  In this review, we examine an extended Bayesian inference method and its
relation to biological information processing. We discuss the idea of combining
two modes of Bayesian inference. The first is the standard Bayesian inference,
which contracts probability space. The second is its inverse, which extends and
enriches the probability space of latent and observable variables. Their
combination has been observed that, greatly, facilitates discovery. Moreover,
this dual search during the updating process elucidates a crucial difference
between biological and artificial information processing. The latter is
restricted due to nonlinearities, while the former utilizes it. This duality is
ubiquitous in biological information process dynamics (`flee-or-fight',
`explore-or-exploit' etc.) as is the role of fractality and chaos in its
underlying nonequilibrium, nonlinear dynamics. We also propose a new
experimental set up that stems from testing these ideas.
