Speaking of sending a record of Bach's music to outer space, NASA has sent phonograph records in 1977 aboard the two Voyager spacecrafts. The contents were selected by a committee chaired by Carl Sagan of Cornell University and aimed to the stories of humans on earth . The contents were natural sounds (wind, thunder, animals), music of from different cultures, greetings in 55 ancient and modern languages, printed messages from the US president Jimmy Carter and U.N Secretary-General Kurt Waldheim. The records also contained images of mathematical and physical quantities, the Solar System, DNA, human anatomy, reproduction, landscapes, plants, animals, food, architecture. The images were annotated with scales of time, size, or mass. They targeted any intelligent extraterrestrial life. (Left): gold aluminium cover designed to protect the gold-plated records from micrometeorite bombardment. It also serves a double purpose in providing the finder a key to playing the record.The explanatory diagram appears on both the inner and outer surfaces of the cover, as the outer diagram will be eroded in time.
(Right):The identical 12-inch gold plated copper records (discs) aboard Voyager 1 and 2.
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The author says that the decision procedure for the Propositional Calculus as a formal system is truth tables. Truth tables can tell whether a propositional expression ( a well-formed string of Propositional Calculus) is true (is a theorem) for all legitimate input values. A truth table has one column for every variable in the expression and one extra column for the result of the expression. Each row is one of the possible values that the variables may have and the last column in every row will contain the result of the expression if the variables had the corresponding values in that row. This is a truth table with one variable (P). The well-formed string is ~P (the negation of P). The truth table gives the value of the expression for all possible values of the variable. This is a truth table for "or" described in the book. The well-formed string is P v Q. The variables are P and Q. For the expression "P or Q" to be true, at least one of P and Q must be true. When both are true then the expression P or Q is true. When only one of them is true then the expression P or Q is true. When both are false then the expression P or Q is false.
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