What this is

Cycles in this version

Each has its own page with the full calibration rationale, sourcing, and paired-data provenance - see all ten cycles.

• Ibn Khaldun — dynastic cycleperiod 120y · peak 1789

  ~120-year cycle of dynastic rise and fall, driven by asabiyyah - the group cohesion that hardship builds and luxury dissolves. Khaldun's five stages, paraphrased from Rosenthal: consolidation → concentration of power → leisure → contentment → waste

  Peak calibration: Project's editorial choice. Anchoring at the French Revolution places the curve at a documented Western inflection point so it can be visually compared against the modern US and global data series this project carries. Khaldun (d. 1406) made no claim about European history; this is the framework being applied here, not extended by him.

  Ibn Khaldun, Muqaddimah (1377)

• Kondratiev waveperiod 54y · peak 1973

  ~50–60 year economic long wave: technological expansion → plateau → stagnation → trough. Kondratiev traced it in price, interest-rate, and production series reaching back to the 1780s

  Peak calibration: Conventional anchor inside the post-WWII K-wave's 1968–1974 turning-point window (oil shock + Bretton Woods end). Other revivalists prefer 1968 (Mandel) or 1971; we use 1973 as the most cited single year.

  Kondratiev, 'Bol'shie tsikly kon'yunktury' (1925); abridged English: 'The Long Waves in Economic Life,' Review of Economic Statistics 17(6) (1935)

• Huntington — creedal passionperiod 60y · peak 1968

  ~60–70 year cycle of American political moralism: surges of 'creedal passion' - when the gap between American ideals and American institutions becomes intolerable - followed by long cynical intervals

  Peak calibration: Midpoint of Huntington's 'S&S Years, 1960–1975' (American Politics, Ch. 7), the period he identified as the fourth American creedal-passion era. Huntington didn't designate a single peak year; 1968 is the interval midpoint.

  Samuel P. Huntington, American Politics: The Promise of Disharmony (Belknap/Harvard, 1981)

• Schlesinger Jr. — liberal/conservative cycleperiod 30y · peak 1970

  ~30-year alternation of American politics between 'public purpose' (liberal/reform) and 'private interest' (conservative/consolidation) eras; the phase lengths are historical approximations of roughly 15–17 years, not fixed half-waves

  Peak calibration: Midpoint of the most recently completed liberal era in the conventional tabulation of Schlesinger Jr.'s scheme (1962–1978). The midpoint is this project's construction, not a peak date Schlesinger states. Taking the midpoints of his dated liberal eras gives roughly 1910 (Progressive), 1939 (New Deal), and 1970 (1960s/Great Society) - intervals of 29 and 31 years, averaging 30 - which is where the 30-year period comes from. The framework descends from Arthur Schlesinger Sr., whose Paths to the Present (1949) tabulated eleven alternating liberal and conservative periods through 1947 averaging 16.55 years each, implying a same-mood recurrence nearer 33 years; his son's streamlined twentieth-century scheme runs closer to 30, and 30 is what is plotted. Note: Schlesinger Jr. himself expected the next liberal turn shortly before or after 1990; a strict 30-year clock from 1970 puts the next cosine peak at 2000. His own forecast and his own period disagree - a plain demonstration of how sensitive a fixed sinusoid is to the anchor and period chosen.

  Arthur M. Schlesinger Jr., The Cycles of American History (Houghton Mifflin, 1986), Ch. 2 'The Cycles of American Politics'; building on Arthur M. Schlesinger Sr., Paths to the Present (Macmillan, 1949)

• Carlota Perez — techno-economic paradigmperiod 55y · peak 2000

  ~50–60 year wave in how each technological revolution is absorbed: installation (finance chases the new technology into a bubble) → turning point (the crash) → deployment (the technology actually spreads - the golden age)

  Peak calibration: Anchored to Perez's 'Turning Point' (2000–2001), the dot-com crash she identifies as the inflection between Installation and Deployment phases of the ICT surge. Her own term is 'turning point,' not peak; we map it to the sinusoid's peak as a mathematical convenience. Read 2000 as the financial-frenzy peak that ends the Installation phase, not a claimed 'paradigm peak' - and note that Perez's 2009 'double bubble' paper treats the dot-com crash and the 2008 credit crash as two parts of one structural episode, which makes any single-year Turning Point a stylization.

  Carlota Perez, Technological Revolutions and Financial Capital (Edward Elgar, 2002)

• Peter Turchin — secular cyclesperiod 150y · peak 2020

  ~150-year US-specific secular cycle (Ages of Discord, 2016): elite overproduction → immiseration (stagnating mass living standards) → state breakdown → reconsolidation. His pre-industrial agrarian cycles in Secular Cycles run ~200–300 years; a separate ~50-year bigenerational cycle stacks on top

  Peak calibration: Center of Turchin's published forecast window for US instability peaking in the 2020s (Nature 2010, Ages of Discord 2016). The 150-year period is specific to his US-compressed grand cycle in Ages of Discord. With our 2020 anchor + period 150, the sinusoid's prior peak lands at 1870 - close to the Civil War instability climax of ~1860 (cos ≈ +0.91 at 1860) but ~90 years off from the Revolutionary War of ~1780, which our sinusoid plots near a trough (cos ≈ −0.81 at 1780). Turchin's actual stated US instability climaxes (1780s, 1860s, 2020s) are not uniformly 150 years apart - gaps of ~80 years (1780s → 1860s) and ~160 years (1860s → 2020s) - so a strict 150-year sinusoid is a forced reduction of a non-uniform cycle. His pre-industrial agrarian secular cycles in Secular Cycles run 200–300 years and his separate bigenerational cycle is ~50 years.

