HT cycles period testing

Method for testing whether a set of detected cycle periods matches Harmonics Theory (HT) predicted periods better than chance.

Version 1.0 — 13 October 2026. Worked out by Ray Tomes with Claude. Reference implementation: ht_period_test.py. Harmonics input: strong-harmonics.csv (columns H, C(H), Cest(H), Str(H), years).

1. Purpose

A cycles analysis of some data (spectrum, CATS, etc.) produces a list of periods. HT predicts a set of periods, each with a relative strength Str(H). This method answers one question:

Do the detected periods lie closer to strong HT-predicted periods than randomly placed periods would?

It rewards multiple precise hits. A miss costs almost nothing; a near-exact match earns a very large score. The result is a p-value from a Monte Carlo test against random periods.

This replaces the earlier "mean log-distance to nearest strong line" test. That test gave every period equal weight, so many mediocre matches could look as good as a few exact ones, and it did not use the accuracy of the data.

2. Inputs

Choosing a

a is a property of the data, not a tuning knob. Use a small value when the periods are very accurate (0.0001 was used for the magnetic reversal periods), and a larger value (0.001, 0.01) for noisier estimates such as spectral peaks from short data. Never adjust a after seeing which value gives the lowest p.

3. Procedure

Step 1 — Strong lines. Take every HT line with Str(H) ≥ the strength limit. Convert years to the unit of the detected periods.

Step 2 — Range. With N detected periods, let

span = log10(P_max) - log10(P_min)

pad  = span / N

range = 10^(log10(P_min) - pad)  to  10^(log10(P_max) + pad)

The range is the periods found plus a margin of span/N each side (one average log-spacing of the found periods).

Step 3 — Score each period. For each detected period P, find the nearest strong line L (searching all strong lines, including any just outside the range, so edge periods are not penalised):

error = |P - L| / P

score = 1 / (error + a)

Step 4 — Fit statistic.

S = sum of score over all N periods

Larger S means a better fit.

Step 5 — Monte Carlo. Repeat many times: draw N random periods uniformly in log period across the range from Step 2, score them exactly as in Steps 3–4, and record the sum. Do this in several batches.

p = (number of random sets with S_random >= S_observed) / (number of random sets)

Report p for each batch and overall, plus the Monte Carlo mean and the 95th and 99th percentile of S for comparison.

4. Chart specification

• x-axis: period, log scale, restricted to the Step 2 range, longest period on the left (descending).

• One vertical line per strong HT prediction, from the bottom of the chart up to its Str(H). The period is written vertically above each line.

• Detected periods are plotted as triangles about 30% of the way up the chart, or lower if needed so they sit below the top of the lowest HT line.

• Title states the range, strength limit and a.

5. How the score behaves

score = 1/(error + a):

• Scores fall roughly as 1/error, so one exact hit is worth many 1% hits. This is what makes multiple hits dominate and misses nearly irrelevant.

• a stops a single exact match from scoring infinity. The maximum per period is 1/a.

• a does not, by itself, make a single lucky hit non-significant. In the worked example below, one near-exact hit (score 5,523) on its own gives p ≈ 0.017 against 6 random periods, and two such hits give p ≈ 0.003. The Monte Carlo test is what decides whether a hit is surprising; a sets how much credit a given precision earns, so it must match the real accuracy of the data. If a is set smaller than the data's true accuracy, small errors in the data are treated as real mismatches; if larger, genuine precision earns less credit.

6. Rules to keep the test honest

1. Fix everything before testing. The period list, strength limit, a, and the unit conversions must be decided first. Trying several strength limits or a values and reporting the best inflates significance. If sensitivity is shown, show all of it (Section 7).

2. Do not trim the list to the best matches. The list must come from the cycles analysis by a rule that does not look at the HT lines (for example all peaks above a significance level). Adding weak periods lowers the apparent significance slightly; removing them to improve p is selection.

3. Collapse clusters. If several detected periods are near-duplicates of the same cycle (within about 1–2%), count the cluster once (use its mean). Otherwise the test counts one cycle many times. (This lowered one earlier result from p = 0.0018 to p = 0.041.)

4. The range depends on the list. Adding or removing a period changes N and the span, so the range, the number of lines, and p all shift. State the range used.

5. Monte Carlo resolution. With 10 × 100,000 trials the smallest reportable p is about 1e-6. If no random set reaches S, report p < 1e-6 rather than 0.

