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My view is that we can reason about organisms living in space because we are one of them. We have a sample size of one, but assuming that properties of differen
by mpoteat 5y ago
My view is that we can reason about organisms living in space because we are one of them. We have a sample size of one, but assuming that properties of different space-faring organisms are distributed normally, it stands to reason that the first sample collected is near to the mean of the underlying distribution.
In other words, imagine a normal distribution with very, very low variance (say, 0.0001). The mean is unknown to you. If you take one sample, your sample will very likely be close to the mean.
- AnimalMuppet 5y agoWithin your argument, what's the justification for assuming low variance?
- mpoteat 5y agoThere is none! Variance could be arbitrarily high I suppose. In the limit, if you assume a uniform distribution, I don't think that a single sample will give you any information about the underlying distribution characteristics. However, for the sake of the argument, variance can be arbitrarily high and still provide increasingly lower amounts of Bayesian evidence. As long as the variance is not unbounded (i.e. as long as the distribution is Gaussian, which I think is a reasonable assumption in nature), you can extract _some_ evidence from a single sample.