I feel I need to point out in this node some of the criticisms that have been made of the Piri Reis map, and in particular Charles Hapgood's interpretation of it.
First of all is the claim that Antarctica is represented on the map. What the Piri Reis map actually shows is the East coast of South America extended towards Africa. Hapgood's explanation is that this was an error introduced on copying from original sources, which showed the correct seperation between Antarctica and South America. But there is a more likely explanation. Ever since Ptolemy, cartographers have theorised a 'counterweight continent' that balances the land masses in the northern hemisphere, keeping the Earth balanced. When South America was discovered, it was tempting for mapmakers to portray it as a northern peninsula of this counterweight continent. The most extreme example is the Lopo Homem map of 1519, where South America stretches right under Africa to join up with Asia, completely enclosing the Atlantic and Indian Oceans. Also see the Contarini map for an alternatively shaped counterweight continent.
Secondly is the claim of amazing accuracy of the map. Hapgood made the map fit by fitting it to four different grids, explaining that it was drawn from four different source maps. Two are parallel but to a different scale. One is rotated 79 degrees clockwise. And the fourth is turned 40 degrees counterclockwise, and to half the scale of the main grid. How did Hapgood come up with all these different placements? By fitting features on the Piri Reis map to features on modern maps. Therefore it is no great wonder that the features are in the correct places! And yet still he admits that two pieces of South America are missing, as well as the Drake Passage and the Palmer Peninsula. And the Amazon River is drawn twice.
Thirdly, the claim that the map shows the Andes just to the east of the West coast of South America. In fact, the map does not show the West coast at all! All that is there is a thin brown line seperating the map from a section of text, not a thick black line like most of the coastlines. The mountains are interesting in that they are in vaguely the same place as the Andes. This deserves further looking into, but doesn't neccessarily mean that the information came from any ancient civilization.
Fourth, the supposed coastline of Antartica without the ice sheet. Hapgood theorises that the original source dates to about 6000 years ago, when the ice was not present. However, most geologists place the date far further back; tens of thousands or perhaps millions of years have passed since antarctica was ice-free. But what about the supposed similarity of the map to present day sonar scans of the antarctic land mass? The problem this time is our modern day accuracy. We have only fuzzy maps of the land beneath the ice. Even then, if the ice were to be removed, the land would look entirely different; the land would become less compressed, while the sea level would rise. We have very little idea what antarctica would look like without ice.
What is the Piri Reis map, then? It is a fairly accurate, but not stunningly so, map of the atlantic that gets very distorted around the southern half of South America, much like the Portugese and Spanish maps of the time. This is understandable given that Piri Reis writes on the map itself that most of his information came from Columbus and Portugese navigators. It is a good map, but there is nothing in it that neccessitates Atlanteans, UFOs, or any other such creations.