Dating Radiocarbon Dating?

Willard F. Libby won the Nobel Prize for Chemistry in 1960 for his part in the development of radiocarbon dating.  The impact of this dating method on archaeology was tremendous.  Colin Renfrew (1979) goes so far as to call the introduction of radiocarbon dating into archaeological research the “Radiocarbon Revolution”.  For such an important event you would think everyone would know exactly when that event occurred.  In researching the prior blog post on the calculation of radiocarbon dates, I noticed that there is no consistent date given for the discovery of the radiocarbon dating method.  The dates people use for the development of radiocarbon dating range from the 1940s into the 1950s.  This imprecision of the dating of the origin of this most important method seems bizarre and a bit ironic.  I decide to settle the matter in my own mind, mainly to satisfy my own curiosity, but also as an examination of the origin of ideas, in which I happen to be very interested.

To get at the date for the origin of radiocarbon dating, we need to know exactly what people mean when they say “origin”.   Few writers offer a specific idea of what they are dating.   Do they mean the first time the idea came into someone’s mind?  Do they mean the first time the basic concepts were demonstrated in the laboratory?  Do they mean the first time the method was successfully tried in the laboratory?  Or do they mean the first time the method and results were published in a professional publication?  The answers to all of these questions are different dates for the origin of radiocarbon dating.  I derived the following chart from R. E. Taylor’s excellent book Radiocarbon Dating, an Archaeological Perspective published in 1987.  Taylor has the best synopsis of the history of radiocarbon dating in chapter 6 of that book.

Year Event Reference
1911 Discovery of cosmic radiation by V. F. Hess Libby 1952
1932 Libby builds the first Geiger-Muller type radiation detector assembled in the United States, and publishes his first official publication. Libby 1932
1933 Development of a  Screen-Wall Counter by Libby Libby 1933, 1934
1934 Radiocarbon produced in the laboratory by Kurie

Forecast of  the existence of natural “cosmic radio-elements” in the atmosphere by Grosse

Kurie 1934

Grosse 1934

1935
1936 Attempt to produce 14C with cyclotron at Berkeley.  This attempt failed because of a mistaken assumption concerning the half-life of 14C.
1937
1938
1939 First published prediction that 13C and 14C formed in nature by cosmic radiation.

Libby and Korff were working separately but along similar lines of research to develop neutron counters.

Libby stated that as soon as he had read Korff’s 1939 paper he thought “that’s carbon dating”.

Korff and Danforth 1939, Korff 1940, and others

Taylor 1987:151

1940 Recognition that 14C half-life was much longer than previously thought. Kamen 1963
1941 Manhattan Project
1942 Manhattan Project
1943 Manhattan Project
1944 Manhattan Project
1945 Manhattan Project
1946 More accurate half-life of 14C by Libby

Libby’s first open acknowledgement of his intention to develop a dating method based on 14C

Libby’s first statement of the basic principles on which 14C dating depend.

Libby 1946

Marlowe 1980

Libby 1946

1947 Libby, Grosse and Anderson conduct initial experiment with biomethane and petromethane to demonstrate the difference in 14C activity and correctness of Libby’s fundamental assumptions.

First published statement that 14C might be used to determine the “ages of various carbonaceous materials”.

Libby 1970

Anderson et. al. 1947a and b.

1948 Improvements of a screen-wall counter specifically for carbon dating by Anderson

First reported 14C age determination on a piece of cypress wood from the tomb of Djoser.

1949 Anderson demonstrates that 14C is relatively constant in the biosphere

Publication of the curve of knowns in “Age determinations by radiocarbon content: checks with samples of known age”

AAA/GSA committee formed to collaborate with Libby

Anderson 1949

Arnold and Libby 1949

1950 First list of provisional 14C dates sent to collaborators.
1951 First list of 14C dates published in Science Arnold and Libby 1951
1952 Libby publishes the first edition of his book, Radiocarbon Dating Libby 1952
1960 Libby wins the Nobel Prize for Chemistry for his work developing the Radiocarbon dating methods

Looking at this table it is apparent that to assign a single year as the “origin” of radiocarbon dating ignores the obvious process of the development of the method.  In fact there was considerable prior art, as they say at the patent office, to even the actual idea of the method, that is not even reflected in this table.  The amount of research into radioactivity before the advent of radiocarbon dating is huge and I will not presume to venture into that material.  More to the point, the discovery in 1911 by V. F. Hess, of cosmic radiation was the key piece of information for future radiocarbon dating researchers.  The knowledge of cosmic radiation lead to speculation of what that radiation did when it encountered earth’s atmosphere and what it produced.  Willard Libby’s own PhD work also laid the foundation for radiocarbon dating through the development of a screen-wall counter in 1933.  It was just such a counter that he later used to derive the first radiocarbon dates.

The year 1939 stands out as the year Libby thought of radiocarbon dating as a possibility.  W. F. Libby and S. A. Korff worked separately but along similar lines to build counters that would be sensitive to neutron radiation.  Korff succeeded in constructing such a counter and was able to demonstrate that thermal neutrons were produced in the upper atmosphere by cosmic radiation.  The neutrons collided with atmospheric nitrogen to form 14C.  This is the basic concept on which radiocarbon dating is based and as soon as Libby read Korff’s 1939 paper stating what he had found, Libby though of the using this for dating.

Between this event and the start of the laboratory development of the radiocarbon dating method, World War II and the Manhattan Project intervened.  Libby participated in the war time effort to separate 235U from 238U for use in America’s atomic bombs but still found time to work on problems related to 14C on the side such as trying to establish the half-life for the isotope.

