Last episode we saw that your neural network can be modeled as a graph, which — we’ll show in this episode — can be viewed as a higher-dimensional simplicial complex. So… what is a simplicial complex??
Higher dimensional spheres, or hyperspheres, are counter-intuitive and almost impossible to visualize. Mathematician Kelsey Houston-Edwards explains higher dimensional spheres and how recent revelations in sphere packing have exposed truths about 8 and 24 dimensions that we don’t even understand in 4 dimensions.
The mathematical material covered includes the basics of number theory (including unique factorization, congruences, the distribution of primes, and quadratic reciprocity) and of abstract algebra (including groups, rings, fields, and vector spaces). It also includes an introduction to discrete probability theory—this material is needed to properly treat the topics of probabilistic algorithms and cryptographic applications.
This textbook contains the content of a two semester course in discrete structures, which is typically a second-year course for students in computer science or mathematics, but it does not have a calculus prerequisite. The material for the first semester is in chapters 1-10 and includes logic, set theory, functions, relations, recursion, graphs, trees, and elementary combinatorics. The second semester material in chapters 11-16 deals with algebraic structures: binary operations, groups, matrix algebra, Boolean algebra, monoids and automata, rings and fields.
Linear Algebra is a text for a first US undergraduate Linear Algebra course. You can use it as a main text, as a supplement, or for independent study. It is Free. The book, the complete answers to all exercises, classroom presentation slides, and a lab manual using Sage, are all available for download, as well as for purchase. The third edition incorporates many suggestions sent by users, including many more beginning exercises, and a new Topic on coupled oscillators and eigenvalues.
The energy associated with psychic activity is not conserved and does not dissipate. I can hear people’s heads exploding as they read those sentences. Typically when I say things like that, a lot people reject the idea; however, they tend to reject the idea because it seems too counter-intuitive, does not fit their expectations, does not fit their biases, does not fit their paradigm, and other things of that nature. This statement is accurate when you look at the relationship psi has to entropy, disorder, and information along with its higher-dimensional structure. Entropy and Disorder There are many different ways Read More
Wormholes, hypercubes, Flatland, and more – Join Neil deGrasse Tyson as he explores time and higher dimensions with comic co-host Harrison Greenbaum and mathematician John Allen Paulos. To start off, Neil explains the concept of a fourth spatial coordinate. Then, our trio compares our knowledge of a possible 4th dimension to the Flatlander’s knowledge of the 3rd dimension in Edwin Abbott’s book Flatland. Ponder the idea that we’re prisoners of our three-dimensions, echoing the shortcomings of Abbott’s two-dimensional beings. You’ll also investigate the film Interstellar and its use of wormholes and the 5th dimension. Physicist James Kakalios, returning guest and Read More
In this post, there is a playlist of video lectures that supplement the book.
How can we capture the unpredictable evolutionary and emergent properties of nature in software? How can understanding the mathematical principles behind our physical world help us to create digital worlds? This book focuses on a range of programming strategies and techniques behind computer simulations of natural systems, from elementary concepts in mathematics and physics to more advanced algorithms that enable sophisticated visual results.
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Public Psychic Matrix For those who want to skip the theory, or have already read the theory, and would like to have access to a matrix, a public one can be found below. For the record, the construct does not attach to all representations of that sigil. It is only attached to the instance of it on the post, so drawing a sigil that does not reference that particular instance won’t do you any good. Matrix Sigil Post Psychic Energy Matrices are a class of amplification constructs I designed. Matrices utilize recursively created fractals to create a resonance via a Read More