-3-
14xi50
3. 'Weights' system
_ represents the unit.
_ = 1/30 (?) of the unit, corresponds to the A fraction _ = 1/32,
being the nearest approximation.
_ = ¼ (?) of the preceding term, apparently corresponds to the A fraction
_ = 1/3, with an extra bar to indicate, perhaps, a 'fraction of a
fraction'.
_ = 1/12 (?) of the preceding term, apparently corresponds similarly
to the A fraction _ = 1/16. or _ = 1/8 ?
There is a difference here in that the terms, instead of all being
fractions of the unit measure, are probably expressed each as fractions
of the preceding item. The reason for this must be that since the system
deals with a more 'abstract' measurement, the smaller terms cannot so
easily be expressed as ideograms; and the fraction system has no conveni-
ent means of registering in one step the excessive ratio of 1440 (?) : 1.
The ratio of the smaller terms, judged purely on the fractional forms,
looks rather more like 3 x 16 = 48 rather than 4 x 12 = 48. Possibly
some fluctuation in the standard progression for the lower terms lies at
the root of this. Or else the value of _ is derived from some quite dif-
ferent explanation: an 'intermediate' ideogram of which _ is then
again a fraction ?
The main reason which you suggest for the difference between the HT
and the Knossos/Pylos fractional systems - the greater area and volume
of trade represented by the latter - seems very much to the point, but
I wonder if you don't exaggerate the clean-cut nature of the change-over.
If the fractional values are based on a common system of reckoning
(and it is merely the manipulation which is different), it isn't clear
to me whether the continuing use of each system side by side is not im-
plicit in the conventions of the other: that is to say:-
1 Whether HT is not actually familiar with the hierarchies of measure-
ment units apparent in Knossos/Pylos, but does not bother to use them
due to the comparatively small amounts dealt with by the accounting sys-
tem;
2 whether Linear B would not be capable of using similar 'compound ali-
quots' to the HT ones when dealing with quantities not bureaucratical-
ly codified, such as fractions of distances etc.
The advantages of the B over the A accounting system are as follows:-
1. By choosing ratio steps of more than 1:2, selected from both the
binary and the ternary systems, greater flexibility and speed can be
achieved in exactly defining complex fractions.
2 This in turn enables the main units of measurement to be made very
large, which is an advantage where large quantities are being dealt
with.
3 A list of items can rapidly be added up 'on paper', which is clearly
extremely difficult on the A system unless the fractions are restric-
ted to ¼, ½ and ¾.
Thus it seems to me that while the Linear B method of manipulating
may be due to a revolution in the actual weights and measures used, the
distinction can be very largely explained as the result of the volume of
transactions involved, and not necessarily as an irreversible historic
change.
I'm afraid this letter is begining to go outside the decent bounds
of comment on your article and starting to chase hares of its own, so
I'll close now. But the question of these fractions is an intriguing one:
I'm grateful to you for stirring me up on the subject, and I'd welcome
further discussion with you on it as the occasion arises.
Yours,
Michael Ventris