Page 50 - Msingi Afrika Magazine Issue 11

MY AFRIKA

Column G column housing the calculations and third to last in column M:
Considering the columns in this for the Ishango prime sieve. Here First we see the number 10 com-
same order, we note that column is where we see doubling and posed of 9+1 in the schematic.
G is the most controversial as representations of the composi- This is because it is contended
this column displays in sequence tions of numbers such as 10 = 5 whether or not the marks form
the four prime numbers between + 5 and possibly also 10 = 9 +1 one group. Or whether this is
10 and 20. Quite typically, the exhibited by the fact that one of really nine marks followed by a
presentation of prime numbers the tally marks in this group is doubtful mark. Similarly, for the
is dismissed by most studies as marked smaller and spaced slight- number 5 composed of 1 + 4,
fortuitous; and not the result ly further apart from the group, only the 4 marks are very clear
of any deliberate or conscious possibly to be distinct from and bold where as the fifth mark
reckoning of the primes. Pletser the others. The arrangement seems to stand further apart
and Huylebrouck [5] are happy to of the middle column displays and is not as clear. Nevertheless,
assert, without justification, that a definite order of calculations because these must add up to
since no awareness of the primes and deductions followed by the factors of 12 (as contended here)
has been previously identified sequence of primes presented as this makes a strong case for the
before the classical Greeks, this results, starting at the foot of the sum of column M not being 46,
possibility is simply eliminated. column. Throughout the top of but rather being 48 (a factor of
The prime sequence on the bone column M we see the doubling 12) and hence the 10 and the 5
actually consists of six primes in of the numbers from 1 to 5 (with being deliberately composed of
sequence starting from the bot- numbers 1 and 2 omitted). In 9 bold marks and by one less
tom of Column M: 5,7, continu- the case of doubling 5 to get 10, bold mark (further apart from
ing to column G: 11,13,17,19. In we see a reversal of the order, so the group) and in the case of the
fairness to this argument for dis- that 10 is written as 5, 4 bold marks and 1 less bold
missing awareness of the primes, mark, again made distinct from
all of the primes could in fact be 10 the group.
taken to be +1 or -1, either side
of multiples in base 6: 6, 12, 18. 5 Column D
But this then does not explain
the rationale for the quite elabo- 5 This column appears to display
rate calculations that take place in a system of numbers in the base
the middle column M. This appears to be a deliberate 10. The four integers would
representation of 10 =5+5, appear to be expressions of
which we will revisit further 10+/- 1 and 20 +/- 1. Column
ahead. D completes the prime sieve
formed by columns G and M by
Referring to figures 1a and 1b, setting the range of the number
we notice that the columns all sequence from which to sift the
sum to totals that are factors of primes. First, the primes in the
12. Columns G and D sum to 60 range n = 1 to 10 are sifted (for
= 5 x 12; whilst column M sums n > 3) by a process beginning
to a total of 48 = 4 x 12. This with the doubling of numbers 1
factoring of twelve in the totals to 5 (excluding 1 and 2). Second-
Fig 1b. De Heinzelin's Detailed Drawing of the of the columns does not look ly, the primes in the range 10 to
Ishango Bone
accidental. It looks very deliber- 20 are then sifted by a process
Column M ate. This has a very interesting beginning with the doubling
bearing on the contention of the of numbers 6 to 10. However,
Column M is seen to be the main numbers that are fourth to last for purposes of economy (we

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