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== Cautionary tales ==
== Cautionary tales ==
Mathematician Olivier Keller, warns against the urge to project our modern culture of viewing numbers everywhere onto the Ishango bone.<ref name=":3" /> Keller exclaims that this practice encourages observers to negate and possibly ignore alternative symbolic materials, those which are present in a range of media (on human remains, stones and cave art) from the Upper Paleolithic era and beyond which also deserve equitable investigation.<ref name=":3" />
While it is exciting to attempt to understand the cultural significance behind this artifact, it is vital to not become wrapped up in dubious hypotheses. Mathematician Olivier Keller, warns against the urge to project our modern culture of viewing numbers everywhere onto the Ishango bone.<ref name=":3" /> Keller exclaims that this practice encourages observers to negate and possibly ignore alternative symbolic materials, those which are present in a range of media (on human remains, stones and cave art) from the Upper Paleolithic era and beyond which also deserve equitable investigation.<ref name=":3" />
Mathematicians Vladmir Pletser and Dirk Huylebrouk, in an analysis responding to Keller, argued that the evidence supports the bone's status as a mathematical artifact.<ref name="PletserandHuylebrouk2">{{cite web |last1=Pletser |first1=Vladimir |last2=Huylebrouck |first2=Dirk |year=2016 |title=Contradictions and narrowness of views in "The fables of Ishango, or the irresistible temptation of mathematical fiction", answers and updates |url=https://arxiv.org/pdf/1607.00860.pdf |eprint=1607.00860}}</ref>


George Joseph, author of "The Crest of the Peacock: Non-European Roots of Mathematics" discredits the simultaneous astrological and computational interpretations of the bone, stating that "a single bone may well collapse under the heavy weight of conjectures piled onto it."<ref>Joseph, George (2011). ''The Crest of the Peacock: Non-European Roots of Mathematics''. Princeton University Press. p. 34.</ref> Keller and Joseph unanimously assert that far-fetched speculations such as these hinder valid research efforts and make light of significant archaeological discoveries.
Dirk Huylebrouck in a review of the research on the object, favors the idea that the Ishango Bone had some advanced mathematical use, stating that "Whatever the interpretation, the patterns surely show the bone was more than a simple tally stick." But also remarks that "to credit the computational and astronomical reading simultaneously would be far-fetched", quoting mathematician George Joseph, who stated that "a single bone may well collapse under the heavy weight of conjectures piled onto it."<ref name=":2" /> Similarly, George Joseph, in "The Crest of the Peacock: Non-European Roots of Mathematics" also stated that "the Ishango bone was "more than a simple tally." And that "Certain underlying numerical patterns may be observed within each of the rows marked." But, regarding various speculative theories of its exact mathematical use, concluded that several are plausible but uncertain.<ref>{{cite book |last=Joseph |first=George Gheverghese |year=2007 |title=The Crest of the Peacock: Non-European Roots of Mathematics" |publisher=Princeton University Press |isbn=978-0-691-13526-7|page=32-34 |url=https://www.ms.uky.edu/~sohum/ma330/files/Crest_of_the_peacock.pdf}}</ref>


==See also==
==See also==

Revision as of 19:10, 9 November 2021

The Ishango bone on exhibition at the Royal Belgian Institute of Natural Sciences

The Ishango bone, discovered at the "fisherman settlement" of Ishango in the Democratic Republic of Congo, is a bone tool and possible mathematical device that dates to the Upper Paleolithic era.[1] The curved bone is dark brown in color, about 10 centimeters in length, and features a sharp piece of quartz affixed to one end, perhaps for engraving.[1] Because the bone has been narrowed, scraped, polished, and engraved to a certain extent, it is no longer possible to determine what animal the bone belonged to, although it is assumed to belong to a mammal.[2]

The ordered engravings etched onto the surface of the bone in a way that has lead people to speculate the meaning behind these marks, including interpretations like mathematical significance or an astrological device. It is thought by some to be a tally stick, as it has a series of what has been interpreted as tally marks carved in three columns running the length of the tool, though it has also been suggested that the scratches might have been to create a better grip on the handle or for some other non-mathematical reason.[3] Others argue that the marks on the object are non-random and that it was likely a kind of counting tool and used to perform simple mathematical procedures.[4][5] Other speculations include the engravings on the bone serving as a lunar calendar. Dating to 20,000 years before present, it is regarded as the oldest mathematical tool to humankind,[1] with the possible exception of the aproximately 40,000-year-old Lebombo bone from southern Africa.

