ABC of the Sukuma Calendar

Edward Anthony Makwaia; Charles Edward Ng’Hwaya Masule

doi:doi:10.11648/j.ijtam.20160202.25

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ABC of the Sukuma Calendar

Edward Anthony Makwaia, Charles Edward Ng’Hwaya Masule

Published in International Journal of Theoretical and Applied Mathematics (Volume 2, Issue 2)

Received: 8 September 2016 Accepted: 21 November 2016 Published: 27 December 2016

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Abstract

The aim of this study had been to document and to astronomically mimic in an algorithm the undocumented ancient lunar calendar of the Sukuma and that of the Nyamwezi sibling tribe of Tanzania which is at the verge of perishing due to the perishing of living memory about that calendar. It had been found that the Sukuma calendar marks its end of the sidereal year at the Sukumaland “Jidiku” position of Earth in its trajectory around the Sun which is the December Solstice astronomically fitting on the Gregorian 23^rd December. The stereotype is that the ancient Sukuma of Kishapu tallied up the elapsing days since the first appearance of the "ndimila" on the horizon day-to-day using 64 pebbles to get to the “Jidiku” and later developed that method of tallying days into the fully fledged “isolo” game of counting pebbles. Subsequent to the determination of the “Jidiku” position, the algorithm to compute the Sukuma lunar New Year was developed basing on the technique of computing the Jewish calendar in essence whereby the number of lunar-tagged days elapsed to the beginning of a 19-year lunar cycle since 01^st January year 0000 get compared with the number of solar days elapsed to the beginning of a 19-year Gregorian cycle since 01^st January year 0000 to get the difference in number of days short to the next new moon which mark the Sukuma lunar New Year lying between 23^rd December and 22^nd January. By adding the number of days short to the next new moon at the beginning of a 19-year Gregorian cycles to a series-tagged increment of days - which is a product of 19 and a within-cycle-relative year of the running year (lying between 0 and 18) - the within-cycle lunar New Year gets computed. The lengths of the consecutive lunar months between two consecutive Sukuma lunar New Years were found to fit in a model of repeating 30-to-29 days. It was further found that the Nyamwezi lunar New Year falls one lunar month before the Sukuma lunar New Year and that a Nyamwezi lunar New Year within a 19-year Gregorian cycle is gotten by adding a series-tagged decrement of days - which is a product of 11 and a within-cycle-relative year of the running year - to the begin-of-cycle number of days short to the next new moon.

Published in	International Journal of Theoretical and Applied Mathematics (Volume 2, Issue 2)
DOI	10.11648/j.ijtam.20160202.25
Page(s)	127-135
Creative Commons	This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.
Copyright	Copyright © The Author(s), 2016. Published by Science Publishing Group

Keywords

Ndimila, Sukuma, Sukumaland, Sukuma Calendar, Sukuma New Year, Nyamwezi, Unyamwezi, Nyamwezi Calendar

References

[1]	Adler, P. J. and Pouwels, R. L.: World Civilizations: To 1700 Volume 1 of World Civilizations, (Cengage Learning: 2007), p. 169.
[2]	Bede, F. W.: The Reckoning of Time, (Liverpool: Liverpool Univ. Pr., 1999), pp. lix–lxiii.
[3]	Bede: The reckoning of time, translated by Faith Wallis (Liverpool: Liverpool University Press, 1999) chapter 62, p. 148.
[4]	Bukurura, S. H.: Indigenous Communication Systems - Lessons and Experience from among the Sukuma and Nyamwezi of West-central Tanzania, Nordic Journal of African Studies 4 (2): 1-16 (1995).
[5]	Butcher, S.: The Ecclesiastical calendar: its theory and construction (Dublin, 1877).
[6]	Law, G.: Regions of Tanzania (Web Resource, 2015) at http://www.statoids.com/utz.html
[7]	McCarthy & Guinot: Julian Day Number (2013), 91–2, at https://en.wikipedia.org/wiki/Julian_day
[8]	Ng’hwaya Masule, C. E.: Enhancements of the Easter Algorithms (1940), American Journal of Applied Mathematics. Vol. 3, No. 6, 2015, pp. 312-320. doi: 10.11648/j.ajam.20150306.21
[9]	Ng’hwaya, C. E.: The Spectacular Rotation of Earth About the Main Axis, American Journal of Astronomy and Astrophysics. Vol. 3, No. 6, 2015, pp. 93-117. doi: 10.11648/j.ajaa.20150306.12.
[10]	Rich, T. R.: The Jewish Calendar: A Closer Look, (2005-2011), http://www.jewfaq.org/calendr2.htm#Essentials
[11]	Schwartz, E.: Christliche und jüdische Ostertafeln, Berlin, 1905, p 104ff.
[12]	Seidelmann, P. K. (ed.): Explanatory Supplement to the Astronomical Almanac, Chapter 12, "Calendars", by L. E. Doggett, ISBN 0-935702-68-7, (University Science Books, CA, 1992).
[13]	Stroeken, K.: Moral Power - The Magic of Witchcraft p. 69. (New York: Berghahn Books, 2012) at: https://books.google.com/books?isbn=0857456601

