• what sets us–humans–apart from other living organisms; inventing is to venture
where others have not, stretching beyond conventional frontiers of time, space,
• what creates new possibilities, sets new standards, brings social and economic
progress and enrichment of knowledge;
• an expression of freedom, of power to create but also (and unfortunately) to
dominate, and may bring social and economic injustice, destruction, and
• birth of the mechanical calculator industry in the 19th century,
• first mechanical calculators started to show up in 16th century; B. Pascal
• calculating aids such as abacus.
• Industrial revolution profoundly impacted the socioeconomic and political landscapes
and socioeconomic conditions all over the world
• 18th and 19th century, mechanical calculators and special look-up table publications,
called mathematical tables, were used to facilitate calculation, veriﬁcation, selection,
categorization, and extraction of data.
• Mechanical calculators of the 19th century were inexpensive (in comparison with total
salaries paid to calculators)
• Knowledge of Past is:
• is a historical voyage through the centuries of human involvement with
calculating and computing;
• begins with the prehistory of computing, when the understanding of numbers and
performing basic arithmetic operations on them was the domain of just a few;
• explores our present-day computing reality, trying to decipher its meaning, to
arrange what we know and understand in a coherent body of knowledge that can
be used to confidently discuss problems faced by our society (such as social
obligations and individual rights and freedoms in the digital age), to understand
where we are and were we are going, or to predict what else is there to invent.
• The microprocessor–the heart of every modern computer–was ”invented”, or rather
offered commercially for the first time in 1971.
• microprocessor is a ‘chip’– contains the CPU
based on the invention of the integrated circuit (1958) which, in turn, was
base on the invention of the transistor (1947),
• Makes our intelligence unique:
• we are aware of what quantities represent, we have abstracted the concept of
numbers from quantities and progressively learned properties of numbers;
• we have named numbers, invented forms of their representation including
symbols to read, write, and record them;
• we have learned to perform complex operations on numbers and use them in
• finger method - that is a method of indicating numbers and counting them using fingers,
is a common origin of many other primitive counting methods. •as ancient as our civilization
• Showing fingers was not the only ancient method of non-verbal expression of numbers.
There were others:
• laying sticks, pebbles, beads, or shells on the ground;
• making marks on the ground with a stick;
• cutting notches or making scratches on a stick or a bone;
• making knots on a string; and many, many more.
• Number systems began to appear around 3,000 B.C.–perhaps even earlier
• Sumerians, Egyptians, Babylonians, Greeks, and Romans, cultures in India and
China, the Mayas and the Incas developed or adopted diverse number systems
and ways to record numbers
• Number two is expressed as ‘||’(two fingers) or ”=” (two sticks, still in use in China and
• For efficient calculations, the Romans used special purpose counters on a board called
counting boards or tables
• These counters were flat surfaces with parallel grooves etched in them
• Numbers: units, fives, tens and so on were represented by beads placed in specific
• ----ooooo hundreds of thousands
--------- tens of thousands
• Roman hand abacus, possibly introduced around 300-200 B.C.
o “I” (units) ”X” (tens), ”C” (hundreds), ”1” (thousands),
• This “modern” abacus was adopted and redefinethin China (suanpan) around the 12 th
century (?) and later in Korea (jupan, 13/14 century) and Japan (soroban, 16 century).
Other refinements of this abacus include Russian abacus (schoty), and Polish abacus
(liczydlo or Slavonic abacus), and many others.
• use of the stick calculator is simple. For instance, to add 32 to 32,031,
we do the following:
1. set the stick calculator to 32,031 by pressing the rightmost stick down until the
digit 1 appears in the window, then pressing the preceding stick until the digit 3
appears es in the window, and so on;
2. press the rightmost stick down 3 times to indicate the addition of 3 units;
3. press the 10s stick down 2 times to indicate the addition of 2 tens;