47 Highpoint,
North Hill,
Highgate,
LONDON, N.6.
14 November 1950.
Dear Bennett,
Your article arrived yesterday, and is extraordinarily interesting.
I don't know which parts Myres was doubtful about, but the analysis of
the Linear B fractional measures seems quite masterly to me.
I made the mistake of reading the article through for the second
time just before going to bed: the result was that I was quite unable
to get to sleep, and in the end was forced to jump out about 3 o'clock
and jot down my reactions to what you had written. If I can sort out
my scribbled notes, here are my comments for what they're worth:-
The values which you have established for the Linear B terms, and
the differences in measuring method compared with the Linear A fractions,
seem to be absolutely convincing; but my own view is that
1 with the exception of ½ , ¼ and 1/8, the values for the Linear A
fractions are not yet satisfactory, and that
2 the distinction between the A and B fractional systems is not quite
as great as you have made out, because, as I hope to show, the B
terms are for the most part nothing more than slightly embellished
versions of the A fractions, with the same basic values maintained.
In reallotting My own suggested values to the A fractions, I have
started from 3 assumptions:
1 That the signs with nucleus _ and _ form two parallel series
of aliquot parts, representing regular and successive halvings of
2 and 3 respectively.
2 That the reason for _ and _ not appearing with ½ is that they
are very small, not that they represent 2/3 and 1/6.
3 That the reduplicated signs represent the lowest terms in the 2
parallel series.
The value of _ = ½ I suppose noone is likely to argue about.
The sign _ = ¼ goes through 3 variations to a express a
"quarter-unit" measure successively ¾ (?), ½ and ¼ full. The last
term of these four ( = 1/16 ) is then reduplicated to show subsequent
halvings.
The sign _ = 1/3 shows a vertical bar cut into 3 parts. its
successive halvings show a progressive simplification of the cross-bars,
until with _ = 1/24 we begin a new cycle of reduplications.
SYNOPSIS OF LINEAR 'A' FRACTIONS (Non-compound forms).
_ = ½ decimal = .5000 your frequency = 59
B i n a r y s e r i e s :
_ = ¼ ···················· .2500 .................... 26
_ = 3/16 or thereabouts········ .1875 ···················· 14
_ = 1/8 ···················· .1250 ···················· 7
_ = 1/16 ···················· .0625 ···················· 9
_ = 1/32 ···················· .0313 ···················· 9
_ = 1/64 ···················· .0156 ···················· 1