5.1 - Introduction
Here, we bring together
certain numerical characteristics of two ancient artefacts,
viz. the opening verse of the Judeo-Christian Scriptures (as
rendered in the original Hebrew) and the standard 8x8
chequerboard (basis of many games, including chess and
draughts).
The total of
unit squares in this arrangement is 64 - significantly, the
smallest non-trivial number that may exist both as square and
cube. Sixty-four is therefore an example of a 'bifigurate'
number - and, in this case, one which may be realised
structurally in either 2 or 3 dimensions.
Observe that
such bifigurates are rare - there being only 10 examples in
the first million natural numbers:
It follows that
the likelihood of a chance encounter with any of these - in
any context - is small. To discover that the 2nd, 3rd and 4th
are intimately involved with the topic in hand - and together
provide a key to our further understanding of fundamental
truths - must therefore be regarded as highly significant.
Let us then
first observe that if the 2nd describes the salient features
of a chequerboard, the 4th must relate to a 'chequerboard of
chequerboards' - a structure which may be depicted thus,
A simpler view
of this structure provides a suitable basis for subsequent
developments:
5.2 -
The Constructions
The 3rd
instance of a square which is also a cube, viz, 729, may now
be placed within the foregoing figure, thus:
Observe that
area C is the product of the two numbers which
are
primary factors of Genesis 1:1 and Genesis
1:1+, respectively;
represent
the difference and sum of the cubes of 4 and
3, respectively; and,
as
trifigurates, combine to exhibit the highest
number of symmetrical forms
The first
simple development is to extend the inner square upwards,
thus generating the two rectangles D and E - each of
considerable interest:
The width of D
is, of course 37 (i.e. 64 - 27) so that the number of unit
squares it contains is 2368 (i.e. 37.64). Remarkably, this
also represents the sum of the CVs of "Jesus" and
"Christ" as evaluated from both New Testament Greek
and Septuagint, thus:
Here, we must
pause to highlight important subdivisions of the lefthand
rectangle, thus:
As may be seen,
2368 = 8.296 (296 being the CV of the 7th word of Genesis
1:1, translated "earth") and 888 and 1480, 3.296
and 5.296, respectively (these in the ratio 3:5 - as found in
the dimensions of the Mercy Seat!).
The
rectangle E encloses precisely 999 unit squares; so here we
have a repdigit of three 9s sharing a border with, (i) its
related cube of 9.9.9 and together with, (ii) the Creator's
Name. How very remarkable!
Now, proceeding
with a symmetrical development of Figure 5.7, we have:
Already the
appearance of an opposed pair of 999-as-rectangle falls in
with the earlier Genesis 1:1 observations concerning the CV
totals 913 + 86 (words 1 and 3) = 203 + 401 + 395 (words 2, 4
and 5) = 999! But do we also find 703 (sum of the remaining
words, 6 and 7) represented in this figure? Yes we do, for
703 is 37th triangular number, and a logical subdivision of
1369-as-square, thus:
Observe that
its triangular counterpart involves the repdigit 666 - a
denary-based symbol of relatively modern vintage which, when
rotated through 180 degrees appears as '999', thus providing
a perfect match with the other components!
This picture
exhibits a particular segmentation of the word CVs of Genesis
1:1, as follows:
913 (word
1) + 86 (word 3) = 999 = 203 (word 2) + 401 (word 4) +
395 (word 5); 407 (word 6) + 296 (word 7) = 703
One further
development is worthy of particular mention. It concerns the
two significant observations, (i) that 703 is 210 units
short of the CV of Bible's first word, 913 and, (ii) that
210 is a rare example of a triangular number which is the
double of another - in this case, 105. Thus, if 105 units be
transferred to G from each of the rectangles E, the following
situation obtains and symmetry is maintained:
The pentagons J
each comprise 894 unit squares and represent the sums of the
CVs of word triplets within Genesis 1:1, thus:
203
(word 2) + 395 (word 5) + 296 (word 7) = 86 (word 3)
+ 401 (word 4) + 407 (word 6) = 894
Thus we have
this alternative representation of the Bible's first verse -
now expressed in terms of its first word and the sums of two
groups of three words:
5.3 -
Interim Observations
