Unprecedented mathematical knowledge found in (Minoan) Bronze Age wall paintings.

Published online: 28 February 2006; | doi:10.1038/news060227-3 Were ancient Minoans centuries ahead of their time? Unprecedented mathematical knowledge found in Bronze Age wall paintings. Philip Ball

Did the Minoans understand the Archimedes' spiral more than 1,000 years before him?

A geometrical figure commonly attributed to Archimedes in 300 BC has been identified in Minoan wall paintings dated to over 1,000 years earlier.

The mathematical features of the paintings suggest that the Minoans of the Late Bronze Age, around 1650 BC, had a much more advanced working knowledge of geometry than has previously been recognized, says computer scientist Constantin Papaodysseus of the National Technical University of Athens, Greece, and his colleagues.

The paintings appear in a building that is still being excavated and restored in the ancient Minoan town of Akrotiri on the island of Thera. A catastrophic eruption of the volcano on Thera, now known as Santorini, around 1650 BC, is thought to have dealt a fatal blow to the Minoan culture. The blast covered Akrotiri, on the island's southern coast, in a thick layer of ash that preserved many buildings and artefacts.

Ten or so buildings have been excavated in Akrotiri so far, including a large one known as Xeste 3, which stands close to the ancient quay. Judging from its large size and extensive wall decorations, Xeste 3 appears to have been some kind of public building, such as a temple or a place for ritual ceremonies.

The most impressive feature of the paintings found in Xeste 3 is a series of spirals, each about 32 centimetres in diameter and embellished with dots. Papaodysseus and his team have shown that these are near-perfect Archimedes' spirals: shapes tightly defined by a simple mathematical formula, in which the distance between the windings is constant.

Some spirals, such as the ones found on snail shells, are common in nature. And others can be easily made by unwinding a thread around a central peg. But the Archimedes' spiral is not like either of these. "Seemingly it does not exist in nature," the researchers say.

"This is the earliest time that such advanced geometric figures have been spotted," says Papaodysseus. "The next such figures appear only 1,300 years later." The team report their work in the journal Archaeometry1.

Papaodysseus and his co-workers admit that they cannot know how much the Theran artists actually understood about the geometric principles they used for the paintings, because no written documents from this period are known to exist.

But he says that, at the very least, "experimentation with geometric tools must lie behind the construction of these wall paintings, as well as an impressive feeling for geometry."

Spiral designs in Xeste 3 were first noticed years ago by archaeologists working at the site. But Papaodysseus says that most people previously assumed that the shapes were painted freehand.

His studies suggest that the curves are just too accurate for that: the edges deviate from their strict mathematical form by typically less than a third of a millimetre. Papaodysseus thinks that this precision was probably achieved by the use of stencils, which appear to have been broken up into six parts to make them easier to transport and the paintings easier to fit to a given space.

The researchers point out one relatively simple way of constructing such a spiral, without knowing the precise mathematical formula for it. One could divide up a circle using a large number of radial lines with equal angles between them, and a large number of concentric circles. A series of dots moving out one radial line and one concentric circle at a time could be joined together into an Archimedes' spiral. But dividing a circle into more than a dozen equal sections is not a trivial task; try it yourself.

Papaodysseus and his colleagues find that the dots decorating the spirals seem to be positioned almost exactly on the radial lines of circles that are divided into 48 sections.

The wall paintings don't in themselves prove that the Therans knew enough geometry to bisect angles. But it certainly looks that way, says Papaodysseus.

Most believed Ramses II to be the pharaoh of the Exodus. That doesn't seem to fit. The latest evidence of the timeline from the Egyptian side places Ramses as late as 925bc as the Shishak that plundered Jerusalem. Others tend to favor Seti I .

Ramses was dated at one point to the 13th century BC. That is substantially later than 1627 and makes the linkage impossible with regard to the volcano theory. Other problems arise here as well. Solomon's reign would be ending in the time of Ramses II, making Solomon a Contemporary of Seti I. Solomon married Egyptian Royalty.
His wife would necessarily come from the court of Seti or Ramses. In any case, neither of them could be the pharaoh of the Exodus. Going backward, you have Solomon's father, David, sitting as Second King of Israel, then Saul who was the first. Saul has linkage with a prior pharaoh under his birth name Lebayou (sp?). This doesn't point to the pharaoh of the Exodus; but, it does rule out who could not have been.

