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Prehistoric Relics Indicating Counting / Mathematical Notation

Mighty_Emperor

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Rather techncial:

Here is Sequence A100000 (this will take a moment):

ID Number:
A100000

URL:
http://www.research.att.com/projects/OEIS?Anum=A100000

Sequence:
3,6,4,8,10,5,5,7

Name:
Middle column of marks found on the oldest object with logical
carvings, the 22000-year-old Ishango bone from the Congo.

Comments:
The other two columns on the rod are: 11, 13, 17, 19 and 11, 21, 19, 9. See
"Deciphering the Bone" at the first Brussels Museum for Natural
Sciences link.
This appears to be the oldest known mathematical object.
"The bone owes its name to the site where it was discovered. Ishango is in
the Congo, 15 km from of the Equator, on the bank of the Edward lake. This
large African lake, one of the sources of the Nile, is 77 km long and 42 km
wide. The area is close to the Virunga National Park and the
Congo-Uganda border." - Brussels Museum for Natural Sciences

References
G. G. Joseph, The Crest of the Peacock: Non-European Roots of
Mathematics, Penguin Books, London, 1992.
D. Olivastro, Ancient Puzzles, Chap. 1 "The First Etches" pp 7-30
Bantam Books NY 1993.
V. Pletser and D. Huylebrouck, The Ishango artifact: the missing base
12 link, Proc. Katachi Univ. Symmetry Congress (KUS2), Paper C11,
Tsukuba Univ., Japan, 18 Nov. 1999; Forma 14-4, 339-346.
Claudia Zaslavsky, Africa Counts, Lawrence Hill Books, New York,
1973.

Links:
Brussels Museum for Natural Sciences, The Ishango Bone Exhibition.
Brussels Museum for Natural Sciences, The Ishango Bone.
Free University of Brussels, Ishango site
D. Huylebrouck, About the Ishango Artifact.

See also:
Sequence in context: A090963 A093064 A004546 this_sequence A083682
A021278 A083349
Adjacent sequences: A099997 A099998 A099999 this_sequence A100001
A100002 A100003

Keywords:
fini,full,nonn,nice

Offset:
1

Author(s):
Dirk Huylebrouck (Huylebrouck(AT)gmail.com), Nov 07 2004

There have been a lot of claims for some of these early incised bones like the Tai plaque:

Marshack, A. (1991) The Taï plaque and calendrical notation in the Upper Paleolithic. Cambridge Archaeological Journal. 1 (1). 25 - 61.

Here is an message from Marshack I found:

Subject: [HM] notched bone
Author: Alexander Marshack <[email protected]>
Date: Mon, 23 Nov 1998 14:48:43 -0500 (EST)

Julio Gonzalez Cabillon:

The incised bone from Ishango, Africa, was merely the first
example of early notation studied and published. This was fully thirty
years ago. Since then a series of such "notational" forms of record
-keeping have been published from far early dates.

I suggest your correspondents check:
Alexander Marshack, THE ROOTS OF CIVILIZATION, 1991, New York:
Moyer Bell Ltd.
Alexander Marshack, The Tai Plaque and Calendrical Notation in
the Upper Palaeolithic, CAMBRIDGE ARCHAEOLOGICAL JOURNAL, Vol 1, No 1,
1991.
Alexander Marshack, 1997. Paleolithic Image Making and Symbolling
in Europe and the Middle East: A Comparative Review. In BEYOND ART:
PLEISTOCENE IMAGE AND SYMBOL. Conkey, Soffer, Jablonski (eds.) California
Academy of Sciences. Via University of California Press.

Formal writing begins with record keeping of the developing
agricultural cultures in the Near East, and then develops in other
agricultural cultures around the world. But pre-agricultural
record-keeping and notations were of a different type, and were not
"linguistic" or arithmetic in the same manner. They were records of
elapsed time, of the periodicities observed in nature, including the
months and seasons. There is evidence for a capacity for counting, but
not of a formal arithmetical system for summing and counting large sums.
There is a huge developing literature on the capacity for non-arithmetical
counting and summing among early cultures, human children, and even
primates. This research has been appearing in a number of disciplines.
My own work has documented such forms of pre-writing, pre-arithmetical
forms of notation and record keeping for almost three decades. The only
systematic effort to disprove these studies, by F. D'Errico, of France,
recently admitted that his more recent studies had confirmed the presence of notation in the Upper Paleolithic, though he does not as yet know why they should have been kept or what the mode of notation consists of.

I suggest that your readers read Stanislas Dehaene, 1997, THE
NUMBER SENSE: HOW THE MIND CREATES MATHEMATICS, Oxford University Press.

Dehaene discusses the neurological and ontological basis for numeracy,
whether or not there is a system of arithmetical counting. I would be
shy of accepting any presumptions about early record-keeping or writing
by those who have not studied the materials and problems at first hand.
The problem of writing, like the problem of language origins, is
extraordinarily complex and should not be left to assumption and
presumption.

Let me know if there are more questions.
Alexander Marshack

Source
 
Some more links for the Ishango bone:

http://www.math.buffalo.edu/mad/Ancient ... hango.html

naturalsciences.be/expo/ishango/en/
Link is dead. This very nice presentation can be accessed via the Wayback Machine:
https://web.archive.org/web/20041228061136/https://www.naturalsciences.be/expo/ishango/en/


http://primes.utm.edu/glossary/page.php ... shangoBone

http://mathworld.wolfram.com/IshangoBone.html

maths.ex.ac.uk/~mwatkins/isoc/african.htm
Link is dead. The MIA webpage can be accessed via the Wayback Machine:
https://web.archive.org/web/20050308231803/http://www.maths.ex.ac.uk/~mwatkins/isoc/african.htm


Someone has even proposed sending the Ishango bone into space (site now gone so Web Archive link provided). Actually the guys site has mvoed here:

etopia.sintlucas.be/~dhuylebrouc ... go_web.htm
Link is dead. Use the Web Archive link cited above.


Although he no longer seems to be suggesting we should send it into space - which is a pity as I like the idea.
 
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