In 1945 Libby moved to the University of Chicago and started to take up the development of carbon dating.  In 1946, Libby first openly talked about attempting to develop a method to date materials with 14C and published his first suggestion of the principles on which radiocarbon dating is based (That is, the balance in living organisms of 14C and the steady predicable decay of 14C in dead organisms). According to Taylor (1987:152) this paper also introduced the term “radiocarbon” for the first time.  According to L. A. Currie (2004: 186)

Like many of the major advances in science, Radiocarbon Dating was born of Scientific Curiosity. As noted by Libby in his Nobel Lecture, “it had its origin in a study of the possible effects that cosmic rays might have on the earth and on the earth’s atmosphere”. Through intensive study of the cosmic ray and nuclear physics literature, Libby made an important series of deductions, leading to a quantitative prediction of the natural 14C concentration in the living biosphere.

The year 1947 was the year for experimentation to see if Libby’s basic assumptions about 14C were correct.  Moving on from the successes of these experiments, Libby and his colleagues entered what Taylor called a micro-Manhattan project for all of 1948 to develop the 14C dating method.  This year saw the first actual dating of material from an archaeological site and a number of improvements in the screen-wall counter to use in measuring 14C radiation.

The next year, 1949 saw the publication of the “Curve of the Knowns” which demonstrated the close correlation between archaeological materials of known ages and estimated radiocarbon dates.  After this the number of estimated dates rapidly increased and the first list of these dates was sent to archaeologists who were collaborating with Libby in 1950 and these dates there subsequently first found in print in 1951.  The next year Libby published his book Radiocarbon Dating, describing the method and the results to that date.

Based on this information it can be said that Libby and his associates developed the radiocarbon dating method between 1939 and 1952 with key developments, discoveries and events in 1939, 1947, 1948 and 1949.  A case can be made, as people have already done, to fix the date for the practical application of the method as 1948 or 1949.

Colin Renfrew’s statement that radiocarbon dating caused a revolution in archaeology brings to mind Ralph Waldo Emerson’s statement that “Every revolution was first a thought in one man’s mind.”  Using Emerson’s criteria you could just as well make a case that 1939 was the origin of that revolution in the mind of Willard Libby.

Bibliography

Anderson, E. C. (1949). Natural Radiocarbon.  Unpublished Ph.D. dissertation, University of Chicago.

Anderson, E. C., W. F. Libby, S. Weinhouse, A. F. Reid, A. D. Kirshenbaum, and A. V. Grosse (1947a) Radiocarbon from cosmic radiation. Science 105:576.

(1947b) Natural Radiocarbon from cosmic Radiation.  Physical Review 72:931-936

Arnold, J. R.; Libby, W. F.

(1949). “Age Determinations by Radiocarbon Content: Checks with Samples of Known Age”. Science 110 (2869): 678–680

(1951). Radiocarbon Dates.  Science 113:11-113.

Bowman, Sheridan (1990). Interpreting the Past: Radiocarbon Dating. Berkeley: University of California Press.

Currie, L. (2004). “The Remarkable Metrological History of Radiocarbon Dating II”. J. Res. Natl. Inst. Stand. Technol. 109: 185–217.

Grosse, A. V. (1934) An Unknown Radioactivity.  Journal of the American Chemical society 56:1922.

Kamen, M. D. (1962) Early History of Carbon-14. Science 140:584-590.

Korff, S. A. (1940) On the contribution to the ionization at sea-level produced by the newtrons in the cosmic radiation.  Terrestrial Magnetism and atmospheric electricity 45:133-134.

Korff, S. A., and W. E. Danforth (1939) Neutron measurements with boron-trifluoride counters.  Physical Review 55:980.

Kurie, F. N. D. (1934) A New Mode of Disintegration Induced by Neutrons.  Physical Review 45:904-905.

Libby W. F. (1932) Simple Amplifier for Geiger-Muller counters.  Physical Review 42:440-441.

(1933) Radioactivity of ordinary elements, especially Samarium and Neodymium: method of detection.  Unpublished Ph.D. dissertation. University of California, Berkeley.

(1934). Reactivity of Neodynium and Samarium.  Physical Review 46:196.

(1946) Atmospheric Helium three and radiocarbon from cosmic radiation.  Physical Review 69:671-672.

(1952). Radiocarbon Dating. Chicago: University of Chicago Press.

(1970) Radiocarbon Dating.  Philosophical Transactions of the Royal Society of London 269A:1-10.

Marlowe. G. (1980). W. F. Libby and the Archaeologists, 1946-1948.  Radiocarbon 22:1005-1014

Renfrew, Colin. (1979) Before Civilization: The Radiocarbon Revolution and Prehistoric Europe. Cambridge, U.K.: Cambridge University Press.

Taylor R. E. (1987) Radiocarbon Dating An archaeological Perspective.  Academic Press, New York.

Published in: on March 6, 2010 at 8:26 pm  Leave a Comment  
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Calculating Radiocarbon Dates

The most important discovery in archaeology in the 20th century was the discovery that the age of archaeological sites and artifacts could be determined by measuring amounts of carbon-14 they contain.  Here is a quick overview of the way in which such dates are calculated using the carbon-14 method, but first you must endure a little bit of background discussion.

The four most common elements in the universe, by mass, are hydrogen, helium, oxygen and carbon, in that order.  In our atmosphere, carbon comes in three varieties, called isotopes.  These isotopes are Carbon-12 (12C), Carbon-13 (13C) and Carbon-14 (14C).  By far the most abundant (98.93%) of the carbon isotopes on earth is 12C.  Almost all of the remaining 1.07% of carbon on earth is 13C.  This leaves just trace amounts of 14C (1 part per trillion) in the total.

