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People have always wanted to study about the people who came before them. Today, many historians argue that we can only understand the present by studying the past. Though archaeology has been around for more than 2500 years, archaeology as a science has not been around for that long. For example, ancient writers like Plato or Pliny the Younger did not use scientific methods; it would take centuries before anyone even thought about that.
Nabonidus, king of Babylon, excavated a more ancient temple during his reign from 556 BC to 539. His daughter put the artifacts they found in the world's first known museum in Ur.
Now we move through the years to a century later. Thucydides (460-395 BC) described how Athenians excavated graves in the Greek island of Delos. He didn't acually excavate the graves, he wrote about them. Many of the ancient "archaeologists" did that.
Plato described about how Atlantis sank. According to Plato, an earthquake caused it to sink beneath the water. The story of Athantis was passed down from generation to generation in his family. The first person in his family to hear about it learned the story from an Egyptian king. Plato later designed a map showing what Atlantis must have looked like.
Plato told people his stories, but imagine if he had actually been there and taken notes! Thet's exactly what Pliny the Younger did. When Vesuvius exploded, he got on a boat and wrote down what he saw from his water view. Most people don't get that chance, they just find ruins and have to make an educated guess. Pliny did this in 79 AD.