  In probabilistic updating one transforms a prior distribution in the light of
given evidence into a posterior distribution, via what is called conditioning,
updating, belief revision or inference. This is the essence of learning, as
Bayesian updating. It will be illustrated via a physical model involving
(adapted) water flows through pipes with different diameters.
  Bayesian updating makes us wiser, in the sense that the posterior
distribution makes the evidence more likely than the prior, since it
incorporates the evidence. Things are less clear when one wishes to learn from
multiple pieces of evidence / data. It turns out that there are (at least) two
forms of updating for this, associated with Jeffrey and Pearl. The difference
is not always clearly recognised.
  This paper provides an introduction and an overview in the setting of
discrete probability theory. It starts from an elementary question, involving
multiple pieces of evidence, that has been sent to a small group academic
specialists. Their answers show considerable differences. This is used as
motivation and starting point to introduce the two forms of updating, of
Jeffrey and Pearl, for multiple inputs and to elaborate their properties. In
the end the account is related to so-called variational free energy (VFE)
update in the cognitive theory of predictive processing. It is shown that both
Jeffrey and Pearl outperform VFE updating and that VFE updating need not
decrease divergence - that is correct errors - as it is supposed to do.
