Quoted from:  Pi in the Sky, by John Barrow. Oxford University Press, 1992. p. 37-38 “English: one/first ; two/second ; three/third ; four/fourth French: un/premier ; deux/second or deuxième ; trois/troisième ; quatre/quatrième German: ein/erste ; zwei/ander or zweite ; drei/dritter ; vier/vierte Italian: uno/primo ; due/secondo ; tre/terzo ; quattro/quarto In each of these […]

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“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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The short video clip below shows the 3D rotations of a 4D object. The deeper questions concern the nature of a “dimension”. How do we know what a dimension is, and if we live in a 3D universe, could we possible also exist in a higher-dimensional universe? it is best to start with simple examples in order to train the mind to think about these questions. The clip below shows a tesseract, which is the four-dimensional analog of a cube. (In geomery, it is called a regular octachoron or cubic prism.) The tesseract is to the cube as the cube is to the square.

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I found this on Wikipedia, reading about prime numbers: “Inevitably, some of the numbers that occur in nature are prime. There are, however, relatively few examples of numbers that appear in nature because they are prime. One example of the use of prime numbers in nature is as an evolutionary strategy used by cicadas of […]

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The Clay Institute offers a prize to anyone who can solve one of these Millenium problems.  Here is a description of the problems from the Institute’s website: Birch and Swinnerton-Dyer Conjecture Mathematicians have always been fascinated by the problem of describing all solutions in whole numbers x,y,z to algebraic equations like x2 + y2 = z2 Euclid […]

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Definition A Fibonacci sequence is easily constructed:  Start with 0 and 1, and for each following number, add the previous two: 0, 1, 0+1=1, 1+1=2, 1+2=3, and so on. Here is the beginning of the sequence:  0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, … The Fibonacci sequence is named after Leonardo of […]

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