Measuring thermodynamic length: https://arxiv.org/pdf/0706.0559.pdf; Chapters 3.1, 3.3 and 3.5 of Amari’s textbook referred to in previous weeks.
Fun with Kullback and Leibler (by Andrew D. Jackson)
For a more formal treatment of submanifolds and induced metrics and connections (that will be useful for next week’s material), see chapters 1.4, 1.9 of Amari’s textbook.
Entertainment and culture: separating the art from the artist
Science does not occur in a vacuum. As much as we’d like to think of it as an idealized quest for the truth of our universe, in reality, this search is often shaped and driven by motivations and ideals formed in the times in which they occur, that may seem wrong (or even abhorrent) in hindsight. For instance, the principle of least action we all know and love, originally formulated by Pierre Louis Maupertuis, was according to him, due to the wisdom of some omnipotent creator, and further proof of his existence.
The formalism of information geometry was first introduced by the statistician C.R. Rao, and was the culmination of his efforts to formalize various proposals to geometrize statistical inference which had sprung up among the Indian statistical community. His doctoral advisor was Ronald Fisher, whose name we’ve also come across several times now, and who himself made profound contributions to the field of statistics. Unfortunately, he was also a eugenicist, and firmly believed that not all races were equal, and that there was a natural hierarchy between them.
Although one can, and should separate the science from the scientist, one shouldn’t forget that sometimes, they are all too human, and susceptible to assuming culturally conditioned priors that do not stand up to subsequent statistical inference with much better data. A good scientist is one who updates their priors with new information, regardless of how strongly held their prior beliefs were. An even better scientist is capable of meta-reasoning about their priors and honestly asking themselves whether they’re dimensionally limited in their reasoning. I often wonder if Fisher would have done either had he been alive in today’s era of genomics, or whether he would have made common cause with those that continue down that path whether publicly, or in omerta as some out there seem to do so.