Interactive visualization of the Time Compression Paradox dynamical system. All data generated from the formal models in the four-paper series.
Five coupled ODEs evolving over 30 years (2025–2055). The compression ratio ρ grows logistically while opportunity space O expands superlinearly. Capital K and expectations E co-evolve through feedback loops.
Paper 1: As AI reduces cognitive price, elastic demand (ε = 1.8) causes total expenditure to increase. Price falls 95% but expenditure grows 11×. The rebound exceeds 100% — classic backfire.
Paper 2: |O(α)| = |O(0)| · ρβ with β = 1.7. The frontier of feasible work expands superlinearly as AI compresses task costs, making previously impossible tasks viable.
How the work multiplier MW varies across opportunity elasticity β and maximum compression ratio ρmax. Darker gold = higher work multiplication.
| β \ ρmax | 10 | 50 | 100 | 500 | 1000 |
|---|
The logistic compression curve ρ(α) = 1 + (ρmax − 1) · σ(k(α − α0)) with inflection at α0 = 10. Current AI capability (~2025) is early on the S-curve.