Cached on August 6, 2009, from Tony Smith's website:

http://www.valdostamuseum.org/hamsmith/Talmud.html

 According to Vedibarta Bam- Tetzaveh web page by Rabbi Moshe Bogomilsky, quoting from the book of Exodus: "... "And you shall place in the breastplate the Urim and the Tumim." (28:30) QUESTION:

What were the Urim and the Tumim, and how did they operate?

ANSWER: The Urim and the Tumim were two inscriptions of the Divine Name. When Moshe was in heaven studying the Torah, Hashem revealed to him the secret of how he should make the Urim and the Tumim. Only Moshe, to whom the secret was revealed, was able to make them, and he placed them into the fold of the breastplate. Therefore, it is not written anywhere that anyone should contribute to the making of the Urim and the Tumim or any instruction to the workers about how to make it.

On the 12 stones of the breastplate were written the names of the twelve tribes, the names of the patriarchs, Avraham, Yitzchak and Yaakov, and also the words "Shivtei Yeshurun" (Yoma 73b). On each stone were six letters, including the name of the tribe, and thus there were 72 letters in total.

When a question was brought before the Kohen Gadol, he would meditate on His Holy name of the Urim. This would cause the letters on the stones of the breastplate to light up or protrude. These letters spelled the answer to the question. However, since they were not in any special order, again the Kohen Gadol would have to meditate on the Holy name of the Tumim and, thus, he would be given Ruach Hakodesh - Divine inspiration - a level of prophecy lower than the one called "nevuah," to arrange the letters properly and convey the correct answer.

In the second Beit Hamikdash, though they had the breastplate, they did not seek instructions from it, either because the power of Ruach Hakodesh was lacking or because they lacked the Urim veTumim. During this period they relied on a bat kol, a voice which emanated from heaven, a level of prophecy lower than Ruach Hakodesh. ...".

According to one of the points of view described in a Jewishgates web page by David E. Lipman: "... Me'am Loez on Tetzaveh: The Ephod and Urim and Tumim ... Exodus 28:30: Place the Urim and Thumim in the breastplate of judgment, and they shall be over Aaron s heart when he comes before God. Aaron will then carry the judgment device for the Israelites before God at all times. ...

... The Urim and Thumim consisted of God's Explicit Name (Shem HaMeforash). This is the great and awesome name of God ... This Name was called Urim and Thumim because of its function. It was called Urim [from the word Uor meaning light]. This was because it enlightened things and explained to Israel the hidden things that they did not know. It was also called Thumim [from the word Utam meaning complete]. This was because it completed and perfected its words, and everything predicted by the Urim and Thumim would come true. ...

... the High Priest ... would gaze at the stones of the breastplate in deep contemplation. ... it would answer ... by accentuating the letters ... These letters were engraved in the stones, but when the priest was meditating on them they would appear to be protruding like the letters on type. ...

... the Urim and Tumim were two separate Divine Names, each of which had its own special function. The Divine Name known as Urim (the "Illuminator") would cause the letters that were necessary for the answer to appear to light up for the priest. ... However, the High Priest still would not be able to understand the answer since he would not know the order of the letters. ... Therefore, there had to be a second Divine Name, known as the Tumim. When the High Priest contemplated this name, he would gain a level of Divine Inspiration approaching prophecy. Then, he would see the order of the letters that were shining, and he would understand how to read them. This second name was therefore called Thummim, the "Completor." It was through this name that the reply was completed.

The Torah does not say, "You shall make the Urim and the Thumim," as it says with regard to the other articles in the Tabernacle. In the case of the other articles, the Torah says, "You shall make an ark; " "You shall make a table;" "You shall make a gold menorah;" and the like. Here, however, the Torah says, "You shall place the Urim and Thumim in the breastplate" without mentioning at all how the Urim and Tumim were made. This is because the Urim and Thumim were not made by man. Neither were they brought as a gift by any human. Rather, they were Divine Names, as we have said, and God gave them to Moses secretly. Now that the Torah states where the Urim and Tumim must be placed, God told Moses, "Place the Urim and Tumim in the breastplate. You know that they are the Divine Names that I gave you secretly." Thus, the Torah says, "the Urim and the Tumim" with the definite article even though the Torah nowhere identifies these objects. This is because, as we have said, they were not the product of human hands. ...".

My conjectures about Urim v'Tumim begins with the assumptions that:

• its purpose, along with the breastplate/stones/letters, is to communicate from the Mind of G-d, considered as the Minds of Spirit Beings, to Humanity;
• the Minds of Spirit Beings communicate thought/information by Quantum Information Theory;
• the Minds of Humanity mostly communicate thought/information by Classical Information Theory.

