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Andrius Kulikauskas: I am working with Math 4 Wisdom participants to create a video for the Summer of Math Exposition contest. The deadline is August 18, 8:00 am.

Binomial Theorem Is a Portal to Your Mind

• Buckminster Fuller - Kirby Urner - Independence vs. Interdependence - basics of root systems - polytopes
• Wisdom competition
• Octahedron
• Cube is dual
• Four kinds of geometry - ways of figuring things out
• Gaussian binomial coefficient
• Finite field with one element - modeling God
• Orthogonal group - binomial theorem
• Grassmanians - real, complex, quaternion
• Divisions of everything - chain complexes, exact sequences
• Bott periodicity - divisions of everything
• Dependence of choices

Zoltar or me at the top of Pascal's triangle

I assume that you are familiar with Pascal's triangle, that you know the binomial theorem, how it counts the number of subsets in a set, and how it is used to calculate probabilities.

I introduce you to the binomial theorem as a portal to your mind, an entry way to the limits of your imagination, the kinds of choices that you can make. I want to show you the learning paths in mathematics that lead up to Bott periodicity, an eightfold framework which organizes the ways of choosing subspaces of vector spaces. I invite you to join the Math 4 Wisdom community, our email discussion group, and in particular, our study group for the mathematics of the divisions of everything, the cognitive frameworks which are the contexts for existence, participation, knowledge and other basic matters. Our intellectual expedition includes those who are learning and teaching high school math as well as those who are investigating advanced mathematics, algebraic topology, Lie theory and quantum physics. We want to appreciate and communicate the subtle but crucial psychological distinctions that even a child faces. We let a child choose - Do you want a carrot or an apple? - and we can frame such questions very differently - Would you like an apple, yes or no? Would you like a carrot, yes or no? Would you like a grape, yes or no?

Our goal is to show that beyond the math on paper there is math in our minds which reflects a more basic language of wisdom. Our greater goal beyond that is to show how it is whimsical and fun to develop a community of independent thinkers who are discovering this shared language. Please join us for this philosophical, mathematical and theatrical adventure from binomial theorem to Bott periodicity!