Cross-power comparison: \(P_{in}\), \(\mathcal{D}_{KL}\), \(\Phi\), \(\mathcal{R}\)

This is the side-by-side table the rest of the essays kept gesturing at. Numbers are rough on purpose; the ratios are the durable signal.

Energy harvested (\(P_{in}\)) — the ceiling on everything else

Three structural facts visible at a glance:

1. China’s \(P_{in}\) is ~2× the USA’s in absolute terms but ~⅓ the USA’s per-capita. China is “rich nation, poor people” in energy terms.
2. USA per-capita is ~16× African per-capita. That ratio is the single largest moral and political fact in the world economy. It cannot be closed by efficiency alone; African \(P_{in}\) has to roughly tenfold for the gap to halve.
3. EU has been shrinking \(P_{in}\) for ~20 years — the only major bloc doing so. Some is real efficiency; a large fraction is offshored energy embedded in imports.

Delusion (\(\mathcal{D}_{KL}\)) — model versus reality

This is a qualitative ranking, not a measurement. The criterion: how large is the gap between the regime’s working forecast and observable base-rate reality, on the questions where it matters?

Important nuance: \(\mathcal{D}_{KL}\) is multiplicative in the denominator of the persistence equation. A Russia-level delusion factor of 2–3× the denominator means the same numerator has to do 2–3× the work. The cost is real and currently being paid in Russia’s case as substrate consumption.

Also important: broadcast \(\mathcal{D}_{KL}\) (propaganda) and internal \(\mathcal{D}_{KL}\) (what the controller actually models) are different. Russia probably has high external, mid internal. China has the opposite issue — middling external, internal rising under personalism. The USA traditionally had moderately low internal \(\mathcal{D}_{KL}\) (think tanks, peer-reviewed open intelligence, market price signals); recently the internal/external gap has narrowed in the worse direction.

What they are made of (\(\Phi\)) — the substrate

Comparable substrate features, rough:

Two observations:

• Africa is the only major substrate with a positive demographic trajectory. Every other listed node is below replacement.
• No single power has all the substrate. The US has people, food, energy, military, and currency but lacks minerals. China has minerals processing, manufacturing, people, but lacks domestic food and energy. Russia has resources and military but lacks people, \(\eta\), and a future. The EU has \(\eta\) and people but lacks energy and military. This is why the world is currently un-hegemonic — no node has all of what another node needs.

The friction load (\(\Gamma\)) — what nobody has settled

Approximate \(\Gamma\) load by node, in equivalent “decade-equivalents” of unresolved files:

\(\Gamma\) enters the denominator with the same multiplicative weight as \(\mathcal{D}_{KL}\). Closing a single decades-old file is worth more for \(\mathcal{R}\) than most growth programmes.

The shelter map (\(\Psi\))

Who is sheltered by whom:

USA  ←  geography, oceans, USD, alliances → shelters EU, Japan, Korea, Gulf, Israel
EU   ←  USA, single market, Euro            → shelters its 27 members
China ← internal market, trade openness     → shelters Pakistan, Cambodia, parts of Africa, Russia (partially)
Russia ← nuclear floor, China               → shelters Belarus, Syria, parts of Sahel, Iran (partially)
Africa ← UN agencies, diaspora, China loans, EU trade → mostly Ψ-importer
Third world ← multi-hedging                  → bracket-as-graph; varies by node
UN    ← post-1945 great-power consensus     → shelters everyone partially

The hegemon question of the 21st century is not “who replaces the US” but “who, if anyone, can credibly offer the third world a \(\Psi\) package that beats the existing one.” Neither China nor Russia individually can; the BRICS+ aggregate doesn’t yet; the West’s \(\Psi\) is conditional on staying internally coherent. The most likely outcome is multipolar \(\Psi\) — different functions sheltered by different blocs — which is just multipolarity stated in persistence-law vocabulary.

The persistence-ratio summary

A rough \(\mathcal{R}\) ranking, decade horizon, structural:

Most major nodes are above the dissolution threshold. The interesting differences are trajectory and what each is overpaying for:

• USA pays in delusion about its own role.
• EU pays in substrate (energy, demographic).
• China pays in concentrated regime risk and demographic clock.
• Russia pays in substrate to keep narrative.
• Africa pays in \(P_{in}\) deficit and unresolved \(\Gamma\).
• Third world pays in \(\Psi\)-rent.
• UN pays in legitimacy when the great powers won’t.

The one variable that dominates the next thirty years

If we had to pick a single FPE variable whose trajectory determines the most about world \(\mathcal{R}\) to 2050, it is African \(P_{in}\) per capita. A continent of 2.5 B people running on 600 W/person is not a steady state — politically, ecologically, or morally. Either it climbs (and the species’ demographic dividend cashes), or it stalls (and the migration vector restructures every other node’s \(\Phi\)).

The persistence law doesn’t decide which. The persistence law just says: this is the load-bearing accounting entry.

Empire collapse proximity (Rus, Chn, US)

Formal hypothesis and scoring: empire_collapse_hypothesis.md.

Ordering: Russia is closest to empire-collapse dynamics; the USA is farthest. None of the three are near state dissolution on a 10-year horizon — the IPS prediction is footprint downscale, not disappearance.

See also

• framework.md — how the terms map
• united_nations.md — the institutional \(\Psi\)
• Per-power essays: usa.md, eu.md, russia.md, china.md, africa.md, third_world.md