In The Field: Were ancient Minoans centuries ahead of their time?

« To be blunt: All dressed up | Main | Early Andean maize unearthed »

Were ancient Minoans centuries ahead of their time?

Unprecedented mathematical knowledge found in Bronze Age wall paintings.

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

Read the story here.

Posted by Nicola Jones on February 28, 2006 04:50 PM | Permalink

TrackBack

TrackBack URL for this entry:
http://blogs.nature.com/cgi-bin/mt/mt-tb.cgi/275

Listed below are links to weblogs that reference Were ancient Minoans centuries ahead of their time?:

» 1000 Bc from 1000 Bc
Surgery is not a modern phenomenon but has its roots in the ancient world.FILENAME: /var/www/im0/htdocs/Musikmesse04/Content/Pear... [Read More]

Comments

It's not at all complicated if you forget the mathematics.

Take a strip of thick material - for instance, a strip of draught excluder tape. Roll it up from one end. Looked at from the side, it will look exactly like the illustration.

Small children, given crayon and paper, will often draw such spirals freehand - not accurately, of course, but you can clearly see what they are trying to draw. It seems to be an instinctive pattern, like concentric circles. Spirals are also very characteristic of Celtic art, produced across Southern Europe from the Black Sea to Ireland during from 1000 BC until they were almost exterminated by the Romans.

Posted by: Peter Lloyd | February 28, 2006 07:49 PM

Its easy to draw an Achimedes spiral without any knowledge of geometry. All you need is a fat stick with a thread tied to it and a pencil tied to the other end. Fix the position of the stick and, keeping the thread tight, draw a line around the stick with the pencil until the pencil is wound up against the stick.

Posted by: Andrew van der Merwe | February 28, 2006 08:53 PM

This research is an apocalypse! Amazing job! Congratulations to Mr. Papaodysseus and his team!

Posted by: Dimitra Pappa | March 1, 2006 05:59 AM

Dear Sirs:

More to the point, since 48 includes a factor of 3, it would appear the Minoans had a technique that would allow them to trisect an angle. Try that yourself.

Posted by: Brian Johnson | March 1, 2006 06:39 AM

This kind of geometrical figure can be seen on the fingureprints or footprints of human. So, by visualizing theirs, these figures can be drawn.
For example, Buddha footprints.

Posted by: Thet Naing Oo | March 1, 2006 08:02 AM

And there is no chance that it is
simply based on a coil of rope is there...?

Posted by: Spud Gun | March 1, 2006 09:48 AM

Re: Minoan spirals. Have seen them. But they are part of a long tradition. Early art is iconographic - it is not always just decorative - it has meaning. The earliest spirals used in a meaningful and iconographic manner that I know of so far, are the ones found in the excavation of mammoth hunter settlements in Siberia dating to about 25,000 years ago. This and other reconisable iconography from that place and time can be seen later in Europe and the Mediterranean. Also China etc. (Ties in with Y chromosome DNA showing migration from Siberia both east and west). The iconography of spirals is likely to refer to the Upper World, Sky or Heavens.
As to Minoan geometry - they had to have some mathematical knowledge to build their vast multi-storied palaces with plumbing superior to that found anywhere else at the time.

Posted by: Heather Hobden | March 1, 2006 12:56 PM

The relevance of this discovery depends on just one word: precision (or lack of it). Shortly: if the pattern is "precise", ancient Minoans had some deep knowledge of geometry, if not it is just one of the many spirals drawn in ancient times, i.e. nothing special.

Spirals are among the archetypal patterns drawn in all cultures even in prehistorical times, see e.g. those in the Megalithic Passage Tomb of Newgrange (Ireland), that date about 3200 B.C. (by the way, they are aligned with surprising astronomical precision to sunrays on the summer solstice). Here is a nice picture of them:

http://www.knowth.com/newgrange-chamber.htm

So, just drawing some type of spiral is only a trivial thing.

More in detail, whereas some types of spiral (logarithmic spirals) exist in nature, e.g. in mollusc shells (they are easy to code in the DNA, just a constant angle of growth of a protective layer of calcium carbonate), some other don't, and Archimede's spiral is an example of the latter.
Archimede's spiral is the easiest you can imagine by abstract mathematical thinking, since in all its points the radius is directly proportional to the angle of rotation w.r.t. a reference radius. Nevertheless you don't find it in nature: it really requires some human thinking (even based on archetypes); e.g. human thinking can easily prompt to roll up some tape-like object and, when this is done, an Archimede's spiral appears, provided that the object has a constant thickness. The only tape-like object available to ancient Minoans that I can figure out is a rope (not sure anyway), so Spud Gun's hypothesis may be reasonable, but I seriously doubt that such a Minoan rope would allow to draw a precise Archimede's spiral (constant thickness ? held against the wall with the drawing ?).
Methods based on a thread tied around a pole/stick and unwound/wound while drawing produce in the end a "Circle evolving curve" that, although quite close to Archimede's spiral, differs substantially in proximity of the centre; furthermoe, also this method would also require a remarkable level of abstract thinking (much more than "copying a coiled rope") and would be already a quite surprising geometry knowledge.

