About B-Theory

Correspondence Matrices
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"No man ever steps in the same river twice, for it's not the same river and he's not the same man." - Heraclitus: 535 – c. 475 BCE

Welcome Traveler: To B-Theory!

I hope you have arrived safely and that who you are now is at least recognizably related to who you were before you arrived here. Perhaps it doesn’t matter really; your belief in yourself brings forth a whole new entity! Who you are or were, and whether or not the “I” that thinks (Descartes: Cogito Ergo Sum) is the same as the one that thought; this is what B-Theory is all about. 

B-Theory is concerned with the state of ‘Being’; both of the ontological and the evolution of the ‘Mind’ and endeavors to model it.

How is this possible? While the modeling of the Mind might seem an insurmountable task, note that the mind, as the whole of our mentality, is affected by both time and biology, each of which are bounded by physical laws. These laws can be described with mathematics. B-Theory hopes to bring about some of the discoveries so as to better understand both who we are and why we are.

There are currently three parts to this work:

The Static:

Thinking of the quote above: Imagine that we were able to take pictures of Heraclitus before and after his stepping in to the river. Treating these snapshots as if they were permanent still frames in time, we look for differences between the man who was Heraclitus and the man he now claims to be. It is the information between these differences that quantify the change and help understand the progression of self. The static projects are as follows:

Propositional Logical Topologies (ProLT): Distinguishability is a the key feature in any topology and is thought to be key in building a ‘Mental Space’. This work puts Aristotelian logic on a topological foundation so as to use principles such as axioms of separation and bridge propositional logic to Algebraic Topology.

Logical Homology Theory: As reasoning can be expressed through semantic languages it is possible that the ability to reason may be embedded in the mind by construction (development). Therefor building a geometric foundation based on logic may give a basis for constructing concepts and ‘thoughts’.

Correspondence Matrices (CM): This work creates linear measurement matrices which are binary matrix equivalents to propositional logical operators. This is needed for… wait for it: hint: it is no accident that the CM’s are formulated in Dirac’s bra-ket representation and are used as measurement matrices as seen in quantum theory. The tools originally developed in this paper were heavily extended to justify discoveries which were found in the process.

Boolean Modules and Vectors: This work develops the notions of B-Modules and Bectors and their associated spaces as well as gives the ability to vectorize logical expressions. This work gives an in depth justification for Correspondence as well as the treatment of logical expressions which can be measured via an inner-product space.


Heraclitus may have been correct when he said: “nothing in this world is constant except change and becoming”. As Minds we only measure ourselves as snapshots in time though we are constantly affected externally. Because of this external affect, brains do not propagate the same signals from moment to moment, there is change. Whatever the mind proves to be, it is inextricably linked to the brain and any change in the brain updates the minds to a new epoch. This is the process of becoming.

Evolutionary Logic: The aim of this project is to give a way to relate real valued functions such as the logistic function in machine learning and neuro-biological processes, to discrete valued propositional logic. By doing so we can bridge discrete values used in the above work in the Static section to continuous valued functions similar to those in the brain.


The work in this section is meant to build a physical foundation for the theory developed in the Static and Dynamic section, to eventually build a Mind. It is much more than this though, it is meant to be a repository for computational tools. As the work in developing the Correspondence Matrices proved quite valuable in other areas (e.g. computation and logic) the other areas are expected to have an impact in multiple areas. B-Theory hopes to build these toolboxes for the community.


B-Theory was started by Brian Droncheff. While the naming of B-Theory came about around the same time Brian released the paper on Correspondence Matrices (March 2018), the initial underlying theory of B-Theory was was born on September 7th, 2008. After attending a philosophy event which Brian organized and spoke concerning neural networks, he had an epiphany which would forever change his outlook on the origin of self-awareness.

Though B-theory may have come about through a search for understanding one’s own mind, it endeavors to be more. Everyone is a scientist by design and it is hoped that some will chose to spend more time in this endeavor and help solve the world’s problems. It is just as important to inspire others to engage in science and other STEM areas as is discovery. B-Theories motivation also lies in promoting science and STEM areas, as well as helping solve the world’s problems.

To B or not to B – that is the question