Carbon-14 has its origin, not in carbon but in another element altogether, nitrogen.   Nitrogen constitutes 78% of the earth’s upper atmosphere and of the nitrogen isotopes; nitrogen-14 (14N) constitutes 99.63% of that total.  The earth’s atmosphere is continually bombarded by cosmic ray particles which collide with molecules to produce free neutrons which in turn collide at a “fairly constant rate” with the molecules of 14N.  These collisions break a proton out of the center of the molecule producing 14C and a free proton.

Basically, 14C has two more neutrons than 12C which makes it unstable, eventually the 14C decays by emitting an electron which changes it back to 14N.  The reversion back to 14N takes place at a constant rate measured by the “half-life” of 14C.  Half-life is the time it takes for one half of any sample of 14C to decay to 14N.  Initially the discoverers of the radiocarbon method determined that the half-life of 14C was 5568±30 years.  Since that time the half-life has been more accurately determined to be 5730±40 years.  The initial estimate is more than just an historical note because in order to stay consistent in presenting results, the developers and users of the radiocarbon dating method still use the original 5568±30 half-life in their calculations.

The proportions of 12C, 13C and 14C in our atmosphere are relatively stable and have been relatively stable for a considerable period of time.  All three isotopes of carbon act relatively the same in forming chemical bonds with oxygen to form carbon dioxide.  So when plants absorb carbon dioxide, the amounts of each isotope of carbon in the plant cells remains in basically the same proportion to that in the atmosphere and a steady state within the plant exists as long as the plant is alive.  Animals absorb this carbon in the same proportions by eating plants or eating animals that eat plants.

When a plant or animal dies, the 14C continues to decay but is not replenished.  By measuring the amount of 14C left in the dead organism the amount of time since death can be accurately determined.  At the present time the radiocarbon method can be used to date organic material between 500 and 50,000 years old. Older than 50,000 years the amount of 14C is too small too be accurately measured as shown on the figure below.

Decay curve for C14 showing the activity at one half-life (t/2). The terms "%Modern", or "pmC" and D14C are shown related in this diagram along with the Radiocarbon age in years BP (Before 1950 AD). http://www.c14dating.com/agecalc.html

At the time of death of an organism, the amount of 14C can be represented by y0 (y-zero or better y-not).  The exponential function pictured above can be stated as

y = y0 e-kt, k>0

The rate of decay for radioactive materials is calculated based on their half-life.  This is a constant (k) that does not have anything to do with how much material is being measured or its age.  There is a half-life formula that can be derived from the exponential function above.

1/2 y0 = y0 e-kt

The y0 on each side of the equation cancel to leave:

e-kt = 1/2.

Taking the logarithm of each side:

ln e-kt = ln 1/2

Which reduces to:

-kt = ln 1/2

or

-kt = ln 2

Rearranging this gives the formula for half-life:

k = ln 2/t.

As an example of how this is used let us suppose we have a sample that has 40% of the radioactivity that was present when the organism died.  The half-life formula for 14C is:

k = ln2/5568

Then

0.4 y0 = y0 e-kt

This becomes:

0.4 = e-kt

This becomes:

0.4 = e-ln2/5568t

Taking the logarithm of each side leaves:

ln0.4 = -ln2/5568 t

From this it is easy to calculate the rough age of the material being dated by:

t = -5568 ln0.4/ln2

= approximately 7360 years before the present.

This is a rough age, to arrive at a more refined estimate; the date needs to be calibrated.  The calibration is needed because the amount of cosmic radiation striking the upper atmosphere fluctuates and so the mount of available 14C also fluctuates.  Researchers have identified the magnitude of these fluctuations by comparing 14C dates with tree ring dates.  This has allowed them to formulate an algorithm to calibrate the 14C dates with the appropriate amount of 14C in the atmosphere.  A simple way to calibrate a date is to sign onto the Queens University of Belfast Calib 6.0 on line program, hit the data input menu button and enter 7360 into Radiocarbon Age BP.  Check Enter Data and then hit the Calibrate button.  This will result in the following data and a date with a 95.4% probability of between cal BC 6372- 6084.  As you can see, the calibrated date is significantly older than the raw data obtained above.

RADIOCARBON CALIBRATION PROGRAM*
  CALIB REV6.0.0
Copyright 1986-2010 M Stuiver and PJ Reimer

Sample ID                                                                        Lab Code                                                                        Sample Description (80 chars max)                                               Radiocarbon Age BP   7360 +/-   55                                              Calibration data set: intcal09.14c  # Reimer et al. 2009            % area enclosed  cal AD age ranges   relative area under                                          probability distribution       68.3 (1 sigma) cal BC 6351- 6310          0.214                                        6263- 6204          0.421                                        6192- 6182          0.044                                        6173- 6156          0.078                                        6145- 6101          0.242                  95.4 (2 sigma) cal BC 6372- 6084          1.000

A radiocarbon dating laboratory will of course do all of the calculations for you and present you with the finished dates, probabilities and handy chart as above.  However it is well that anyone actually submitting dates do calculations like this on their own in order to understand how the laboratories arrive at their dates.  In addition, those just reading archaeological reports can profit from an ability to do the above calculations in order to understand the radiocarbon dates of archaeological sites and artifacts.  Those who would like to know more could not go wrong by acquiring the books by Bowman, Libby, Renfrew and Taylor listed below.

Bibliography

Bowman, Sheridan  1990  Interpreting the Past.  Radiocarbon Dating. University of California Press/British Museum

Libby, Willard F.  1965  Radiocarbon Dating. Phoenix Books.  University of Chicago Press, Chicago and London.

