In this essay, I will argue that the analysis of Sandberg et al. is flawed in a number of key respects, and as a result the Fermi Paradox remains an open question. Here I briefly list the key problems with the Sandberg et al. paper, before proceeding to discuss each in more detail.

  1. The method used of multiplying uncertainties of many small numbers, most of which have an upper bound of one, is biased towards yielding a result of a high probability of Earth being unique, while also leading to various dubious results.
  2. The key result of the paper is driven largely by uncertainty in the parameter fl, which is modeled in an unusual way without clear justification.
  3. Adoption of slightly different (and I believe more plausible) modelling choices and parameter values yields totally different results, which do not result in the Fermi paradox being dissolved. I illustrate this by re-estimating the Sandberg et al. models using different parameters and modelling assumptions.

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The potential for abusing multiplication of fractions to give extremely low numbers is well known. A particularly egregious example of this can be found in the work of Christian apologist Tim McGrew, who estimates the prior probability of having the evidence we do pertaining to the resurrection of Jesus at less than 10^-40, on the basis of multiplying together supposedly independent probabilities of each of Jesus’ disciples separately experiencing a hallucination.

There is nothing biased or weird in multiplication of probabilities yielding small numbers. It is the correct model for calculating joint probability P(A,B) = P(A|B)P(B) or P(A)P(B) if A,B independent. The issue with McGrew's calculation is not that multiplying independent events is "biased", it is that the model itself is wrong (the disciples' hallucinations are not plausibly independent, and there are additional issues concerning the transmission of factful account of events anyway).

Likewise, the correct move of incorporating "number of possible avenues by which life may emerge" is not to add more probabilities into multiplication, you'd include sum terms.

If one wants to criticize the model, that is of course possible, but that is a different point. The are also numerical issues with working with small floating numbers, but usually they can be avoided with careful applications of logs.

abiogenesis being so early on Earth is 100% survivorship bias

Being early on earth was not necessary for survival. Similarly, being early for the formation of stars of suitable temperatures also wasn't especially favored by anthropics. Neither of those things had to happen.

Great post! I moved a lot toward a rare-earth view when I learned of the Sandberg paper, and this post has me back to unsure. Glad I read this.