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Edward Anthony Makwaia, Charles Edward Ng’Hwaya Masule. (2016). ABC of the Sukuma Calendar. International Journal of Theoretical and Applied Mathematics, 2(2), 127-135. https://doi.org/10.11648/j.ijtam.20160202.25

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Edward Anthony Makwaia; Charles Edward Ng’Hwaya Masule. ABC of the Sukuma Calendar. Int. J. Theor. Appl. Math. 2016, 2(2), 127-135. doi: 10.11648/j.ijtam.20160202.25

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AMA Style

Edward Anthony Makwaia, Charles Edward Ng’Hwaya Masule. ABC of the Sukuma Calendar. Int J Theor Appl Math. 2016;2(2):127-135. doi: 10.11648/j.ijtam.20160202.25

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@article{10.11648/j.ijtam.20160202.25,
  author = {Edward Anthony Makwaia and Charles Edward Ng’Hwaya Masule},
  title = {ABC of the Sukuma Calendar},
  journal = {International Journal of Theoretical and Applied Mathematics},
  volume = {2},
  number = {2},
  pages = {127-135},
  doi = {10.11648/j.ijtam.20160202.25},
  url = {https://doi.org/10.11648/j.ijtam.20160202.25},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ijtam.20160202.25},
  abstract = {The aim of this study had been to document and to astronomically mimic in an algorithm the undocumented ancient lunar calendar of the Sukuma and that of the Nyamwezi sibling tribe of Tanzania which is at the verge of perishing due to the perishing of living memory about that calendar. It had been found that the Sukuma calendar marks its end of the sidereal year at the Sukumaland “Jidiku” position of Earth in its trajectory around the Sun which is the December Solstice astronomically fitting on the Gregorian 23rd December. The stereotype is that the ancient Sukuma of Kishapu tallied up the elapsing days since the first appearance of the "ndimila" on the horizon day-to-day using 64 pebbles to get to the “Jidiku” and later developed that method of tallying days into the fully fledged “isolo” game of counting pebbles. Subsequent to the determination of the “Jidiku” position, the algorithm to compute the Sukuma lunar New Year was developed basing on the technique of computing the Jewish calendar in essence whereby the number of lunar-tagged days elapsed to the beginning of a 19-year lunar cycle since 01st January year 0000 get compared with the number of solar days elapsed to the beginning of a 19-year Gregorian cycle since 01st January year 0000 to get the difference in number of days short to the next new moon which mark the Sukuma lunar New Year lying between 23rd December and 22nd January. By adding the number of days short to the next new moon at the beginning of a 19-year Gregorian cycles to a series-tagged increment of days - which is a product of 19 and a within-cycle-relative year of the running year (lying between 0 and 18) - the within-cycle lunar New Year gets computed. The lengths of the consecutive lunar months between two consecutive Sukuma lunar New Years were found to fit in a model of repeating 30-to-29 days. It was further found that the Nyamwezi lunar New Year falls one lunar month before the Sukuma lunar New Year and that a Nyamwezi lunar New Year within a 19-year Gregorian cycle is gotten by adding a series-tagged decrement of days - which is a product of 11 and a within-cycle-relative year of the running year - to the begin-of-cycle number of days short to the next new moon.},
 year = {2016}
}

