STUDY OF NUMBER

Press, Volume LXVII, Issue 20273, 26 June 1931, Page 17

STUDY OF NUMBER

SCIENTIFIC SOCIETY. PROFESSOR SADDLER'S ADDRESS "The* pioneers in the realm of mathematics were the Greeks," stated Professor W. Saddler, F.E.S., in liis opening remarks to the Scientific Society last evening. Professor Saddler delivered his presidential address to the Society upon "The Historical Development of Number." The Greek philosophers, continued the speaker, had a profound contempt for those who looked ou arithmetic as a mere mechanical art. They left -the purely logical and scientific side to the Sophists, the school-teachers of the age. Tho initiators in the renowned Greek school of geometry were Pythagoras and his followers. The school of Pythagoras was said to have discovered harmonic progressions in the notes of the musical scale by finding the relation between tho length of a string and the pitch of its vibrations. The supreme achievement of Pythagoras was the discovery of the irrational number —that the length of the diagonal of a square of side one foot ■was incommensurable. To the Greeks these diagonals were'new magnitudes, and geometrical lengths, but were they numbers? For the time this shattered the whole of Euclid Book Vl.—destroyed the fabric of their geometry, la fact, the Pythagoreans kept the irrationals' secret as long as possible, and it was looked on as an act of fate when tho man who divulged the secret perished by .shipwreck.

Search for Harmony. Pythagoras, the dreamer and philosopher, searched for the principle of homogeneity in the universe. He found a connexion between number and tlie origin of all things. Thus harmony'depended upon musical proportionnothing but a mysterious number relation. i Where harmony was thero were numbers. So the order and beauty of tho universe had its origin in numbers. There . were seveu planets in the heavens and seven notes in the musical scale. Thus the spiritual ear of Pythagoras discovered in the planetary motion a wonderful harmony of the spheres.. Professor Saddler outlined the number systems of the ancients. With Arabic numerals and the introduction of zero enmo the dawn of mathematical progress. The earliest arith moticians seemed to be the Hindus who used dots for numbers. The problem caused by irrationals was solved by Eudoxus and placed i n Euclid Book X. This theory t lasted till sixty years ago, when Dedekind re- . vised it. Algebra arose from generalised arithmetic, nationals gitve rise 'o irrationals, which were fitted to tho svstem. Algebra came as an arithmetic with symbols for number?), and served as an intellectual instrument for putting clear the qualitative Aspect of the world To talk sense was to talk in quantities. _ The only Greek mention of algebra is in the work of aiiout 230 A.D. Much earlier mention of algebra was found in tho Egyptian Ahmes Papyrus, about 2000 B.C. Ihe greatest algebraical discoveries were, however, made l>v tho Hindus. They used tho negative root, both for use as a quantity and to indicate direction. The form and spirit of modern terms of arithmetic were essentially Indian. They made advances in trigonometry, and perfected a notation of numbers. '

Study of .Mathematics. Mathematics differed from other sciences in that it used elusive symbols and unreal images in & spirit QX adventure, not akin to other arts. •'t pursued apritely symbols just as a child might do. Bertrand Russell tiefined mathematics as "such that we never know what we are talking about and don't know if what we are saving is true." "The justification," continued Professor' Saddler, "for the use of symbolism in mathematics is that we coulti not. get very far with it. The growth of symbolism had bean Blew. Not until 1600 did Leibnitz introduce indices, and not till much lfltar did Euler complete the gap in mathematics by adding imaginary numbers. A new development in mathematics was discovered in the modern era by an Irishman, Sir William Hamilton. Hie found a new kind of algebra not obeying the commutativo law'which, developed into the vector theory, BBd the famous theory of quaternions. Professor Saddler now showed a series of slides illustrating the numerical systems "Of the ancients. A vote of thanks to Professor Saddlor was proposed by Dr Denham, and carried. Mr T. H. McCombs seconded the vote of thanks on belialf of the students.