Tony Smith's Home Page


The Talmud is a detailed expansion of the Torah. The Schottenstein Edition of The Talmud is published by ArtScroll. An 18-volume English translation of the Talmud is available in CD-ROM format from Soncino Press. Rabbi Adin Steinsaltz has written a multivolume work, The Talmud: The Steinsaltz Edition (Random House), which includes a A Reference Guide, in which he says:

"... The ultimate purpose of the Talmud is ... to seek out truth. ... The Talmudic dialectic can be compared to an inquiry in pure science, particularly in the sphere ... of mathematics. ...".

Some parallels between the Talmud and present-day science are drawn by Andrew Goldfinger in his book Thinking About Creation (Aronson 2000). Here are some quotations from his book, along with my comments, on some subjects, including:

Here, on some other subjects, are some quotations from other sources, along with my comments:


"... If we open the Bible to the book of Ezekiel we find that the prophet has written ... of the revelation ... , known as the Account of the Chariot, ... he received from God. ... The information ... is so esoteric that ... we have no hope of understanding it unless we can find a teacher who is privy to the oral explanation that Ezekiel communicated to his students. ... The Talmud ... Chagiga ... warns that the true meaning of the Account of the Chariot ... should only be taught to one person at a time. ...".

The entire Book of Ezekiel is carved on a set of 64 marble and granite tablets in raised letters on a square grid and in continuous script, now in Jerusalem.

Teaching only one person at a time is a standard practice of Taoism. There are interesting correspondences between Torah-Talmud-Kabbala and Taoism-Buddhism.


"... if we open the Torah and start reading at the book of Genesis, we encounter ... not one, but two, stories of creation. ... the presence of two sequential creation stories ... does not signify two creations. ... There are different names used for God in each of .. the two stories ... The oral tradition tells us ... different names indicate different ways in which God interacts with the world. When we experience God as the source of chessed, of loving kindness, we call him Hashem ... when we experience God as the source of g'vurah, of strength and justice, we call Him Elokim. ...

,,, In the first story, the name used is Elokim, God as the source of law, the creator of a natural ... universe ...

... in the second story ... name ... for God: HaShem Elokim, indicating both justice and mercy. ...

... The Talmud tells us ... that the true explanation of the story of creation should only be taught to two at once. ... Just as argument is seen, by the Talmud, as the way to eventually discover what is true, so is honest dialog ... the only way to stimulate and achieve growth. ...".


"... In the first story ... The Torah starts with, "In the beginning, Elokim created ..." The word used for "create" is bara, which ... occurs principally in only three contexts in the entire Torah. The first use ... refers to the creation of the universe. The second is on the fifth day ... the creation of the great creatures of the sea. Finally, it is used to refer to the creation of man on the sixth day. According to the Ramban ... Nachmanides, thirteenth-century ... commentator ...and Sforno ... commentator, 1475-1550 ... [bara] ... indicates a creation of somenthing from nothing, Yesh MeAyin ... All other acts were the transformation of something already existing into something else. ... The initial state of the physical universe is described as being Tohu VaVohu ... The Talmud ... Chagigah ... identifies Tohu as a green or yellow line surrounding the world ... and Vohu as stones in the depth of the waters. ... the book of Isaiah .. refers to the line of Tohu and the stones of Vohu. ... the Ramban ... sees the Tohu VaVohu as a formless and malleable substrate from which all other matter was formed ... Rashi ... eleventh-century ... commentator ... does explain the terms in combination as referring to an astonishing emptiness ... Rabbi Samson Raphael Hirsch describes ... Tohu VaVohu ... as "astonishingly chaotic" ... Kabbalah (the esoteric part of the Torah) tells us that God created and destroyed many worlds before this one. ... some scholars ... assume that ... they were destroyed without a trace. ...".

"... God made a statement, "let there be light", and light came into being. ... The Torah goes on to say that He ... separated the light from the darkness. ... When the Torah refers to light, is it talking about the sea of massless particles that existed before the single force was hidden? If so, we have perfect consistency between the scientific and Torah views. ... Rashi ... eleventh-century ... commentator ... quotes the Talmud ... Chagiga ... It says that God separated out some of the primeval light and hid it away for a future time when it would be used by the righteous. This light will extend through all space, and with it it will be possible to see from one side of the universe to the other. ...".

