Math 4 Wisdom. "Mathematics for Wisdom" by Andrius Kulikauskas.

Upcoming Videos

Here is a list of upcoming videos that I'm working on.

Coming Soon

Here I order the videos in groups, in terms of the order in which I intend to release the top video in each group.

Sociology Study Group

Aslam's methodology
24 Ways of Figuring Things Out in Biology

Math for Divisions of Everything

John Harland: Complex numbers. Part II. (junior level)
Andrius Kulikauskas, Kirby Urner: Binomial theorem
Andrius Kulikauskas: Investigating Bott periodicity
Andrius Kulikauskas: SU(2) (junior level)
John Harland: Quaternions. (junior level)
Francis Howard: SU(2) (senior level)

Wondrous Wisdom

The Meaning of Life: We Internalize (Perspectives), God Immortalizes (Positivity) I will look over my slides and then record this video.
Needs and Operating Principles
Doubts and Counterquestions
Expectations and Emotional Responses
Values and ... ?

Language of Wisdom Study Group

Conversation with Jere Northrop

Fivesome for Decision Making

Almost Completed: From Moments to Distribution: Learning from John Harland
Grad-Curl-Divergence (John Harland: The Anti-Curl) Record in late March or April.
Classification of orthogonal Sheffer polynomials
Time and Space as Representations of Decision-Making

Landscape of Truth and Value

Investigation of the landscape of truth
Session with philosophy subgroup of Friends of Wisdom
Conversations on Relationships with Truth. With Jinan KB, Bill Pahl, Thomas Gajdosik, John Harland, Jon Brett, Kirby Urner, Silvijus Pokštas

24 Keys to Math

I will regularly collect and share material, and look for new sources of problems.
Algebraic Ways of Problem Solving
- Center
Collect ways of problem solving in geometry.

Threesome for Participation

Zig Zag Lemma
Mathematical Beauty Awakens the Imagination

Foursome for Knowledge

Exercises: Examples of the foursome.
Conversation with Thomas and John
Conversations with Michael Schreiber
Yoneda Lemma: The Natural Isomorphism
Yoneda Lemma as a Knowledge Switch

6 Conceptions

Grothendieck's six functor formalism
Classifying adjunctions

Sevensome for Logic

Investigate the kinds of dualities.

What is geometry?

Conclusions from examples of problem solving in geometry.
The relation of Lie theory to geometry.
Four classical families express the symmetry of counting and the duality of counting forwards and backwards.

Training to Think

Learning to think without words

All Upcoming

Here is a list of all of the videos I currently envision.

Wondrous Wisdom

Overview of Wondrous Wisdom

I present what I know of the language of wondrous wisdom with a series of videos based on slides which I talk about.

Wondrous Wisdom Research Updates

From the big picture to the role of wisdom
Relating the counterquestions, the wisdom exercises and the flow of experience
Investigating meaningful experiences
Possibly...
- God Doesn't Have To Be Good (Gospel of John)
- God Doesn't Have To Be Good (My Life Experiences)

Wondrous Wisdom Future Research

Analyze God and Other Ultimates

4 Reservations

Counterquestions

Examples: Doubts and Counterquestions
Exercises: Examples of Doubts (from every day life)
Exercises: Examples of Doubts (from literature)
Exercises: Examples of Doubts (from Scriptures)
Answers to Exercises
8 Counterquestions: Framework for Intelligence
Engaging the Violent
Exercises: Examples of Structures
Answers to Exercises
Truths of the Heart and of the World

Four reservations

Operating principles for Needs
Counterquestions for Doubts
Directions of the good for Expectations
Investigations for Values

Application: Peacemaking for Russia and Ukraine

My letter to the Russian government.
An Epistemological Portrait of Russian Federation President Vladimir Putin.

Math for God: From Binomial Theorem to Bott Periodicity

Binomial Theorem: Gateway to God in Math

Pascal's triangle. Calculate, what is the probability that in a family with 3 children there are 2 girls and 1 boy?
Calculate, for example, (1 + 0.01)^n, which is to say, what happens when you have small growth, as with an interest rate of 1% ?
The geometry of squares and cubes (in 3 dimensions but also in higher dimensions), how they grow, (x+h)^n, where h is small.
Derivatives of powers of x, which we can also understand in terms of slopes.
Prove the binomial theorem, "n choose k", in different ways, counting subsets of sets. One way is to use mathematical induction.
Relate the binomial theorem to the Euler characteristic and Betti numbers.
Consider the Gaussian binomial coefficient, how it counts subspaces of vector spaces over a finite field F_q. And we can imagine what happens when q goes to 1.
Relate the binomial theorem to the binomial distribution and enter the world of probability and statistics but also orthogonal polynomials.
Discuss the Grassmannian and how it relates to Bott periodicity.

