Hieroglyphic Representation Of Numbers 631i

Hieroglyphic Representation of Numbers As soon as the unification of Egypt under a single leader became an accomplished fact, a powerful and extensive istrative system began to evolve. The census had to be taken, taxes imposed, an army maintained, and so forth, all of which required reckoning with relatively large numbers. (One of the years of the Second Dynasty was named Year of the Occurrence of the Numbering of all Large and Small Cattle of the North and South.) As early as 3500 B.C., the Egyptians had a fully developed number system that would allow counting to continue indefinitely with only the introduction from time to time of a new symbol. This is borne out by the macehead of King Narmer, one of the most remarkable relics of the ancient world, now in a museum at Oxford University. Near the beginning of the dynastic age, Narmer (who, some authorities suppose, may have been the legendary Menes, the first ruler of the united Egyptian nation) was obliged to punish the rebellious Libyans in the western Delta. He left in the temple at Hierakonpolis a magnificent slate palette—the famous Narmer Palette—and a ceremonial macehead, both of which bear scenes testifying to his victory. The macehead preserves forever the official record of the king’s accomplishment, for the inscription boasts of the taking of 120,000 prisoners and a of captive animals, 400,000 oxen and 1,422,000 goats.

KING NARMER  

This pharaoh of ancient Egypt is also associated with the legendary name of Menes. He ruled as the King of Egypt during the period in ancient Egyptian history known as the Early Dynastic Period.

NARMER PALETTE  

It was found at Hierakonpolis and depicts the unification of the two lands of Upper and Lower Egypt. The palette also depicts ceremonial of sacrifice of the defeated.

BOOK OF THE DEAD  

Also known as “Book of Coming Forth by Day” or "Book of emerging forth into the Light". It consists of a number of magic spells intended to assist a dead person's journey through the Duat, or underworld, and into the afterlife.

HIEROGLYPHICS   

formed from two ancient Greek words: hieros 'holy' + glyphe 'carvings' which described the ancient holy writing of the Egyptians sacred signs picture script

EGYPTIAN NUMBER SYSTEM       



as early as 3000 BC Hieroglyphic system. Used papyrus as *paper* Base 10 “grouping” system Symbols can repeat 9 times The Egyptians had a number system that used eight different symbols. The eight symbols are:  1 is shown by single stroke  10 is by an upside down u  100 is by a curved rope  1,000 is by a lotus flower  10,000 is by an upright bent finger  100,000 by a tadpole  1,000,000 by a person holding up his hand as if in great astonishment  10,000,000 by a rising sun Symbols in the Egyptian number system.

10,000,000

How would you write 3,244?

  

How would you write 21,237?

The value of the number represented was not affected by the order of hieroglyphs. The reading and writing of Egyptian numbers was not a positional system. It also involves operation like addition and subtraction

ADDITION involving EGYPTIAN NUMBER SYSTEM Addition and subtraction caused little difficulty in the Egyptian number system. For addition, it was necessary only to collect symbols and exchange ten like symbols for the next higher symbol. This is how the Egyptians would have added, say, 345 and 678. Add 345 and 678.

Subtraction was performed by the same process in reverse. Sometimes “borrowing” was used, wherein a symbol for the large number was exchanged for ten lower-order symbols to provide enough for the smaller number to be subtracted, as in the case

The Greek Alphabetic Numeral System Around the fifth century B.C., the Greeks of Ionia also developed a ciphered numeral system, but with a more extensive set of symbols to be memorized. They ciphered their numbers by means of the 24 letters of the ordinary Greek alphabet, augmented by three obsolete Phoenician letters (the digamma for 6, the koppa for 90, and the sampi for 900). The resulting 27 letters were used as follows. The initial nine letters were associated with the numbers from 1 to 9; the next nine letters represented the first nine integral multiples of 10; the final nine letters were used for the first nine integral multiples of 100. The accompanying table shows how the letters of the alphabet (including the special forms) were arranged for use as numerals.

Because the Ionic system was still a system of additive type, all numbers between 1 and 999 could be represented by at most three symbols. The principle is shown by

For larger numbers, the following scheme was used. An accent mark placed to the left and below the appropriate unit letter multiplied the corresponding number by 1000; thus ′β represents not 2 but 2000. Tens of thousands were indicated by using a new letter M, from the word myriad (meaning “ten thousand”). The letter M placed either next to or below the symbols for a number from 1 to 9999 caused the number to be multiplied by 10,000, as with

With these conventions, the Greeks wrote

To express still larger numbers, powers of 10,000 were used, the double myriad MM denoting (10,000)2, and so on. The symbols were always arranged in the same order, from the highest multiple of 10 on the left to the lowest on the right, so accent marks sometimes could be omitted when the context was clear. The use of the same letter for thousands and units, as in

gave the left-hand letter a local place value. To distinguish the numerical meaning of letters from their ordinary use in language, the Greeks added an accent at the end or a bar extended over them; thus, the number 1085 might appear as

The system as a whole afforded much economy of writing (whereas the Greek alphabetic numerical for 900 is a single letter, the Egyptians had to use the symbol required the mastery of numerous signs.

nine times), but it

Multiplication in Greek alphabetic numerals was performed by beginning with the highest order in each factor and forming a sum of partial products. Let us calculate, for example, 24 × 53:

The idea in multiplying numbers consisting of more than one letter was to write each number as a sum of numbers represented by a single letter. Thus, the Greeks began by calculating 20 × 50 (κ by ν), then proceeded to 20 × 3 (κ by γ), then 4 × 50 (δ by ν), and finally 4 × 3 (δ by γ). This method, called Greek multiplication, corresponds to the modern computation.

The numerical connection in these products is not evident in the letter products, which necessitated elaborate multiplication tables. The Greeks had 27 symbols to multiply by each other, so they were obliged to keep track of 729 entirely separate answers. The same multiplicity of symbols tended to hide simple relations among numbers; where we recognize an even number by its ending in 0, 2, 4, 6, and 8, any one of the 27 Greek letters (possibly modified by an accent mark) could represent an even number. An incidental objection raised against the alphabetic notation is that the juxtaposition of words and number expressions using the same symbols led to a form of number mysticism known as “gematria.” In gematria, a number is assigned to each letter of the alphabet in some way and the value of a word is the sum of the numbers represented by its letters. Two words are then considered somehow related if they add up to the same number. This gave rise to the practice of giving names cryptically by citing their individual numbers. The most famous number was 666, the “number of the Beast,” mentioned in the Bible in the Book of Revelation. (It is probable that it referred to Nero Caesar, whose name has this value when written in Hebrew.) A favorite pastime among Catholic theologians during the Reformation was devising alphabet schemes in which 666 was shown to stand for the name Martin Luther,

thereby ing their contention that he was the Antichrist. Luther replied in kind; he concocted a system in which 666 forecast the duration of the papal reign and rejoiced that it was nearing an end. Readers of Tolstoy’s War and Peace may recall that “L’Empereur Napoleon” can also be made equivalent to the number of the Beast. Another number replacement that occurs in early theological writings concerns the word amen, which is αµην in Greek. These letters have the numerical values

totaling 99. Thus, in many old editions of the Bible, the number 99 appears at the end of a prayer as a substitute for amen. An interesting illustration of gematria is also found in the graffiti of Pompeii: “I love her whose number is 545.”