Cycle No. 09 · Empirical · contested
Modelski — long cycle of world leadership
110-year sinusoid Leading economy · GDP share: the record the verdict counts, drawn below on its own scale. A shape that looks alike is not a test.
Modelski · Does it hold up?
Not testable on the record that exists — and that is the finding, not a dodge.
The paired record (Leading Economy's Share of World GDP) runs 152 years: 1.4 of the 3.0 full periods this site requires before it will run a test on a 110-year claim. Roughly 178 more years of that measurement would reach the floor.
This is not a verdict about this theory in particular: 0 of the 9 paired constructions on this site clear that floor. Long-cycle claims are hard to test because the records are short, not because the theorists are careless.
~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
- Period
- 110 years
- Reference peak
- 1945
- Paired data
- Leading economy · GDP share
Peak calibration
Move the peak yourself: calibrate this cycle →
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). This site draws the one period around 1945 (1890–2000). Repeated back from 1945, a 110-year cosine would put 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.
CaveatThe 110-year period is this project's midpoint of Modelski's 100–120-year range, and he states the concept 'does not connote strict cycles.' The paired series measures the largest economy - not his naval/global-reach construct - and under that mechanical rule the 1870s–1881 leader is Qing China, not Britain.
Confidence classification: Empirical · contested — an empirical literature exists on the claim, and it is disputed. It grades the theorist's own evidence for the period; a paired data series is a separate comparison this site added. Every cycle on this site is drawn as at most one period of a pure sinusoid, cut at today where that period has not ended yet, built from one documented period and one documented reference peak, each taken from the theory or, where it gives none, chosen by this site — a deliberately naïve construction, so that disagreement between theories rather than parameter fitting is what you see. See about for why this site draws each cycle once, not as a repeating wave.
Where this curve plots its extrema
Computed from period 110 and reference peak 1945, over the one period this site draws (1890–2000). These are positions of this construction, not dates claimed by the theorist.
- Peaks
- 1945
- Troughs
- 1890 · 2000
Paired data series
Leading Economy's Share of World GDP
% of world GDPThe largest single economy's share of the summed GDP of the countries Maddison covers that year, with the leader named per year (Maddison Project Database 2023, 2011 PPP $); trimmed to 1870+, and the covered-country denominator grows over time - see provenance. The rule - largest economy - is mechanical, fixed without reference to Modelski's leadership succession
Why this pairingEconomic size as a deliberately imperfect correlate of world leadership - a proxy for a correlate of Modelski's naval/global-reach construct, not the construct itself. Mechanical by design (the largest economy per year, never hand-picking his hegemons), so its divergences show: under Maddison PPP the 1870–1881 leader is Qing China (not Britain, Modelski's naval leader) and China leads again from 2014. The series' all-time maximum, 31.6% in 1945, falls on the reference peak - a descriptive coincidence under a denominator whose coverage is thinnest early, not independent validation of the theory.
- Source
- Maddison Project Database 2023 (Bolt & van Zanden, 2024, J. Econ. Surveys, DOI 10.1111/joes.12618)
- License
- CC BY 4.0
Spectral verdict
Insufficient data — no test possible · 1.4 of 3.0 required periods
The Leading Economy's Share of World GDP record spans 152 years — 1.4 of the 3.0 full periods this site requires before testing a 110-year claim. No test was run and no p-value exists: the honest verdict is that the record is too short to test the claim at all.
“Insufficient data” is an eligibility outcome under the site's pre-registered 3.0-period rule - the test is declined, not failed - and is not evidence for or against the theory.
This pairing has no p-value. Separately, this site's secondary cross-grid panel borrows a theory's period and sets it against a record that theory is not paired with, so none of its re-pairings is this theory's own claim. This page's record, Leading Economy's Share of World GDP, was set against 2 other theories' periods: Schlesinger Jr.'s 30 years and Turchin's 50 years (lowest p 0.398). None of these 2 reached p < 0.05 under either noise model. All 19 re-pairings, cell by cell →
Target period 110 years · Insufficient data — no test possible · 1.4 of 3.0 required periods
Swipe sideways for the whole figure
Wider than this window: use the arrows at its edges to see the rest, or click it to open it full size
No test was run: this record covers 1.4 of the 3.0 full periods the pre-registered test requires, so the spectrum in the figure is descriptive only. Had the record qualified, the test would be a harmonic regression at the exact stated period against an AR(1) red-noise null (99,999 bootstrap draws). Read the protocol under spectral testing on the methods page, or fetch the machine-readable verdicts.json.
Reuse this
Kooi, D. (2026). Sinusoidal History: Modelski — long cycle of world leadership. https://sinusoidalhistory.com/cycles/modelski · DOI 10.5281/zenodo.21998618. Paired data series: Leading Economy's Share of World GDP (Maddison Project Database 2023 (Bolt & van Zanden, 2024, J. Econ. Surveys)), CC BY 4.0.
Our code and the original chart files are MIT-licensed as our own work. The plotted data stay under their upstream terms, listed above: CC BY series carry their attribution requirement with them, and a series with no explicit license is shown here without any grant we can pass on. Reuse our figures and code with attribution; honour the data terms for the plotted series.
Open this cycle in the interactive chart to calibrate its peak and period against the data, or compare it with the other nine on one axis.