Skip to comments.Unprecedented mathematical knowledge found in (Minoan) Bronze Age wall paintings.
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.
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.
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.
Great Minds think alike.
Sometimes mathematical concepts are dimly anticipated before being formally defined. The spiral might have been determined through fooling with compass/protractor techniques, but its full meaning would be hard to understand without the benefit of the Pythagorean theorem. There would have to be a comparison between how deeply Archemedies understood the properties of the object and how well the Minoans understood it. You aren't going to get that from one picture.
That is true, but the interesting thing here is the minoan culture influenced the later greek culture in many ways.
Including art and mythology. Then why not mathematics?
It is ofcourse possible that Archimedes just saw the drawings and got inspired. But i leaves other options aswell.
"the powerful influence that the Minoan culture had on the later classical Greek culture"
I think this date is actually 1628BC and the same time as the Jewish Exodus from Egypt. The volcano plume would have had to be 30 miles high to be seen from Egypt..."staff by day, torch by night."
The most recent eruption of Pinatubo in the Phillipines was 26 miles high and the one in/around Alaska was greater than 30 miles high.
The Minoans had far more advanced navies than surrounding countries, it wouldn't surprise me if their mathematics were advanced as well.
Everytime I hear about some culture supposedly inventing the mathmatical concept of 0, I never believe it
"Moses called down a host of calamities upon Egypt until the pharaoh finally freed the Israelites. Perhaps he had the help of a comet impact coupled with a volcano.
A volcano destroyed the island of Santorini in the Aegean Sea (between today's Greece and Turkey) around the middle of the second millennium B.C. Researchers Val LaMarche and Kathy Hirschboeck suggest the volcano might be associated with tree-ring evidence for several years of intense cold beginning in 1627 B.C
. "Could that form the basis for strange meteorological phenomena recorded in the biblical book of Exodus? In the book of Exodus, which describes events a few hundred kilometers from Santorini, we read of a pillar of cloud and fire, a lingering darkness, and the parting of the Red Sea. An enormous column of ash must have hung in the sky over the eruption (the Israelites pillar of cloud by day and fire by night?), and the volcano doubtless caused a tsunami, or tidal wave (which could have drowned a pharaoh's army)."
"The Exodus story is traditionally dated to either the thirteenth or fifteenth century B.C. Those dates, however, depend ultimately on identifying the Pharaoh of the Oppression, and historians have never proven to which ruler that infamous title referred."
Sure you did, ever hear of a chalkboard? Erasable walls just hadn't been invented yet.
Ever hear of the math major that had a constipation problem? He got a pencil and worked the problem out.
.....But dividing a circle into more than a dozen equal sections is not a trivial task; try it yourself. ......
Absurdly simple. Divide it into six by taking radial arcs, split one and do it again from tne mid point.
Not true. Every mathematician and math instructor I have ever known "did math on a wall". Back in those days, they were called "blackboards".
I guess the dude wouldn't have got as much newsprint if he speculated "Maybe it was just an accident...?"
Another one of the "I think I found Atlantis near Cuba" crowd.
Nothing to do with atlantis and he is not suggesting it.
It isnt like finding archimedes spiral on a rock in africa or easer island, the minoans have influenced the greek in a great manner.
To find two identical spirals among two cultures of which one was the older and was known to have influenced the other (and perhaps vice versa) is enough to raise questions concerning the origin of the spiral.
And the math that it required.
Hexagons are found in both math and nature. But if I draw a hexagon, that doesn't mean I invented life in a test tube.
The parallels between math and art are well known. Sometimes art is just that - art. A testing and discovery of forms and figures.
the Pythagorean says, "all is number", I say...To all -- please ping me to other topics which are appropriate for the GGG list. Thanks.
- How many finger am I holding up?
- What about letters?
- Must have been a big number that you smoked.
- What's the number for 9-1-1?
New Ice-Core Evidence
Challenges the 1620s age for
the Santorini (Minoan) Eruption
Gregory A. Zielinski, Mark S. Germani
Journal of Archaeological Science
Volume 25, Issue 3
March 1998, Pages 279-289
13 July 1997
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"To find two identical spirals among two cultures of which one was the older and was known to have influenced the other (and perhaps vice versa) is enough to raise questions concerning the origin of the spiral.
And the math that it required."
Maybe they just saw a snail and admired the spiral shape of the shell. No math needed, but it is a perfect expression of the golden mean.