6. Statistics are one-sided: p is the chance that random periods do at least as well.

7. Different tests are not comparable. p-values from this method cannot be compared with those from the earlier mean-closeness test.

7. Worked example — magnetic reversals, 1.11 Ma cycle paper

This paper is available on viXra at https://vixra.org/pdf/2610.0033v1.pdf

Detected periods (Ma): 1.1101, 1.2286, 3.3335, 2.2683, 0.74026, 2.7629. Strength limit 0.9, a = 0.0001.

Range: 0.576 – 4.284 Ma (span 0.6535 in log10, pad 0.1089); 26 strong lines in range.

• Observed sum S = 10,471.

• Random sets: mean S ≈ 897; 95th percentile ≈ 2,939; 99th ≈ 6,988.

• p = 0.00069 (10 batches of 100,000: 0.00057 to 0.00079).

The result rests on the first three periods (about 10,230 of the 10,471). The last three are weak or no matches. A paper should say this.

Sensitivity (reported for transparency, not for choosing)

Removing any one period leaves p below 0.02. Note that the "only best three" row is a selected subset and should not be quoted as the result.

8. What to report in a paper

• The detected periods and how they were obtained (data, method, any significance criterion).

• Strength limit, a and the reason for it, the test range, number of strong lines in range.

• Per-period nearest line, relative error and score.

• Observed S, Monte Carlo mean and 95th/99th percentile, p per batch and overall, number of trials.

• The fact that the test is dominated by the best few matches, if so.

• Any sensitivity checks, shown in full.

9. Reference implementation

ht_period_test.py (Python 3, numpy; matplotlib for the chart).

python ht_period_test.py \

  --periods 1.1101 1.2286 3.3335 2.2683 0.74026 2.7629 \

  --period-unit Ma \

  --harmonics strong-harmonics.csv \

  --str-min 0.9 --a 0.0001 \

  --batches 10 --trials 100000 \

  --label "Magnetic reversal cycles" \

  --out chart.png

--period-unit accepts yr, kyr, Ma, Ga, months, days. The script prints the range, the per-period table, S, the Monte Carlo summary and p, and writes the chart described in Section 4.

10. Possible future extensions

• Build this into the interactive chart tool (inputs: periods, strength limit, a).

• Add automatic cluster collapsing with a stated tolerance.

• Add a "run all with the same pre-registered settings" mode for comparing several datasets fairly.

Oct 11, 2026 · @Ray Tomes

Introduction

I have found a cycle of 2.701 years in C14 data and a cycle of 2.697 months in Milan rainfall. Their ratio is 12.018 ± 0.022, consistent with an exact 12:1 harmonic relationship. Because Dewey's common cycles have ratios of 2 and 3 there are many instances of ratio 12 between them (2x2x3).

Neither period is one of Dewey's well-known cycles. A search of the literature and the FSC cycles catalogue shows they are not rare either. This report lists every report found within ±2% of either period (2.646–2.754 years and 2.646–2.754 months, i.e. 80.5–83.8 days), plus near misses.

My findings

The ratio is 32.412 / 2.697 = 12.018 ± 0.022, under 1σ from exactly 12. A factor of 12 (2² × 3) is one of the most commonly expected harmonic ratios.

The monthly period is not simply three solar rotations. Three Carrington synodic rotations (3 × 27.275 days) give 81.83 days, about 0.2 days or 2σ short of 82.03 days. Nor is it related to the solar Rieger cycle, which is close to 154.7 days; half of that is 77.35 days.

Reports near 2.70 years (32.4 months)

The closest independent match is an FSC lake-levels cycle at exactly 2.701 years, identical to my C14 value.

Kononovich & Shefov note the solar QBO was first found in the early 20th century, and describe it as a wave train whose period and amplitude decrease, which explains the spread of reported periods. The 33-month FSC entries sit at the edge of the window and are likely Dewey-era round-number estimates.

Near misses: 2.8 yr in the Sun's equatorial rotation rate around 1990 (wavelet study, +3.7%); FSC lake levels at 2.59 yr (−4%) and 2.905 yr (+7.5%).

Reports near 2.70 months (82.2 days)

All independent reports near 82 days come from solar and cosmic-ray data; none appears in the FSC catalogue.

