**An Oracle Restored**

One of the principal
reasons for the 'Mt.Sinai encounter', recorded in Exodus 25-31,
was to instruct Moses as to the precise details of construction
of the portable sanctuary that would function as God's dwelling
place on earth - the ** tabernacle** -
together with its furnishings, and manner of use.

Concerning the high-priestly vestments, we read particularly of the
oracle - the ** Urim and Thummim** (Ex.28:30)
- provided for the guidance of the people in difficult and
uncertain times. Details are lacking of the nature and use of
these items

[Link to a Web site on the Tabernacle]

In Ian Mallett's paper *The
Breastplate of Judgment*^{(2)}, attention is drawn to the many
interesting features attending the matrix of integers formed from
the characteristic values (hereafter "CVs") [Appendix 2] of the breastplate names:

**2. The contiguous multiples of 37**

- The
following attributes, predicated upon 37
^{(3)}and its multiples, may be readily ascertained:

- The value of the
matrix (i.e. the sum of its components) is 3700, or
10^2x37
^{(4)} - Of these, the 6 occupying 'odd' positions total 1850, or 50x37, and the 6 occupying 'even' positions, the same
- The first 9 form a square; they total 2812, or 76x37
- The remainder - forming the final row of 3 - total 888, or 24x37
- The first value is 259, or 7x37
- The remaining values in the square may be grouped into 4 connected pairs - each representing a multiple of 37, thus:

At (a), we have the breastplate matrix and observe that it may be divided into 6 regions, here designated I, II, III, IV, V and VI - as at (b) - such that the sum of the name CVs within each region is a multiple of the uniquely-symmetrical number 37 - as represented at (c) - the corresponding multipliers of 37 being depicted at (d).

We read in John's
Gospel, "He was in the world, *and the world was made by
him*, and the world knew him not." (ch.1, v.10).
Remarkably, the breastplate is imprinted with our Creator's
'signature' - the bottom row (value 888) conveying the encoded
name, 'Jesus', and the connected block above (value 1480), the
title, 'Christ', thus:

And we further observe powerful symbolism in the fact that the ratio, name:title, represented numerically by 888:1480, or 3:5, is identical with that of the sides of the mercy seat (Ex.25:17-22) - central element in tabernacle worship! [Details concerning the derivation of the characteristic values of the Creator's name and title are given in Appendix 3.]

The foregoing facts lead directly to a pythagorean view of the breastplate - one in which the Lord's Name plays an essential role.

As we have just seen, the breastplate matrix (value 100x37) may be divided into two blocks, thus:

Here, it may be observed that the square roots of the multipliers of 37, {6,8,10} form a pythagorean triple that is a simple multiple of the classic case, {3,4,5}! Four such triangles are generated when a square of side 10 units is rotated by 36.87° (nearly 37°!) within a centred square of side 14 units, thus:

The sum of these squares is 296 - a number that has already been shown to be an essential feature of the breastplate.

It has already been observed that the sum of the odd-numbered names is precisely one half of the total, and therefore equal to the sum of the even numbered names. However, as revealed below, there is another arrangement which halves the structure numerically, and two which divide it in the ratio 1/4:3/4, thus:

Further, in 925, we
have the value of the Creator's name and title, as derived from
the English analogue of the Hebrew alphabetic numbering scheme^{(5)}. A computer simulation reveals
that about 5% of equivalent random sets exhibit these combined
properties.

We observe that 7 of the 12 integers in the array exhibit interesting relationships of the form,

Multiple (M) / Divisor (D) = Quotient (Q)

Thus:

259(the 1st) /7(the 6th) =37570(the 5th) /30(the 3rd) =19162(the 10th) /54(the 4th) =3570(the 5th) /95(the 9th) =6

The order of appearance of these elements in the matrix is as follows:

259 30 54 570 7 95 162

i.e. M D D M D D M

and we observe symmetry in the types represented, and between types, thus:

Further, an examination
of the four quotients (Q) - 19, 3, 37, and 6 - reveals them to be
significant and related **figurate**^{(6)} numbers, thus:

There are a number of points of contact between the numerical features of the breastplate, as outlined above, and those of the Hebrew Bible's first verse:

