This page is a sub-page of our page on Category Theory.

///////

**The sub-pages of this page are**:

• Algebraic Thought

• Semantic meta-network for communicative quality assurance

///////

**Related KMR-pages**:

///////

**Other relevant sources of information**:

• A legacy for living systems, Gregory Bateson as Precursor to Biosemiotics, Springer, 2008.

• Semiotic Engineering

• Algebraic Semiotics, by Joseph Goguen

///////

**Human Algebras**:

• Norm-Critical Innovation Algebra

• Discourse Algebra

• Social Algebra

• Socially Responsible Algebra

• Social Calculus

• Knowledge Algebra

• Business Algebra

• Ethical E-Commerce

**Matrix Algebras**:

• Matrix Algebra

• Linear Algebra

• Projective Geometry

**Polynomial Algebras**:

• Some basic algebraic concepts

• Rings of Polynomials

• Disambiguating plus

**Category Theory**:

• Category Theory

• Algebraic Thought

///////

**Other related sources of information**:

///////

**HumCat: The Human Category**

1. **The category of human beings**

**Starting point: Human thinking can be modeled as instantiations of thought patterns **

A thought can be seen as the instantiation of a kind of blue-print that we will refer to as a thought pattern, a thought-schema, or sometimes just a schema when the context is unambiguous. This is very similar to how databases are constructed by specifying a (database) schema and then populating the database by instantiating this (abstract) schema with (concrete) entries of data items – as well as with relations between some of these – in accordance with the rules and constraints provided by the schema.

1.1. **Human information**

The complementary view to Shannon’s perspective, the human perspective on communication, has been taken by a number of scholars. It is best represented by the famous definition of information given by Gregory Bateson (1972): “Information is a difference that makes a difference.” Hence, the first difference is mapped into the mind of the agent and combined with the cognitive state of the agent into the second difference.

Let us introduce the term ‘pattern’ to mean a collection of objects with (directed) relations between some of them. If we think of a difference as a form of pattern, then Bateson’s definition translates into “information is a pattern that creates another pattern”. Moreover, this creation is due to the presence of a third pattern, the pattern, which represents the cognitive state of the agent involved. We will often refer to the latter type of pattern as a schema.

Hence, we can expand Bateson’s definition in the following way:

*Information is a difference that makes a difference to me,
by allowing me to connect a pattern that is new to me
with the patterns that I know from before*.

Category theory is a universal pattern language for mathematics that has been developed during the last 75 years. It is concerned (in increasing order of importance) with patterns, relations between patterns and relations between such relations.

Since knowledge is expressed in terms of patterns, we can say that in Bateson’s model of information, knowledge is developed and “makes a difference” by connecting patterns. In category theory such connections are created by the construction of limits and colimits.

///////

**Negozilla**:

///////

**Interpreting objects through concepts**:

///////

**Monitoring and connecting information flows by knowledge tentacles**:

///////

**What we agree on and what we obey**:

///////

**We as the limit and colimit of Me and You**:

///////

** Leviathan** as the

*limit*and

*colimit*of his Subjects:

///////

**Mental modeling**:

///////

**Interpreting an Object through a Model**:

///////

**Evolving a Cultural Reference Model**:

///////

**Physically and mentally augmented senses**:

///////

**Overview of Human Communication**:

///////

**Explicitly and tacitly supported communication loop**:

///////

**2-agent conversational knowlecule**:

///////

**Sharing explicit knowledge in a knowledge bundle**:

///////

**The React –> Preact –> Act loop**:

///////

**Functorial and non-functorial patterns**:

///////

**Functorial and non-functorial relations between energy theories**:

///////

**Henry supports Sally**:

///////

**Multi-level commutativity**:

///////

**Pullback of Thoughts, Feelings, and Beliefs**:

///////

**Read-Write interaction loop**:

///////

**A difference that makes a difference**:

///////

**How a difference makes a difference**:

///////

\, {\mathbb 2}^{P_{rePatterns}} \, \stackrel {N_{owPatterns}} {\longrightarrow} \, {\mathbb 2}^{P_{ostPatterns}} \,

\, {\mathbb 2}^{P_{rePats}} \, \stackrel {N_{owPats}} {\longrightarrow} \, {\mathbb 2}^{P_{ostPats}} \,

• Expansion of Time into a Laurent series of moments

///////

**Pullback from FunctorCategories Mind –> Cat**:

///////

**Looking through functor categories**:

///////

**Aware schema mappings**:

///////

**Unaware schema mappings**:

///////

**Read-write loop through glasses**:

///////

**Read-write loop with glasses and implicit templates**:

///////

**Anastomotic reticulum 1**:

///////

**Anastomotic reticulum 2**:

///////

**Read-write loop through anastomotic reticulum**:

///////

• Divisibility Graph at Wolfram MathWorld.

Lattice of **limits** (= agreements) and **colimits** (= coherent actions):

///////

**Dual glasses – limit and colimit for the fish system**:

///////

///////

**Concept improvement process**:

///////

**Intensive and extensive semantics**:

///////

**Rules ∆ Examples**:

///////

**Interpreting and expressing thoughts 1**:

///////

**Interpreting and expressing thoughts 2**:

///////

**Communicating through thought-graphs**:

///////

**Mapping a thought-square 1**:

///////

**Mapping a thought-square 2**:

///////

**Mapping a thought-square 3**:

///////

**Mapping a thought-square 4**:

///////

**Mapping a thought-square 5**:

///////

**Mapping a thought-square 6**:

///////

**The Conzilloscope**

///////

**Two cognitive agents modeling a situation in Me^3 + You^3**:

///////

**Two cognitive agents modeling a situation 2**:

///////

**Two cognitive agents modeling a situation 3**:

///////

**Two cognitive agents modeling a situation 4**:

///////

**Conscious and Sub-Conscious Communication**:

///////

**Communication model for Human Atolls**:

///////

**Me^3 and You^3**:

///////

**SECI-based Intra/Inter Communication model**:

///////

**SECI-based Intra/Inter Communication model of type Me^2 <=> You^2**:

//////

**Consciousness is a mathematical pattern** (Max Tegmark at TEDxCambridge 2014):

//////