Near misses:

• 84 d (+2.2%): strongest peak in Bai & Sturrock's 1966–76 spectrum (NASA NTRS); also sunspot activity in cycle 23, with 85 d in the southern hemisphere (cycle 23 study).

• 86 d (+4.6%): sunspot areas in cycle 22 (Springer).

• 78 d is excluded: it is half the ~154.7-day solar cycle, not this period.

Discussion and suggested tests

The 2.70-year period appears across solar, atmospheric, hydrological and economic data; the 2.70-month period so far only in solar and cosmic-ray data, plus Milan rainfall. That pattern fits a real but minor cycle, which may be why Dewey never singled it out.

Suggested follow-ups:

• Trace the FSC 2.701-year lake-levels entry to its original source: which lake, what span, who reported it.

• Look for other subdivisions of 2.70 years in the same data: 1/2 (16.2 mo), 1/3 (10.8 mo), 1/4 (8.1 mo), 1/6 (5.4 mo). Matches at similar precision would strengthen the harmonic family.

• Check whether the solar 79–83 day reports cluster near 82.0 days when re-measured with longer data.

The FSC entries come from the parts of the catalogue I had to hand; a full export may contain more. Readers who know of other reports near either period are invited to add them here.

Sources

• Kononovich & Shefov – Quasi-biennial variations of solar activity (2002)

• Zharkova et al. – Periodicities of solar activity and solar radiation (2023)

• Time variations of the solar neutrino flux (wavelet analysis)

• Oláh et al. – Multiple and changing cycles of active stars II

• Short-term periodicities in the Sun's surface rotation

• Özgüç & Ataç – North and south major flare periodicities, cycle 20

• López Comazzi & Blanco – Periodicities in neutron monitor counting rates (2022)

• Search for a clock related to the solar 154-day complex (Bai & Sturrock)

• Periodicities in sunspot activity during solar cycle 23

• Short-term periodicities in sunspot areas during solar cycle 22

• Tomes – Solar 154-day cycle (CRI)

• Foundation for the Study of Cycles period tables, via the Cyclos catalogue

Here are the cycles-related articles and papers that appeared during September 2026, grouped by forum section. Each item states a specific period. Individual items will also be posted in their own sections.

Scientific Cycles

Cosmology & Astronomy

• Non-linear dynamo waves in magnetized shear flows: a candidate mechanism for the solar cycle (arXiv 2609.30367, Perimeter Institute, Sept 2026). The authors model a shear-driven dynamo wave in the Sun's near-surface shear layer. It gives stable 11-year polarity reversals and also a modulation with an 88-year period, which is in the Gleissberg range. Field strengths and flow speeds are compared with observations.

Geology & Paleontology

• Grand Canyon rocks preserve a 1.2-billion-year record of Earth and the Moon (ScienceAlert, 26 Sept 2026; Lantink et al., Nature Geoscience). Rhythmic layering in the Hakatai Shale records Milankovitch cycles from about 1.25 billion years ago. The authors derive a precession period of about 15,730 years. That implies the Moon was at about 53.8 Earth radii and a day lasted about 19 hours.

Climate & Weather

• IRI ENSO Quick Look, mid-September 2026 (Columbia University IRI, 21 Sept 2026). The weekly Niño 3.4 index reached +3.0 °C. All 22 models forecast a very strong El Niño through the 2026–27 summer/winter. It may rank among the strongest events on record in the 2–7 year ENSO cycle.

Market Cycles

Stock Markets

• US Stocks: Why September Weakness May Be Worth Watching (Matrixport, 4 Sept 2026). Includes a chart of S&P 500 performance through the 4-year presidential cycle. It notes that September has been the weakest month over the last 25 years, and weaker still in midterm years such as 2026.

Commodities

• Sir Gold, the Oil Baron, and Dr. Copper: 15 Stocks for the Supercycle (Thierry Borgeat, The Market/NZZ, 8 Sept 2026). Includes a gold chart showing a 7–8 year cycle, with tops in 1974, 1980, 1987, 1994, 2003, 2011 and 2020, and the next projected around 2028. It also refers to a 39-year cycle of falling interest rates that ended in 2020. (Part 1 appeared on 31 Aug.)
• The commodities supercycle question (Real Assets Adviser, 1 Sept 2026; subscription required). An interview with Aberdeen's Bob Minter. It draws on a data series of the producer price index divided by the S&P 500 going back to 1870.