- both reveal 37 to be the dominant factor (a feature heralded by their totals: Gen.1:1 = 2701 = 37 x 73; breastplate matrix = 3700 = 37 x 100;
- the total of Gen.1:1 divides thus: 2701 = 999 + 999 + (999 - 296); the breastplate total may be written, 3700 = 999 + 999 + 999 + (999 - 296), or 2701 + 999; indeed, as the following figure reveals, this combination is actually present (as are the many multiples of 296, as we have already seen):

- the factors of 2701, viz 37 and 73, and of 703 (i.e. 999 - 296), viz 19 and 37, are richly figurate; the same structures are implied by the breastplate data as Figure 8 reveals (observe that 6 x 6-as-triangle symmetrically disposed about 37-as-hexagon yields a hexagram of 73);
- the multipliers of
37 in both Gen.1:1 and Creator's name (ie 73 and 64,
respectively) are themselves related to 37: 73, by digit
reversal, and 64, by the cube suggested by the hexagonal
form of 37
^{(3)}.

Clearly, they are the work of one supreme author!

As has been
demonstrated in an earlier paper ^{(8)}, 2368 and 2701 - symbols of the
Creator and Creation, respectively - are also objects of
considerable significance per se in the field of **numerical
geometry**^{(9)}. Both exhibit compound symmetries which
take the form of two-dimensional arrangements of uniform
three-dimensional elements^{(10)}

.

Here we observe 37
cubes - each of 64 units^{(11)} - set out as a regular hexagram.
Remarkably, the figure is harmonised by the fact that these cubes
are represented in two-dimensions by numerical hexagons - each of
37 units^{(3)}! The total represented is 37x64, or 2368
- the characteristic value (CV) of the Lord (Appendix 3).

In the next diagram,
2701, or 37x73 - the CV of Gen.1:1 - is depicted as a hexagram of
73 gnomons - each of 37 units^{(3)}.

Figure 10 may now be centred and superimposed on Figure 11, thus:

The 'halo' of 36
visible gnomons (blue) embodies 36x37, or 1332 units, and the
total represented by the whole is thus 1332+2368, or 3700 units -
** the sum of the 12 breastplate names!** However, it
should not go unnoticed that

Alternatively, the last diagram may be perceived as the augmentation of Figure 11 by a hexagram of 37 smaller cubes - each of value 27 (i.e. 3^3). Clearly, the value represented by this hexagram would be 27x37, or 999. We observe that both 999 and 2701 are present in the breastplate - and form a significant division of it [Figure 9].

The fact that these
constructions are hybrid - incorporating both two- and
three-dimensional elements - is itself symbolic: it mirrors the
dual nature of Jesus who was both *perfect man* and *God!*

Referring again to
Figure 2 we observe that the division of the figure into two
groups of 5 and 7 tiles, respectively, establishes further links
with the Gen.1:1 phenomena. Thus we find that 37 is the
arithmetic mean of 25 (= 5^2) and 49 (= 7^2) and, again, the *centroid
element*^{(12)} of the 73rd numerical triangle (an
alternative representation of Gen.1:1^{(8)}) is found to occupy the 25th
position in the 49th row!

The phrase, ** I am
Alpha and Omega...**, occurs three times in the text of the
Bible's last book (Rev.1:8, 21:6, 22:13) - its final appearance
being followed by the words,

Consulting Appendix 3, we observe the following numerical implications of this arrangement:

CV() = 532; CV() = 800; their sum = 1332 = 36 x 37

The more obvious expressions of the phrase would have involved either the names, or the symbols, of both letters, with the following numerical implications:

CV() = 532; CV() = 849; their sum = 1381
= a prime number

CV(A) = 1; CV() =
800; their sum = 801 = 3 x 3 x 89

and the final possibility of symbol followed by name:

CV(A) = 1; CV() = 849; their sum = 850 = 2 x 5 x 5 x 17

Clearly, the only arrangement to yield a multiple of 37 is precisely that found in the text! - and we observe that the particular multiple, 1332 - representing 'Alpha and Omega' - is that which not only accompanies 2368 ('The Lord') in the breastplate matrix [Figure 2] but also functions as the outline hexagram ('the halo') in the representation of 'The Lord of Creation' [Figure 11(c)]!!