Shoshenq I's Chief Archetect is recorded in a generational family tree that has been dated to year 26 of the reign of Darius I. Also listed in that family tree is the cheif architect of Ramses. So these aren't fixed dates for the beginnings and endings of the reigns, it just tells us who was reigning at a given snapshot in time. Shoshenq was reigning by the family tree in 776. Ramses II was in 925.
We know Seti I reigned into his 90s. And the Amarna letters
tie Saul to Ankhenaton. Saul was the first King of Israel after the Exodus. The letters to Pharaoh from Saul tie in nicely to biblical events recorded. Ankhenaton reigned under the name Amenhotep IV. This would rule out the conjecture about Tutankhamun being the firstborn son killed at passover.

Linkages have been drawn between Joseph and Amenemhet III which seem to support the later timeline - framing things in as it were. The Bar Joseph waterway from that period still bears Joseph's name. What seems problematic to me is the explosion of kings in the 13th Dynasty combined with the imprecision of dating in general. There are also a lot of assumptions made as to when many of the Kings ruled. Some dynasties seem to have been co-ruling instead of ruling in dynastic order - a kingdom divided between upper and lower Egypt as it were. Not altogether unexpected; but, a blind eye seems to prevail in attempt to stretch the timeline for reasons obvious to some and embarrassing to others when the corrections are made. I find it interesting the linkages made at Megiddo to Solomon. A building not matching his recorded building style and requirement is identified as his in preference over one that matches it precisely. Why? Because the one matching doesn't match the presumed "layer" in which Solomon is expected to be found. Faced with the contradiction, the hard evidence of the matching structure is abandoned in preference to the conjectural dating method of the layers. IMHO, this is a lot of what is wrong with science today. Ideologies get in the way of methodology. One should be following the evidence.

Anyway, I'm off to bed. Have fun with it.

The valcano idea is tossed in because these guys want "naturalistic" explanations for things they can otherwise not explain. It's never enough for them to say "I don't know" or to take the scripture literally. People want to force supernatural into a natural explanation. When they can't they tend to avoid the subject rather than admit their ignorance. That is pride.

I like the jacketed sulfur pellets from the area of Sodom and Gamorah. I've never seen a natural explanation for them, yet there they are. Volcanos don't produce them nor is there one near by to explain them if volcanoes did produce them. And further, there is no explanation for the specific places they fell to the exclusion of others - that is unless one takes scripture at it's word and God at His.

The sulphur pellets are fairly small - about the size of a golf ball as I remember. The core is pure sulphur with an outher jacket or casing that I'm not sure about the makeup of.. The interesting thing about them is that they burn so hot, they are found imbedded into solid rock that they melted their way into as it were.

http://www.wyattmuseum.com/images/wpe3.jpg

http://www.exchangedlife.com/wyatt/images/sulphurball.jpg

http://www.exchangedlife.com/wyatt/images/aaron.jpg

There used to be some pretty good shots of these posted at Wyatt's website. I found a few.

I don't know if the casing is a result of impacting something or not. It's just something I remembered seeing in other photos.

I think the numbers I remember seeing are that most sulphur deposits are in the range of 30-40 percent pure. These pellets are 95 plus percent pure and burn at 5000 to 6000 degrees. Very nasty little buggers as it were. My understanding is that they produce ash that is denser than normal - heavier. And looking at the remains of Gamorah, that isn't tough to believe.

Disclaimer: Opinions posted on Free Republic are those of the individual posters and do not necessarily represent the opinion of Free Republic or its management. All materials posted herein are protected by copyright law and the exemption for fair use of copyrighted works.

· join list or digest · view topics · view or post blog · bookmark · post a topic · subscribe ·
	Gods Graves Glyphs	Just updating the GGG info, not sending a general distribution. To all -- please ping me to other topics which are appropriate for the GGG list. GGG managers are SunkenCiv, StayAt HomeMother, and Ernest_at_the_Beach
·Dogpile · Archaeologica · ArchaeoBlog · Archaeology · Biblical Archaeology Society · · Discover · Nat Geographic · Texas AM Anthro News · Yahoo Anthro & Archaeo · Google · · The Archaeology Channel · Excerpt, or Link only? · cgk's list of ping lists ·