History

The Ishango bone was found in 1950 by its true hhh? Belgian Jean de Heinzelin de Braucourt while exploring what was then the Belgian Congo.[6] It was discovered in the area of Ishango near the Semliki River. Lake Edward empties into the Semliki which forms part of the headwaters of the Nile River (now on the border between modern-day Uganda and D.R. Congo). The bone was found among the remains of a small community that fished and gathered in this area of Africa. The settlement had been buried in a volcanic eruption.

The artifact was first estimated to have originated between 9,000 BC and 6,500 BC, with numerous other analyses debating the bone to be as old as 44,000 years.[5][7] However, the dating of the site where it was discovered was re-evaluated, and it is now believed to be more than 20,000 years old (from between 18,000 BC and 20,000 BC).[8][9]

Professor Heinzelin brought the Ishango bone to Belgium, where it is now stored in the treasure room of the Royal Belgian Institute of Natural Sciences in Brussels.[10] Several molds and copies were created from the petrified bone in order to preserve the delicate nature of the fragile artifact while being exported.[10] A written request to the museum is required to see the artifact, as it is no longer on display for the public eye.[10]

Interpretations

First (sometimes called "center") column (invisible in picture), from bottom to top
Second (or "right") column (to the left in picture), from bottom to top
Third (or "left") column (to the right in picture), from bottom to top

Mathematical

The 168 etchings on the bone are ordered in three parallel columns along the length of the bone, each marking with a varying orientation and length.[1] The First column, or central column along the most curved side of the bone, is referred to as the M column, which is French for Milieu.[1] The Left and Right columns are respectively referred to as G and D, or Gauche and Droite in French.[1] The parallel markings have led to "various tantalizing hypotheses" such as that the implement indicates an understanding of decimals or prime numbers. Though these propositions have been questioned, it is considered likely by many scholars that the tool was used for mathematical purposes, perhaps including simple mathematical procedures or to construct a numeral system.[5]

Discoverer of the Ishango bone, De Heinzelin, suggested that the bone was evidence of knowledge of simple arithmetic.[1]The third column has been interpreted as a "table of prime numbers",[11] as column G appears to illustrate prime numbers between 10 and 20,[1] but this may be a coincidence.[5] Historian of mathematics Peter S. Rudman argues that prime numbers were probably not understood until the early Greek period of about 500 BC, and were dependent on the concept of division, which he dates to no earlier than 10,000 BC.[12]

More recently mathematicians Dirk Huylebrouck and Vladimir Pletser, have proposed that the Ishango bone is a counting tool using the base 12 and sub-bases 3 and 4, and involving simple multiplication, somewhat comparable to a primitive slide rule. However they have concluded that there is not sufficient evidence to confirm an understanding of prime numbers.[1][4][2][13]

Anthropologist Caleb Everett in his book, ""Numbers and the Making of Us", has also explained of the object that "the quantities evident in the groupings of marks are not random", and are likely evidence of prehistoric numerals.[5] He suggests that the first column may reflect some "doubling pattern" and that the tool may have been used for counting and multiplication and also possibly as a "numeric reference table".[5]

Astrological

Alexander Marshack, an archaeologist from Havard, speculated that the Ishango bone represents numeric notation of a six-month lunar calendar.[1][2][8] Marshack made a diagram comparing the different sizes and phases of the moon with the notches of the Ishango bone.[10] There is some circumstantial evidence to support this alternate hypothesis, being that present day African societies utilize bones, strings, and other devices as calendars.[1] This has led Claudia Zaslavsky to suggest that the creator of the tool may have been a woman, tracking the lunar phase in relation to the menstrual cycle.[14][15] This is countered with the argument that Marshack overinterprets the data and that the evidence does not support lunar calendars.[16]