Again, in the context
of the first verse of the Bible (Gen.1:1) - that 'treasure-trove'
of numerical geometry ^{(7)}^{(8)} - we find a similar
association: the central Hebrew word is formed from the first and
the last letters of the alphabet; immediately preceding it is
'Elohim', meaning 'God' - the Creator!

It seems abundantly obvious, therefore, that He who created all things and designed the breastplate is also the One who inspired the writing of the Book of Revelation!

email: vernon.jenkins@virgin.net

Link to *Double
Indemnity*

This page was last modified 2006-03-11.

(1) The Urim and Thummim were clearly more than the equivalent of a pair of dice (as some have contended) for God did not always provide an answer (1Sam.14:36-37, 28:6). The response came either by a voice from heaven or by an impulse upon the mind of the high priest. This oracle was of great use to Israel (e.g. Nu.27:21, 1Sam.23:6-12).

(2) Obtainable from PALMONI RESEARCH, 4 Tynesdale, Whitby, Ellesmere Port, CH65 6RB, U.K.

(3) As an integer, thirty-seven has unique geometrical properties: 37 uniform squares or circles (as appropriate) can be arranged to fill any one of three symmetrical frames - octagon, hexagon, or hexagram; in hexagon form, it represents a typical 2D view of a cube of dimension 4, i.e. a stack of 64 unit cubes; it is also the difference between the cubes of 4 and 3. These features are illustrated in the following diagrams:

Clearly, 37 is
associated with 16 axes of symmetry, and in this sense it is the
most symmetrical of all numbers. But, in addition, as a denary
object, it provides a basis for many interesting mathematical
recreations (see *The Ultimate Assertion: Evidence of
Supernatural Design in the Divine Prologue*, CEN Tech.J.,
vol.7(2), 1993, Appendix, pp.192-196).

(4) This appears significant since the breastplate was itself a square, and 10 is a highly significant number: a prominent feature of human anatomy, principal radix of man's number systems from the beginning, and collective unit in the now near universal principles of decimalisation and metrication.

(5) In Appendix 2, an outline is provided of the historically-attested Hebrew alphabetic numbering scheme. If the Roman alphabet is superimposed on this, and the values 500, 600, 700, and 800, assigned to the extra four letters W, X, Y, and Z, we then have a modern equivalent of this ancient scheme. Under this regime, the name 'JESUS' would assume the value 515 (i.e. 10+5+100+300+100), and the title 'CHRIST', 410 (i.e. 3+8+90+9+100+200); 'JESUS CHRIST' would therefore become 925, or 5^2x37.

(6) In the context of this page a * figurate
number* is one which, when represented as a set of
uniform circular or spherical counters, completely fills a
polygonal or polyhedral frame. Examples are illustrated above.

(7) Such data are presented in the *The Beginning of Wonders* and in a number of printed
documents, including *The Ultimate Assertion: Evidence of
Supernatural Design in the Divine Prologue*. Please email the
author for details.

(8) See for example *The Arbiters of Truth*

(9) *Numerical geometry*
describes the study of those two- and three-dimensional
structures that involve both number and form, i.e. the figurate
numbers. These lie close to the heart of mathematics, and the
symmetries represented are absolute in the sense that they are
independent of radix, of time, and of place.

(10) Here, the 4th solid gnomon (= 37, difference between the 4th and the 3rd cubes) and the 4th cube (= 64 units) are symbolically represented by

(11) The 'units' referred to in this
account are the unit cubes which function as *counters* in
the construction of the diagrams.

(12) One in every three numerical
triangles is built around a single counter which then functions
as the *centroid element* - i.e. that which is equidistant
from each of the three sides. Such a triangle is the 73rd.

(13) See also Colossians 1:16

(14) The writer is indebted to Captain Richard Prendergast for drawing his attention to this interesting anomaly.

Jacob fathered 12 sons by four women: his wives, Leah and Rachel; and his concubines - maidservants of Leah and Rachel - and surrogate mothers, Zilpah and Bilhah (Gen.29:31-35; 30:1-24; 35:16-18). The following table lists the names of the sons, in order of birth, with their respective mothers.

