Abacus logic
Encyclopedia
A logical abacus is a mechanical digital
computer
.
Also referred to as a "logical machine", the logical abacus is analogous to the ordinary (mathematical) abacus
. It is based on the principle of truth table
s.
Before numbers were even invented, counting devices were used to perform everyday calculations; one of this devices was the abacus, which provided merchants good and accurate data when buying and selling goods.
The abacus was not created as we know it today, but was rather a continuous improvement throughout the ages. "Later day abaci had grooves for small pebbles and later yet wires or rods on which counters could freely move back and forth" (Bogomolny). The most recent form know of the logical abacus is a frame made often out of wood which holds firmly a set various rods or wires with freely sliding beads mounted on them (Georges).
It is constructed to show all the possible combinations of a set of logical terms with their negatives, and, further, the way in which these combinations are affected by the addition of attributes or other limiting words, i.e., to simplify mechanically the solution of logical problems. These instruments are all more or less elaborate developments of the "logical slate", on which were written in vertical columns all the combinations of symbols or letters that could logically be made out of a definite number of terms. These were compared with any given premises, and incompatible ones crossed off. In the abacus the combinations are inscribed each on a single slip of wood or similar substance, which is moved by a key; incompatible combinations can thus be mechanically removed at will, in accordance with any given series of premises.
The principal examples of such machines are those of William Stanley Jevons
(logic piano), John Venn
and Allan Marquand
.
In the modern world, the abacus as we know it today looks nothing like it did when it was originally invented. In the ancient times, the abacus was a really simple device that was used to count numbers; this included addition and substraction only. Nowadays, the abacus still keeps its essence of the frame with rods and beads moving freely on the rods, but is much more developed. The newest know abacus invented by Lee Kai-chen contains four decks, in which more complex operations can be made; "multiplication and division are easier using this modified abacus and includes instructions for determining square roots and cubic roots of numbers" (Georges).
Digital
A digital system is a data technology that uses discrete values. By contrast, non-digital systems use a continuous range of values to represent information...
computer
Computer
A computer is a programmable machine designed to sequentially and automatically carry out a sequence of arithmetic or logical operations. The particular sequence of operations can be changed readily, allowing the computer to solve more than one kind of problem...
.
Abacus
The abacus, also called a counting frame, is a calculating tool used primarily in parts of Asia for performing arithmetic processes. Today, abaci are often constructed as a bamboo frame with beads sliding on wires, but originally they were beans or stones moved in grooves in sand or on tablets of...
. It is based on the principle of truth table
Truth table
A truth table is a mathematical table used in logic—specifically in connection with Boolean algebra, boolean functions, and propositional calculus—to compute the functional values of logical expressions on each of their functional arguments, that is, on each combination of values taken by their...
s.
Before numbers were even invented, counting devices were used to perform everyday calculations; one of this devices was the abacus, which provided merchants good and accurate data when buying and selling goods.
The abacus was not created as we know it today, but was rather a continuous improvement throughout the ages. "Later day abaci had grooves for small pebbles and later yet wires or rods on which counters could freely move back and forth" (Bogomolny). The most recent form know of the logical abacus is a frame made often out of wood which holds firmly a set various rods or wires with freely sliding beads mounted on them (Georges).
It is constructed to show all the possible combinations of a set of logical terms with their negatives, and, further, the way in which these combinations are affected by the addition of attributes or other limiting words, i.e., to simplify mechanically the solution of logical problems. These instruments are all more or less elaborate developments of the "logical slate", on which were written in vertical columns all the combinations of symbols or letters that could logically be made out of a definite number of terms. These were compared with any given premises, and incompatible ones crossed off. In the abacus the combinations are inscribed each on a single slip of wood or similar substance, which is moved by a key; incompatible combinations can thus be mechanically removed at will, in accordance with any given series of premises.
The principal examples of such machines are those of William Stanley Jevons
William Stanley Jevons
William Stanley Jevons was a British economist and logician.Irving Fisher described his book The Theory of Political Economy as beginning the mathematical method in economics. It made the case that economics as a science concerned with quantities is necessarily mathematical...
(logic piano), John Venn
John Venn
Donald A. Venn FRS , was a British logician and philosopher. He is famous for introducing the Venn diagram, which is used in many fields, including set theory, probability, logic, statistics, and computer science....
and Allan Marquand
Allan Marquand
Allan Marquand was an art historian at Princeton University and a curator of the Princeton University Art Museum.Marquand was the son of Henry Gurdon Marquand, a prominent philanthropist and art collector. After graduating from Princeton in 1874, Allan obtained his Ph.D. in Philosophy in 1880, at...
.
In the modern world, the abacus as we know it today looks nothing like it did when it was originally invented. In the ancient times, the abacus was a really simple device that was used to count numbers; this included addition and substraction only. Nowadays, the abacus still keeps its essence of the frame with rods and beads moving freely on the rods, but is much more developed. The newest know abacus invented by Lee Kai-chen contains four decks, in which more complex operations can be made; "multiplication and division are easier using this modified abacus and includes instructions for determining square roots and cubic roots of numbers" (Georges).