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TY  - JOUR
T1  - ABC of the Sukuma Calendar
AU  - Edward Anthony Makwaia
AU  - Charles Edward Ng’Hwaya Masule
Y1  - 2016/12/27
PY  - 2016
N1  - https://doi.org/10.11648/j.ijtam.20160202.25
DO  - 10.11648/j.ijtam.20160202.25
T2  - International Journal of Theoretical and Applied Mathematics
JF  - International Journal of Theoretical and Applied Mathematics
JO  - International Journal of Theoretical and Applied Mathematics
SP  - 127
EP  - 135
PB  - Science Publishing Group
SN  - 2575-5080
UR  - https://doi.org/10.11648/j.ijtam.20160202.25
AB  - The aim of this study had been to document and to astronomically mimic in an algorithm the undocumented ancient lunar calendar of the Sukuma and that of the Nyamwezi sibling tribe of Tanzania which is at the verge of perishing due to the perishing of living memory about that calendar. It had been found that the Sukuma calendar marks its end of the sidereal year at the Sukumaland “Jidiku” position of Earth in its trajectory around the Sun which is the December Solstice astronomically fitting on the Gregorian 23rd December. The stereotype is that the ancient Sukuma of Kishapu tallied up the elapsing days since the first appearance of the "ndimila" on the horizon day-to-day using 64 pebbles to get to the “Jidiku” and later developed that method of tallying days into the fully fledged “isolo” game of counting pebbles. Subsequent to the determination of the “Jidiku” position, the algorithm to compute the Sukuma lunar New Year was developed basing on the technique of computing the Jewish calendar in essence whereby the number of lunar-tagged days elapsed to the beginning of a 19-year lunar cycle since 01st January year 0000 get compared with the number of solar days elapsed to the beginning of a 19-year Gregorian cycle since 01st January year 0000 to get the difference in number of days short to the next new moon which mark the Sukuma lunar New Year lying between 23rd December and 22nd January. By adding the number of days short to the next new moon at the beginning of a 19-year Gregorian cycles to a series-tagged increment of days - which is a product of 19 and a within-cycle-relative year of the running year (lying between 0 and 18) - the within-cycle lunar New Year gets computed. The lengths of the consecutive lunar months between two consecutive Sukuma lunar New Years were found to fit in a model of repeating 30-to-29 days. It was further found that the Nyamwezi lunar New Year falls one lunar month before the Sukuma lunar New Year and that a Nyamwezi lunar New Year within a 19-year Gregorian cycle is gotten by adding a series-tagged decrement of days - which is a product of 11 and a within-cycle-relative year of the running year - to the begin-of-cycle number of days short to the next new moon.
VL  - 2
IS  - 2
ER  -

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Author Information

Edward Anthony Makwaia

Bank of Tanzania, Dar-Es-Salaam, Tanzania
Charles Edward Ng’Hwaya Masule

Institute of Mechanical Engineering, Mechanical Process Engineering and Environmental Technology, Dresden University of Technology, Dresden, Germany

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Edward Anthony Makwaia, Charles Edward Ng’Hwaya Masule. (2016). ABC of the Sukuma Calendar. International Journal of Theoretical and Applied Mathematics, 2(2), 127-135. https://doi.org/10.11648/j.ijtam.20160202.25

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ACS Style

Edward Anthony Makwaia; Charles Edward Ng’Hwaya Masule. ABC of the Sukuma Calendar. Int. J. Theor. Appl. Math. 2016, 2(2), 127-135. doi: 10.11648/j.ijtam.20160202.25

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AMA Style

Edward Anthony Makwaia, Charles Edward Ng’Hwaya Masule. ABC of the Sukuma Calendar. Int J Theor Appl Math. 2016;2(2):127-135. doi: 10.11648/j.ijtam.20160202.25