Renfrew, Colin 1979 Before Civilization: The Radiocarbon Revolution and Prehistoric Europe. Civilization: The Radiocarbon Revolution and Prehistoric Europe. Cambridge University Press, Cambridge.

Taylor (1987) Radiocarbon Dating: An archaeological perspective. Academic Press, London

Weir, Maurice D., Joel Hass and Frank R. Giordano 2008 Thomas’ Calculus Early Transcendentals, eleventh edition.  Based on the original work by George B. Thomas Jr.  Pearson Addision Wesley Boston.

Wikipedia contributors, “Radiocarbon dating,” Wikipedia, The Free Encyclopedia, http://en.wikipedia.org/w/index.php?title=Radiocarbon_dating&oldid=343525845 (accessed February 24, 2010).

Published in: on February 27, 2010 at 4:51 am  Leave a Comment  
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Book Review: Roman Britain

The University of Oxford, Department of Continuing Education has an online course entitled “Exploring Roman Britain”.   The text for this course is Roman Britain by Martin Millett.  I was interested in taking this course, but other interests have intervened, so I purchased the book to read on my own.  Those living in the UK would profit immensely by taking the course, as the resident cost for the extra instruction is quite reasonable.  For those who, for one reason or another, cannot take the course, this book provides a valuable introduction to a fascinating period in the history of Britain.

Roman Britain is published by B. T. Batsford Ltd in their English Heritage series.  The author first published this book in 1995 and after some revisions published the revised edition in 2005.  I am reviewing the revised edition in paperback form that has a $22.95 retail price in the US.

The author is impeccably qualified to write a book like this one concerning the Roman period in British history.  He is a professor of Classical Archaeology at the University of Cambridge and a Fellow of Fitzwilliam College.  In addition, he has extensive previous experience in teaching at other universities and in archaeological fieldwork, not only in Britain but also in Spain and Italy.

The book has 144 pages of heavy good quality paper and measures 7.5 by 9.75 inches, which has a comfortable feel in the hand while reading.  Inside the book the text is laid out in single 3.5 inch columns that allow plenty of space for illustrations, photographs and detailed captions.  The publisher should be commended for producing a paperback with quality printing and materials for a reasonable price that does justice to a book with the imprint of English Heritage.  I do have a quibble about the color in the photographs.  The photographs appears slightly washed out similar to what happens to old slide film.  I cannot decide if the color problem is the fault of the originals or the printing reproduction.

The text is divided into a detailed introduction and six chapters.  Millett’s approach is to interpret the history of Roman Britain through the archaeological record.  This has several advantages.  First the archaeological evidence of the Roman period in Britain is extensive and one of the best preserved periods in British history.  Second the archival records of this period are, for various reasons, spotty, written by people far distant from Britain or missing all together.  By approaching the topic through the archaeological record, Millett provides a wonderful illustration of the explanatory power of archaeological data in general.

In the introduction, Millett presents a table of the main historical texts concerning Roman Britain and this provides a timeline from Julius Caesar’s expeditions into Britain in 55 BC and 54 BC to St Germanus’ possible last visit to Britain in AD 435-7.  If you lose your way through the book you can always refer to this table to find where what you’re reading fits into the overall chronology of things.  The introduction also contains a series of maps that show the Roman campaigns in Britain and the distribution of many of the sites associated with them.  Finally, Millett discusses the character of the archaeological record for the Roman period in Britain.

The first chapter discusses the peoples of Britain and divides them up into geographical regions: Southern and Eastern England; Wales, Western and Northern England; Southern and Central Scotland; and finally Northern Scotland and Ireland.  Millett describes the population as a diverse people.

There was no single communal identity that unified those living in these islands.  The concept of ‘Britons’ was imposed by Mediterranean peoples in the way modern Western society has conflated all indigenous South Americans as ‘Indians’.  Page 23

After this discussion of the peoples of each area the author reviews the attempts at estimating a population figure from the limited data available and arrives at an estimate of 3.6 million for the whole of the British Isles during the Roman period.  While he admits this is a rough estimate it does put the periods’ history in better context for me to have an idea of the size of the population involved.

At the end of this first chapter Millett describes the agriculture and the manufacturing and commerce of the period.  This amounts to seven short pages.  Here is my only significant disappointment with this book.  Full disclosure as they say in the stocks and bonds industry, I should reveal that my interest in archaeology is in the history of technology and I would therefore be most interested in an involved discussion of the Roman influence on the technology of Britain.  Millett’s interests lie elsewhere and it would be unfair to criticize his book because he did not follow my interests.  But I will nevertheless point out to those interested in a detailed discussion of the technology of the Roman period, this is not the book in which you will find it.

In the second chapter Millett discusses the way in which the Roman imperial system exerted its authority over Britain.  In this system Rome empowered indigenous leaders to rule small city states and allow the central government to maintain a relatively small occupying force.  The trappings of the imperial system engendered administrative centers and thus varying degrees of urbanization in an otherwise largely rural countryside.  In this discussion Millett distinguishes between the administrative towns as public towns, small towns without administrative roles and rural settlements which included the Roman villas adopted by many locals as displays of power, wealth and prestige.

Chapter three covers the character of the Roman civil administration and the occupying army in Britain.  Chapters four and five examine the Celtic art traditions and their Romanization and the impact of the Roman conquest on the religion of both the native inhabitants and the conquerors.  Finally, chapter six discusses the end of Roman rule in Britain and the gradual invasion of the Saxons.

