Page 189 - Coincidences in the Bible and in Biblical Hebrew

COINCIDENCES IN THE BIBLE AND IN BIBLICAL HEBREW
168
168 COINCIDENCES IN THE BIBLE AND IN BIBLICAL HEBREW
(namely, those in the basic set) are employed for each interpolation or extrapolation.
We reemphasize that if the assumption of linearity is invalid (that is, the null hypoth-
esis is true), then CNV and WF values are completely unrelated, and the interpolated
and extrapolated new entries in Table 12.3 (those added to the basic set) would just
add noise (they are not expected to align themselves on a straight line). Adding noise
would strengthen the tendency of observations to support the null hypothesis.

The final complete set of observations used, either in toto or by a subsample,
for any of the linear regression analyses that follow, is displayed in Table 12.3.
Observations belonging to the basic set are underlined.
The added entry for argaman will be addressed later on. This color has a
known CNV , yet it is not included in the set of elementary colors of Table 12.1.

Therefore, it will be added to the basic set later on, in a separate analysis, which
will be based on an extended basic set.

To calculate by interpolation CNV values for colors in the set of elementary

colors but not in the basic set, the following formulae were used (these may be
easily derived from trigonometric considerations):

Interpolation (always based on the adjacent two basic-set observations, N 0 is the
unknown CNV ):

N 0 = {N 1(f 2 – f 0) + N 2(f 0 – f 1)} / (f 2 – f 1)

Where:
N i–CNV value for point i (i = 1, 0, 2, where “0” index the point with unknown

CNV (the interpolated middle point); 1 relates to the adjacent point with known

CNV and the smaller WF (first interpolating point); and 2 relates to the adjacent
point with known CNV and the higher WF (the second interpolating point);
f i–WF for point i (i = 1, 0, 2); all values of f i are known, and used for the

interpolation.

Extrapolation (same notation as before; extrapolation was used only to obtain the

CNV of violet, and was obtained based on CNV and WF values of the two colors
preceding it, with known CNVs—namely, basic-set observations; N 2 denote here
the unknown CNV):

N 2 = {N 0 (f 2 – f 1) – N 1 (f 2 – f 0) } / (f 0 – f 1)