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About the Fundamental Law of Inequality: UPDATED Aug 2023

My co-author Greg Warr and I finally published our book on this subject: "Exposing Nature's Bias: the Hidden Clockwork behind Society, Life and the Universe." It is the culmination of more than 10 years of research and unifies the emergent properties of many systems. it explains why greed dominates financial systems, why Zipf's law of word frequencies is present in all books, why the genome has been so stable for over 3.6 billion years, why some proteins are so long, why software structure is pre-determined independently of its developers or the technology they use and in indeed why power-laws dominate all discrete systems in the universe.

Published - June 2022

** Availability at **

** Availability at **

Here's more of the story so far ...

Jul 2023

Protein copying in the domains of life

Proteins are exactly copied around the domains of life and viruses according to a very precise power-law. This behaviour is predicted by the FLI and you wouldn't find it unless the maths told you where to look. The graphs are plotted using the splendid European Molecular Biology Lab data from 2007-2021 in snapshots. We have been trying to publish this for a couple of years but biological journals always find an excuse to reject it even though it can be independently tested. This copying is partly caused by HGT (Horizontal Gene Transmission) and partly by VGT (Vertical Gene Transmission). You might like to check it out for yourself.

It turns out that viruses play an essential part in this mechanism making it harder to claim that viruses are not alive. From the point of view of Information Theory, there is no sensible distinction.

May 2022

Universal Inverse Symmetry in all genomes

Watch how the universal symmetry of DNA gradually degrades as genomes decline in size from the extraordinary axolotl, down to the viruses such as Covid-19 which are a million times smaller. Every group of N adjacent nucleotides is repeated but in inverse symmetry, behaviour enforced by the FLI.

The same progression but this time showing the power-law in N-tuple behaviour (adjacent groups of N nucleotides) enforced by the FLI. All genomes look like this showing how DNA has an underlying stability over its 3.6 billion years in spite of evolutionary pressures.

October 2019

A general proof of Zipf's law

The first general proof of Zipf's law for all discrete systems. Download

Strong evidence of an information-theoretical conservation principle linking all discrete systems

A complete general theory of why disparate discrete systems such as the proteome and collections of computer software share identical properties such as their length distributions. There's a lot more to come. Download

CoHSI V; Identical multiple scale-independent systems within genomes and computer software

The genome and hexadecimal software dumps have exactly the same information properties. Download

CoHSI IV; Unifying Horizontal and Vertical Gene Transfer - is Mechanism Irrelevant ?

Shows that CoHSI correctly predicts the rate at which proteins are copied across all domains of life, demonstrating that viruses are fundamental to this process. Download

CoHSI III: Long proteins and implications for protein evolution

Shows that the longest protein depends only on the size of the protein aggregation and demonstrates that this leaves a recognisable footprint in the phylogenetic tree including evidence of a previously undocumented mass extinction. Download

CoHSI II; The average length of proteins, evolutionary pressure and eukaryotic fine structure

Why protein average length is highly conserved and unusual fine structure identified in the Eukaryota. Download

CoHSI I; Detailed properties of the Canonical Distribution for Discrete Systems such as the Proteome

A comprehensive exploration of the properties of the CoHSI equation. Download

September 2017

Conservation of Hartley-Shannon Information (CoHSI) in discrete systems

The length distribution of discrete systems such as the complete Proteome, collections of Software in any language and digital Music all obey the following equation

Here N is the number of ways M components each with size ti beads made up from ai different colours can be arranged. For components large compared with their alphabet, this asymptotes to a power-law

It has nothing to do with natural selection, human volition or any other action other than the natural behaviour of large random systems. It is an emergent property and in important ways, software and protein structural properties are therefore identical.


Heiland Lecture, CSM, Golden CO, 07-Mar-2018

NIST Lecture, Boulder CO, 06-Mar-2018

May 2015

Conservation of Information in Proteins

In proteins, CoHSI predicts the remarkable constancy of average protein length and also why very long proteins exist. PLOS ONE download

Like all my recent work, complete computational reproducibility packages are provided which are capable of reproducing each diagram, table and statistical result using entirely open source. As an example, for this paper it can be found at Reproducibility package

and a tutorial in how to build reproductibility packages is given here. How to build reproducibility packages

April 2014 - Software's Hidden Clockwork

Lengths of software components measured in tokens

Unique alphabets of software components measured in tokens

Just like proteins, all software systems have a hidden clockwork which forces them into the same component size and alphabet size distributions whatever they do, whoever wrote them and whatever technology or language was used. Just watch as both the lengths and alphabets of 100 million lines of C, C++, Java, Fortran, Ada and Tcl-Tk asymptote to the CoHSI distribution in 1/2 million line chunks.

IEEE TSE preprint