The book ends with a list of places to visit including museums and archaeological sites and a list of books for further reading.  This is followed by a short general glossary and an index.  I can’t help but think that Millett did not have a hand in putting together the glossary as it contains the statement “that the 14C in living organisms decays to 12C after their death at a known rate”.  This is not a mistake a seasoned professional would make as it is well known that 14C decays to 14N.

Martin Millett covers a lot of ground both figuratively and geographically in this short book and he does it with a clear, unpretentious and informed manner.  This book is well worth adding to your library.  If you are thinking of visiting the UK with the intention of visiting some Roman sites, by all means read this book first.  The pleasure of your experience will be greatly increased by the reading of this volume.

Published in: on February 21, 2010 at 11:47 pm  Leave a Comment  
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Three Reasons 2012 will not be the End of the World

Presented by Columbia Pictures and Sony Pictures International

According to some people, who base their belief on the Maya calendar, the world will end on December 21, 2012.  We have heard quite a bit about this impending end of the world because of the 2009 disaster movie aptly named 2012.  Since the movie came out the press has lost some interest.  This probably occurred because 2008 and 2009 were such back to back financial disasters; people have had to contend with real problems.   Never fear, the hustlers, the quick buck hucksters and the publicity seekers among us will be stepping up their game in the near future (I make this prediction based on the alignment of certain astrological signs in my cat’s food with his water dish).   The DVD of the movie will be released soon so I thought I would get my shot across their bow before they open up on us in earnest.

Think back little over 10 years to the Chicken Little disturbance that these same people made about the supposed Y2K bug in computers that was to bring on the Armageddon.  The survivalists were in full flower and it was both funny and sad when January 1, 2000 rolled around and nothing what-so-ever happened.  Some people were left with expensive drafty bunkers and mounds of freeze dried meatloaf.  You would think everyone would have learned a lesson.  However, as P. T. Barnum never really said, “There’s a sucker born every minute” and there are always people on the lookout to take advantage of them.  Here are three reasons not to listen to them.

(1) The Maya Calendars are Cyclic. I did say calendars with an “s”.  People say that the Maya calendar ends on December 21, 2012.  Which one?  The Maya had a number of calendars and the feature that they all shared is that they were cyclic.  They repeated themselves.  They repeated themselves.  They repeated themselves.

The Mayan calendars are true wonders of the ancient world which apparently had their origin about 2600 years ago among earlier Mesoamerican civilizations.  While other groups such as the Aztecs also inherited these calendars, it was the Maya who extended them to the highest art/science.  One interesting feature of the calendars is the fact that they contained the concept of zero, a true intellectual breakthrough.

The calendars were complex affairs but based on the simple fact that people have 20 fingers and toes rather than our system of 10 based on just our fingers.  Their solar calendar had cycles consisting of 20 days (the end cycle being the exception was only 5 days long to bring the total for each year to 365 days.  Years were grouped into cycles of 20 which were intern grouped into 20 by 20 cycles of 400 years called baktuns.    This solar calendar regulated mundane activities such as administrative and  agricultural events.

The Maya also divided time into a number of other cycles, the most important being the 260 day sacred round or tzolkin for religious events.  The sacred round was a cycle of thirteen numbers (13 being a sacred number among the Maya) that worked like clock gears with twenty day names (20 being another sacred number).  These gears meshed with the solar calendar mentioned above with the cycle of 365 days and based on the solar year.  National Geographic’s depiction of this system gives us a good view of the complexity and beauty of these intermeshing systems.  The interlocking wheels of numbers and named days from the sacred round and the solar round produces a 52 year cycle in which no two names reoccur together in any 18,980 day cycle or Calendar Round.

The Calendar Round and How it Worked (after National Geographic, December 1975, in Schele and Freidel 1990:80)

Other Mesoamerican peoples such as the Aztecs, adopted this 52 year cycle as their highest system.  Sylvanus Morley 1968 page 234 states that

The Aztecs believed that the world would come to an end at the close of one of these 52-year periods, and on the last night of the xiuhmolpilli, the population of Tenochtitlan (Mexico City) withdrew to the hills surrounding the city to await the dawn.  When the sun rose on the morning, there was general rejoicing, the Sacred Fire was rekindled, the houses were cleaned and set in order, and the business of life was resumed.  The gods had given mankind another 52-year lease on life.

As we know the world never did end at any of these 52-year cycles, but I am sure the threat of such an end kept many of the calendar keepers and priests in well compensated jobs, cushy accommodations and powerful positions.  Nothing ever really changes in human relations.

(2) The Long Count Calendar does not end

The Maya had a longer view of time than the Aztecs with the use of another calendar now called the Long Count.  The Maya began the Long Count calendar based on a ballpark estimate of when the earth was created, which was August 11, 3114 BC.  This calendar had a 360 day year divided into eighteen 20 day months and these 18 month years were turn divided into 20 year groups and these in their turn were again divided into further groups of 20 and so on and on, with no end in sight.  This table from Sylvanus Morley 1969 page 237 shows the divisions of the Long Count system.  The divisions below baktuns were actually rarely ever used and it is no mystery why, none have ever occurred.

Divisions of Time in the Maya System

20 kins (days) 1 uinal 20 days
18 uinals 1 tun 360 days
20 tuns 1 katun 7,200 days
20 katuns 1 baktun 144,000 days
20 baktuns 1 pictun 2,880,000 days
20 pictuns 1 calabtun 57,600,000 days
20 calabtun 1 kichiltun 1,152,000,000 days
20 kinchiltuns 1 alautun 23,040,000,000 days

It doesn’t take Robert Feynman to see that there is a pattern here.  Outside of the 18 uinals that are limited by our solar year, the Maya kept to their sacred 20 divisions.  It is curious that today Mesoamerican archaeologists are somewhat divided as to when the Long Count calendar cycle resets to zero.  Some think the cycle resets at 13 baktuns and others, for obvious reasons, think that the calendar runs to 20 baktuns as shown in the above table (which would be approximately 4770 AD).  It is the thirteenth baktun that ends on December 21, 2012.

