Page 49 - Msingi Afrika Magazine Issue 11

MY AFRIKA

Society of African Earth Scientists,
Email: saescentists@hotmail.co.uk the African continent (that is, 3rd
century BC Alexandria, Egypt) [2].
Yet the Ishango bone is dated as
22,000 years old by carbon dating
his paper aims to show of the bone inscriptions houses the [3]. This would mean that Central
that the Ishango bone, calculations of the Ishango Sieve. Africa precedes Greek invention of
one of two bones discov- All numbers deduced in the mid- the prime sieve of Eratosthenes by
Tered in the 1950s buried dle calculation column relate to a at least 19,700 years! Furthermore,
in ash on the banks of Lake Edward process of elimination of the non- the discovery throws into question
in Democratic Republic of Con- prime numbers from the sequence the Greek origins of mathematics;
go (formerly Zaire), after a nearby of numbers 1,2,3,4,5,6,7,8,9,10 since the method of elimination
volcanic eruption, is the world's first (although numbers 1 and 2 are of Eratosthenes closely resembles
known mathematical sieve and table omitted). The act of elimination is that of the Stone Age Ishango
of the small prime numbers. The proven by the display of the num- mathematicians. It may well have
bone is dated approximately 20,000 bers deduced in the middle column; been an idea transmitted earlier to
BC. namely: 4, 6, 8, 9, and 10 and the the ancient Egyptians before the
subsequent omission of these same Greek conquest of Egypt. We note
Key to the demonstration of the numbers from the following list a similarity between the Ishango and
sieve is the contention that the an- leaving only: 5, 7 at the bottom of ancient Egyptian uses of doubling
cient Stone Age mathematicians of column M. used in conjunction with addition
Ishango in Central Africa conceived to undertake more complex mathe-
of doubling or multiplication by 2 in This elimination process described matical tasks. The suggestion is that
a more primitive mode than mod- above is repeated to obtain the the Greeks merely usurped the the
ern Computer Age humans, as the primes 11,13,17,19 when eliminat- scientific knowledge and status of
process of "copying" of a singular ing non-primes from the sequence the Egyptians. It is worthy of note
record (that is, a mark created by a 11,12,13,14,15,16,17,18,19,20. that Eratosthenes was the director
stone tool as encountered in Stone However, only calculations for the of the library at Alexandria and
Age people's daily experience). Sim- sequence 1 to 10 (for numbers therefore had access to many works,
ilarly, the doubling of any number above 2) are displayed in column M; for which he could claim to be the
was, by logical extension, a pro- as if to exemplify the Ishango Sieve originator. The same is true of other
cess of copying of any number of method for the benefit of posterity. Greeks, such as Euclid; if, indeed
records (marks) denoting an inte- they were ethnically Greek at all,
ger, thereby doubling the exhibited 1. Introduction rather than Egyptian. This has never
number (marks). Some evidence for been satisfactorily substantiated.
this process of "copying" and thus This paper aims to show that the
representing numbers as consisting Ishango bone, one of two discov- The Ishango bone, first discovered
of "copies" of other numbers, is ered in the 1950s buried in ash by the Belgian Professor Jean de
displayed on the bone and can still on the banks of Lake Edward in Heinzelin de Brouhart in the 1950s
be found to exist in the number Democratic Republic of Congo [4], is a 10 cm long curved bone
systems of modern Africans in the (formerly Zaire) after a nearby which has 168 notches distributed
region. volcanic eruption [1], is the world's along three columns on the bone
first mathematical sieve and table (shown in the diagram below)
Unlike previous speculations on the of the small prime numbers. This which are now commonly referred
use of the bone tool by other stud- pronouncement will be greeted with to as columns G, M and D after
ies, the ancient method of sieving astonishment in many circles, for the French terminologies for Left
of the small primes suggested here various reasons. Firstly, it has been (Gauche), Middle (Milieu) and Right
is notable for unifying (making use the established view in modern (Droite).
and explanation of) all columns of times, that Eratosthenes of Cyrene
the Ishango bone; whilst all num- (276-194 BC), the ancient Greek
bers exhibited form an essential director at the world-famous library
part of the primitive mathematical at Alexandria in ancient Egypt was
sieve described. Furthermore, it is the inventor of the first mathemat-
stated that the middle column (M) ical sieve for the prime numbers on

Figure 1a. A Schematised Represen-
WWW.MSINGIAFRIKAMAGAZINE.COM tation of the Marks on the Ishango ISSUE 11 | MAR/APRIL 2021 49
Bone Arranged in Three Columns
Left (G), Middle (M) and Right (D