*Ad hominem * attacks on Heyerdahl aside, he and his associates apparently really did manage to raise an Easter Island statue without any advanced technology. As mentioned by a previous poster, the methods used to build the Egyptian pyramids and monuments such as Stonehenge are still open to question.
Throughout Ireland there are stone fences which have stood for centuries without mortar. It is no trick to sort and stack thousands upon thousands of rocks neatly together so that they will make stable, nearly level, walls–all you need to do is make precise measurements of the contours of each stone and the right computer software. It is thought that fire and pressure were used to force the rocks into breaking up and collapsing into the proper formations, but, as I understand it, nobody is really sure.
This explanation for how the stone fences were fashioned was only proposed in the 20th Century. It was also in the past century that some techniques used by ancient metalurgists were reconstructed–unfortunately, I don’t have a cite for this.
No one is sure how the interior of a Greek trireme was designed. These were ships with three rows of oars arranged one atop the other. The oars in the topmost row would have been positioned at such an extreme angle that it appears they would have been impossible to work.
A number of modern cities have buildings and monuments arranged so that they form geometric patterns. A prime example is Washington, D.C. From the top of the Washington Monument one can go to the four sides of the building and look out directly on The Jefferson Memorial, The Lincoln Memorial, The Capitol and The White House. These and various other cites are said to be aligned with the front door of the Custis-Lee Mansion. Standing in front of John F. Kennedy’s grave one sees The Washington Monument bisect the Lincoln Memorial.
All of this was done with the benefit of various surveying and measuring techniques which were well understood by the 18th Century. In ancient and Medieval times, however, people in various parts of Europe were apparently able to make similar arrangements, placing structures such as temples and, later, cathedrals, at precise distances and along precise alignments.
Lines which can be drawn on maps to show these exact positionings are known as “ley lines”, as in England many of them are found in areas with place names ending in “ley”, an old word for field. (Hence names such as Ashley and Wheatley). Just how people managed to do this precise work of placement nobody knows.
At the beginning of Raiders of the Lost Ark there is a sequence where Harrison Ford is “chased” by a huge stone ball. There actually are stone balls of this sort, in a variety of sizes, scattered throughout the jungles of Costa Rica. How ancient people managed to carve them seems to be anyone’s guess.
Among the objects found in the tomb of Tutankhamen is a carved vase with beautful decorations which are only visible when the vase is lit from the inside. It is not clear how artists were able to do work of this sort.
I’ve heard it said many times that no one is sure exactly how the Stradivarius family was able to do such fine work.