If the light corresponds to the forces of nature, it is interesting that:

What other forces of light might now be hidden and available for future use by the righteous? Perhaps examples might include: phenomena related to


"... the second day. Only one thing was created. It is called the Rekiah ... it does separate the "waters above" from the "waters below". ... In the Talmudic tractate Chagiga, ben Zoma reports that ... the Rekiah is only three-finger-widths wide. ...".

If you consider the Rekiah to be a separator, not of two parts of 3-dim space, but of two parts of 4-dim spacetime, and

if you consider the Rekiah to be a separator of our expanding universe at a particular time, with the "waters below" corresponding to our universe prior to Rekiah time, and the "waters above" corresponding to our universe after Rekiah time, and

if you consider the width of the Rekiah to be 3 cm (one cm per finger-width), so that the time of Rekiah is 3 cm / 300,000 cm/sec = 10^(-5) sec, and

if you consider that the time of Rekiah refers, not necessarily to its duration, but to its time after the big bang of our universe,

then look at what happened in our universe at age 10^(-5) sec:

According to the standard cosmological model as described in The Early Universe by Kolb and Turner (Addison-Wesley 1994), at page 72: "... At a temperature of about 100 to 300 MeV ( t =approx= 10^(-5) sec ) the Universe should undergo a transition associated with... color confinement, after which the strongly-interacting particles are ... baryons ... and ... mesons ...".

Could the Rekiah be related to the quark/hadron phase transition of our expanding universe, the time when protons and neutrons first congealed out of the pre-existing quark soup ?

If so, since color force gluons mix 4-dim SpaceTime dimensions with 4-dim Internal Symmetry Space dimensions, the Rekiah could be the region in which SpaceTime goes from 4-dim to (4+4)=8-dim.



"... Babylonian Talmud Taanis 6a ... speak[s] of a deep primal separation between the ultimate reality and the world as we know it. This separation is the result of an event called the tzimtzum. ... The Torah Temima [... comment on the words "malei nima" from ... Chagiga...], in discussing the Rekiah, contrasts mans's sloppiness ... with God's precision. The verb he uses for precise specification is tzamtzeim, which derives from the same root as tzimtzum. Perhaps the torah Temima is hinting at the identification of the Rekiah with the tzimtzum. ... God is an absolute entity, without attributes and without structure. ... Far from being too complex for us to understand, God is actually too simple. ... if God is a perfect simple unity, how could He give forth a seemingly imperfect world of complex structure? ... we come to the idea of the tzimtzum. In human language, God ... condensed HIs perfect being to allow room for the imperfect worlds to exist. ... The Hebrew word for the universe is HaOlam, wihich comes from the root 'oLaM, meaning to hide or conceal. ... Since the tzimtzum involves the concealment of God's unity in the imperfect multiplicity of the world, the work of creation consists ... of the creation and maintenance of diversity. ... although God is the only force operating in the world, He conceals His presence and presents us with a multiplicity of less real forces. it is these forces that seem most real to us, since we are bound to the physical world, and it is only after we have broken the conection to this world and enter the afterlife, the World of Truth, that we can achieve a clearer picture of what is going on. ... ".

If the Rekiah is one example of tzimtzum condensation/phase transition related to the quark/hadron phase transition of our expanding universe, the time when protons and neutrons first congealed out of the pre-existing quark soup,

then other examples of tzimtzum condensation/phase transition may correspond to other events described in The Early Universe (Addison-Wesley 1994) by Kolb and Turner (on pages 72 and 74 and in chart on page 73) as occurring at various ages of our universe:

  • ions and electrons combine to form atoms, with matter decoupling from radiation and the Universe itself being the surface of last scattering for the microwave background radiation, at about 10^13 sec (about 300,000 years); and
  • matter density equals radiation density at about 10^11 sec (about 3,000 years); and
  • nucleosynthesis during ages from 10^(-2) sec to 10^2 sec; and
  • the quark-hadron phase transition at age about 10^(-5) sec; and
  • electroweak symmetry breaking at age about 10^(-11) sec; and
  • the Planck time at age about 10^(-43) sec.