Here I should note that, since human minds have Quantum Consciousness, some human minds can communicate directly by Quantum Information Theory resulting on occasion in direct enlightenment of some individuals, but most inter-human communication is by written/spoken/gesture language using Classical Information Theory.

Given the above, my conjectures are:

• Urim takes Quantum Information in the form of the Quantum Code [[256,0,24 ]] whose word length 256 corresponds to the 256 Odu of IFA and to the dimensionality of the Cl(1,7) Clifford Algebra of the D4-D5-E6-E7-E8 VoDou Physics model ) and transforms it into Classical Information in the form of the Golay Code C24 [24,12,8]. Thus it is said that Urim is like the light of observation that acts to decohere the superposed Quantum State to produce an observed decohered Classical State.
  • Note that [[256,0,24]] has 256 qubits, only 2^0 = 1 word ( a coherent state of superposition of many possibilities ), and minimum distance 24 corresponding to the dimensionality of the Leech Lattice.
  • Note that [24,12,8] has 24 classical binary bits, 2^12 = 4,096 words, and minimum distance 8 corresponding to the dimensionality of the E8 Lattice.  
• The breastplate contains an array of 72 letters on stones corresponding to 3 binary 24-bit words of the Classical Golay Code C24 [24,12,8]. Each of the 3 columns of stones would carry 1 word. Each of the columns could then be regarded as an array of 4 rows, each row being 1 stone with 6 letters, making up a 4x6 array of letters, corresponding to the 4x6 array structure of the MOG (Miracle Octad Generator) and the hexacode C6 [6,3,4], whose letters are in the 4-element Galois Feild GF(4) and whose 3^4 = 64 words have 6 letters.
• Tumim corresponds to symmetry structure of the Golay Code C24 [24,12,8], including its Steiner system S(5,8,24) and its symmetry group, the Mathieu group M24 of order 24x23x22x21x20x48. The symmetry/perfection/truth of Tumim allows for determination of whether or not each of the 3 words of the breastplate/stones/letters belongs in C24 and for correction of errors. Computational techniques of Tumim include the MOG and the hexacode C6.

Here, paraphrasing from the books

• Sphere Packings, Lattices, and Groups by J. H. Conway and N. J. A. Sloane (Springer, Third edition 1999),
• From Error-Correcting Codes Through Sphere Packings to Simple Groups, by Thomas M. Thompson (MAA 1983),
• A Course in Combinatorics, by J. H. van Lint and R. M. Wilson (Cambridge 1992),
• Designs and Their Codes, by Assmus and Key (Cambridge 1992),

are some details about those mathematical structures:

Error-correcting codes were discovered in mid-20th century after R. W. Hamming got irritated by his computer stopping when it encountered an error, causing him to realize that if his computer could detect errors it should be able to locate and correct them.

C24 is a binary Golay code [24,12,8] is a code of length 24, dimension 12, and minimal distance 8 over the binary field F2. Of the 2^24 sets of 24 zeroes and ones, 2^12 = 4096 are in C24. They can be divided into classes:

• 1 that has 24 zeroes;
• 759 that have 16 zeroes and 8 ones;
• 2,576 that have 12 zeroes and 12 ones;
• 759 that have 8 zeroes and 16 ones;
• 1 that has 24 ones.

The symmetry group of C24 is M24, where M24 is the simple Mathieu group of order 24x23x22x21x20x48. M24 has several interesting subgroups, including:

• PSL2(23)
• the sextet group 2^6:3xS6
• the octad group 2^4:A8 = 2^4:GL4(2)
• PSL3(4) = M21
• the trio group 2^6:(S3xL2(7)) = 2^6:(S3xL3(2))
• the Mathieu group M23
• the Mathieu group M22 and M22:2
• the Mathieu group M12 associated with the Steiner system S(5,6,12) and the ternary Golay code C12 [12,6,6] with 3^6 = 27x27 = 729 words. C12 can be constructed using Rubik-icosahedron twist-permutations.

An octad is a Golay codeword of weight (distance from the origin) 8. The octads of C24 constitute a Steiner system S(5,8,24). The Steiner system S(5,8,24) is a set with 24 points and a collection of distinct 8-subsets (called blocks) such that any 5-subset is contained in exactly 1 block.

The MOG is a 4x6 binary array, so that it would carry 24 bits of information.

The hexacode C6 is a 3-dimensional code of length 6 over F4. C6 has 36+12+9+6+1 = 64 = 2^6 = 4^3 = sqrt(4^6) hexacodewords.

The Mathieu group M24 is transitive on trios consisting of three disjoint octads. The subgroup fixing a trio is a group 2^6:(S3xL2(7)) it being significant that L2(7) is isomorphic to L3(2). and is Klein's group of order 168 = 7x6x4, and is the automorphism group of the Hamming binary code H7 [7,4,3].