Interest Rates

• Cycle Mismatch Shapes New Markets: A Deep Dive into the First Full Round of the Sixth Kondratiev Wave (Deep News via Tiger Brokers, 22 Sept 2026). The chief economist of China Fortune Innovation Fund argues that the Fed's rate hike on 17 Sept ended the first asset-pricing cycle of the sixth Kondratiev wave. He also discusses phase mismatch between the Kondratiev, Kuznets, Juglar and Kitchin cycles. This is an interpretive piece rather than a data study.

Bitcoin & Cryptocurrency

• Bitcoin's 4-Year Cycle: What the Record Shows in 2026 (Bitcoin.com, data as of 17 Sept 2026). It tabulates all four halving-linked 4-year cycles and the current drawdown of about 40%. It also scores analysts' "cycle is dead" calls against "cycle holds" calls.

Also noted (late August 2026)

• Infradian rhythms of human heart rate reveal distinct multiday cycle periods in healthy adults (EBioMedicine, 22 Aug 2026). Wearable data show heart-rate cycles from weekly to monthly to seasonal.
• A study in Science (27 Aug 2026) used a 1,000-year coral record and found that recent ENSO temperature swings exceed anything in the preindustrial part of the record.

No qualifying September items were found for Botany, Physics & Geophysics, Sociology, Astrology, Wave Structure of Matter, Exchange Rates, Methods, Mathematics, Music and Harmonics, Scientists and Researchers, or Conferences.

Abstract. The origin of biological rhythms—from the heartbeat to circadian cycles—
remains an open question in systems biology. Denis Noble has argued that the genome
does not encode a “master clock,” yet organisms exhibit coherent periodicities. We
propose that these rhythms are rooted in a fundamental inertial resonance of matter itself.
The Universal Particle Principle (UPP) derives a 1second timescale from the proton’s
geometry, linking quantum chromodynamics, gravitation, and the fine structure constant.
Independently, the Geesink/Meijer (GM) Acoustic Quantum Code reveals a discrete 12
band spectrum, normalized by octaves, in which the proton appears at 1.5 Hz and 1.333
seconds per cycle—exactly the harmonic ratios 3/2 and 4/3 predicted by the proton’s
quark content and spherical geometry. This convergence is not coincidental; it is a
structural bridge between quantum geometry and acoustic spectral quantization.
Extending to genetics, Pythagorean ratios such as 3/2 are known to appear in molecular
parameters of the genetic code (Petoukhov & Boulay). The Biogenic hypothesis of the
UPP-model and GM-model could be further supported. We thus propose a unified
framework in which the proton acts as a geometric clock, the GM scale as its harmonic
spectrum, and the genetic code as its biochemical readout. The framework yields testable
predictions for exoplanetary architectures, chronobiology, and mitochondrial dynamics.

• Watch Full Video: 26  
•  

• 💡 Would you like to create a study quiz or flashcards to test your knowledge on these cycles?

What the experts say

The official position, stated plainly on the USGS geomagnetism FAQ, is that magnetic reversals show no periodicity at all — they are described as random events, occurring at irregular intervals with no discernible pattern governing when the next one will happen. The chart below, built from the standard reversal timescale, is offered by USGS as the illustration of that irregularity: a chaotic sequence of black and white bars with no obvious rhythm to the eye.

(Chart: reversal timescale to ~80 Ma, black/white polarity bars, source: geomag.usgs.gov/faq.html)

What the same chart shows once marked

Overlay two simple markers on that same "irregular" record — red dots at 1.11 million year intervals, green bands at 9 million year intervals — and the picture changes. The markers land on genuine structure in the reversal pattern across the full ~80 Myr span, not just in one cherry-picked stretch. There are additional fluctuations beyond these two periods, but the two markers themselves track real features of the record the "no pattern" verdict says shouldn't be there.

(Chart: same timescale with red 1.11 Myr and green 9 Myr markers added, source: ray.tomes.biz)

Confirming it independently

A visual match on one chart could be coincidence, so the same reversal data was tested with two independent, unrelated analytical methods:

Spectral analysis (Lomb–Scargle periodogram). Run on the last 30 million years of reversal data (122 reversal boundaries), this method searches for periodicities directly in the frequency domain, with no reference to the 1.11 Myr figure built in beforehand. It returns a cluster of peaks, the tallest of which sits at 1.110 Myr — flanked by clean harmonics at 0.740 Myr (2/3 of 1.11) and 3.334 Myr (3× 1.11).