Among the scholars that think the calendar cycle ends with 13 baktuns are Linda Schele and David Freidel 1990 page 82.  They state that (using December 23 instead of December 21)

In the near future Maya time also approaches one of its great benchmarks.  December 23, 2012 will be 13.0.0.0.0, the day when the 13 baktuns will end and the Long Count cycles return to the symmetry of the beginning.

It is important to note they also state that

The Maya, however, did not conceive this to be the end of this creation, as many have suggested.  Pacal, the great King of Palenque, predicted in his inscriptions that the eightieth Calendar Round anniversary of his accession will be celebrated eight days after the first eight-thousand-year cycle in the Maya calendar ends.  In our time system, this cycle will end on October 15, 4772.

In other words, which ever side is correct on the end of the Long Count calendar, time goes cycling on and on forever.

(3) The Maya are not worried! Yes the Maya still exist and still live in Central America as their ancestors did for millennia.  You would think that if any one would be worried about the end of the world, as predicted by the Maya calendar, it would be the Maya themselves.  But this is not the case at all.  The New Age prophets of doom are outsiders.  Funny they know more about the Maya than the Maya do themselves.  This New Age knowledge is supposed to be about something that is as fundamental as the end of everything!  I am not buying this at all and neither are the Maya.  I can just imagine them saying to each other that the New Age hysteria is “So Aztec”!

P. T. Barnum really did say,   “Without promotion something terrible happens… Nothing!”  The modern day sharps and city slickers know this just as well as Barnum and will be promoting 2012 so that they can insure that nothing terrible, like nothing, happens to them.

Sources:

Morley, Sylvanus G.  (Revised by George W. Brainerd)  1968  The Ancient Maya.  Stanford University Press.  Stanford, California

Schele, Linda and David Freidel  1990  A Forest of Kings, The Untold Story of the Ancient Maya.  William Morrow.  New York.

Published in: on February 8, 2010 at 2:56 am  Comments (1)  
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Previously on Lost: Tawaret

I make no secret of the fact that I am totally addicted to the television program LOST.  I am as curious as the next viewer about how this final season will play out.  One of the intriguing mysteries is the gigantic statue of Tawaret that at the current show time survives only as a foot.  It will be interesting to see how the writers explain the meaning of the statue without beating us over the head with ancient Egyptian mythology.

Tawaret was an Egyptian goddess that protected women during pregnancy and childbirth.  She was also associated with the annual flooding of the Nile and the renewal of the fertility of the farm lands along the banks of the river.  There are obvious connections with Tawaret in the story line of the series involving the difficulties of pregnant women on the Island.  I am hoping that the writers leave some of these things for the views to figure out.  Another aspect of Tawaret is that she was known as the one who restrained the evil god Set from doing fowl deeds.  The storyline might be running in this direction considering the fellow living in the foot of the statue and the other man who wishes to kill him.

Newsweek, in this week’s edition, may have hit the right attitude when they stated that “it’s more fun when you stop trying to figure it out and just roll with it”.

Published in: on January 26, 2010 at 10:39 pm  Leave a Comment  
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Free Read: The British Museum’s Online Publications

Free online research papers are available on The British Museum Web Site.  These include a wide variety of publications involving museum procedures, artifact analysis and field studies.  A list of these research publications are on this publications page.  An example that should interest many is:

Cleaning and Controversy: the Parthenon sculptures 1811-1939

This research paper concerns the sculptures taken by Lord Elgin from the Parthenon in 1811 and given to The British Museum.  The paper is not about the history of the sculptures but about the controversial cleaning of the sculptures that occurred in the 1930s.  To the museums credit they have attempted to lay out the whole controversy for public scrutiny.  It is well worth the read to get a fuller understanding of all of the controversies surrounding these important historical treasures.  The introduction states:

In the late 1930s the art dealer Lord Duveen offered the Trustees of The British Museum a purpose-built gallery to house the ‘Elgin Marbles’.  In 1937-8, while the sculptures of the Parthenon were being prepared for installation in this new gallery, a controversial cleaning of some of the sculptures took place.  A major press scandal ensued. . . Fascinated by the scandal of it, people have tended to make up their own version of its consequences.

In another section of The British Museum site they list the British Museum Technical Research Bulletins.

One of these papers concerns the iconic cat sculpture known as the “Gayer-Anderson cat” and provides a lot of insight into the history of this wonderful artifact.

A new look at an old cat: a technical investigation of the Gayer-Anderson cat

The abstract of this paper states that:

The Gayer-Anderson cat is one of the best-known objects in the collections of the British Museum’s Department of Ancient Egypt and Sudan. It is a life-size cast copper alloy figure of a cat sitting upright, probably dating to the Egyptian Late Period (around 600 bc). Despite the iconic nature of the sculpture no scientific or technical examination had been made of the piece until recently. This article describes a full technical investigation within the context of the archaeological and religious significance of the object. This revealed that the figure, although now repaired, had suffered an unexpected level of damage in the past. It also showed evidence of the original manufacturing techniques used. Indications were also found of the possible original appearance of the object, including the use of polychromy.

Another section of the site contains the British Museum Studies in Ancient Egypt and Sudan (BMSAES)

An example of one of these studies is the very interesting  One accident too many?

This study briefly describes the injuries observed on the skeletal remains of a man who lived during the Kerma Period in ancient Sudan and offers explanations for the discrete injuries based on parallels discussed in clinical literature, particularly literature from non-industrialized regions.