Cautionary tales

While it is exciting to attempt to understand the cultural significance behind this artifact, it is vital to not become wrapped up in dubious hypotheses. Mathematician Olivier Keller, warns against the urge to project our modern culture of viewing numbers everywhere onto the Ishango bone.[2] Keller exclaims that this practice encourages observers to negate and possibly ignore alternative symbolic materials, those which are present in a range of media (on human remains, stones and cave art) from the Upper Paleolithic era and beyond which also deserve equitable investigation.[2]

George Joseph, author of "The Crest of the Peacock: Non-European Roots of Mathematics" discredits the simultaneous astrological and computational interpretations of the bone, stating that "a single bone may well collapse under the heavy weight of conjectures piled onto it."[17] Keller and Joseph unanimously assert that far-fetched speculations such as these hinder valid research efforts and make light of significant archaeological discoveries.

See also

References

  1. ^ a b c d e f g h i j k Huylebrouck, Dirk (2019), "Missing Link", Mathematics, Culture, and the Arts, Cham: Springer International Publishing, pp. 153–166, retrieved 2021-10-19
  2. ^ a b c d e Association pour la diffusion de l'information archéologique/Royal Belgian Institute of Natural Sciences, Brussels (n.d.). "Have You Heard of Ishango?" (PDF). Natural Sciences.
  3. ^ Rudman, Peter Strom (2007). How Mathematics Happened: The First 50,000 Years. Prometheus Books. p. 63. ISBN 978-1-59102-477-4.
  4. ^ a b Pletser, Vladimir (2012). "Does the Ishango Bone Indicate Knowledge of the Base 12? An Interpretation of a Prehistoric Discovery, the First Mathematical Tool of Humankind". arXiv:1204.1019 [math.HO].
  5. ^ a b c d e f Everett, Caleb (2017). Numbers and the Making of Us: Counting and the Course of Human Cultures. Harvard University Press. pp. 35–36. ISBN 9780674504431.
  6. ^ de Heinzelin, Jean: "Ishango", Scientific American, 206:6 (June 1962) 105--116.
  7. ^ Gerdes, Paulus (1991): On The History of Mathematics in Africa South of the Sahara; African Mathematical Union, Commission on the History of Mathematics in Africa.
  8. ^ a b Marshack, Alexander (1991): The Roots of Civilization, Colonial Hill, Mount Kisco, NY.
  9. ^ Brooks, A.S. and Smith, C.C. (1987): "Ishango revisited: new age determinations and cultural interpretations", The African Archaeological Review, 5 : 65-78.
  10. ^ a b c d Stewart, Ian; Huylebrouck, D.; Horowitz, David; Kuo, K. H.; Kullman, David E. (1996-09-01). "The mathematical tourist". The Mathematical Intelligencer. 18 (4): 56–66. doi:10.1007/BF03026755. ISSN 0343-6993.
  11. ^ Williams, Scott W.: "Mathematicians of the African Diaspora" The Mathematics Department of The State University of New York at Buffalo.[1]
  12. ^ Rudman, Peter Strom (2007). How Mathematics Happened: The First 50,000 Years. Prometheus Books. p. 64. ISBN 978-1-59102-477-4.
  13. ^ Plester, Vladimir; Dirk Huylebrouck, Dirk. "An Interpretation of the Ishango Rods" (PDF). /www.researchgate.net.
  14. ^ Zaslavsky, Claudia: Africa Counts: Number and Pattern in African Culture, L. Hill, 1979.
  15. ^ Zaslavsky, Claudia: "Women as the First Mathematicians", International Study Group on Ethnomathematics Newsletter, Volume 7 Number 1, 1992|January 1992.
  16. ^ Robinson, Judy. 1992. Not counting on Marshack: a reassessment of the work of Alexander Marshack on notation in the Upper Palaeolithic. Journal of Mediterranean Studies 2(1): 1-16.
  17. ^ Joseph, George (2011). The Crest of the Peacock: Non-European Roots of Mathematics. Princeton University Press. p. 34.

Further reading

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