Perfect for defending yourself against a man armed with a banana.
Posted on 03/02/2006 5:01:38 AM PST by S0122017
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.
Unnatural design
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.
A feeling for maths
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.
Experiments with geometry must lie behind the construction of these paintings.
Constantin Papaodysseus, National Technical University of Athens, Greece.
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 key question is how the stencil itself was made.
Splitting a circle
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.
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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.
I don't have time this morning to run it down, but suspect this is in reality a very early instance of the Golden Mean. The spiral is generated by plotting values developed graphically by various multiples of Golden mean rectangles.
The Golden Mean is used in the construction of the Great Pyramid so Minoan usage might not be all that big a deal.
By the way, the spiral is incorporated into the geometry of a pine cone so it won't roll down hill.
I think we routinely underestimate ancient societies.
I don't think it is unreasonable to think that at various times in history (and prehistory) some discoveries were made that perhaps only barely missed connection with other ideas that would have launched technologies centuries earlier. I cannot imagine what was lost in the burning(s) of the library at Alexandria... things that took centuries to rediscover and build upon.
Seems like every time I connect to the internet, somebody's got a new date for the Thera catastrophe.
Just once I'd like to see "Minoan-Egyptian Dictionary found." Or "Board Game Pieces for Phaistos Disk Found."
I always thought Crete was the leader in civilization until for some unknown reason, possibly attacks from mainland Greece, they ceased to be.
What ever the reason, Crete has always fascinated me.
The Linear B Tablets and Mycenaean Social, Political, and Economic Organization
Lesson 25, The Prehistoric Archaeology of the Aegean
Revised: Friday, March 18, 2000 | Trustees of Dartmouth College
Posted on 08/29/2004 11:19:46 PM EDT by SunkenCiv
http://www.freerepublic.com/focus/chat/1202723/posts
6 posted on 08/30/2004 3:43:06 PM EDT by SunkenCiv
http://www.freerepublic.com/focus/chat/1202723/posts?page=6#6
The Phaistos Disk
various | various | various
Posted on 09/22/2005 11:12:35 AM EDT by SunkenCiv
http://www.freerepublic.com/focus/f-bloggers/1489304/posts
ping
We're currently studying Crete, the Minoans and Greece with my first grader. It really is fascinating. (We made a Mycenaean helmet out of paper mache.)
Anyway, we went to see "Greece" at the Imax a few days ago, and I wish that I had realized that Santorini was actually Thera, as a lot of the first part of the film was based there. I would recommend seeing this production when it gets to your area.
I only wish we could travel to the Mediterannean (sp) to visit it first hand. The scenery was breathtaking!
Without taking a stand on the accuracy of the claim, the article states that the Archimedes spiral is not found in nature, and it specifically mentions that snail shells do not follow that pattern.
Perfect for defending yourself against a man armed with a banana.
I remember reading about the Ionian civilization on the east coast of the Adriatic duringthe Greek era. If they had garnered a little more power and support from the Greeks, the industrial revolution could have started 2000 years earlier than the Rennaissance.
Interesting
Information at this site would refute those claims.
http://goldennumber.net/
A way-cool site; however, I don't see where it addresses the article's claim that the Archimedes spiral does not match natural patterns such as snail shells.
Archimedes certainly did not invent geometry. Ancient civilisations in Iraq, India and China demonstrate that they knew the subject well. Writings have been found, such as student excercise tablets from temples in Babylon.
One link to a discussion of mathematics in Babylon is: http://www-groups.dcs.st-and.ac.uk/~history/HistTopics/Babylonian_mathematics.html
A link to a short discussion of Early Geometry: The Babylonians, Egyptians & Chinese: http://library.thinkquest.org/C0110248/geometry/history1.htm
The above link even says, "The Pythagorean Theorem, although named after Pythagoras, was actually already known in ancient times.". It goes on to say why the writers think so.
In answer to your question, I think Archimedes published material that he was taught, added some original work and called the whole body of work his own. More a plaigarist than a Korean fake.
Still the idea that math may be a lot older makes sense to me. And it does certainly makes it likely that Archimedes was at least inspired by Minoan designs, perhaps more.
http://www.ualr.edu/~lasmoller/fibonacci.html
It's also heavily used in finance to analyze economic cycles.
BUMP
You have been watching the movie "Phi"?
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