But that is just a direct consequence of the pdfs being near-constant, as we've agreed.Expand full comment
 That doesn't sound right to me either.Expand full comment
 Thanks Robin. It was the repeated refs to the distributions being exponential that threw me. While technically correct, they made it harder for me to see that you were really comparing Earth’s durations with sets of values obtained by N repeated draws from a *nearly uniform* distribution over [0,W-S], after discarding those sets whose sum exceeded W-S.Expand full comment
 Yes the pdf is near constant, but no we aren't using any more than the total time constraint.Expand full comment
 "if an oasis succeeds in doing all its required hard steps within its W-S duration, then the time durations required to do each of the hard steps are all drawn from the same (roughly exponential) distribution, regardless of the value of E for those steps!"OK but isn't the pdf for each of these time durations nevertheless essentially constant over the relevant N-dimensional region (in which the ith duration Di is at most W-S for all i)? And if so, why would you expect the observed values for Earth to be any closer than what’s implied by the constraint that the Di sum to no more than W-S?Why I think the pdfs are essentially constant: By the definition of 'hard step', the expected value E of each step >> W. But for an exponential distribution, E = 1/L (writing L for lambda), so 1/L >> W => LW << 1 => L(W-S) << 1 => the value L*exp(-LDi) of the pdf of the (un-truncated) exponential distribution for Di is always, within the relevant truncation region, roughly L.Expand full comment
 Yes, there are surely many constraints and factors I'm not considering above. And if they correlate with the features I examine, my analysis could be misleading.Expand full comment
 That would be about future filters. This post is focused on explaining data with past filters.Expand full comment
 You must discuss the "political" filter in a future post. I'm afraid that's the one that may be key, at least for us https://www.nationalreview....Expand full comment
 You can represent a chance of something causing extinction via a try-once step.Expand full comment
 Any ideas about positive and negative filters?Positive ones: thing that should happen, like sex.Negative ones: thing which should not happen like large asteroid impacts or wrong genetics.Expand full comment