1. | REUBEN | Leah |

2. | SIMEON | Leah |

3. | LEVI | Leah |

4. | JUDAH | Leah |

5. | DAN | Rachel/Bilhah |

6. | NAPHTALI | Rachel/Bilhah |

7. | GAD | Leah/Zilpah |

8. | ASHER | Leah/Zilpah |

9. | ISSACHAR | Leah |

10. | ZEBULUN | Leah |

11. | JOSEPH | Rachel |

12. | BENJAMIN | Rachel |

Jacob's favorite son, Joseph, sold into slavery through the treachery of his elder brothers, ultimately became Pharaoh's 'right-hand man', married an Egyptian, and fathered two sons, MANASSEH and EPHRAIM (Gen.41:50-52). These two particular grandsons of Jacob were destined to become proxies for their father in the above list. The tribes - now numbering 13, and each identified by the name of its progenitor - remained in Egypt for some 400 years. Following the Exodus, and before entering the 'promised land', a significant event took place: at God's command, the sons of Levi were set apart and dedicated to His service; in due course, they would therefore not feature in the apportionment of the land between the tribes (Deut.10:8-9). Accordingly, we deduce that the name of Levi would not appear on the breastplate, for the high priest who bore it would himself have been of that tribe; again, as we have seen, Joseph would have been represented by his two sons. A reading of Nu.1 confirms these facts.

Many centuries after
these events occurred, it became the practice to use Hebrew
letters as numerals. All written words and names have since
become fairly interpretable as numbers. Details of the Hebrew *alphabetic
numbering scheme* are given in Appendix 2. The names of the tribes of Israel
(assuming it is these that were engraved on the jewels of the
breastplate), in progenitor birth order, and with their full
numerical interpretations, are listed in the table below along
with their Strong's reference number bracketed. [Note: to verify
these Hebrew spellings you may access www.blueletterbible.org using the relevant reference number.]

* In contrast to the other 11, the Hebrew rendering of the name Zebulun occurs in different ways - as detailed below:

Observe
that the column headed 'Freq(uency)' records the number of times
each variation occurs in the Old Testament text; and that headed
'CV', the numerical values to be associated with these. For the
purposes of the current exercise, it is clear that latter may be
read either as **101** or **95**.
However, the latter is preferred here because, (a) it relates to
the most frequent of the variations, (b) it is this value that
raises the total of the 'Tribes of Israel' to a significant
multiple of 37, and the one which establishes many of the
internal breastplate characteristics.

It is worth noting that this layout corresponds with the engravings on the two onyx stones mounted on the shoulderpieces of the ephod (Ex.28:9-12).

The following diagrams present a summary of the matters discussed above.

The breastplate is here represented as a tiled rectangle - the tiles being numbered from right to left, in the Hebrew manner - with the omitted names, Levi and Joseph, shown in their proper positions, by order of birth.

Here, finally, is the breastplate prepared for analysis as a 4 x 3 matrix of name CVs:

The Hebrew alphabet has 22 letters - five with 'end forms', i.e. variants used only when words end with one or other of these letters. From circa 200 BC, as the following table reveals, each letter was made to function as a numeral - thus copying the earlier Greek model (c 600 BC).

The
practice that existed then was to record numbers on an *additive*
basis, i.e. the value represented by a string of letters was
simply the sum of the tabular values assigned to each. The *characteristic
value* (CV) of a conventional Hebrew word, name, or phrase, is
obtained in this manner. As an illustration of the procedure, the
characteristic value of the name *SIMEON* is derived below.
We observe that all Hebrew reading proceeds from right to left.

Thus, CV (SIMEON) = 50 + 6 + 70 + 40 + 300 = 466

The Greek alphabet is an ordered set of 24 upper/lowercase pairs of characters. The position and numerical value of each letter of each of these pairs is detailed below:

This scheme was introduced circa 600 BC for the purpose of recording numbers on an additive basis, the missing values, 6 and 90, being represented by non-alphabetic symbols. Thus, every string of letters was potentially a number - interpreted by summing the tabular values of the letters.

As a unique example of
this procedure, the *characteristic value*s (CVs) of the
Lord's Name and Title are evaluated below:

Observe that the letter values appear above and their respective sums below.