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Digital culture
Prolegomena to Educatio Digitale
Thursdays 10:15  11:45, Hardenbergstr. 33, R110
daniel@udkberlin.de
Semester 0 :: Historical Context
Session 3 :: Between Antiquity and Rennaissance
Question of the day
What is a digit ?
Etymology of the word "digit"
 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 ProtoIndoEuropean root *deik "to show"
MariamWebster dict. definition of a "digit"

 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

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
Our definition "digit"
 a symbol denoting/representing a natural number ("a numeral")
 we'll work with four systems of numerals
 roman: I, V, X, L, C, D, M
 decimal: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9
 binary: 0, 1
 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)
Muhammad ibn Musa alKhwarizmi (c. 780  850 A.D.)
 persian scholar from goldenage 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
House of Wisdom of Baghdad
 8th century  12th century :: goldenage 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
Liber Algebræ et Almucabola
"an algorithm" to solve quadratic equation
If some one says: "You divide ten into two parts: multiply the one by itself; it will be equal to the other taken eightyone times."
Computation: You say, ten less a thing, multiplied by itself, is a hundred plus a square less twenty things, and this is equal to eightyone things. Separate the twenty things from a hundred and a square, and add them to eightyone. It will then be a hundred plus a square, which is equal to a hundred and one roots. Halve the roots; the moiety is fifty and a half. Multiply this by itself, it is two thousand five hundred and fifty and a quarter. Subtract from this one hundred; the remainder is two thousand four hundred and fifty and a quarter. Extract the root from this; it is fortynine and a half. Subtract this from the moiety of the roots, which is fifty and a half. There remains one, and this is one of the two parts. (1831 English Translation)
Arithmetics: Dixit algorizmi...
 Kitāb alJam‘ watTafrīq biḤisāb alHi("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: positionbased and including 0
Leonardo Fibonacci of Pisa (c. 1175 c. 1250)
 "the most talented Western mathematician of the Middle Ages"
 his book Liber Abaci (1202) popularized the HinduArabic 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
Fibonacci's sequence :: Rabbits
"Suppose a newlyborn pair of rabbits, one male, one female, are put in a field. Rabbits are able to mate at the age of one month so that at the end of its second month a female can produce another pair of rabbits. Suppose that our rabbits never die and that the female always produces one new pair (one male, one female) every month from the second month on.
How many pairs will there be in one year?"
http://www.maths.surrey.ac.uk/hostedsites/R.Knott/Fibonacci/fibnat.html
Fibonacci's sequence :: Spiral
modus Indorum :: the method of Indians
"The nine Indian figures are:
9 8 7 6 5 4 3 2 1
With these nine figures, and with the sign 0 which the Arabs call zephir any number whatsoever is written..."
Leonardo Fibonacci of Pisa :: Liber Abaci :: The Book of the Abacus
Abacus homework
 Watch some videos about addition, subtraction and multiplication on an Abacus (e.g. https://www.youtube.com/watch?v=jwabVzlobZI)
 You can validate the activitycredit for this course by:
 Teaching Your fellow students how to multiply 121 x 121 on an Abacus.
 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.
Feedback 0 :: 3 questions
 What do I like about the course?
 What I do not like?
 What are my wishes?