By Karl Menninger
'The historian of arithmetic will locate a lot to curiosity him the following . . . whereas the informal reader could be intrigued through the author's greater narrative ability." — Library Journal
This ebook isn't just a desirable advent to the idea that of quantity and to numbers themselves, hut a multifaceted linguistic and ancient research of the way numbers have built and developed in lots of varied cultures. Drawing on facts from historical past, literature, philosophy and ethnology, famous German pupil Karl Menninger. recounts the improvement of numbers either as they're spoken (and written as phrases) and as symbolic summary numerals that could he without problems manipulated and combined.
Despite the tremendous erudition the writer brings to the subject, he continues a gentle tone all through, proposing a lot of the knowledge in anecdotal shape. furthermore, nearly three hundred illustrations (photographs and drawings) and lots of comparative language tables serve to augment the textual content. the writer starts off with a lucid therapy of quantity series and quantity language, together with the formation of quantity phrases in either Indo-European and non-IndoEuropean languages, hidden quantity phrases and the evolution of the quantity series. He then turns to written numerals and computations: finger counting, folks symbols for numbers, alphabetical numerals, the "German" Roman numerals, the abacus and extra. the ultimate part issues the improvement of our modem decimal procedure, with its position notation and 0, according to the Indian quantity method, and its advent to the West during the paintings of the Italian mathematician Fibonacci. the writer concludes with a evaluate of spoken numbers and quantity symbols in China and Japan.
"The e-book is principally sturdy on early counting and calculating units: primitive tally sticks, the knotted cords of historical Peru, the flowery finger symbols as soon as used for numbers, counting forums with movable counters, and naturally the abacus." — Martin Gardner, Book World
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Additional info for Number Words and Number Symbols: A Cultural History of Numbers
Rak-Sell of Singapore, the overdue J. Ruska of Berlin, R. Schlösser of Hannover, and ok. Vogel of Munich. i'm quite beholden to Mr. Wolfram Müller of Frankfurt and Tokyo. Heppenheim an der Bergstrasse Spring 1958 KARL MENNINGER record of Phonetic Symbols ś represents a valid among s and sh š is reported like sh in English “shoe” č is reported like ch in English “church” ə represents a suppressed or murmured e, just like the final syllable in “America” þ in Gothic and outdated Nordic is said like th in English “three” ě corresponds to Russian ye ḷ, ṃ, ṛ symbolize syllabic sounds, with out vowels q is reported like ok ṷ is a semivowel, among u and w Contents Preface record of Phonetic Symbols quantity series AND quantity LANGUAGE advent The quantity series The summary quantity series The quantity series Used Concretely NUMBERS with no phrases NUMBERS AS ATTRIBUTES NUMBERS AS ADJECTIVES enlargement of the quantity series by way of Supplementary amounts NUMBERING via hands AND feet ideas of the quantity series SUCCESSION AND workforce GROUPINGS of upper RANK GRADATION by means of STEPS GROUPINGS within the GRADUATED quantity series 20-GROUP “MAN” quantity LANGUAGE AND quantity SYMBOLS ancient Gradations REPRESENTING THE GRADATION quantity structures in line with GRADATIONS OF VIGESIMAL GRADATIONS IN eu quantity SEQUENCES THE AINU quantity series legislation Governing the Formation of quantity phrases SUCCESSION OF MAGNITUDES BACK-COUNTING OVERCOUNTING extra methods OF FORMING quantity phrases the 1st STEPS past TEN Our quantity phrases Indo-European kinfolk Languages SURVEY OF LANGUAGES AND quantity phrases the unique INDO-EUROPEAN LANGUAGE the person INDO-EUROPEAN LANGUAGES The Non-Indo-European Languages The which means of Our quantity phrases pictures at the back of THE innovations OF dimension AND quantity SEMANTIC FADING OUR INDO-EUROPEAN quantity phrases was once There a Babylonian impression on Our quantity series?
Luther acknowledged in a single of his Tischreden, Wenn gott sihet, dass wir undanckbar sind, so lässet er uns durch den teuffel einen guten schilling geben, “If God sees that we aren't grateful, he we could the satan provide us an outstanding shilling,” a colloquial expression for a drubbing of 12 or perhaps 30 blows. within the dialect of Silesia the note Schilling has been shortened to Schilg, as in ein Schilg Eier, “a dozen eggs,” and has been inflated to the indefinite which means of “many” within the expression schilgemal (literally: Schilg occasions potential a dozen times).
Fig. ninety five the advance of alphabetical writing, from the Egyptian (column 1)` during the Phoenician (2) to the Hebrew (3), Greek (7), Latin (11), and Germanic (12) alphabets. The Greeks gave their letters numerical values (9), and the Hebrews (5) followed an analogous trend. Column thirteen exhibits the numerical values assigned to the Runic characters. hence we come to the 3rd very important fulfillment of the Greeks: the letters have numerical values in line with their fastened order within the alphabet (column 9). This tying of the letters to numbers which the Greeks invented then used to be passed again to the Semitic donors of the letters themselves: Hebrew followed the alphabetical numerals (column 5), and so they went from there to Syriac and thence to Arabic.
Even German folkways supply an engaging instance of “knot-writing” within the Miller’s Knots, utilized by millers of their transactions with bakers as much as the start of the 20 th century (see Fig. 90). Fig. ninety Miller’s knots used to point quantities and types of flour. the actual knots illustrated right here have been utilized in the province of Baden. The miller needed to “write down” someway the quantities and the categories of flour and meal inside the sacks he brought. For this function he could use the draw strings that tied the mouths of the sacks.
French tapestry approximately three × three m. Musée de Cluny, Paris. allow us to stick with this instance with the interesting French illustration of mathematics personified on a really huge pictorial tapestry (Fig. 199). mathematics, as one of many seven liberal arts, is seated at a counting desk (a bureau), the place she exhibits her exclusive scholars the best way to use counters (jetons) to shape numbers taken from a booklet. two times during this representation we learn the quantity 1520, that's most likely the date. The impressive factor is that the fabric at the desk has no strains; yet such clean reckoning cloths existed, as we will see presently (Fig.