NUMBERS AND COUNTING.

Otago Witness, Issue 3831, 16 August 1927, Page 72

NUMBERS AND COUNTING.

DR

BELL'S ADDRESS

'At the annual meeting of the Cbamben ot Commerce on Friday, evening Dr Bell’ ot Otago University, made some remarks’ on numbers and counting, which proved most interesting to men who deal with figures every day of their business lives. mP/ BeI A Said that in the British Museum there are writings on mathe? matics produced 3500 years ago and be. lioved to be founded on earlier writings dating more than 1000 years further uack. lhe usual method of multiplying made its appearance in books on arithme, tic barely 500 years ago. Long division appeared somewhat later. Six hundred yeans ago long division was a process that could only be accomplished by the most expert mathematician, and multiplication was about as far as the average university student could hope to attain to in his mathematical studies.

As soon as man had possessions and began to count them a number system became a necessity. It was said that the vocabularies of some of the poorest ano most uncivilised tribes contained no word lor numbers beyond 3 or 4. Any lar"er quantity was “a great lot.” “As the mental and material acquisitions of men increased the need to extend his number system grew. The need for employinthe process of counting led very early to the method of grouping units. Men be"au to count by tens or by sixes. The reateu for choosing 10 was obvious, but various choicenV n ad bee " giVen fOr tbf * pi, ? ■ was sai d that the ancient Babylonians thought the year contained -60 days, so they divided the circle into 0 degrees and becoming accustomed to counting by sixes they divided the day ii to 24 hours The early Greeks used alphabetic symbols, and the Romans an additive system. The origin of V in th" va°r™ an sjstem ba4l beea explained in arious ways. Some thought it represented the hand with open fingers. Our pi esent system was usually called tho Arabic system, but though it came to us the a iFnd the JS U had its origin ainoug the Hindus Why was it that, while tho netablc .contributions to the R, m d P, hll^°P b y ot the world, and the Rom ai Ks to its laws, their number sysHinrl eie Poetically unknown, and the Hindu system was now in general use’ It was because some unknown Hindu first oOt his idea of place-value in a numSnteTo m and , b ® cause the Hindus invented a symbol for zero. Hindus worn great mathematicians. Kudu astronomers carried the use of these numerals to Ba"hdad, whence boat-traders made them known over the east of the Mediterranean along the north of Africa, and into Spain and Italy. They did not become widely known in Europe till about 1300 A.D. lhe earliest written forms showed considerable variations, but after the invention of printing there was little change in the forms of the symbols, and they remained to-day what they were 450 years ago. The power of modern computation was due largely to the efficient system of numeration making use of the idea of place-value and to the invention of decimal fractions. These fractions were not used, or understood, until the IGth centurv, and the first book wdiich dealt clearly with them was not published until 1585. It was interesting to note the results of these struggles towards arithmetical efficiency in our everyday vocabulary. Calculations were often performed on a table with pebbles or metal discs, which were thrown on and counted. Hence to-day we spoke of a shop-counter. The bank teller was a familiar personage, and was more nearly related, etymologically at least, to the tailor than he usually imagined. Before the common use of paper, accounts were kept by tally sticks. Notches were cut in a rod to indicate the amount paid, and the rod was split, each party keeping a section. The wrnrd “tally” came from the French word “tailler.” to act, from which the word “tailor” was also derived. Hence the phrases “an account tally,” to “tally up,” and so on. A “tale” was a sum. “Wo spend our years as a tale that is told.” The speaker also gave the origin of tho words “stock.” “folio,” and ‘’exchequer,” in a very interesting manner.

Dr Bell was warmly thanked for his address.