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Annoyance comments on Cascio in The Atlantic, more on cognitive enhancement as existential risk mitigation - Less Wrong
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If the correlation is sufficiently small, it can be lower than the error rate in detecting it.
And though the two concepts are distinct, in this context they're the same. Implication and statistical correlation can be the same when what's implied is a likelihood instead of a certainty.
I can't tell if I disagree with you in a substantive way or just in your word usage (i.e., semantics). Can you please translate this assertion into math?