth wave lands in August 1965, 93 months late. The clock does not survive its first out-of-sample wave.
4. Go to the spectrum on the white null. 32, 24, 21.3 months all clear the band. This is what every eyeball analysis of this file has ever seen.
5. Switch to red. One survivor beyond a year: none. The 12.0-month seasonal towers at eleven times the noise. Tap it and read what it means.
6. Go to the schedule. Four rails at one rate. Cover the labels and try to tell the record from the Poisson rail. Then tap the gauge and read what five intervals can prove.
7. Toggle Mars on the index. The 1952 triangle sits two months left of the 536 spike. Tap it, then read the epoch numbers with and without it.
8. End on the file. Read The Exhibit, then The Wobble, then Must Mislead, in that order: what the graph was, what the record is, and why no dial can reach the thesis.

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

In one line: the Blue Book monthly record is REPORTED, spliced from its three published sources with every yearly sum re-derived and the nine self-disagreements pinned rather than repaired; the Mars dates are MEASURED astronomy; the trend, the wave set, the periodogram with its two null bands, the CV gauge and the Mars epoch test are MODELLED arithmetic with every model choice on a visible dial and every stochastic figure seeded, re-derived by scripts/wave-schedule-tune.mjs before the build passes; and whether the rhythm is a schedule of reinforcement is a READING the bench declines to make, hanging the schedule and the bursts at exactly equal size. Turn the dials, switch the null, and watch what a rhythm is worth.

• Edward U. Condon (dir.), "Scientific Study of Unidentified Flying Objects", Section V Chapter 2, Table 1: "Number of UFO Reports Received each Month by Project Blue Book", January 1950 through 1968 as printed (Bantam edition; NCAS and SHG transcriptions cross-checked cell by cell for this bench). The chapter's own caption on the fluctuations, the press-publicity table for 1952 and the Grudge Report No. 6 quotation are from the same chapter.
• Project Blue Book desk records preserved by Rob Mercer: "From the Desks of Project Blue Book: Sightings and Statistics, 1947-1969" (The Black Vault), for the hand-drawn 1947-1949 monthly histograms, the 1966-1969 "Statistical Data" sheets, and the 1949 sheet's three mutually inconsistent totals.
• Air Force fact sheet, "Unidentified Flying Objects and Air Force Project Blue Book": yearly totals 1947-1969 summing 12,618.
• Jacques Vallée, "The Invisible College" (E. P. Dutton, 1975; Anomalist Books 2014), Chapter 9: Figure 3 and its caption, the index-construction sketch, and the reinforcement-schedule argument. Quotations follow the 2014 printing; page references approximate. Reviewed in this site's culture wing.
• C. B. Ferster and B. F. Skinner, "Schedules of Reinforcement" (Appleton-Century-Crofts, 1957), cited in the book as "Patterns of Reinforcement": the schedule taxonomy and the extinction-resistance result the book borrows.
• Jacques Vallée, "Challenge to Science: The UFO Enigma" (with Janine Vallée, Regnery, 1966), for Vallée's own examination and abandonment of the Michel Mars-opposition correlation.
• Mars opposition dates 1948-1969 from the standard astronomical almanac record; synodic period 779.94 days.
• Sputnik 1 (4 October 1957) and Sputnik 2 (3 November 1957) launch dates; Levelland, Texas, 2-3 November 1957; Life, "Have We Visitors From Space?", 7 April 1952; Washington National radar events, 19-20 and 26-27 July 1952; Dexter and Hillsdale, Michigan, 20-21 March 1966, and the 25 March 1966 press conference.