i=0;
		while (true) {
			i=i+1;
			print i;
		}
		

1. Lectio :: Mythology
   • Hephaistos
   • Pygmallion
   • Pythagoras
2. Disputatio :: Myths of a digital world
3. Exercitio :: A letter to Your digital self
4. Video :: The 2^nd rennaissance I.

• a male counterpart to Pallas Athena
• gives skill to artists
• god of blacksmiths, metalworking, carpenters, craftsmen, artisans, sculptors, metallurgy, fire, and volcanoes
• son of Zeus and Hera
• husband of Aphrodite
• often depcited as "lame and crippled"
• known as Vulkan among Romans

• Hermes' helmet and sandals, Achiless' armor, chariot of Helios
• chain-link net for Aphrodite & Ares
• Pandora's pithos (also known as "Pandora's box")
• first documented automata

• Wheel tripods to bring stuff to Olympos and back (Iliad, ca. 8th century B.C.)
• golden and silver dogs and lions which could bite invaders of the palace of Alkinoos (Odyssea, ca. 8th century B.C.)
• Talos, a giant made of bronze to protect Europa in Crete (Argonautica, 4th-3rd century B.C.)
• Aetos Kaukasios, a robotic eagle eating Prometheus' liver (Poeticon Astronomicon, 1st century B.C.)

• described in 10^th book of Ovid's metamorphoses, but potentially derived from older myth from island of Cyprus
• an archetypical story about a thing which becomes conscious thanks to a divine intervention
• Can You think of another stories or modern myths with similar plot ? (note them down, we'll speak about them in a minute!)

• a half-mythological, half-historic personage
• first man to call himself a philosopher ("lover of wisdom")
• important contributions to mathematics (e.g. Pythagorean theorem, Theory of Proportions etc.) and music (e.g. Pythagorean tuning, musica universalis etc.)

• triangle distributing numbers 1 to 10 in four rows
• many levels of symbolism (Unity / Power / Harmony / Kosmos; Fire / Air / Water / Earth; Point / Line / Triangle / Tetrahedron )

and then said creators: faciamus hominem ad imaginem et similitudinem nostram

and then said humans: faciamus machinam ad imaginem et similitudinem nostram

1. Repetitio :: Mythology
2. Questio :: What is a machine ?
3. Lectio :: Antiquity
   • Antikythera mechanism
   • Heron of Alexandria
   • other traditions
4. Exercitio :: Introduction to Abacus
5. Disputatio :: What is NOT a machine ?

• English word machine comes through Middle French from Latin machina, which in turn derives from the Greek (Doric μαχανά makhana, Ionic μηχανή mekhane "contrivance, device, engine", a derivation from μῆχος mekhos "means, expedient, remedy")
• Greek "mekhane" was potentially derived from Proto-Indo-European root *magh- meaning "to be able, have power." Linguists believe that English words like may, might, magi, magic, make or German words like machen, Macht etc. are derived from the PIE-root *magh.

• Any device that transmits a force or directs its application.
• An efficient and well-organized group of powerful people.
• A person who acts with the mechanical efficiency of a machine.

• an ancient Greek analogue computer used to predict astronomical positions and eclipses for calendar and astrological purposes decades in advance
• created sometimes around 2nd-1st century B.C., discovered in 1902
• complex clockwork of at least 30 bronze gears

• greatest experimenter of antiquity
• teacher at Musaeum
• author of works like Pneumatica, Automata, Mechanica, On the dioptra, Belopoeica, Catoptrica, Geodesia, Geoponica etc.
• father of cybernetics

• holy water dispenser
• windwheel organ
• Hero's engine (aeolipile)
• 10-minute long fully mechanical theater piece involving a first "programmable" robot

"When King Solomon stepped upon the throne, a mechanism was set in motion. As soon as he stepped upon the first step, the golden ox and the golden lion each stretched out one foot to support him and help him rise to the next step. On each side, the animals helped the King up until he was comfortably seated upon the throne. No sooner was he seated than a golden eagle brought the great crown and held it just above King Solomon's brow, so that it should not weigh heavily on his head."

We'll discuss the Persian & Arab traditions next week.

• less interested in "crude", hardware-oriented disciplines of robotics and mechanics (an exception: "The story of a mechanical girl")
• more interested in "subtle", software-oriented disciplines of mathematics and logics
  • Shulba Sutras :: texts concerning the Srauta ritual which describe the geometry related to fire-alter construction

• Watch some videos about addition, subtraction and multiplication on an Abacus (e.g. https://www.youtube.com/watch?v=jwabVzlobZI)
• You can validate the activity-credit for this course by:
  1. Teaching Your fellow students how to multiply 121 x 121 on an Abacus.
  2. Proposing the highest possible number which answers the question "How many distinct numbers can one unambiguously represent on an abacus with 10 marbles on 10 rows ?" and demonstrating why it is true.

