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The Ādam Paradox Hypothesis 197
3.The Probability
Under APH: The chance of finding such a mismatch is very small (<10%),
because APH expects symbols and expansions to line up.
Under gradualism: It’s more likely (~70%), because gradualists expect
population to rise slowly and not depend on a single symbolic “ignition.
”
Simplified version:
Under APH (<10%)
APH predicts:
Symbols trigger population growth.
Therefore, expansions and symbols should appear close together in time
(within a few thousand years, not tens of thousands).
So if you imagine many possible worlds consistent with APH:
In 90%+ of them, symbols and expansions overlap.
In fewer than 10%, random noise in dating methods or short-lived
anomalies might make them look separated.
That’s why we set the chance of a >20k mismatch as very small: <10%.
Under Gradualism (~70%)
Gradualism predicts:
Population growth is driven by climate, resources, or slow adaptation.
Symbolic artifacts can show up much later, as “icing on the cake.
”
If you run this scenario in many possible worlds:
It’s actually likely (more than half the time) that expansions appear first.
Archaeology already shows expansions in Africa ~100kya, but sustained
symbols only ~70kya — that’s a 30k mismatch.
So the probability of mismatch is much higher here — roughly 70%.
These aren’t lab-measured probabilities. They
’re theoretical likelihoods used to
compare models. It’s a way of saying: If we look at the evidence, which story
fits better?
In short:
<10% under APH = a mismatch would be an anomaly, not the norm.
~70% under Gradualism = mismatches are expected and fairly common.