Nature thoughtfully provided our earliest ancestors with a simple aid of computation — a digital computer in the
strictest sense of the word — copies of which may be seen
in active use in any school-room where the youngest generation is counting on its fingers. In making this provision,
nature unwittingly established the decimal base, with its
10 digit values as a natural mode in which the human race
might express its numerical ideals.
In the beginning — to borrow a phrase — there was the
abacus. This little device came into, being some 2,000 years
ago and still is the most widely used calculator on earth.
In some areas of the world it is the only known counting
device.
The word calculation itself comes from the earliest form
of abacus which consisted of lines drawn on the ground,
with small limestone pebbles to represent numbers. The
Latin word calcis means lime or limestone and the Latin
word calculus, which grew out of it, first meant a small piece
of limestone and later was expanded to mean any pebble
used in counting.
The abacus (from abax, an ancient Greek word for slab)
was a direct result of early efforts to count. When primitive
man satisfied his need for food and shelter, he began seeking
ways of expressing himself. His first writings were the rudimentary drawings on cave walls, the notches on the trees.
The earliest were simply representations of what we find
in nature — the sun, the moon, the animals he hunted. Soon,
however, he wanted to express how many animals he had
killed in a hunt, how many children he had, and .so forth.
Such was the development of symbols to indicate one, several,
and nuiny.
The next step was a big one — devising symbols to express
specific quantities. The first two were, quite naturally,
a two and a five; two because man had two hands, five because
he had five fingers. And by combining the symbols for hands
and fingers, he could express many different specific quantities. In such unprofessorial way man took his first plunge into
the mathematical world and came up with a revolutionary
concept — how to count. For then man acquired a scientific tool with which he could break up the universe into its
component units and thus master the size and shape of things.
- The numbers now in use are of comparatively recent origin,
not more than a thousand years. They are known as HinduArabic figures, because they originated in India and were
introduced to Europe by the Arabs.
The abacus makes use of this two-five or biquinary notation system.
The abacus is a most remarkable instrument — a computer
of great ingenuity capable of being made with the simplest
tools.
But the abacus has its shortcomings — otherwise we'd
all still be using it. It cannot carry over tens from one line
to another and the counting of beads is the basis for addition
and subtraction only. As man constantly expanded his
mathematical horizons this became an increasingly vexatious problem.
/
Nevertheless, the elementary basis of operation of any
digital computer, however complex, is the same as that of the
old-fashioned abacus.
ASSIGNMENTS
I. Comprehension questions:
I. What is the simplest way of computation? 2. Is finger
counting practised in our times? 3. Where does the decimal
base of numeration come from? 4. What did the limestone
pebbles represent in counting? 5. What is the etymology
of the term calculation? 6. What is the origin of the word
abacus? 7. What lies in the basis of two-five system of
numeration? 8. Who invented numbers and introduced them
to Europe?
II. Discussion questions:
1. Why do the people use the abacus in the time of scientific and technological progress? 2. Did nature provide man
only with a decimal base of numeration? 3. How does the
abacus function? 4. How did the first mathematical symbols
come into existence? 5. What are the shortcomings of the
abacus? 6. What have abacus and computer in common?
7. What do we call the abacus's native sister in Ukrainian?
I. What is the simplest way of computation?
Answer: The simplest way of computationa is a digital computer in the
strictest sense of the word
2. Is finger counting practised in our times?
Answer: Yes,it is in active use in any school-room.
3. Where does the decimal base of numeration come from?
Answer: Nature unwittingly established the decimal base, with its
10 digit values as a natural mode in which the human race
might express its numerical ideals.
4. What did the limestone pebbles represent in counting?
Answer: to represent numbers
5. What is the etymology of the term calculation?
Answer: The word calculation itself comes from the earliest form
of abacus which consisted of lines drawn on the ground,
with small limestone pebbles to represent numbers.
6. What is the origin of the word abacus?
Answer: The abacus (from abax, an ancient Greek word for slab).
7. What lies in the basis of two-five system of numeration?
Answer: Devising symbols to express specific quantities. The first two were, quite naturally, a two and a five; two because man had two hands, five because he had five fingers.
8. Who invented numbers and introduced them to Europe?
Answer: they originated in India and were introduced to Europe by the Arabs.
II. Discussion questions:
1. Why do the people use the abacus in the time of scientific and technological progress? - people use it as a physical aid to keep track of the sums, the carrys, etc
2. Did nature provide man only with a decimal base of numeration?
3. How does the abacus function? - it is a calculation tool used by sliding counters along rods or grooves, used to perform mathematical functions.
4. How did the first mathematical symbols come into existence? - they were signs for the depiction of numbers — ciphers, the appearance of which apparently preceded the introduction of written language.
5. What are the shortcomings of the abacus?
6. What have abacus and computer in common?
7. What do we call the abacus's native sister in Ukrainian?