Intersections: Where Art and Science MeetBach "The Musical Offering recursion in music", Escher " recursion in art", Gödel " incompleteness requires recursion," and Heisenberg "uncertainty in the universe" 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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Intersections: Where Art and Science Meet Bach "The Musical Offering recursion in music", Escher "recursion in art", Gödel "incompleteness requires recursion,"
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Intersections: Where Art and Science MeetBach "
The Musical Offering recursion in music", Escher "recursion in art", Gödel "
incompleteness requires recursion," and Heisenberg "uncertainty in the universe"
Wednesday, January 25, 2012 first time offered at noonin 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
Canons 14th 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
• http://en.wikipedia.org/wiki/Mathematics_and_art • 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.
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
• 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.
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.
• For example: 6936=23x31x172 • and 1200=24x31x52
• are two numbers satisfying the hypothesis of the theorem that can be written as the product of prime numbers.
• 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.
• 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.
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