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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
Some music
• Bach: Endlessly Rising Modulation Canon (with score!) 8 minutes and 18 seconds.
• J.S. Bach - Crab Canon on a Möbius Strip 3 minutes and 7 seconds.
Crab Canon
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
notation•
http://www.lluisvives.com/servlet/SirveObras/jlv/08140629733581728654480/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_cano
n-in-the-unison1.jpg
jaques clemens
O virgo splendens
Jaques Clemens
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.
Mathematics and Art
• 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.
Hand with Reflecting Globe, Self-portrait lithograph 1935
Metamorphosis II woodcut 1930-1931 (3 panels 19.5 cm x 400 cm)
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
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.
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.
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.
• 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.
Geometry
• Euclidian• Hyperbolic• Spherical and Elliptic• Geometric Algebra • Clifford/Geometric Algebra study group at Mo
ntgomery College meeting since 2007 faculty and students together transforming the understanding of the universe at the college, the Cliffhangers!
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
Romantic/Quantum Uncertainty
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 Planck’s constant, h or ħ.
Chapter 5 Opener
Figure 5.8 Annotated
Figure 5.12 Unannotated
Figure 5.15
Figure 5.18
Figure S4.7
Figure 16.1 Unannotated
Figure 16.1 Annotated
Horse Head Nebulae in Orion
Astronomers Use Photoshop
Interest Rates
• 1.02^33=1.92223• 1.0233=1.92223• 1.022^33=2.050• 1.02233=2.050
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