# Symmetry…

## The Universal Structures of Reality

“The purpose of Logic was to develop a system of thought that could be able to distinguish between Good and Bad Reason “ …

“People think that mathematics is complicated. Mathematics is the simple bit, it’s the stuff we can understand. It’s cats that are complicated”…

- John Conway

Mathematics is the science of uncovering and abstracting *Patterns *in our emergent complex *Material World.*

*Numbers *abstract counts whereas *Groups* abstract *universal structures* and *relationships *— codifying the ideas of *Symmetry.*

We make sense of the World through these *relationships *and *interdependencies.*

The *Physical World *— *Material World *— embedded into *Metaphysics* — *Mental World* — embedded into a *Theory of Logic*.

“Bad reasoning as well as good reasoning is possible; and this fact is the foundation of the practical side of logic”…

- Charles Sanders Pierce

2oth Century US Philosopher* Charles Sanders Peirce *outlined how it is through *Abduction *that new* ideas a*nd *theories *emerge about our *Material World.*

“Abduction is the process of forming an explanatory hypothesis. It is the only logical operation which introduces any new idea; for induction does nothing but determine a value and deduction merely evolves the necessary consequences of a pure hypothesis”…

- Charles Sanders Peirce

Rather than embracing a* universalist* *(absolutism* — i.e. binary, certain) tradition of Logic *Charles Sanders Peirce* believed our Human capacity to re-inteprete language and assign different universes to *quantifiers *— through *semantic* relationships — *hypothesis,* *abduction *and *context *— enables us to *Reason a*nd make sense of the World.

It is through these *Mental Structures* — *Relationships *— that we create *Mental Models of the World*.

When the structure satisfies the defining *Axioms* of the *Theory* it becomes a *Model *— *Propositional Theorems *— that could be deduced from a series of *Axioms*.

Building on the core principles of *Logic* and *Algebra* outlined by *Euclid *in his work titled *Elements* from ~300BC. which explored this geometric methods of *Reasoning*.

We create *mental models* of this world —* patterns* and *relational structures *— and match these against our *Material World*.

Concepts and objects — *Epistemology*, *Ontology,* *Axiology *and *Geometry *— mapped in high dimensional *Conceptual Spaces* that leverage the unique qualities of our *Geometric Mind*.

The closer these structures and relationships align with our *Actions *& *Experiences* in the *Material World *the more they provide* certainty* and *simplify *complexity.

Narrowing the *Reality Gap*.

Uncovering *Universal Structures,* *Known Knowns *and abstracting *Ground Truths*.

Reductionism as opposed to emergence.

Symmetries as opposed to breaks in Symmetries.

*Reason *and *Logic *require the *integration *of our *Mental World *and *Material World*

Rationalism with Empiricism

Idealism with Pragmatism

The Semantic, Geometric, and Algorithmic Mind

Abduction, Induction, and Deduction

Experience, Perception, and Abstraction

The Reflexive, Transitive and Symmetric.

The principles of *Symmetry* are at the very core of *Good Reason,* *Logic* and our understanding of *Reality.*

Forming the foundational principles for a range of *heuristics* in areas such as *Geometry,* *Group Theory*, *Physics*, *Ethics *and at the same time uncovering order and regularity from an emergent complex *Material World.*

*Symmetry* is also a foundational principle of *Nature* — People , Animals, Plants, Planets, Leaves, Fruit, Flowers, and Spiderwebs are all Symmetrical.

A harmony between our *Mental World *of a*bstraction* and *Material World *of *experience*.

Universal Mental World & Material World Structures of Reality.

*Symmetry* is a statement on the actions you can take and preserve these *universal structures*.

A *Group* is a statement about all the actions you can take and preserve structures.

A *structure* is a Model if it satisfies the defining *axioms *of that *Theory *— *Model Theory.*

A *Periodic Table of Finite Simple Groups *— All the ways things can be *Symmetrical *— atoms of abstract *Universal Structures* — Algebraic structures of *Symmetries *— that are the building blocks of *patterns* and *structures* of our complex* Material World*.

From low dimensional *simple Groups* to high dimensional complex *Monster Groups*.

*Symmetry *enables for the *compression* and *simplification* of *Complexity *— *Reductionism *— with *Groups* through the abstraction of universal structures being the basis of *Algebra*, *Good Reason* and *Logic*.

It provides the *topology* to map the basis of *Concepts.*

*Isomorphism* enables us to map equivalent forms and structures — equal shapes and forms.

*Asymmetry *in our *Material World *highlights the *Limits of Logic — *the *Limits of Knowing — the Limits of Reason*.

A break in *Symmetry* is *Emergence*.

“Without the application of the Principle of Symmetry to the Quality of Reason — all that is left is a “Marketplace of Ideas” — a relativism of Ground Truths and Ground Motives …

- The Complexity Void

“Intelligence, Data Science, Learning and Reason all require the integration of our Mental World and Material World.

An Embodied Abstraction.

The application of the Principle of Symmetry and the Quality of Reason” …

- The Complexity Void

## Footnotes:

[To be added shortly ]