1. Repetitio :: Antiquity
2. Narratio :: L'histoire de fille mecanique
3. Questio :: What is a digit ?
   
   
4. Lectio :: Dark ages
   • al-Khwarizmi
   • Fibonacci
   
   
5. Exercitio :: Abacus II.
6. Disputatio :: Your feedback

• digit (n.)
  in English since late 14c., "numeral below 10," from Latin digitus (french: "doigt") "finger or toe" (also with secondary meanings relating to counting and numerals), considered to be related to Proto-Indo-European root *deik- "to show"

1. • any of the Arabic numerals 1 to 9 and usually the symbol 0
   • one of the elements that combine to form numbers in a system other than the decimal system
   • digits , slang : the digits of a telephone number
2. any of the divisions in which the limbs of most vertebrates terminate, which are typically five in number but may be reduced (as in the horse), and which typically have a series of phalanges bearing a nail, claw, or hoof at the tip

• a symbol denoting/representing a natural number ("a numeral")
• we'll work with four systems of numerals
  1. roman: I, V, X, L, C, D, M
  2. decimal: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9
  3. binary: 0, 1
  4. hexadecimal: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, a, b, c, d, e, f
• other systems of numerals are also possible (e.g. base64)

• persian scholar from golden-age of islamic science
• his name Latinized as "Algorithmi" (Port. "guarismo" and Spanish "algarismo" mean digit)
• since 820 A.D. the astronomer and head of the House of Wisdom in Baghdad
• contributions to Algebra, Arithmetic, Astronomy, Trigonometry, Geography

• 8th century - 12th century :: golden-age of islamic science
• integration of Persian and Arabic into one cultural realm
• translation of Greek and Roman works into arabic
• extension of antique knowledge, e.g. Brothers Musa
• more practical than Greek stuff

• book about solving quadratic equations
• principial mathematical text-book of European Universities until 16th century
• al-ğabr ("forcing", "restoring") operation :: moving a deficient quantity from one side of the equation to the other side
• al-Muqabala ("balancing" or "corresponding") operation :: subtraction of the same positive quantity from both sides
• presented in ordinary text
  Al-kitāb al-mukhtaṣar fī ḥisāb al-ğabr wa’l-muqābala, The Compendious Book on Calculation by Completion and Balancing

• Kitāb al-Jam‘ wat-Tafrīq bi-Ḥisāb al-Hi("The Book of Addition and Subtraction According to the Hindu Calculation")
• Arabic original of the book has been lost
• 12th century translation by Adelard of Bath (starting with "so said alKhwarizmi") introduced Hindu numerals in the west
• Hindu numerals: position-based and including 0

• "the most talented Western mathematician of the Middle Ages"
• his book Liber Abaci (1202) popularized the Hindu-Arabic numeral systems in Europe
• travelled extensively around the Mediterranean coast, meeting with many merchants and learning about their systems of doing arithmetic
• first one to describe Fibonacci sequence

• What do I like about the course?
• What I do not like?
• What are my wishes?

1. Repetitio :: Between Antiquity and Rennaissance
2. Narratio :: Wheat and chessboard legend
3. Questio :: What is an algorithm ?
   
4. Lectio :: Between renaissance and Age of Reason
   • Descartes & Pascal
   • Leibniz
5. Exercitio :: Binary counting.
6. Presentatio :: BYOD or not BYOD in an elementary school ?

• algorithm (n.)
  ...

• a procedure for solving a mathematical problem in a finite number of steps that frequently involves repetition of an operation
• a step-by-step procedure for solving a problem or accomplishing some end
Name some examples of an algorithm.

• polymath
• at 23-years of age, his dreams pose him in front of a question: Quod vitae sectabor iter?
• establishement of scientific method (based on "doubitatio")
• "Cogito ergo sum", mind-body dualism
• cartesian coordinate system, analytic geometry ...

• polymath
• in 19years of age started to build first mechanical calculators ("Pascalines")
• ground-breaking works in mathematics (Pascal's triangle), geometry (Pascal's theorem), physics (Pascal's law), theology (Pascal's wager)
• develops first public transport in the world
• dies young, last words: "Puisse Dieu ne jamais m'abandonner"