Kotov commensurability analysis. A completely different method, applied independently to the same reversal times, searches for a base period whose small integer multiples best explain the observed boundary spacings. It turns up its own set of peaks — and several of them land on fractions and multiples of the very same 1.11 Myr figure: 0.1851 Myr (1/6), 0.5555 Myr (1/2), and again 0.740 Myr (2/3), each matching to within a fraction of a percent.

The folded cycle. A third, more direct check: take all 30 million years of reversal data and fold it on top of itself at exactly 1.11 Myr — stack every cycle on the same phase axis and average. If 1.11 Myr means nothing, folding should wash the record out into flat noise. It doesn't:

The folded curve is a smooth, single-humped wave — a clear swing from roughly −0.6 to +0.6 across the cycle, not a scatter of unrelated points. Folding the same data at nearby periods (1.05, 1.20, 1.30 Myr) collapses this back into a much flatter, noisier curve — confirmation that the effect is sharply tied to 1.11 Myr specifically, not a generic property of the data.

Two unrelated methods, run independently on the same underlying reversal data, converge on the same number family, anchored at:

1.11 million years

with a consistent ladder of related periods around it:

This is not a single suspicious spike buried in noise. It's a coherent, self-consistent family of related periods, recovered twice, by two different techniques, from data that mainstream geomagnetism treats as fundamentally patternless.

The planetary connection

The geomagnetic evidence stands on its own. But there is an independent reason to expect a period near 1.11 million years to show up somewhere — because it already has, in the dynamics of the outer solar system, entirely apart from anything to do with Earth's magnetic field.

The reference. Bertotti & Farinella, Physics of the Earth and the Solar System (Kluwer, 1990, p.312), state that Uranus and Neptune exchange orbital energy over a 1.1 million year cycle. This is a real, well-established result of numerical solar-system integrations — the LONGSTOP project (Milani, Carpino et al., a 100-million-year integration of the outer planets) and a follow-up 210-million-year integration by Applegate and colleagues (1986). Uranus and Neptune sit near — but never lock into — a 2:1 mean-motion resonance; their mutual perturbation produces a slow, cyclic exchange of orbital energy, with Neptune's orbit growing while Uranus's shrinks, then reversing.

The more precise figure, from the primary source (Carpino, Milani & Nobili, based on LONGSTOP 1B), gives this period as 1.119 million years. Bertotti & Farinella simply rounded it to "1.1 Myr" in their text. This is a near-resonant beat rather than a true resonance, and it drifts somewhat in period over time rather than staying perfectly fixed.

A second, independent planetary period. There is also a fixed secular cycle in the outer solar system, generated differently: the angle between Jupiter's and Uranus's perihelion directions (Δϖ) librates around 180° (the two perihelia staying roughly opposite each other), with a period set by the difference between the two planets' perihelion precession rates, g5 (Jupiter) and g7 (Uranus). Using the modern catalogue values (g5 = 4.2575″/yr, g7 = 3.0868″/yr):

Period = 360° ÷ (g5 − g7) = 1,296,000″ ÷ 1.1707″/yr ≈ 1.107 million years

Unlike the Uranus–Neptune beat, this figure is a stable secular frequency difference — not drifting, and computable to high precision from measured planetary orbital data alone.

Closing the loop. This second figure is the one that matters most personally: it matches a note of "1.108 Myr" recorded decades ago, from a source that had since gone untraceable despite repeated searching — including repeated attempts using AI search tools, which consistently came up empty. The reference was finally recovered from an old notebook, and the number holds up under recalculation from first principles: 1.107 Myr, against a remembered figure of 1.108 Myr — agreement to within a few parts in a thousand.

So the solar system independently produces two neighboring periods, both close to 1.11 Myr, from two different physical mechanisms:

Fitting the harmonic cascade. The 1.107 Myr figure also slots cleanly into the existing 586 Myr harmonic cascade (586 → 293 → 146.5 → 73.3 → 36.6 Myr, descending by powers of 2): 586 ÷ 528 = 1.10985 Myr, where 528 = 2⁴ × 3 × 11 — a legal harmonic combination, and one that reuses the same factor of 11 already present in 293 ÷ 11 = 26.65 Myr, the mass-extinction cycle. The planetary period is not just numerically close to 1.11 Myr; it fits into the same harmonic structure already used elsewhere in the framework, using no new large primes.

