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Intersections: Where Art and Science Meet Bach "The Musical Offering recursion in music", Escher "recursion in art", Gödel "incompleteness requires recursion," and Heisenberg "uncertainty in the universe" BachThe Musical OfferingEscherrecursion GödelincompletenessHeisenberguncertainty Wednesday, January 25, 2012 first time offered at noon in The Morris and Gwendolyn Cafritz Foundation Art Center, CF101 at the Takoma Park/Silver Spring Campus of Montgomery College by Rupert Chappelle, IT person and Musician extraordinaire Dr. Harold Alden Williams, Planetarium Director

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Some music Bach: Endlessly Rising Modulation Canon (with score!) 8 minutes and 18 seconds. Bach: Endlessly Rising Modulation Canon J.S. Bach - Crab Canon on a Möbius Strip 3 minutes and 7 seconds. J.S. BachCrab Canon on a Möbius Strip

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Crab Canon

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Canons 14 th Century Music Here are three canons from the 14th century both image and in notation http://www.sca.org.au/bardic/rbom/O_Virgo_splendens.PDF http://www2.cpdl.org/wiki/index.php/File:LV_21v.jpg O virgo splendens. three note motif inverted, pitch shifted and varied - obvious in the original notation http://www.lluisvives.com/servlet/SirveObras/jlv/0814062973358172865 4480/ima0046.htmhttp://www.lluisvives.com/servlet/SirveObras/jlv/0814062973358172865 4480/ima0046.htm http://www.sca.org.au/bardic/rbom/Laudemus_Virginem.PDF http://www.sca.org.au/bardic/rbom/Splendens_Ceptigera.PDF Laudemus Virginem http://www.lebrecht.co.uk/blog/wp- content/uploads/2010/03/36174_canon-in-the-unison1.jpg jaques clemens http://www.lebrecht.co.uk/blog/wp- content/uploads/2010/03/36174_canon-in-the-unison1.jpg

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O virgo splendens

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Jaques Clemens

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In Escher's picture Circle Limit III, 1959, the map from a given fish to the one in front of it is a hyperbolic transformation. hyperbolic transformation

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Mathematics and Art http://en.wikipedia.org/wiki/Mathematics_and_a rt http://en.wikipedia.org/wiki/Mathematics_and_a rt Some of Escher's tessellation drawings were inspired by conversations with the mathematician H. S. M. Coxeter concerning hyperbolic geometry. [54] Relationships between the works of mathematician Kurt Gödel, artist M. C. Escher and composer Johann Sebastian Bach are explored in Gödel, Escher, Bach, a Pulitzer Prize- winning book.tessellation H. S. M. Coxeterhyperbolic geometry [54]Kurt GödelM. C. EscherJohann Sebastian BachGödel, Escher, BachPulitzer Prize

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Drawing Hands strange loopstrange loop

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Hand with Reflecting GlobeHand with Reflecting Globe, Self-portrait lithograph 1935

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Metamorphosis II Metamorphosis II woodcut 1930-1931 (3 panels 19.5 cm x 400 cm)

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WaterfallWaterfall lithograph 1961

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RelativityRelativity lithograph 1953

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Medieval Education (community college, first two years) Trivium Grammar: thing as it is symbolized: EN101 Logic: thing as it is known: PL190 Rhetoric: thing as it is communicated: RD120, SP108 Quadrivium Arithmetic: Numbers, Counting what: MA101 Geometry: Numbers in Space, Shape, Where is it? MA105 Music: Numbers in Time, When: MU110 Astronomy/Cosmology: Number in Space & Time, became Science in general. AS101, BI101, CH100A, GL101, ME101, PC101, and PH105

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Gödel Recursively axiomatizable first-order theories that are rich enough to allow general mathematical reasoning to be formulated cannot be complete, as demonstrated by Gödel's incompleteness theorem. Gödel's incompleteness theorem

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Fundamental Theorem of Arithmetic In number theory, the fundamental theorem of arithmetic (or the unique-prime-factorization theorem) states that any integer greater than 1 can be written as a unique product (up to ordering of the factors) of prime numbers.number theoryintegerup tofactorsprime numbers For example: 6936=2 3 x3 1 x17 2 and 1200=2 4 x3 1 x5 2 are two numbers satisfying the hypothesis of the theorem that can be written as the product of prime numbers.hypothesis theorem

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Fundamental Theorem of Algebra Every non-zero single-variable polynomial with complex coefficients has exactly as many complex roots as its degree, if each root is counted up to its multiplicity.multiplicity Or every non-constant single-variable polynomial with complex coefficients has at least one complex root. Equivalently, the field of complex numbers is algebraically closed. polynomialcomplexcoefficientsrootfieldcomplex numbersalgebraically closed

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Geometry Euclidian Hyperbolic Spherical and EllipticElliptic Geometric Algebra Clifford/Geometric Algebra study group at Montgomery College meeting since 2007 faculty and students together transforming the understanding of the universe at the college, the Cliffhangers! Clifford/Geometric Algebra study group at Montgomery College

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Medieval Education (community college, first two years) Trivium Grammar: thing as it is symbolized: EN101 Logic: thing as it is known: PL190 Rhetoric: thing as it is communicated : RD120, SP108 Quadrivium Arithmetic: Numbers, Counting what: MA101 Geometry: Numbers in Space, Shape, Where is it? MA105 Music: Numbers in Time, When: MU110 Astronomy/Cosmology: Number in Space & Time, became Science in general. AS101, BI101, CH100A, GL101, ME101, PC101, and PH105

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Romantic/Quantum Uncertainty

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Heisenberg Uncertainty Principle

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What is knowable and measurable Interaction is what is important not consciousness, the universe continues now whether you are conscious of it or not. You can not know where something is and know at what momentum (velocity with attitude) to arbitrary precession at the same time. You can not know what the energy is and know what it time of emission or absorption is to arbitrary precession. The universe is pixilated around Plancks constant, h or ħ.

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Chapter 5 Opener

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Figure 5.8 Annotated

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Figure 5.12 Unannotated

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Figure 5.15

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Figure 5.18

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Figure S4.7

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Figure 16.1 Unannotated

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Figure 16.1 Annotated

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Horse Head Nebulae in Orion

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Camille Flammarion

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Astronomers Use Photoshop

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Interest Rates 1.02^33=1.92223 1.02 33 =1.92223 1.022^33=2.050 1.022 33 =2.050

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