How rational are we? We might say that this question, revised, is, "How Bayesian are we?" Do we correctly combine probabilities, taking into account combinations of our prior beliefs and understandings of the evidence completely correctly?
If we believe neuroscientists, humans are maybe Bayesian.. If you look at the cognitive science literature, that is so clearly not true-- people invent models in which humans just randomly drop data as a correction to the Bayesian framework that keeps the Bayesian framework in place. But perhaps the scientific community as a whole is Bayesian. After all, the scientific community is supposed to be special in some way. It is supposed to be more than the sum of its parts, not less, in its quest for what might be called "truth". In class, we've been reading through Kuhn's take on the science of science. I wondered what happened around the time of a crisis, in which the current paradigm (what's in the textbook and what everything thinks is the right way to interpret the data) is in competition with a new potential paradigm. The process of deciding between the old paradigm and the new paradigm is messy, filled with persuasive tactics, and might not even happen. For instance, without chaos theory, our understanding from Newtonian mechanics of the perigee of the moon was off by a factor of two for decades-- but nobody abandoned Newtonian mechanics for that reason. But beyond the mess, might the actual outcome be just decided by a simple application of Bayes rule? In this paper, they argue just that. Basically, at a scientific crisis, you start evaluating the likelihood of each potential paradigm for explaining the data, and encode your prior beliefs about the likelihood of each potential paradigm. Part of this prior belief might be based on aesthetic or a resistance to change. But aesthetic comes into play in the likelihood too. If a paradigm can explain too much, as you would see with Ptolemaic astronomy for example, it is actually less likely in a likelihood sense than a heliocentric theory once you integrate over all possible parameters. One question I have is: how close is the scientific community to Bayesian? Can someone evaluate this from data in some way? It'd be very hard to do so, but I already think that the structure of Kuhn's science of science prohibits pure Bayesianism for the scientific community. To be a Bayesian, you have to evaluate posterior beliefs correctly, as they become your priors, but the new paradigm is not even evaluated to have a probability before the scientific crisis sometimes. Sometimes, with special relativity, its framework is introduced prior to the revolution, but its prior is never evaluated based on all the previous data collected. Therefore, its prior is never correct, and Bayesianism can never be achieved by the scientific community. Still-- how close, as a community, do we come?
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