I didn’t mean ‘similar’. I meant that it is equivalent to Bayesian updating with a lot of noise. The great thing about recursive Bayesian state estimation is that it can recover from noise by processing more data. Because of this, noisy Bayes is a strict subset of noise-free Bayes, meaning pure rationality is basically noise-free Bayesian updating. That idea contradicts the linked article claiming that rationality is somehow more than that.
There is no plausible way in which the process by which this meme has propagated can be explained by Bayesian updating on truth value.
An approximate Bayesian algorithm can temporarily get stuck in local minima like that. Remember also that the underlying criterion for updating is not truth, but reward maximization. It just happens to be the case that truth is extremely useful for reward maximization. Evolution did not achieve to structure our species in a way that makes it make it obvious for us how to balance social, aesthetic, …, near-term, long-term rewards to get a really good overall policy in our modern lives (or really in any human life beyond multiplying our genes in groups of people in the wilderness). Because of this people get stuck all the time in conformity, envy, fear, etc., when there are actually ways of suppressing ancient reflexes and emotions to achieve much higher levels of overall and lasting happiness.
As its the case with an myopic view on any Bayesian inference process that involves a lot of noise. The question is just whether rationality is about removing the noise, or whether it is about something else; whether “rationality is more than ‘Bayesian updating’”. I do not think we can answer this question very satisfyingly yet.
I tend to think what Cumming says is akin to saying something like: “Optimal evolution is not about adapting according to Bayes rule, because look at just how complicated gene expression is! See, evolution works by stories encoded in G, A, C and T, and most of them get passed on even though they do not immediately help the individual!”