Expected float entropy, relationships and consciousness
The question of whether there is a class of mathematical structures that have the property of consciousness may seem bizarre, daunting and yet perhaps on reflection important. It has received little attention from mathematicians probably because mathematics cannot be introduced in the absence of concrete definitions.

It is however of interest to biology, neuroscience, computer science, mathematics and theoretical physics, an example of the latter being Max Tegmark’s "Mathematical Universe Hypothesis" and its variations; see arXiv.org. Whilst it is sensible to approach such questions with caution and humility it is also reasonable for scientists to try to make progress in this area. In this respect I have writer papers proposing that relationships (isolated under expected float entropy minimisation) may play an important role in consciousness.

The theory stems from information theory and introduces a version of conditional Shannon entropy that includes relationships as parameters. It turns out that, for nonrandom systems, certain choices for the relationship parameters are isolated from the rest in the sense that they give much lower expected float entropy values and, hence, the system defines relationships. Since consciousness is awash with relationships and associations the theory may be relevant to consciousness. For those interested, below are various resources including a release of the GUI software (runnable .jar files) developed for researching the theory.
 From Learning to Consciousness: An Example Using Expected Float Entropy Minimisation. Entropy article 2019. pdf
 QuasiConscious Multivariate Systems. Complexity article 2015. pdf
 QuasiConscious Multivariate Systems. Preprint 2015. pdf
 QuasiConscious Multivariate Systems. ASSC conference poster 2015. pdf
 (Download URFinder3.7)
 (Download URFinder3.7 development source files)
 (Download RasterSampler1.0)
 (Download RasterSampler1.0 development source files)
 Mathematical theories of consciousness. News item and case study on www.maths.ox.ac.uk 2016. Web Page
URFinder is for finding relationship parameters that minimise expected float entropy in the case of small systems. It can also be used to implement Monte Carlo methods and produce expected float entropy histograms. RasterSampler is used for sampling pixels, in a chosen configuration, from digital photographs. When reading the published Complexity article “QuasiConscious Multivariate Systems” please note that the copy editing introduced an error on the 19th page (page number 143). The equation in question should say .