By fixing two points of the 24 we obtain the Mathieu group M22 which is the stabilizer of the Steiner system S(3,6,22) obtained by deleting those two points from all octads of S(5,8,24) that contain them both.

According to a Jewish Celebrations web page by Reb Yosef:

"...  Commentary from the Stone Edition Chumash: ... Ramban adds that Moses himself wrote this Name [or Names], because only he had the spiritual knowledge and greatness to know what had to be done. This is why the Urim v'Tumim is not mentioned among the vestments and artifacts of the Tabernacle that were made by artisans or contributed by the people.

During the waning years of the First Temple Era, King Josiah realized that Eretz Yisrael would be conquered and, fearing that the most sacred parts of the Temple would fall into profane hands, he removed the Urim v'Tumim from the Breastplate and hid it, and he also hid the Ark containing the Tablets, and the anointment oil. None of them were found during the period of the Second Temple. While their absence denoted a diminished degree of holiness, it did not prevent the performance of the Temple service. It did mean, however, that from that time onward, the Kohen Gadol could not present Israel's urgent questions for God's response. ...".

Since the Urim v'Tumim has not been available for over two thousand years, it is understandable that there exist various opinions about what it is. My opinion is that my conjecture may be near the truth. However, you can find many other opinions, such as some of those stated on a web page of the International Standard Bible Encyclopedia:

"... 4. Recent (Critical) Views: The view most generally held today is that the Urim and Thummim were two sacred lots, one indicating an affirmative or favorable answer, the other a negative or unfavorable answer ... Efforts have been made to support the view that the Urim and Thummim themselves were sacred lots on the basis of analogous customs among other peoples (e.g. pre-Islamic Arabs ... and Babylonians ...".

My personal opinion is that, although the Urim v'Tumim and breastplate with stones and letters might be regarded as a divination system, it is much more sophisticated than two affirmative/negative lots, and its relation to other divination systems is correspondingly much more sophisticated. For instance:

• the 72 letters might correspond to the 72 root vectors of the exceptional Lie algebra E6 which root vectors are related to Aperiodic Tilings

;

• and the 72+6 = 78 dimensions of E6 might correspond to the 78 cards of Tarot;
  • and the 22 Major Arcana cards (including 0) of Tarot might correspond to the Hebrew alphabet;
• and the structure of 28+17+33 = 78-dimensional E6 might be contained in representations of the 256-dimensional Clifford Algebra Cl(1,7) of IFA in a way that is structurally similar to the D4-D5-E6-E7-E8 VoDou Physics model:
  • 28 dimensional bivector representation;
  • plus 17 = 1 + 2x8 dimensional complexification of 8 dimensional vector representation;
  • plus 33 = 1 + 2x16 dimensional complexification of 8+8 = 16 dimensional spinor representation.

According to  a Yale Alumni Magazine web page, by Dan Oren '79, '84MD:

"... The two Hebrew words (Urim v'Thummim) at the center of the official Yale seal

appear eight times in the Hebrew Bible. Jewish sources considered them oracular gems worn by the high priest Aaron. And their presence in Leviticus 8:8 - the middle verse of the Pentateuch - suggests that they identify the book on the Yale seal as the Bible itself. ...

... To the ancient Hebrews, the Urim and Thummim reflected the oracular will of God. To the Puritans who shaped early Yale, that oracular will was represented by Jesus. ...

... If we return to the Latin Lux et Veritas, a remaining question is of how the common translation from that era of Thummim as "perfection," became Veritas or "truth." By 1735 (the year before the Yale seal began to appear on Yale diplomas), under the stimulus of Jonathan Edwards, theological battles between "New Lights" and "Old Lights" were raging in Connecticut. The "New Lights" attacked the established order by questioning the value of education outside of understanding Jesus. Many "Old Lights" thought religious knowledge was central to an education, but hardly sufficient for one. The latter opinion prevailed at Yale. Mathematics and metaphysics, insisted Yale's leaders, had to go hand in hand with theology and ethics. By choosing to translate Urim V'Thummim as Lux et Veritas, it seems -- in contrast to the one-dimensional approach of Harvard -- Yale insisted that its college offered the essentials of proper learning: the "light" of a liberal education and the "truth" of an old New England religious tradition....".

[ Here I cannot resist adding a comment that the letter Y has the same structure as the Dynkin diagram

for the D4 Lie algebra used in to the D4-D5-E6-E7-E8 VoDou Physics model (which I sometimes represent in a different but mathematically equivalent way, such as flipped vertically or flattened to a T shape). ]