Still another example from this same series is:

Pottery production at Hierakonpolis during the Naqada II period: Toward a reconstruction of the firing technique

Recent excavations at HK11C Operation B at Hierakonpolis have revealed remains of pit-kilns dated to the Naqada II period, in which mainly straw-tempered modeled rim jars were produced. This discovery is valuable not only for the new data it presents for the study of Predynastic pottery, but also for providing an opportunity to reconsider ancient pottery production techniques. To evaluate the firing technique used in the HK11C kilns, an integrated analysis was conducted, which included ICP-AES, SEM, and in-depth observations of the surface stains on pottery from Hierakonpolis.

These are just a few of the publications available, explore the site on your own to find what strikes your fancy!

Published in: on January 24, 2010 at 8:25 pm  Leave a Comment  
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Four Reasons Why An Archaeologist Should Examine District 9

Archaeology of the present might seem like a bizarre undertaking, but it provides a unique view of current events and human behavior; often hidden or overlooked by the press, public and other scientific disciplines.  James Symonds (i) recently wrote a special plea for archaeologists to communicate to the public and the press the unique perspective that contemporary archaeology can bring to the study of human behavior.  He cites the example of Lisa Hill digging a contemporary campsite in England.  Hill (ii) stated that contemporary archaeology,

“. . .is something to do with actually engaging with the present from a different perspective. There are things you can learn by excavating and applying archaeological techniques that you can’t get from photographs or oral history. It is definitely worth doing.”

I have thought of many different examples that illustrate the useful perspective of contemporary archaeology, but one that struck me as being both persuasive and fun is in the realm of science fiction.

If you have seen the recent movie District 9 (iii), you know that in the movie an alien spaceship arrived above Johannesburg, South Africa in 1982.  The spaceship contained about one million intelligent (kind of) arthropod-like bipeds.  The leadership of this group died in some sort of epidemic and the remnants of this alien population were given asylum on earth.  The aliens have a “hive mentality” and the population that remains consists of what would be analogous to worker bees without the queen.  After some conflict with local South Africans the aliens were confined to a camp inside Johannesburg called District 9 and their management was turned over to a company called Multinational United (MNU).  The time period for the start of the movie is 20 years later in 2002 when it is decided to move the now 1.8 million aliens 200 kilometers north, away from any human population center, to a new camp called District 10.  At the end of the movie, in 2010, the relocation of the aliens has been completed and the alien population is now 2.5 million.

The movie shows a number of people who have been employed to study the aliens.  There are biologists, military experts and management functionaries.  It is evident from the movie that MNU knows relatively little about how the aliens actually lived in District 9.  A through survey of the area before it is burned would answer some of the pressing questions facing MNU about the aliens.  Here are four reasons why MNU should hire at least one archaeologist before destroying what is left of District 9 (and making a sequel movie to District 9).

(1) Population:  When the aliens arrived in 1982 there were one million, in 2002 there were 1.8 million and now 8 years later there are 2.5 million.  This represents a troubling acceleration in population growth.  This acceleration is occurring in spite of the fact that MNU conducts an aggressive program to destroy the alien nurseries.  How is this possible?  The aliens are reproducing like a typical invasive species and MNU needs to understand their reproduction cycle if they are going to cope with this population explosion.  An archaeologist could help identifying these characteristics by mapping their activity areas in the portion of the district still intact.  Where are their nurseries and how it is possible with the strict population controls that their numbers are dramatically increasing?

(2) Social organization: The movie informed us that the leadership died before the spaceship got to earth, but the aerial view of part of District 9 clearly shows order.  Rectangular layout and parallel streets shows some order to the dwellings.  How do the aliens arrive at this order without leaders?  What is this hive mentality?  An archaeologist studying the layout of the settlement could identify patterns that would provide insight into the social organization of the aliens even without their leaders.

(3) Technology: MNU has studied the weaponry of the aliens extensively but ignored the other evidence of the alien’s technology.  The alien’s ability to build their habitations in District 9 out of scraps shows a good deal of adaptability.  But this is offset to some extent by some curious signs that the aliens have some serious limitations.  For example, the photograph above shows the typical size of an alien and the typical size of the alien build doorway.  The alien is 2 feet taller than humans but builds their doorways to human scale.  What is going on?  Are they blindly mimicking how humans build their houses, without imagination using materials they scavenge or have they never lived in such dwellings and have no concept of building them to their scale?  A through survey of the alien constructed buildings would provide MNU with a clearer picture of their technological capabilities.

(4) Diet and Economy: The aliens were housed in District 9 from 1982 until 2002 and left behind a mountain of debris that can provide answers to a number of questions that have so far eluded the MNU and government officials alike.  For example, the alien preference for canned cat food can be easily mapped.  How much did they consume?  Where did it come from?  What portion of their diet did the cat food represent?

These are just four of the questions that MNU needs to be asking and the answers can be partly obtained through the work of an archaeologist.  MNU I await your call.

Published in: on January 19, 2010 at 6:18 pm  Leave a Comment  
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What? Slaves didn’t build pyramids! Now what do we do with all of these stupid posters?

Egyptian archaeology workers ferrying sand in trolleys on rail tracks in front of the Great Pyramid, in Giza, Egypt, Monday, Jan. 11, 2010. Egyptian archaeologists discovered a new set of tombs belonging to the workers who built the great pyramids, shedding light on how the laborers lived and ate more than 4,000 years ago, the antiquities department said. (AP Photo/Amr Nabil)

The latest news from Egypt:  Slaves did not build the Pyramids!(i) This sounds like a story that NBC’s Chuck Todd twittered about recently concerning the Mark McGwire steroid scandal.

