How the numbers were chosen

Normalization

Every overlaid data series is rescaled to the interval [-1, 1] using its own minimum and maximum over the visible window. The eight cycle curves are sinusoids of unit amplitude (theamplitude_normalized field on every cycle is 1.0). The vertical axis is therefore dimensionless: visual peak heights do not represent real-world magnitudes, only relative shape over time. That is convenient for eyeballing shape against a normalized sinusoid, and it is lossy: it hides absolute magnitude and makes level differences invisible. Two points stand out:

• A series with one enormous spike (e.g. global conflict deaths in WWII) compresses every other variation toward a thin band. The visible shape near the peaks is real; the visible shape away from them is attenuated.
• Because normalization is per-series, you cannot compare amplitudes across series. Only across time within a single series.

Why Pearson is the wrong tool

The calibration panel reports a Pearson correlation between the data series and the cycle curve. Pearson assumes two things this context violates:

• Phase sensitivity. For two sinusoids of the same period, Pearson r reduces to cos(Δφ), where Δφ is the phase offset between them. A perfect cosine evaluated over one full period has r = 1 with itself, r = 0 with a quarter-period shift, and r = −1 with a half-period shift — even though all three are the same cycle in any structural sense. Pearson therefore measures phase alignment, not cyclic similarity, and the calibration slider primarily moves r by changing Δφ.
• Independence of observations. Time series are autocorrelated, so classical Pearson significance tests are anti-conservative on data like ours: the effective sample size is smaller than the row count, and naive p-values overstate significance. The calibration drawer therefore reports the r value but not a p-value.

The panel exposes Pearson anyway because the single most important question - "how much is the peak-year choice doing?" - is visible just from watching the correlation change as you move the slider. That diagnostic use is valid. Treating the number as a test statistic is not.

Better tools for cyclic data include cross-correlation at varying lags, the Fourier periodogram (or Lomb-Scargle for unevenly sampled records, which the present series are not), and wavelet decomposition for non-stationary signals. These are flagged for future work.

Missing and sparse data

The curves cover 1600–2050. Every data series has shorter coverage. DW-NOMINATE: 46th Congress–present (1879–current); Fernald TFP annual series 1948–present, displayed 1948–present (the 1948 and 1949 values use a clipped, asymmetric window because a true 5-year centered window only becomes available at 1950 — treat the first two displayed points as edge artifacts); Project Mars conflict data 1800–2011; WID top-1% wealth modern coverage 1913–most-recent (with five earlier decadal points spliced from secondary sources, see below); Maddison US/world GDP share trimmed to 1870+ (earlier years have unstable country coverage); V-Dem 1789–present; Stimson Policy Mood 1952–2024. Gaps are simply absent from the chart - nothing is interpolated. If a series fails to load, its legend entry shows "data unavailable" and the rest of the viz keeps working.

Two finer caveats. The modern WID/Saez–Zucman US top-1% wealth series begins in 1913; the five pre-1913 points (1820, 1850, 1880, 1900, 1910) come from earlier historical sources spliced via OWID/ WID and have wider standard errors. The TFP 5-year centered rolling average is this project's derivation from Fernald's annual dtfp_utilcolumn (utilization-adjusted TFP growth), not Fernald's own published series; the build script keeps clipped (asymmetric) windows at the boundaries rather than dropping rows, so 1948 = mean of {1948, 1949, 1950} and 1949 = mean of {1948, 1949, 1950, 1951} — read those endpoints with appropriate skepticism.

A third caveat. The Maddison rebuild forward-fills each country's GDP between sparse benchmark observations but does not back-fill before each country's first observation. Many non-Western countries enter Maddison only at 1950, so the world denominator is systematically smaller pre-1950 than post-1950 — biasing US share of world GDP upward for early years. The 1870 value (~10.6%) and the magnitude of the 1870→1945 climb should both be read as "US share of countries Maddison covers in that year," not "US share of world GDP" literally.

Notes on individual pairings

V-Dem with Strauss-Howe, not Huntington. An earlier draft of this project paired V-Dem with Huntington as a secondary signal alongside DW-NOMINATE. We moved it to Strauss-Howe so each cycle would have exactly one paired series. Both are arguments. The Strauss-Howe pairing reads V-Dem's recent decline as a Fourth-Turning institutional-stress signal; the Huntington pairing would have read it as the trough side of a creedal-passion cycle. The data is the same; the framing differs.

Project Mars covers conventional wars only. The conflict-deaths series registers years like 2010 as zero because no qualifying conventional war (interstate or civil war between states with differentiated militaries causing ≥500 deaths) was active that year — even though other conflict datasets (UCDP, COW, PRIO) record substantial casualties in 2010 (Afghanistan, Iraq, Mexican drug war). The series therefore measures conventional-war intensity, not all conflict deaths; read drops to zero accordingly.

No paired series for Perez. The techno-economic paradigm story is harder to reduce to a single century-long series. TFP growth is paired with Kondratiev because the Kondratiev framing is more directly about productivity surges; Perez tells a richer story about installation and deployment phases that no single time series captures cleanly.

Stimson Policy Mood with Schlesinger Jr. Of the eight cycles, Schlesinger's pairing is the closest the site gets to a direct measurement: Stimson's index is, by construction, an estimate of US public preference for liberal vs. conservative domestic policy — exactly what Schlesinger's cycle claims to track. The catch is coverage: the series only starts in 1952, so only Schlesinger's most recent two completed swings (mid-50s trough → late-60s peak → late-70s trough) sit inside the empirical window. The pre-1952 shape of the Schlesinger curve cannot be stress-tested against the paired data; treat the calibration drawer's Pearson r accordingly.

See each series' per-source provenance file for full retrieval and processing notes.