Finally, if the discovered Archimede's spiral shows a precision that rules out "free drawing", and is distinguished from a circle evolving curve enough to rule out the use of a thread, then the only construction method I can figure out is splitting of the circle as described by the authors, and the discovery is a major one; otherwise it will be just another attraction on a touristic island.
Has anyone read the original article on "Archaeometry" ? I am not enough motivated to subscribe just for reading it.

Posted by: Fabio Corsi | March 1, 2006 02:05 PM

Fascinating story. May change the history of geometry and art.
Well done to the whole contributors.

Posted by: P. M. | March 1, 2006 02:25 PM

SPIRAL :It's as simple as a thethered pen around a stick
and as complicated as concept of God.Like a spiral the universal unwound
from a devine source Energy will all return to concentrate into the same Energy to explode again to create a Big Bang !

Posted by: askkaz | March 1, 2006 04:50 PM

I have actually read the original article, and the evidence is really impressive. In what seems a really good work of pattern recognition they can reject statistically the idea of spirals being of logarithmic or 'circle involute (stick+thether+pen)' at 99,9% confidence, and confirming the linear type at 99,9% confidence. One excerp from the article pinpointing at the accuracy of the paintins: 'We would like to point out that the average distance between the actual and prototype spirals of the first class is between 0.14 and 0.20 cm. If this error is divided by the corresponding spiral radius, then an average percentage error between 1.2% and 1.4% is obtained. Concerning the second prototype spiral class, the average distance is about 0.08 cm, while the corresponding average percentage error is 1.1%.'. Also they report about other geometrical drawings that supports the idea of the artist knowing to construct 16, 32 and 48 polygons.

If this finding pass the scrutiny of other experts, we must have to reconsider the early history of maths. May be the Greeks do not have invented much of the maths attributted to they nowadays, but only put in paper it. It is very exiciting to see that knowledge supposed to begin at middle first millenia BC actually is at last 1000 years older.

Posted by: Carlos Moreno Martinez | March 1, 2006 08:00 PM

While surfing the web, performing my routine search for articles on the Minoan culture, I came across a mention of a similar artifact. The infamous Phaistos Disc has a similar geometric pattern, albeit a bit more crude.

Other instances of this pattern in middle bronze age Minoan ritual artifacts have shown up, but so far, their meaning is unclear.

Posted by: Rebecca | March 2, 2006 12:19 AM

Very very very good

Posted by: ANASTASIA STROUMPOULI | March 2, 2006 07:14 AM

Well done!!! One of the most admirable and fascinating discoveries I have ever read.

Posted by: Kyriaki M. | March 2, 2006 11:55 AM

One example in nature of an Archimedes spiral is that of the millipede when coiled in its threatened pose.

Posted by: Steve Williams | March 8, 2006 05:16 PM

The spirals of this type being drawn, in such ancient times should not come as any big suprise. There way be no mathematics behind it but simply people of the time drawning items in there environment. Just look at simple snail shells, they have the same pattern. Look at a coiled snake. We may be looking to far into this.

Posted by: Josh Steven Gray | March 13, 2006 04:25 PM

Seeing as how I have just begun (re)reading S. Cuomo's 'Ancient Mathematics' (ISBN 0-415-16495-8), this piece has fired a spark. The possible implications are astounding, IF we are indeed not making a mountain of a molehill.

Posted by: Christopher Gazaway | April 1, 2006 12:47 AM

l think very very good article.

Posted by: resimler | May 1, 2007 06:42 PM

Well done!!! One of the most admirable and fascinating discoveries I have ever read.

Posted by: araba | June 4, 2007 01:53 PM

thanks for informations .can i get comment rss for this article ?

Posted by: resim | June 11, 2007 10:34 AM

i had read the original article . it seem very good. thanks.

Posted by: Arabalar | June 11, 2007 10:53 AM

1,000 years earlier ??? very very interesting discovery. Thank you.

Posted by: Güzel Resimler | June 13, 2007 04:09 PM

Well done!!! One of the most admirable and fascinating discoveries I have ever read.

Posted by: resimler | June 17, 2007 12:26 AM

in the full story .. there is some wrong thing about math.
isn't it ?
maybe we can't use math.

Posted by: arabalar | July 3, 2007 03:11 PM

very very good article!'!

Posted by: bebek resimleri | July 10, 2007 01:10 AM

i think very good!!

Posted by: DigitalBoutiques | July 14, 2007 10:21 PM

i think not very good article because very good:)

Posted by: resimler | July 14, 2007 10:24 PM

Good work.Take a strip of thick material - for instance, a strip of draught excluder tape. Roll it up from one end. Looked at from the side, it will look exactly like the illustration.

Posted by: Bilgi | July 21, 2007 11:35 PM

thanks.

Posted by: muhabbet | August 1, 2007 07:45 PM

i think not very good article because very good:)

Posted by: Resim | August 28, 2007 12:03 PM

its nice article .. thanks

Posted by: turkey travel map | August 31, 2007 05:20 PM

Well done!!! One of the most admirable and fascinating discoveries I have ever read.

Pos

Posted by: MSN Resimleri | September 7, 2007 01:34 PM

in the full story .. there is some wrong thing about math.
isn't it ?
maybe we can't use math.

Posted by: Güzel Resimler | September 7, 2007 01:35 PM