Other McGwire-related breaking news items today: Sun rises in the east; Earth is round; the alphabet contains 26 letters; dog bites man.

Did someone really believe that slaves built the pyramids?  Sure some people take the Hollywood film history as gospel, but people who have anything beyond a cursory acquaintance with the history of Egypt would not have made this mistake.  The news did trace the story back to Herodotus who visited the pyramids about thousand years after their construction.

The ancient Greek historian Herodotus once described the pyramid builders as slaves, creating what Egyptologists say is a myth later propagated by Hollywood films.

My opinion is that Herodotus was lead astray by one of the ubiquitous Egyptian guides that make stuff up as they go, as they do to this day.

Anyway, there are all of these posters on Google that mimic the awful management posters you will encounter in a the typical cubical office.  These mimics use the pyramids as their photographic example.  Personally, I hate the original posters because they are lame exhortations to the workers to slave on for their management masters.  I guess I will have to find some others to use on my office walls.  None-the-less these are still classic, for example how about this one.

Or take this one that is a little more subtle.

Looking at it from another angle, you can define slavery in fairly broad terms so the posters may not be far wrong after all.  Take a look at this cartoon along these lines.

Update: So if slaves did not build the pyramids, who did?  Probably you will not get a more suscinct explanation than the one in Encyclopedia of the Archaeology of Ancient Egypt Compiled and edited by Kathryn A. Bard and published in 1999 (page 909).  When discussing the construction of the pyramids she states that:

The sheer size of the royal pyramid complexes required large numbers of unskilled as well as skilled laborers. In the absence of large-scale slavery in the Old Kingdom, a system of corvée labor developed in which all citizens could be conscripted for part of the year. Ancient Egypt was an agrarian society and peasant farmers, who made up the bulk of its population, were the majority of the conscripted laborers. During the Nile’s annual inundation when no farming could be done, farmers were put to work. Housing, clothing and feeding of the work teams was provided by the state, perhaps utilizing women as weavers and food preparers, as later records show that women could also be conscripted. Hardly anyone seems to have been exempt from the corvée system, including priests and high officials, who might be pressed to act as overseers of those repairing dikes, building fortifications, or moving colossal stone blocks and carved monuments. Well-to-do Egyptians were buried with so-called servant statues, which provided proxies to do the work. Possibly this indicates that many rich Egyptians bought out of the corvée by hiring a substitute, or giving a bribe.

Published in: on January 14, 2010 at 5:55 pm  Leave a Comment  
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Figuring the Volume of the Great Pyramid and Similar Structures

I was looking in Wikipedia’s entry for the Great Pyramid of Giza(i) which states that the volume of this pyramid is approximately 2.5 million cubic meters.  It got me thinking, now how in the world did they figure this out?  I have come to the conclusion that they used integral calculus.  They know that the pyramid’s base is a nice square measuring 230.37 meters on a side.  The height of the pyramid is known to be 146.478 meters.  So to arrive at a solution for the volume you could make the height the x-axis for the problem.  The limits of integration would therefore be x = 0 and x = 146.478.  The idea of integration is that you slice the pyramid into an infinite number of squares, in this case from top to bottom and compute the area of each square.

The area of the base square is 230.37 meters squared or 53070.3369 square meters.  To restate this as a formula to compute the all of the squares in the pyramid, you need to divide the 230.37m. base by 146.478m. height to obtain 1.57272764511 ratio base to height.  You can then use this in a formula (1.57272764511x)2 squared for each of the pyramid slices.  Taking the integral (you can use a calculator like the TI-89 or just add one to the exponent, making it 3, and then multiply by the reciprocal, which would be 1/3 ) of this you arrive at .824490748564 x3.  Plugging in 146.478 for x gives you 2,591,212.26949 cubic meters.  Close to Wikipedia’s approximation.

The Great Pyramid from space by the GeoEye-1 satellite from PopSci

Popular Science 2009

I have been thinking of all kinds of uses this process of integration could have, where have I been all of this time?

Published in: on January 13, 2010 at 1:18 am  Leave a Comment  
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A Bailout for Tyrannosaurus?

Fossil skull of Proceratosaurus, looked after in the collections of London's Natural History Museum. It is the oldest-known relative of T. rex and it lived 165 million years ago. (Credit: Image courtesy of Natural History Museum of London) from ScienceDaily

ScienceDaily(i) has a article about a fossil named Proceratosaurus found almost 100 years ago but only recently recognized as the oldest known relative of the Tyrannosauridae (that eventually included the well known Tyrannosaurus rex). This got me thinking about the current state of curation in museums in the United States.  There is a huge backlog of archaeological, historical and paleontological material (always has been) that needs to be accessioned, cataloged and inventoried according to Office of Inspector General Museum Collections: Accountability and Preservation Report(ii).  There is no doubt that many more things like Proceratosaurus sit in boxes and on shelves in museums waiting to be discovered.

Museum jobs are typically well paid and while I have no numbers, there are certainly professionals who are now unemployed that could be put to work clearing away these accessioning and cataloging backlogs.  I have unemployed neighbors on both sides of me and on down the street both ways.  The unemployment level is said to be 10% but the real unemployment level that includes those who have given up looking for work is much higher.  We need a jobs bill.  A jobs bill that includes museum collection management would first and foremost help unemployed professionals in many fields and would second help preserve the collections we have all over the United States.   Who knows what treasures we will find by sending these now unemployed explorers into our national attics?

Published in: on January 9, 2010 at 7:07 pm  Leave a Comment  
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