Living vs. cumulative dead through history, 10,000 BCE to 2100 CE

dead_living.py

"""Living vs. cumulative dead through history, 10,000 BCE to 2100 CE.

Cumulative births anchored to PRB (Haub & Kaneda 2022) era totals (~117B by 2022).
Living interpolated from standard population benchmarks; post-2022 follows UN WPP 2024
medium variant. Dead = ever-born - living.
"""
import numpy as np
import matplotlib.pyplot as plt
from matplotlib.ticker import FuncFormatter

# PRB era cumulative births, scaled to hit 117B at 2022.
prb_cum = [
    (-10000, 0.9),
    (-8000,  1.2),
    (1,      51.1),
    (1200,   79.9),
    (1650,   93.8),
    (1750,   97.2),
    (1850,   101.6),
    (1900,   104.7),
    (1950,   108.4),
    (2000,   113.9),
    (2022,   117.0),
    (2050,   117.0 + 0.130 * 28),
    (2100,   117.0 + 0.130 * 28 + 0.115 * 50),
]

# Living population benchmarks (millions)
pop_knots = [
    (-10000, 4), (-8000, 5), (-1000, 50), (1, 300), (1000, 310),
    (1500, 500), (1650, 500), (1750, 795), (1800, 980), (1850, 1260),
    (1900, 1650), (1950, 2520), (1970, 3700), (2000, 6070), (2022, 7960),
    (2050, 9700), (2086, 10300), (2100, 10200),
]

years = np.arange(-10000, 2101)

cum_years = np.array([c[0] for c in prb_cum])
cum_vals = np.array([c[1] for c in prb_cum]) * 1e9
cum_births = np.interp(years, cum_years, cum_vals)

knot_years = np.array([k[0] for k in pop_knots])
knot_pops = np.array([k[1] for k in pop_knots]) * 1e6
pop = np.exp(np.interp(years, knot_years, np.log(knot_pops)))

dead = cum_births - pop
ratio = dead / pop

# x = years before 2101, log-scaled then inverted so modern era gets spread
# out on the right and ancient era gets compressed on the left.
x = 2101 - years

def year_fmt(val, _):
    y = 2101 - val
    if y <= 0:
        return f"{-y+1} BCE"
    if y < 1000:
        return f"{int(y)} CE"
    return f"{int(y)}"

fig, (ax1, ax2) = plt.subplots(2, 1, figsize=(10, 7), sharex=True)

ax1.plot(x, dead / 1e9, color="#444", lw=2, label="Cumulative dead")
ax1.plot(x, pop / 1e9, color="#c44", lw=2, label="Living")
ax1.set_xscale("log")
ax1.set_yscale("log")
ax1.invert_xaxis()
ax1.set_ylabel("People (billions, log scale)")
ax1.set_ylim(0.001, 200)
ax1.grid(which="both", alpha=0.3)
ax1.legend(loc="upper left", framealpha=0.9)
ax1.set_title("The living, the dead, and their ratio (10,000 BCE – 2100 CE)")

ax2.plot(x, ratio, color="#2a7", lw=2)
ax2.set_xscale("log")
ax2.set_yscale("log")
ax2.set_ylabel("Dead per living (log scale)")
ax2.set_xlabel("Year")
ax2.set_ylim(1, 3000)
ax2.grid(which="both", alpha=0.3)

# Put ticks at recognizable years
tick_years = [-10000, -3000, -1000, 1, 1000, 1500, 1800, 1900, 1950, 2000, 2050, 2100]
tick_x = [2101 - y for y in tick_years]
tick_labels = ["10000 BCE", "3000 BCE", "1000 BCE", "1 CE",
               "1000", "1500", "1800", "1900", "1950", "2000", "2050", "2100"]
ax2.set_xticks(tick_x)
ax2.set_xticklabels(tick_labels, rotation=30, ha="right")
ax2.minorticks_off()

plt.tight_layout()
out = "/Users/emptysquare/co/emptysquare-hugo/emptysquare/content/the-dead-majority/dead-living.png"
plt.savefig(out, dpi=150)
print("saved", out)