The convergence. Three independent lines of evidence — the geomagnetic reversal record (spectral analysis, Kotov commensurability, and phase-folding, all converging on 1.11 Myr), the Jupiter–Uranus secular perihelion cycle (1.107 Myr, matching a 35-year-old notebook figure), and the Uranus–Neptune energy exchange (1.119 Myr) — all land on the same narrow timescale, arrived at by entirely different physical mechanisms and analytical methods. None of these three was fitted to match the others after the fact; each comes from its own independent calculation.

Different people have different ideas of what the aether is. It may be a tensile medium or it may flow or it may be made up of particles that bounce about. Funny, that sounds like solid, liquid and gas. So it is important to state which of these our ideas are based on. Because light can be polarised I prefer to think of it as transverse waves and favour a tensile medium. But LaFreniere showed that you can get polarised waves without a tensile medium.

My plan for the aether.

1. It is a tensile medium so that any distortion tries to undo, itself because it makes a force to do that.

2. The standard wave equation as used in Maxwell's equations is the basis and will therefore work for all electromagnetic waves.

3. This will be a surprise - space is Euclidean, and time is absolute. Have I gone mad? Do I not know about GR? I will explain how WSM can explain GR in Euclidean space and absolute time. I consider this a major part of the way forward and will explain the details later.

4. The wave equation is linear. This explains why light can travel across the Universe in every direction and through every point without getting in its own way. It is well known that linear equations can be combined and that multiple waves do not interact. This is taught as fundamental physics.

5. Except that it is wrong. When transverse waves travel through each other they do interact although that interaction is extremely small unless the waves have very high amplitude. For a very long time I was stating that the fundamental equation had to be non-linear. And it might be. But you can get interaction with a linear equation with transverse waves. That is because displacements in the medium do vector addition and as the waves go back to their original position they are working on a different part of the aether.

6. When trying to model particles in these conditions, it is very easy to get equations that cause the aether to fold over itself which is rather untidy and probably unphysical. So it may be that another condition is required and that is that the aether is incompressible. An alternative is that compressing it is very difficult. I remember people saying that Maxwell's equations were originally written in quaternions and later converted to vector form as we know them. Some claim that this lost a part of the meaning. That part may related to this aspect of things.

7. I am possibly on my own here, but I do not believe that any solution can be found without recognising the role of harmonics theory in the various frequencies floating about in the Universe. The second thing that I will follow up with is details of harmonics theory understanding of particles, isotopes and such. The little waves ride on the bigger waves and so on all the way up, although the direction of causes is all the way down.

8. The universe does not work from the bottom up but from the top down. That is why string theory was always doomed to fail and Harmonics theory has so many successes.

Those that have also tried to work with these concepts may well have very many different ways of looking at things. Good, let us try multiple different ways and see what works.

Have fun

Ray

https://youtu.be/dsYauWjGWIU?si=s96IjK7FIEAtjWSN

Internal Clocks: Chronobiologists have discovered that thousands of genes and physiological processes—such as core body temperature, hormone levels, blood pressure, and alertness—follow a dual oscillation, peaking and dipping every 12 hours rather than just once a day. Biological "Rush Hours": This 12-hour cycle creates secondary peaks of metabolic and genetic activity around dawn and dusk, helping the body manage daily shifts in energy demands.The Post-Lunch Dip: The minor drop in alertness and body temperature that humans typically feel about 12 hours after the middle of the night (usually early-to-mid afternoon) is a direct reflection of this internal rhythm interacting with our sleep-wake cycle. Midday Naps in Past and Traditional Societies.

The Siesta Tradition: Across Mediterranean, Middle Eastern, Latin American, and parts of Asian history, a post-midday rest or siesta was standard practice.Beating the Heat: Societies naturally paused work during the hottest hours of the afternoon when ambient temperatures peaked and physical labor became inefficient or dangerous. Biphasic Sleep: This habit forms part of a biphasic sleep pattern (sleeping in two distinct daily blocks, such as a shortened night plus a daytime nap), which was widely practiced before industrial work schedules enforced a single, continuous 8-hour block of night sleep.