excuse me addressing this response to you, but you have reiterated a
criticism mounted by various 'traditionalists', and it is convenient to post
this response here.
I go a little outside the terms of your original statement in taking 'random
clumpings' to be equivalent to 'overly concentrated due to use of ordinal
values', but my response is in regard to often encountered 'critiques' of
one ordinal system, and 'clumping' and 'concentration' are not unrelated
terms when they appear in 'critiques' (more often a priori dismissals,
though not in your case) of that system.
> On 25/09/2007, Bill Heidrick <heidrick@...> wrote:
> Also, it is my own opinion
> > that the various patterns of association of numbers and English letters,
> > including Crowley's own in his marginalia to Liber Trigrammaton, seem to
> > yield no better than random clumpings of idea convergence.
as compared to what? Taking the Greek and Hebrew data as it is, the
supposedly 'larger' number range of Greek and Hebrew is really a more
dispersed number range. EQ values are more concentrated, while Greek and
Hebrew numerations have large gaps in the series (as in Liber D) and the
range of Greek reduces to a third - or less - of the apparent range when one
takes into account traditional 'fudge factors' like Colel (where a
difference of one between numbers is disregarded, thus 665=666=667).
Then we have the random choice of numeration of many letters in the
'Hebrew-English' system. About any word can be given so many different
values that the whole system is virtually meaningless in mathematical or
scientific terms. It is far less rigourous than English systems where each
letter has only one value and spelling is pre-determined.
*The Dispersal of Liber D's Gematrias.*
Is there any justification for criticising the distribution of gematria
values in an ordinal system by comparison with a decimal system? If such a
critique is to be immune to the countercharge of 'Phormionism' an impartial
examination of the distribution of values in a decimal system is a necessary
preliminary. There is no sign that such an examination has ever been
undertaken by those mounting the critique, in contrast � it must be said
-with those of whom the critique is made!
Since this critique almost invariably originates from a Thelemic school
which advocates the establishment of a baseline ending in 1947, it is
entirely justifiable for my response to be based on examination of Crowley's
Hebrew gematria dictionary, Liber D.
In Liber D's range of 1-3321 less than 800 numbers are given any gematria
correspondences, the ratio of the actual to the apparent is approximately
26%. Minor gaps begin after 221 widening into significant hiatuses after
500, so that - curiously enough - 777 is the 666th number with a gematria
value attached. These hiatuses increase considerably after 800, so that by
1000 only 745 numbers have attached gematrias. Following this the gaps widen
to the degree that many pages of the text in Equinox I.8 consist of blank
columns. Between 1755 and 3321 we find a grand total of two gematrias.
Unsurprisingly Regardie condensed the text in editing it for 'The Qabalah of
Aleister Crowley' in order to save a great deal of space.
Disregarding the many cases where only one gematria accompanies a number,
many of the gematrias included are not worth consideration. For example the
'Hebrew' values of the names of demons derived from the shoddy scholarship
of the incompetent and incontinent Dr. Rudd. Others, such as various
spellings of Crowley's name might also be justifiably omitted. Of course
Liber D is far from being the final word on Hebrew gematria, even Crowley
says of it that 'none of the editors claim to possess even the smallest
degree of scholarship'. Nevertheless, the charge that an ordinal system of
gematria produces results that are 'too condensed' compared to decimal
systems simply invites the response that decimal systems by contrast are
'too dispersed'. The likelihood is of course that 'density' and 'dispersion'
are simply inherent qualities of the respective approaches, and that neither
disqualifies the other from consideration.
Notes on dispersal/concentration in Greek gematria. The use of Colel permits
comparison between gematrias where the value is one less or one more than
another gematria. So for instance 1747 (666+1080) is 'the same as 1745 and
So in Greek gematira 1746 'the cup of Jesus' is the same as 1745 'the
virgin, pearl of the kingdom' and 1747 'offspring of a virgins womb'. Well
okay, trouble is though that 1745 is also one more than 1744, and 1743 is
one less, so 1744, 'the divne man' is the same as 1743 'first created' and
1745 'Father, Son, Spirit'.
Which of course means that 1743 in effect is the same as 1747!
With rules such as this 'random clumpings'; are much easier to find, and the
supposed greater range of the numerical values obtained with decimal based
gematria collapses in on itself dramatically. One might guess that 'colel'
derives from Kollao, meaning 'glue, to stick together or join', chuck enough
of that kind of glue in the system and associative clumping is only to be
expected. From an impartial perspective the supposed ascendancy of decimal
systems over ordinal systems is non-existent.
(For reasons of brevity, as well as of avoiding technical complexity, I omit
from this response an account of Hebrew gematria using ordinal values. Such
a study is not without its virtues, and is easily justified upon observing
that the ordinal values of the Hebrew alphabet are the only values employed
in the relevant scriptures. Those wishing to pursue this line of
investigation might begin by examining divine and angelic names.)
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