  Peter Turchin, Secular Cycles (Princeton, 2009, with Nefedov); Ages of Discord (Beresta, 2016); End Times (Penguin, 2023)

• Ray Dalio — Big Cycleperiod 75y · peak 1950

  Big Cycle of imperial rise and fall: rising → top → declining → reset, tracked through debt, reserve-currency status, and internal order. Dalio puts long-term debt cycles at about 50–75 years; this curve uses 75, the top of his range. He also describes a longer ~250-year empire arc

  Peak calibration: Per Dalio Ch. 5: 'these measures of the United States' powers relative to its own history reached their peaks in the 1950s immediately after the Allies won World War II.' The 1950 anchor comes from Bridgewater's ~250-year empire-score chart, while the 75-year period is this project's selection from the 'about 50 to 75 years' range Dalio states for long-term debt cycles - he does not assert 75 specifically. The two are different constructs in Dalio's framework; using one's peak to anchor the other forces our sinusoid to peak again at ~2025, which Dalio does not assert (the empire-score chart shows decline post-1950, not a second peak). Treat this curve as a forced single-cycle reduction of two stacked Dalio cycles. Separately, our paired data (US share of world GDP) peaks at 1945 because of war-production effects; the cycle and the data deliberately differ by ~5 years, reflecting the difference between Dalio's composite empire score and a single GDP-share series.

  Ray Dalio, Principles for Dealing with the Changing World Order (Avid Reader Press, 2021)

• Strauss-Howe — saeculumperiod 84y · peak 1955

  ~80–90 year saeculum - about one long human life - in four ~21-year turnings driven by generational replacement: high → awakening → unraveling → crisis (the 4th turning)

  Peak calibration: Anchored to the post-WWII American High (~1955), the most recent completed First Turning peak in Strauss-Howe's saeculum. With period 84, the trough of this construction lands at 1997 (1955 + 42) and the next peak at 2039; the predicted Fourth-Turning Crisis climax (~2020) therefore sits on the rising arm of the sinusoid (cos ≈ +0.15), neither at a trough nor a peak. The framework actually has two cultural highs per saeculum (the 1T High and the 2T Awakening), so reducing it to a single sinusoid is a forced choice; we use the structural High. There is no peak-year anchor that aligns the predicted Crisis climax with either a sinusoid peak or trough.

  William Strauss & Neil Howe, The Fourth Turning (Broadway Books, 1997)

• Modelski — long cycle of world leadershipperiod 110y · peak 1945

  ~100–120 year long cycle of world leadership - global war → world power → delegitimation → deconcentration - tracked through naval and global-reach preponderance. Plotted here at 110 years, the midpoint of his stated range

  Peak calibration: Start of the US world-power phase in Modelski's own dating: Table 2.1 of Long Cycles in World Politics (1987, p. 40) dates the American cycle's phases 1914–1945 (global war) and 1945–1973 (world power), and Table 2.2 (p. 42) dates US oceanic supremacy from 1944, when the US crossed his threshold of one-half of the world's capital-ship assets. The 110-year period is this project's midpoint of the '100 to 120 years' range Modelski states in his encyclopedia treatment ('Long Cycles in Global Politics,' UNESCO-EOLSS), where he also warns that the long cycle 'does not connote strict cycles' - treat the fixed sinusoid as a stylization he explicitly disclaims. The 1987 book brackets the same range: it reports that 'in four of the cases, the average interval of time between the attainment of naval preponderance by one power and by its successor is 120 years' (p. 42) and speaks of 'the recurrence of global wars at intervals of about one century' (p. 218). Anchored at 1945, a 110-year cosine puts its earlier peaks at 1835, 1725, 1615, and 1505, against Modelski's own world-power phase starts of 1815 (Britain II), 1714 (Britain I), 1609 (the Netherlands), and 1516 (Portugal): misses of +20, +11, +6, and −11 years. The fixed period reproduces his sequence only loosely, and the drift grows toward the present.

  George Modelski, Long Cycles in World Politics (Macmillan / University of Washington Press, 1987); period range and non-strict-cycles disclaimer from Modelski, 'Long Cycles in Global Politics,' UNESCO-EOLSS

• Turchin (50y) — fathers-and-sons cycleperiod 50y · peak 1970

  ~50-year 'bi-generation' oscillation in US political violence, superimposed on the longer secular cycle - spikes of unrest roughly every two generations, once living memory of the last convulsion fades

  Peak calibration: Most recent stated peak, in Turchin's own words: 'a 50-year oscillation superimposed on the secular cycle, with peaks around 1870, 1920, and 1970' (Journal of Peace Research 49(4), 2012). With period 50 and peak 1970, this sinusoid's prior peaks land exactly on his other two stated peaks (1870 and 1920) and the next lands at 2020. Turchin himself extends the sequence to 'around 2020' in the same paper, while explicitly calling that a simple projection rather than a scientific prediction; it also coincides with the instability forecast of his separate 150-year secular cycle, so the two Turchin curves on this site peak together at 2020 by construction, not as corroboration. The paper attributes the mechanism to the 'fathers-and-sons' dynamic - an additional process he treats as distinct from the core structural-demographic theory - and prefers the term 'bi-generation cycles,' with recurrence 'roughly two generations (40–60 years)'; 50 is the headline number and the one used here.

  Peter Turchin, 'Dynamics of political instability in the United States, 1780–2010,' Journal of Peace Research 49(4) (2012): 577–591