Community Discussion list Contact Andrius Kulikauskas m a t h 4 w i s d o m @ g m a i l . c o m +370 607 27 665 Eičiūnų km, Alytaus raj, Lithuania Thank you for your support! Patreon Paypal to ms@ms.lt Bookshelf Thank you! Upload Upcoming Videos Here is a list of upcoming videos that I'm working on. Coming Soon Here I order the videos in terms of the order in which I intend to release them. Math 4 Wisdom Vision Welcome to Math 4 Wisdom I am interviewing participants, collecting key slides, thinking through the text. My application to the Scholarship Workshop I need to select slides and visuals. I am collecting and organizing my material, preparing a presentation for John Harland and Michael Schreiber, sharing findings and asking questions at Mathstodon and Zulip and StackExchange. Yoneda Lemma: The Natural Isomorphism Yoneda Lemma as a Knowledge Switch Application: Peacemaking for Russia and Ukraine Fred Kayiwa's "Vision for Our Future" Create a template and a playlist Jinan's "Vision for Our Future" Jeff Buderer's "Vision for Our Future" My own "Vision for Our Future" My interviews with Kirby Urner and with others Wondrous Wisdom Almost Completed: God's Will: Love the Imperfect The Meaning of Life: Internalization and Immortalization I will look over my slides and then record this video. 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 Binomial Theorem: Gateway to God in Math I will start preparing slides. 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. 24 Keys to Various Disciplines 24 Ways of Figuring Things Out in Biology Conversations Conversations with John, Jon... Conversation with Jinan Exact sequences and divisions of everything Bott Periodicity (Presentation and discussion relating to John Baez's lecture) Collect material, prepare slides. Compare with John Baez's presentation. 4 Reservations Examples of 8 Counterquestions Threesome for Participation Mathematical Beauty Awakens the Imagination 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. Sevensome for Logic Investigate the kinds of dualities. 6 Conceptions Grothendieck's six functor formalism All Upcoming Here is a list of all of the videos I currently envision. 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. From the big picture to the role of wisdom Relating the counterquestions, the wisdom exercises and the flow of experience Investigating meaningful experiences Possibly... Wondrous Wisdom Future Research Analyze God and Other Ultimates 4 Reservations 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 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 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. 24 Keys to Various Disciplines 24 Ways of Figuring Things Out in Biology Buckminster Fuller's 24 Ways of Figuring Things Out
Šis puslapis paskutinį kartą keistas March 21, 2023, at 12:47 PM