Here are two computer-animated videos from Youtube that demonstrate some properties of knots, the relations between knots and space, and how we arrive at hyperbolic space. Easy to watch, and very informative.   Part Two:   Related posts: Klein Bottle Tesseracts: from 3 to 4 Dimensions. 0 to 6 dimensions and back – simple rotation. […]

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This is the title of a talk by James Carse.  He wrote a wonderful little book, Finite and Infinite Games, in 1986. The following talk applies the dialectic of finite and infinite games to the question of warfare and religion.   Related posts: Finite and Infinite Games Gödel: The modern development of the foundations of mathematics […]

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Below there is  an interesting video inspired by numbers, geometry and nature, created by Cristóbal Vila. Nature looks complex, but the underlying principles are simple, for instance the Fibonacci Series of numbers.  The natural beauty and complexity we see all around us is deeply astonishing, but what’s even more astonishing is all the math behind […]

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How do you turn a sphere inside out, without punching a hole into it? It is possible,as you can see in the transformations in this fascinating video: Related posts: Mathematical Problems Klein Bottle Unsolved Millenium Problems Tesseracts: from 3 to 4 Dimensions. 0 to 6 dimensions and back – simple rotation. Hyperbolic Space The German […]

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Murray Gell-Mann developed the theory of quarks, the fundamental particles that constitute the atomic core. Here is an excerpt of his biography from the Nobel prize website. Continue reading

“There are two approaches to mathematical infinity. It can be seen as defining limiting cases that can never be realized or as existing in some philosophical sense. These mathematical approaches parallel approaches to meaning and value that I call absolutist and evolutionary. The absolutist sees ultimate meaning as something that exists most commonly in the form of an all powerful infinite God. The evolutionary sees life and all of a creation as an ever expanding journey with no ultimate or final goal. There is only the journey. There is no destination. This video argues for an evolutionary view in our sense of meaning and values and in our mathematical understanding. There is a deep connection between the two with profound implications for the evolution of consciousness and human destiny.” (Paul Budnik)

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This is a simple computer-simulated rotation from a point, which has 0 dimensions, to a line (1 dimension), a square (2), a cube (3), all the way up to 6 dimensions, and then down. Multi-dimensional objects are much more complex than we can imagine.   Related posts: Tesseracts: from 3 to 4 Dimensions. Klein Bottle […]

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