J. W. Mason

Mathematical Institute
University of Oxford
United Kingdom

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Welcome to my home page

I have long been interested in questions concerning the extent of the fundamental significance of mathematical structures. This page gives details of my research in the area of mathematical theories of consciousness, and also on spaces and algebras of functions.

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.

Brain image

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 non-random 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
  • Quasi-Conscious Multivariate Systems. Complexity article 2015. pdf
  • Quasi-Conscious Multivariate Systems. Preprint 2015. pdf
  • Quasi-Conscious Multivariate Systems. ASSC conference poster 2015. pdf
  • Download (Download URFinder3.7)
  • Download (Download URFinder3.7 development source files)
  • Download (Download RasterSampler1.0)
  • Download (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 “Quasi-Conscious Multivariate Systems” please note that the copy editing introduced an error on the 19th page (page number 143). The equation in question should say p_{4}\not=p_{1}+q_{1,2}+q_{1,3}.

Spaces and algebras of functions

In March 2012 I received my PhD in Mathematics from the School of Mathematical Sciences at the University of Nottingham, UK. My PhD research was mainly in the area of spaces and algebras of functions with an emphasis on Banach algebras and the generalisation of some existing theory over all complete valued fields and rings. My research on generalising Uniform algebras involves the use of functional analysis, Galois Theory and non-Archimedean analysis which is an interesting combination of theory. My publications in this area are available below.

I thank my supervisor Dr. J. F. Feinstein for his guidance and enthusiasm. On this site you can find out more about my research and academic activities.

Maple plot

Publications and Beamer presentations Also see arXiv.org

  • ThesisUniform Algebras Over Complete Valued Fields. PhD. Thesis, University of Nottingham 2012. pdf
  • From Learning to Consciousness: An Example Using Expected Float Entropy Minimisation. Entropy article 2019. pdf
  • Quasi-Conscious Multivariate Systems. Preprint 2015. pdf
  • Consciousness and the structuring property of typical data. Complexity article 2012. pdf
  • A survey of non-complex analogs of uniform algebras. In Function spaces, Contemp. Math. AMS 2011. pdf
  • An inductive proof of the Feinstein-Heath Swiss cheese classicalisation Theorem. Proc. AMS 2010. pdf
  • Generalising uniform algebras over complete valued fields. Function Spaces 2010 at SIUE, USA. Beamer
  • An intuitive proof of Heath's Theorem on Swiss cheese sets. BMC 2008 at the University of York, UK. Beamer

Useful links

London Mathematical Society
Institute of Mathematics and its Applications
American Mathematical Society
MR Lookup
Search arXiv.org
School of Math. Sciences, U. of Nottingham UK
Joel Feinstein's Home Page
Mac Tutor History of Mathematics archive
Mathematics Genealogy Project
Julia and Mandelbrot set Explorer
Images of Mathematicians on Postage Stamps
Turing Year logo

Page view.

Conference participation

  • The Nineteenth Annual Conference of the ASSC, Paris France 2015. Web site.
  • The Sixth Conference on Function Spaces at SIUE USA 2010. Web site.
  • Banach Algebras 2009, Stefan Banach International Mathematical Center, Bedlewo, Poland. Web site.
  • The Sixtieth British Mathematical Colloquium 2008, University of York, UK. Web site.

Photos from Function Spaces 2010. For more photos see here.

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Maintained by J Mason.