Movement of Ideas Across Space and Time

Movement of Ideas Across Space and Time

The Number Zero and Place Holding

The Maya were a great civilization in pre-colonial America, occupying territory in southern Mexico, Guatemala, and Belize. They developed hieroglyphic writing and the concept of zero as a number to use in mathematical operations. They also inventeda place-value numbering system which is the only efficient way to denote large numbers and to use them in mathematical computations. The Maya made these advances in mathematics hundreds of years before any other civilization.
By 1500 B.C.E., the Maya had settled in villages and employed agriculture to grow corn, beans, and squash. They built large stone buildings, had pyramid temples, made paper from the bark of trees, and wrote in books. The Maya were excellent astronomers, and they developed a calendar. The Maya worked metals such as gold and copper. At its height, the Mayan civilization had approximately 40 cities with populations from 5,000 to 50,000.
The classical period of Mayan civilization lasted from approximately 250 C.E. to 900 C.E. and declined for reasons that are not known. By the 16th century, when Europeans came to Central America, Mayan civilization had subsided into small agricultural villages.
The Maya used a base of 20 (from 10 fingers and 10 toes) grouped in sets of five (one for each hand and foot). Numbers were expressed in dots (for one), bars (for five), and a shell for zero.
Zero is not an easy concept. Mathematics started when people began counting objects, for example, cows, sheep, and jars of olive oil. It was practical and not theoretical. Ancient peoples (except for the Maya) had no concept of zero or of negative numbers. When the ancient Babylonians needed to start counting large numbers of objects, they developed the place-value system long before the Maya civilization existed. For a thousand years, the Babylonians used a place-value system without a zero. 2106 would be written in the same way as 216. The Babylonians relied on the context in which the number was used to clarify which number they meant.

Note:We still use context in the interpretation of numbers in limited situations. For example, if you go to a store to buy candy and the clerk tells you the cost is two-fifty, you know he or she means $2.50. But if you are buying a dining room table at a furniture store and the clerk tells you that it costs two-fifty, you know that the dining room table costs $250.

Our place-value base ten numbering system works as follows. The term digit refers to an Arabic numeral (1,2,3,4,5,6,7,8,9 or 0) within a larger number. Thus the digit "5" appears twice in the number 1,345,561. The location of a digit within the number indicates the power of the base to which it relates. Because we use a base of 10, the digit not only refers to its own value but it is multiplied by the power of ten that corresponds to its position within the number. We start with the one's place. That is very straightforward, like counting on our fingers. The first place to the left is the ten's place (101). The digit in the ten's place is multiplied by 101(i.e. 10) to determine how much it adds to the value of the number. Thus, the number 61 = one plus 6 X 101. The second place to the left of the one's place is the hundred's place (102). The digit in the hundred's place is multiplied by 102(i.e. 100) to determine how much it adds to the value of the number. Thus, 561 = 1 + 6 X 101plus 5 X 102. The digit in the million's place (106), which is the six places over from the one's place, adds its own value multiplied by 1,000,000 to the value of the number. Therefore the number 1,345,561 means 1 + 6 X 101+ 5 X 102+ 5 X 103+ 4 X 104+ 3 X 105+ 1 X 106.
The Babylonians used a base of 60 that serves the same purpose as the number 20 in the Mayan system and the number 10 in our system. After the Babylonians had counted to 59, they put a one in the next place to the left, the 60's place.
In about 400 B.C.E., the Babylonians began to use a slash mark to show that there was nothing in a particular place. 2016 would be written 2/16. Thus, they used the slash mark as a "place holder." This is one of the primary uses that we make of zero but the Babylonians didn't recognize that zero was itself a number that could be used in mathematical computations.
The Ancient Greek golden age began in the third century B.C.E. and was based on geometry, which measures the length of lines. Geometry deals with positive numbers and doesn't need zero. Nor did the Greeks have place-value numbers even though they were more advanced than the Babylonians in many aspects of civilization.
The Romans (5th century B.C.E. - 5th century C.E.) didn't have the zero either, and even though Roman civilization was very advanced and flourished hundreds of years after the Babylonian civilization, the Romans didn't use the place-value numbering system.
The first society other than the Maya to discover the concept of zero as both a placeholder and a number for use in mathematical calculations were inhabitants of the Indian subcontinent in Asia. They developed a ten-based, place-value system using the antecedents of 1,2,3,4,5,6,7,8,9 & 0. By about 600 C.E., after several hundred years of development, these numbers were standard in India. Thus, the Indians treated zero as a number and used it in computation, at the same time as or a few hundred years after the Maya.

