TR研究ADITIONSOFANCIENTSCHOLARSHIP方案.docVIP

TRADITIONS OF ANCIENT SCHOLARSHIP In this course we will deal with ideas about the physical world around us, finally leading to quite fundamental issues, namely, space and time. It will be useful to look at these ideas from an historical point of view – when and where did these ideas appear, and who contributed to our present understanding of the world? The short answer to this question is people from nearly all over the world, stretching over a very long time span. Science is a quantitative subject so we need some amount of mathematics to deal with it. Where did our math come from? The earliest recorded significant work in mathematics comes from Mesopotamia about 3500 BCE where the Sumerians developed the place value system in arithmetic. We use this system today. For us the number 1997 means 1*1000 + 9*100 + 9*10 + 7*1. The Sumerians did not use a decimal system, but a mixture of decimal and sexigesimal: For them the number 1997 would equal 1*600 + 9*60 + 9*10 + 7*1 (=1237 in our notation, a completely different number). The important thing is that they developed the place value system, allowing addition, subtraction, multiplication, and division, just as we do these things. Using Roman numerals, with no place system, these operations are so complex that they were regarded as magical. The oldest recorded long division problem appears on a Sumerian clay tablet written 4600 years ago. It probably came from a training school for Sumerian priests, who played the role of accountants and lawyers among other things in their society. In this problem someone wants to pay workers to do a job. They will be paid seven volumes of rice apiece, each volume being about 0.7 modern liters. He has 1,163,242 of these volumes. So the question he has is, how many workers can he pay? Clearly we need to divide 1,163,242 by 7, as we all learned how to do in grade school. The Sumerian student was using a mixed decimal and sexigesimal system, but the process is the same, and there it