Math tutorials

Q-analogue of Binomial Coefficients

I want to make a video about the q analogue of the binomial coefficients and how we get the mythical "field with one element" when we take the limit q goes to 1. That is important for modeling choice when we have only one choice to choose from. I think this is relevant for modeling God.

Structure of Finite Fields

Understand the structure of finite fields of cardinality {$q^n$} and then consider what happens when we take the limit {$q\rightarrow 1$}. This should give insight into modeling {$F_1$}.

Calculating representations of Clifford algebras as relevant for Bott periodicity

Raudys Hierarchy of Statistical Methods

Understand the Raudys hierarchy and how it may express the divisions of everything.

(1) the Euclidean distance classifier;
(2) the standard Fisher linear discriminant function (DF);
(3) the Fisher linear DF with pseudo-inversion of the covariance matrix;
(4) regularized linear discriminant analysis;
(5) the generalized Fisher DF;
(6) the minimum empirical error classifier;
(7) the maximum margin classifier.

Threesome for Participation

Mathematical Beauty Awakens the Imagination

I made a picture in a talk I gave in Lithuanian http://www.ms.lt/sodas/Mintys/MatematikosGrožisŽadinaVaizduotę

I gave this as an example of mathematical beauty where our mind can break out of the limits of what we can see. I compare that with the visual beauty of the Mandelbrot set, which exemplifies Christopher Alexander's 15 properties of life, including three related to one (good shape), all (local symmetry of background), many (positive, concave space).

Animating the 4-simplex. Visualizing 4 dimensions with 5 points.

I wonder how best to animate the 4-simplex. I know some Python. I should learn the basics of Manim.
I draw a tetrahedron (four points - four dimensions) and introduce a fifth point at the center (which becomes a fifth dimension when I wiggle it around). Using Pascal's triangle we see how the row for an edge 1 2 1

becomes the row for a triangle 1 3 3 1 (one center, three vertices, three edges, one face) becomes the row for a tetrahedron 1 4 6 4 1 (one center, four vertices, six edges, four faces, one volume) becomes the row for a 4-simplex 1 5 10 10 5 1 (one center, five vertices, ten edges, ten faces, five volumes, 1 4-dimensional-cell)

Foursome for Knowledge

I will make many short videos about the Yoneda Lemma and how it functions as a knowledge switch relating the four levels of knowledge: Whether, What, How, Why.

Yoneda Lemma and the four levels of knowledge

General idea as a knowledge switch
Natural Isomorphism
Interpreting the Natural Isomorphism
Example: Cayley's Theorem
More examples
The foursome: overview
Examples of the foursome
The foursome as a building block
The foursome: exercises
The foursome: discussion of answers
In terms of Kan extensions
Isbell duality
Coends and ends?

Norman Anderson's Information Integration Theory

Investigate how averaging (by the unconscious) is teased apart as addition and multiplication (by the conscious).

Yates Index Set Theorem

Explain what this says about the foursome of levels of knowledge: Whether, What, How, Why.

Classifying adjunctions

The Fundamental Theorem of Covering Spaces

This is part of my study of adjunctions with the goal of classifying adjunctions. This particular adjunction is an equivalence. I have been studying algebraic topology at the New York Category Theory Meetups and you are welcome to join us.

Fivesome for Decision Making

Time and Space as Representations of Decision-Making

Orthogonal Sheffer polynomials

Classification of orthogonal Sheffer polynomials
Combinatorics of Hermite polynomials

Minkowski space and Moebius transformations

The Fivesome, Quadraticity and the Eccentricity of the Conics

Sevensome for Logic

Eight dualities

Investigate the kinds of dualities.

Shu-Hong Zhu's Thesis

Present as an example of the sevensome. And relate to linear fractional transformations.

Six Conceptions

Symmetric functions of the eigenvalues of a matrix

Seeking a relation to the six representations, for example, a connection with Hopf algebras.

{$K^{-1}K=I$} and nonexistence of an involution

Set this up as a problem where the nonexistence of an adjunction indicates the nonexistence of a combinatorial interpretation for an involution.

Grothendieck's six functor formalism

24 Keys to Math

24 Ways of Figuring Things Out in Math

Surface structure and deep structure Completed.
Groups of ways of figuring things out (4, 4, 3, 4, 6, 3)
Talk on visualizations as the source of paradox
Overviewing the entire system
Investigating further...

I want to make videos about the 24 ways of figuring things out in mathematics.

Visualization as Restructuring and thus a Source of Logical Paradox

24 Keys to Various Disciplines

24 Ways of Figuring Things Out in Biology
Buckminster Fuller's 24 Ways of Figuring Things Out