The Arabs from the Middle East would trade with the Indians. They saw how advanced the Indian numbering system was, and they adopted it. Arabs refer to the numbers 0 - 9 as "Indian numbers." From the Middle East, these concepts spread to Europe in the 11th century C.E. where the numbers 0 - 9 are called the "Arabic numbers." By this time the Mayan civilization had reached its peak and had been in decline for about two hundred years. The use of zero and the place-value system was gradually adopted throughout Europe from the 12th century to the Renaissance in the 14th century.
As the Mayan civilization declined, its mathematics was lost. Zero and the place-value numbering used by the modern day inhabitants of North and South America came back to the lands of the Maya with the Spaniards as they colonized the Americas.

The Finger, also calledthe Birdor theDigitus Infamis

Remember when one of the gang members gave Mr. Escalante the finger? Where did this gesture come from? How did it get to the Latino boy in Southern California?

Different hand signs mean different things in different cultures. For example, the "thumbs up" sign means "good going" or "everything's OK" in the U.S. and many other places. However, in the Middle East, parts of West Africa, Russia, Australia and other places it is very derogatory. The "OK" sign formed by linking the thumb and the first finger to make a rough circle is accepted as a sign of approval in the U.S. and many other countries. However, in Latin America it is a gross insult, being the equivalent of calling someone an "a__ hole." In parts of Europe this means "nothing," and in Japan it means something like "give me change."
The extended middle finger has been an insulting gesture from the time of the ancient Greeks and Romans, and perhaps before. The first reference to "the finger" appears in a play called "The Clouds" written in 423 B.C.E. by the Greek dramatist Aristophanes. The play contains a scene in which a character has a debate with the great philosopher Socrates. Like many others who tried to debate with Socrates, the character gets a little angry and then gives Socrates the finger.
The Romans adopted much of their culture from the Greeks. Roman sculpture is very much like Greek sculpture. The Roman gods are similar to the Greek gods. Much of Roman literature was based on Greek literature. The Romans also adopted some Greek obscenities, including the finger, which was a well-established Roman insult. They had two names for this gesture, the "digitus infamis," roughly translated as the "infamous finger" and the "digitus impudicus" meaning the "indecent finger."
Roman culture spread to Europe with the conquests of the Roman Empire. The Roman influence came to the U.S. through the European settlers along two pathways. European culture came directly to North America through colonization and also indirectly through emigration of Europeans to Central America and Mexico and then from there, to the U.S. Angel's friend could have inherited the gesture in either of these two ways. (He could have learned it from U.S. culture or it could have been part of his Latin American heritage.) In any case, the origins of "the finger" stretch back to ancient Greece some 2,500 years ago.

Modern society has many things that are new, such as computers, the Internet, cars, airplanes, space travel, and electronic music. However, a lot of what we use or experience every day has come rather directly from ancient civilizations. A few of the thousands of examples are:Babylon:writing; the 60-minute hour; the 12 lunar months in a solar year; the city-state; a written legal code (Hamurabi); place-value numbers;ancient Israel:monotheism, morality-based religion; the Old Testament, the teachings of Jesus Christ; the concept of time as progressing forward rather than history being cyclical or not progressing at all;ancient Greece:geometry; philosophy; democracy; the Olympic Games; classical sculpture; drama; humanistic outlook;ancient India:zero, Arabic numerals;ancient Rome:representative government (the Roman Senate); the balance of powers in government; the alphabet;Renaissance Europe:scientific method, humanistic outlook (recovered from the Greeks);Medieval England:the concept of individual rights and limited government (from Magna Carta); the common law.