2021.06.02 In a few months, I hope to start producing videos presenting math for wisdom. Here I am writing out thoughts for my first video, an introduction of my intentions for Math 4 Wisdom. I am thinking of doing a 3 minute version and a 20 minute version.
Summary of goals
- Address the shortage of materials for appreciating, contemplating, exploring advanced mathematical topics and especially, gaining a sense of the big picture.
- A sort of guide for mountain climbers.
- Show the usefulness of wisdom as a guide in making sense of mathematics and the relevance of various mathematical topics to expressing wisdom.
- A bit like an alternative reality for wizards except its real - Jesus, Buddha, Mohammed, Harry Potter.
- Show the reality of cognitive frameworks.
- Way to engage those who might work together.
- Find support and income to get by.
General idea of my philosophy
- Relate the definite and the indefinite.
- Math is most definite. So show how the indefinite relates.
- For example, how axiomatic mathematics is inspired by nonaxiomatic premathematics.
General approach
- Ways of figuring things out in math.
Goals for math
- Overview all of math - the areas, concepts, questions, results...
- Identify and appreciate the key concepts behind mathematics.
- Understand and apply the nature of mathematical beauty.
Cognitive frameworks
- Language of absolutes
- ABC's - twosome, threesome, foursome
List examples of topics that I will explore and
- Bott periodicity and the eight-cycle of divisions of everything.
- SU(2) and transformations of mood.
- 4 classical Lie families and 4 geometries.
- Six visualizations and paradox.
- Yoneda lemma and the foursome.
- Sheffer polynomials, quantum physics and the fivesome.
- Adjunctions and divisions of everything.
- Grothendieck's six operations, the natural bases of the symmetric functions and the six representations.
- Yates Index Theorem, the jump hierarchy and the foursome.
- Godel's Incompleteness Theorem and the three-cycle.
- {$F_1$} and God's going beyond himself.
- Seven-eight kinds of duality.
- Shu-Hong's equation and the sevensome.
- Norman Anderson's theory and modeling thinking fast and slow.
- Ways of figuring things out in other fields: neuroscience, chess, physics, biology, Jesus, Gaon of Vilna, my philosophy.
Goals for Math 4 Wisdom
- Express my concepts in terms of math.
- Show that my concepts are relevant and fruitful in math.
- Present a language for
- Foster a community.
Goals for wisdom
- Main ways the indefinite is important.
- Solve technical issues.
- Relate different houses of knowledge.
Goals for language
- Create a language for working together as a scientific community.
- I look to math as a standard of truth for such expression, for such a language.
Goals for community
- Support inclusive harmony of self-realization of all people - "meaningful inclusion".
- Shared question, "How to love each other more"
- Sharing life experiences, deepest values, investigatory questions, etc.
- My personal goal is to express myself fully as I wish for others as well.
- So I am expressing myself through arts and with examples from all of life.
Elementary examples
- Amounts and units. Combine like units, list differing units. Type theory.
- Comparing the price of a sandwich {$\frac{4}{3}\frac{2}{3}=\frac{8}{9}$} as illustrating that algebra is thinking step-by-step.
- Trigonometry: Every rectangle is half a triangle.
- Extending the domain.