The series of tzimtzum might be a series of phase changes with each successively higher energy tzimtzum revealing more and more symmetry, as in the sequence:

  • condensation of atoms from plasma; and
  • condensation of matter structure from smooth radiation; and
  • condensation of nuclei from neutrons and protons; and
  • condensation of neutrons and protons from quarks; and
  • condensation of massive weak bosons from electroweak bosons and Higgs scalars; and
  • condensation of 4-dim spacetime from 8-dim spacetime.

"... The Torah tells us that there is only one ... true force ... God. But ... God keeps Himself hidden ... through the process of the tzimtzum ... The hidden parts of the Torah tell us that the world we perceive is but the tip of the iceberg, that there are much deeper levels of reality that are hidden from us. ... underlying it all is God ... this deepest level of reality is forever beyond our grasp. ...".

Further levels of tzimtzum might involve phenomena related to:

Some concepts related to tzimtzum are shevirat ha-kelim ("breaking of the vessels") and tiqqun ("restoration").



"... While the first creation story could be taken to be a treatise on ... the origins of the physical universe ... with the second story ... man ... ( The ... Hebrew ... word adam indicates a human being, whether male or female ) ... is the central figure, and all of creation is seen to be but the arena within which he acts. ...

... The Torah says that Adam ... could not find an ezer knegdo, a helper against him, ... a helper to engage in dialogue with him, so that he could realize his true spiritual potential ... In the Midrash we find that ... Adam was both male and female ... God caused Adam to fall into a deep sleep, and He then took flesh from his side and formed ... a woman. ... God fissioned this single being into two separate ones ... the attraction between a ... male ... and a woman is the desire to reunite that which was split apart. ... only through marriage (with dialog) can the unification occur. ...

... man was created with two conflicting drives, the Yetzer HaTov, ... that holy spark within us that gravitates toward God ... , and the Yetzer HaRah, the drive that, if unguided, leads to evil ... the Torah tells us how to turn ... Yetzer HaRah ... toward good. ...

... the person ... focussed on clothing or sensual pursuits is pained by the loss of a physical body and experiences the afterlife as a punishment, while the person emotionally invested in Torah is finally able to achieve higher levels of understanding than were ever possible during life and so feels deeply rewarded ...".

"... Torah scholars are impervious to the fire of Gehinnom. (see Nefesh HaChaim 4:17) ... Beis HaLevi (Derush section 13) elaborates: Gehinnom could conceivably be for either of two purposes: (a) to punish a person for the evil he performed in his lifetime; or (b) to cleanse his soul of sins ... In truth, Gehinnom serves both these purposes. Most persons are in Gehinnom for a maximum of twelve months and then merit entrance into the World to Come ... Nimos asked R' Meir if every person who descends to Gehinnom ascends from it to Gan Eden; R' Meir answered ... But if a person ... is entirely evil ... there is no part of him that would remain to enter Gan Eden, Therefore, he never ascends from Gehinnom. ...". (From Talmud Bavli / Tractate Chagigah, The Gemara, The ArtScroll Series / Schottenstein Edition, Mesorah Publications Ltd. (1999) 15b 1,5)


 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:

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:


Here, paraphrasing from the books

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.


Here are some more comments on the history of Urim v'Tumim:  

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:



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). ]



What about Torah study by non-Jews?  

"... a non-Jew who studies the details of the seven Noahide laws, which are incumbent on him, deserves the honors due a Kohen Gadol (Sanhedrin 59a). The study of the seven Noahide laws may lead him to study most of the precepts of the Torah (Meiri to Sanhedrin 59a; see Responsa, Rama section 10). ...

... Noahide Laws - the seven commandments given to Noah and his sons, which are binding upon all gentiles. These laws include the obligation to have a body of civil law, and the prohibitions against idolatry, immorality, bloodshed, blasphemy, stealing and robbing, and eating limbs from a live animal. ...". (From Talmud Bavli / Tractate Chagigah, The Gemara, The ArtScroll Series / Schottenstein Edition, Mesorah Publications Ltd. (1999) 13a 3)



Tony Smith's Home Page