Copy | Download

@article{10.11648/j.ijtam.20160202.25,
  author = {Edward Anthony Makwaia and Charles Edward Ng’Hwaya Masule},
  title = {ABC of the Sukuma Calendar},
  journal = {International Journal of Theoretical and Applied Mathematics},
  volume = {2},
  number = {2},
  pages = {127-135},
  doi = {10.11648/j.ijtam.20160202.25},
  url = {https://doi.org/10.11648/j.ijtam.20160202.25},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ijtam.20160202.25},
  abstract = {The aim of this study had been to document and to astronomically mimic in an algorithm the undocumented ancient lunar calendar of the Sukuma and that of the Nyamwezi sibling tribe of Tanzania which is at the verge of perishing due to the perishing of living memory about that calendar. It had been found that the Sukuma calendar marks its end of the sidereal year at the Sukumaland “Jidiku” position of Earth in its trajectory around the Sun which is the December Solstice astronomically fitting on the Gregorian 23rd December. The stereotype is that the ancient Sukuma of Kishapu tallied up the elapsing days since the first appearance of the "ndimila" on the horizon day-to-day using 64 pebbles to get to the “Jidiku” and later developed that method of tallying days into the fully fledged “isolo” game of counting pebbles. Subsequent to the determination of the “Jidiku” position, the algorithm to compute the Sukuma lunar New Year was developed basing on the technique of computing the Jewish calendar in essence whereby the number of lunar-tagged days elapsed to the beginning of a 19-year lunar cycle since 01st January year 0000 get compared with the number of solar days elapsed to the beginning of a 19-year Gregorian cycle since 01st January year 0000 to get the difference in number of days short to the next new moon which mark the Sukuma lunar New Year lying between 23rd December and 22nd January. By adding the number of days short to the next new moon at the beginning of a 19-year Gregorian cycles to a series-tagged increment of days - which is a product of 19 and a within-cycle-relative year of the running year (lying between 0 and 18) - the within-cycle lunar New Year gets computed. The lengths of the consecutive lunar months between two consecutive Sukuma lunar New Years were found to fit in a model of repeating 30-to-29 days. It was further found that the Nyamwezi lunar New Year falls one lunar month before the Sukuma lunar New Year and that a Nyamwezi lunar New Year within a 19-year Gregorian cycle is gotten by adding a series-tagged decrement of days - which is a product of 11 and a within-cycle-relative year of the running year - to the begin-of-cycle number of days short to the next new moon.},
 year = {2016}
}

Copy | Download

TY  - JOUR
T1  - ABC of the Sukuma Calendar
AU  - Edward Anthony Makwaia
AU  - Charles Edward Ng’Hwaya Masule
Y1  - 2016/12/27
PY  - 2016
N1  - https://doi.org/10.11648/j.ijtam.20160202.25
DO  - 10.11648/j.ijtam.20160202.25
T2  - International Journal of Theoretical and Applied Mathematics
JF  - International Journal of Theoretical and Applied Mathematics
JO  - International Journal of Theoretical and Applied Mathematics
SP  - 127
EP  - 135
PB  - Science Publishing Group
SN  - 2575-5080
UR  - https://doi.org/10.11648/j.ijtam.20160202.25
AB  - The aim of this study had been to document and to astronomically mimic in an algorithm the undocumented ancient lunar calendar of the Sukuma and that of the Nyamwezi sibling tribe of Tanzania which is at the verge of perishing due to the perishing of living memory about that calendar. It had been found that the Sukuma calendar marks its end of the sidereal year at the Sukumaland “Jidiku” position of Earth in its trajectory around the Sun which is the December Solstice astronomically fitting on the Gregorian 23rd December. The stereotype is that the ancient Sukuma of Kishapu tallied up the elapsing days since the first appearance of the "ndimila" on the horizon day-to-day using 64 pebbles to get to the “Jidiku” and later developed that method of tallying days into the fully fledged “isolo” game of counting pebbles. Subsequent to the determination of the “Jidiku” position, the algorithm to compute the Sukuma lunar New Year was developed basing on the technique of computing the Jewish calendar in essence whereby the number of lunar-tagged days elapsed to the beginning of a 19-year lunar cycle since 01st January year 0000 get compared with the number of solar days elapsed to the beginning of a 19-year Gregorian cycle since 01st January year 0000 to get the difference in number of days short to the next new moon which mark the Sukuma lunar New Year lying between 23rd December and 22nd January. By adding the number of days short to the next new moon at the beginning of a 19-year Gregorian cycles to a series-tagged increment of days - which is a product of 19 and a within-cycle-relative year of the running year (lying between 0 and 18) - the within-cycle lunar New Year gets computed. The lengths of the consecutive lunar months between two consecutive Sukuma lunar New Years were found to fit in a model of repeating 30-to-29 days. It was further found that the Nyamwezi lunar New Year falls one lunar month before the Sukuma lunar New Year and that a Nyamwezi lunar New Year within a 19-year Gregorian cycle is gotten by adding a series-tagged decrement of days - which is a product of 11 and a within-cycle-relative year of the running year - to the begin-of-cycle number of days short to the next new moon.
VL  - 2
IS  - 2
ER  -

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