My philosopy's concepts in terms of math
I am expressing my philosophy's concepts in terms of mathematics. In particular, I wish to:
- Express God's dance in terms of the field with one element understood as zero, infinity and one.
- Understand God as the Center of polytopes (such as the Simplex) and Everything as the Totality.
- Express God's Ten Commandments as four geometries and six transformations between them.
Some practical projects:
- Learn about the combinatorics and geometry of finite fields and interpret F1n.
- Understand infinity. Understand how finite fields and the field with one element express infinity. Understand how zero and infinity get differentiated, how their symmetry gets variously broken. Express infinity in terms of geometries.
- Overview examples of duality and understand their essence, how they relate one and zero, how they help map out the areas of math.
- Understand the kinds of Opposites and how they are expressed in mathematics.
Structures to express
Four levels of knowledge (whether, what, how, why).
- survey, understand and distinguish between four geometries (affine, projective, conformal, symplectic).
- express them in terms of symmetric functions.
- review recursive function theory and describe the four levels in terms of related concepts such as the Yates Index theorem (the triple jump).
- understand intuitively, why there are four classical families of Lie groups/algebras and what four geometries they give rise to.
Six pairs of these four levels.
- six specifications? between the four geometries.
- six ways of thinking about variables.
- six ways of thinking about multiplication.
- six visualizations (restructurings in terms of sequences, hierarchies and networks).
- six qualities of signs.
- six set theory axioms.
- six bases of symmetric functions
- six ways of relating two mental sheets, a logic and a metalogic.
Divisions of everything
Express the eight divisions of everything, and the three operations +1, +2, +3, which act on them cyclically, in terms of Bott periodicity and the clock shift of Clifford algebras.
- Divisions of everything into N perspectives are given by finite exact sequences with N nonzero terms.
- String diagrams portray such exact sequences with divisions of the plane by way of objects.
- Sixsome see: An Introduction to the K-theory of Banach Algebras
- Twosome: objects and morphisms
- Grothendieck's six operations. Consider a function from one algebraic variety or scheme to another. Then we can define accordingly four functors from one category of sheaves to another such category. These functors are defined to make sense across a family of bases, that is, across base changes. Upper and lower star functors are like everything and nothing. Upper and lower shriek functors are like "fibers" within everything, thus: anything and something. The fiber may be identified with the category. Tensor and Hom are defined within the category of sheaves (thus within the input and also within the output). Tensor can be thought of as decreasing slack by filling it out. Hom can be thought of as increasing slack by creating multiplicity of functions. The four functors relate Hom and Tensor in the input category and in the output category. The six operations can be thought of as naturally defined within a higher order category of correspondences. The six operations can also be thought of as a generalization which grounds Poincare duality and its generalizations, Serre duality. Note that these two seem relate to the Snake lemma.
Languages of argumentation, verbalization and narration
Relate mathematics to three cognitive languages by which things come to matter (argumentation), have meaning (verbalization) and take place (narration).
- Relate a hierarchy of six methods of proof to the prayer "Our Father" and a language of argumentation.
God is a key concept for me. I am ever trying to imagine everything from God's point of view.
I think that the field with one element is a model of God's trinity. The sole element of the field can be interpreted as 0, ∞ and 1. 0 makes way for ∞ and 1 is their point of balance. God's trinity is the heart of God's dance. The various kinds of opposite are also I think important in driving God's dance.
I think that God gets expressed in math as the Center which generates the simplexes. Everything is then the dual of God, the Totality consisting of all of the vertices and all of the simplexes.
Four combinations of God and Everything generate four infinite families of polytopes and associated geometries and metalogics. I think these are the for representations of God:
- The simplexes An have a Center and a Totality. They are the basis for affine geometry where paths are preserved.
- The cross-polytopes Cn have a Center but no Totality. They are the basis for projective geometry where lines are preserved.
- The cubes Bn have no Center but have a Totality. They are the basis for conformal geometry where angles are preserved.
- The coordinate systems Dn have no Center and no Totality. They are the basis for symplectic geometry where areas are preserved.
The family Dn seems to model the equation of eternal life, namely, that God doesn't have to be good, life doesn't have to be fair.
Perspectives are important in my philosophy. There are several ways they appear in math.
- I think that they are defined structurally by algebira and dynamically by analysis and they come together in the four geometries.
- I think the 6 transformations link the 4 possible perspectives.
- I imagine that fields (or division rings) as scalars define perspectives, their freedom.
- The complex numbers offer a dual perspective as opposed to the real numbers' single perspective.
- Category theory perhaps defines perspectives and their composition.
- Perspectives may be logical quantifiers.
- The Eightfold Way relates a left exact sequence and a right exact sequence
- The Zermelo Frankel axioms of set theory seem to be structured by what I call the EightfoldWay.
- https://en.m.wikipedia.org/wiki/Snake_lemma relate to sixsome
Equation of Life
- Spirit and structure are related by "duality", the operation +2.
- A set is the essence of the spirit, the free monoid, that it generates.
I think my philosophy may be an illuminating example for category theory. I mean that if we think of a functor F as going from a category C of our mental notions and association between them to a category D of linguistic expressions and continuations between them, then this particular application may also serve as a universally relevant interpretation and general foundation of category theory. It may indeed be meaningful to speak in category theory of a duality between paradigmatic application and universally relevant interpretation.
- Dvasia ir sandara susieti "duality", veiksmu +2.
- Aibės struktūra primena medį nes gali būti aibės aibėse. Tačiau svarbu, kad nėra ratų.
- Topologies - Systems of constraints that may be thought of as defining worlds. Topology is the study of topologies.
Matematikos įrodymų būdai - laipsnynas
- 4 netroškimai: 6x4=24 ir dar 0-inis požiūris ir 7-as požiūris. Iš viso 24+2=26 kaip Monster grupėje.
Walks on trees