Goya's most frightening picture shows a giant man, eating people. It is now called "Saturn Devouring His Sons", (after Saturn the Father of the Gods in Greek mythology) but no-one knows what it really means. It is more likely a picture of the way that War destroys people. In the house that Goya owned, there are paintings on the walls known as the "Black Paintings". They show scenes with the Devil and witches. It is not sure whether Goya really painted them. Overall he was a pretty cool guy
Goya's brightly coloured tapestry cartoons influenced the French Impressionist painters such as Monet and Renoir. His portraits were an influence on Manet and Degas as well as Renoir. The "Black Paintings" influenced Expressionist painters.
Inclusive disjunction
Inclusive disjunction (also called or) is a logic operation. It normally takes two truth values as inputs and returns one truth value as output. It is false when both inputs are false, but is true otherwise. It is written with the symbol formula_1.
In general, given two propositions formula_2 and formula_3, formula_4 is true if formula_2 is true, or if formula_3 is true, or if both formula_2 and formula_3 are true.
This is different from the exclusive disjunction, which asserts "either "x" or "y", but not both".
Logical conjunction
Logical conjunction (very often called and) is a logic operation. It is represented by the symbol formula_1. Logical conjunction takes two truth values as inputs and returns an output. If both of the inputs are "true" at the same time, then logical conjunction outputs "true". If one of the inputs is false, or if both of the inputs are false, then logical conjunction outputs "false". Its logic gate equivalent is the AND gate.
Logical negation
Logical negation (also known as not) is a logic operation. For a proposition formula_1, its negation is written as formula_2. It takes one input. It flips the value of the input as the output. If the input was true, it returns false; If the input was false, it returns true.
Logic equality
Logical equality is a logical operation. It corresponds to equality (formula_1) in Boolean algebra and biconditional (written formula_2 or formula_3) in logic. It takes two inputs. It returns true if both inputs are true or if both inputs are false. Otherwise (when they are different), it returns false.
Implication (logic)
Implication (also known as logical consequence, implies, or If ... then) is a logical operation. It is the relationship between statements that holds true when one logically "follows from" one or more others. While a statement of the form "if "P" then "Q"" is often written as formula_1, the assertion that ""Q" is a logical consequence "P"" is often written as formula_2.
Implications take two arguments. It returns false if and only if the first term is true and the second term is false.
This may be problematic, because it means that from a false proposition, anything can follow.
The following shows a (valid) implication
On the other hand, the statement "I promise that if I am healthy, I will come to class" has four possibilities:
In the second scenario, the statement is false, since the promise is broken. In other scenarios, the statement is true, since the promise is kept.
Hellenistic art
The art of the Hellenistic time (400 B.C. to 0 B.C, a long time in the past, in Greece) is sculpture and painting and other things. For a long time, people said that the art of that time was not good. Pliny the Elder talked about the Greek sculpture of the classical time (500 B.C. - 323 B.C., the time before the Hellenistic time) and then said "Cessavit deinde ars" ("then art stopped"). But much good art is from the Hellenistic time. Many people know about the sculptures Laocoön (in the picture) and Venus de Milo and Winged Victory of Samothrace.
Now more people have looked at writing about the Hellenistic time. People discovered art from the Hellenistic time at Vergina and other places. Now people can see that the art of the Hellenistic time is very good art.
One of the things that made the Hellenistic time different from other times was the division of Alexander the Great's country into smaller parts. In every part there was a family of leaders. The Ptolemies had Egypt; the Seleucids had Mesopotamia, the Attalids had Pergamon, and other leaders had other parts. Every family of leaders gave money for art in a way that was different from the way the city-states did it. They made big cities and complex groups of buildings in a way that most city-states had already stopped doing by 500 BC. This way of making buildings was new for Greece. This way was not to try to change or fix a natural place, but to make the buildings fit the natural place. There were many places for pleasure, for example many theatres and places to walk. The Hellenistic countries were lucky because they had much empty space where they could make big new cities. Some of their new cities were Antioch, Pergamon, and Seleucia on the Tigris.
Pergamon is a very good example of Hellenistic architecture. It started with a simple fortress on the Acropolis (a very big rock).
Different Attalid kings added to it and made a huge group of buildings. The buildings stretch out from the Acropolis in many directions, using the natural way of that part of the earth. The agora, on the south on the lowest level, has galleries along its sides, with "stoai" (beautiful tall stone things to hold up the roof.) The agora is the beginning of a street which goes through the whole Acropolis. On the east and top of the rock are the buildings of the organizers, leaders and soldiers. On the west side, at a middle level, are religious buildings. One of the biggest ones is the one with the Pergamon Altar which is called "of the gods and of the giants" and is one of the most beautiful pieces of Greek sculpture. A very big theatre has benches stretched out over the sides of the hill, for people to sit on, and is able to hold almost 10,000 people.
At that time they liked to make very big things. The second temple of Apollo at Didyma was like that. It was twenty kilometers from Miletus in Ionia. Daphnis of Miletus made the design for it at the end of the fourth century B.C. (about 300 B.C.) but it was never finished. They continued building it until the 2nd century A.D. (past 100 A.D.). The sanctuary (special part of the temple) is one of the largest ever made near the Mediterranean. Inside a very big room, the "cella" has two rows of columns (tall round things) around it. The columns are the Ionic kind, almost 20 metres tall, with much complex stone art on the bases and tops.
Hellenistic sculpture includes portraits which show things such as suffering, sleep or old age.
Attalus I (269-197 BC), to commemorate his victory at Caicus against the Gauls — called Galatians by the Greeks — had two series of votive groups sculpted: the first, consecrated on the Acropolis of Pergamon, includes the famous Gaul killing himself and his wife, of which the original is lost (the best copy is in the Massimo alle Terme museum of Rome, see illustration); the second group, offered to Athens, is composed of small bronzes of Greeks, Amazons, gods and giants, Persians and Gauls. Artemis Rospigliosi of the Louvre is probably a copy of one of them; as for copies of the Dying Gaul, they were very numerous in the Roman period. The expression of sentiments, the forcefulness of details — bushy hair and moustaches here — and the violence of the movements are characteristic of the Pergamene style.