Sunday, May 21, 2017

The Greco-Roman Egyptian Alpha-Numerals Theory, or the “Ahmestrahan” Numerals

(Update 2022:  The author has substantially modified his position on this post since the time it was first posted.  This is mostly for archival purposes.)

 The Greco-Roman Egyptian Alpha-Numerals Theory, or the “Ahmestrahan” Numerals

I will be presenting two separate theories on Egyptian “Alpha-Numerals.”  This article is the first one.  This article is inspired by the statement in Facsimile #2 of the Book of Abraham, Figure 11, which states, “If the world can find out these numbers, so let it be. Amen.”  Yet, if one looks at the symbols pointed to, they are not conventional Egyptian numeric characters, but they are actually conventional Egyptian Alpha-characters.  This means that they are the characters typically representing “text” in the Egyptian language.  But this is not unexpected with regard to the Book of Abraham, because the rest of the characters thought of as “text,” both in the Facsimiles of the Book of Abraham, as well as in the Kirtland Egyptian Papers that present character translations, are not the conventional Egyptian translations of said characters.

Here is a link to a companion piece to this article by one of my partners, Vincent Coon, that contains his opinions and research on this matter:

Anyhow, this first article in the series is a presentation of how late Egyptians could have associated their uni-literal (single-consonantal) characters with the Greek-Hebrew-Semitic Alpha-Numeric system.  It doesn’t really answer very well with evidence  the question of which system of representation would have been used for Bi-literal, Tri-literal and Determinative characters, but does make a suggestion.  So, we start out with the Book of Abraham Facsimile #2, the Hypocephalus of Sheshonq, Figure 11.

The following is the original form of the hieroglyphs in the Hypocephalus in figure 11.  In the original, they go from right to left:

Here is the copy that was in the Kirtland Egyptian Papers, which gives us a separate view of what Joseph Smith's scribes originally saw before them, but there is no essential difference:

Here are the characters flipped so they go left to right:

Here are the characters transformed into regularized hieroglyphs, along with a transcription into the way they are read in Egyptian, as shown by Hugh Nibley in One Eternal Round:

(Hugh Nibley, One Eternal Round, p. 327)

These particular hieroglyphics, the way they are “read” in Egyptian, translate to, “O God of the sleeping ones from the time . . . “  They are part of a larger message continued on in the other panels, in totality, saying, “O God of the sleeping ones from the time of the creation.  O Mighty God, Lord of Heaven and Earth, of the hereafter, and of his great waters, may the soul of Osiris Shishaq live.”

Yet, as we noted above, Joseph Smith commented on this, saying, “If the world can find out these numbers, so let it be. Amen.”

What are we to make of this?  Well, it is the same exact problem as elsewhere in the explanations for the Facsimiles, as well as in the Kirtland Egyptian Papers.  The way Joseph Smith translated this is not to “read” them, but as with the rest of the symbols, he gave interpretations to characters that were treated singly as single pictographs, rather than concentrating on what they “say” in Egyptian.  It is quite true that they can be read conventionally, but that was not what he was doing here.

Referring to  Figure 4 of the Hypocephalus, Facsimile #2, Joseph Smith says “Answers to the Hebrew word Raukeeyang, signifying expanse, or the firmament of the heavens; also a numerical figure, in Egyptian signifying one thousand; answering to the measuring of the time of Oliblish, which is equal with Kolob in its revolution and in its measuring of time.”  There was no text in figure 4 to read.  This is a statement about the picture itself, and the picture itself was said to be a numerical character in Egyptian.  This is the figure of the god Sokar on the boat, extending out his wings.  And this says that it answers to the Hebrew word raqia (another way to transliterate “raukeeyang,” which does indeed mean the expanse of the heaven in the Hebrew language.  The action of Sokar’s extending his wings would seem to be symbolic of the idea of expanding, or expanse.  While some Egyptologists endeavor to deny the fact, LDS apologists have successfully and reasonably defended the fact that Sokar in this context, in his ship as shown, is indeed symbolic of the number 1000.  But remember, this is entirely an interpretation based on the picture.  There is no text here in the figure to interpret.

We have the same exact issue above with figure 11.  Each hieroglyph in figure 11 is a separate little picture, when separated out singly.  And each one needs to be interpreted separately, on its own merits, to figure out which number it represents, the same as how Sokar on the boat was a figure representing a number.  What the text “says” here has nothing to do with the little pictures themselves, and we must segregate these two concepts in order to come to a proper understanding to what is going on.  We must come to know that the pictures themselves can be representational on their own, in an entirely separate scope, from what they “spell out.”  So, the first step, then, is to separate out each hieroglyph, and analyze them, even though combinations of these hieroglyphs may actually compose a larger number, much like how 1 and 0 can compose the number ten, although whatever system is at work here for these to be interpreted as numbers is not immediately obvious.  But it isn’t strange that Egyptian symbols that are used to write out text could have been used as numbers.  Precedents are the fact that both the Hebrew and Greek alphabets were used for numbers.  Similarly, our own alphabet, named the Latin alphabet, was used by the Romans for their numerals.  We didn’t get our own numbers that we use now until the middle ages from the Arabs.  How many times have you seen in the credits of a movie the year the movie was made in Roman numerals, composed of letters from the Latin Alphabet, the very alphabet we use?  The letter I is the number 1.  The letter V is the number five.  The letter X is the number ten.  The letter L is 50.  The letter C is 100.  And the letter M is 1000.  And so, in the case of Roman Numerals, the letters are not used to spell out anything.  They are used in a separate context as numbers.  There is nothing alien about this concept whatsoever, and it is a phenomenon that is very well-attested historically.  There is nothing crazy about Joseph Smith’s assertion that symbols from the “Egyptian Alphabet” could be used numerically.  We just somehow must figure out which system is being used in these characters for numeric representationalism.  The best way to do this is to not limit ourselves to one system, but to make more than one suggestion, and over time, the best system may win out, with enough research.  But for now, we make multiple suggestions.

As I have shown in other articles on this blog, the whole Alphabet itself is derived from a set of Egyptian Hieroglyphics ( 30 symbols) originally repurposed  to represent constellations of the Lunar Zodiac (a set of 30 constellations representing lunar stations or “mansions” that overlap the regular 12 constellations of the Zodiac  on the ecliptic.  I have identified these constellations and matched them up one by one with each proto-letter of the earliest alphabet called the Proto-Sinaitic by some scholars.  So the whole regular Alphabet as we know it is actually “reformed Egyptian,” from a certain point of view.  But this set of characters was later modified by the Phoenicians and adopted by the Greeks.
As Georges Ifrah, a very important French scholar on numbers, has pointed out, however, there is actually a myth that the Phoenicians used their letters as numbers:

It has long been asserted that, long before the Jews and the Greeks, the Phoenicians first assigned numerical values to their alphabetic signs and thus created the first alphabetic numerals in history.
However, this assumption rests on no evidence at all.  No race has yet been discovered of the use of such a system by the Phoenicians, nor by their cultural heirs, the Aramaeans . . .
The numeral notations used during the first millennium BCE by the various northwestern Semitic peoples . . . are very similar to each other, and manifestly derive from a common source . . . (The Universal History of Numbers, p. 227).

Ifrah then goes on to show the evidence of a separate system of Semitic numbering that was used among them that was NOT alphabetic at all, up until the JEWS adopted the system of the GREEKS for Alpha-Numerals much later on.  In other words, it was the GREEKS that invented the use of alpha-characters as numbers, not the Phoenicians, or Semites like the Jews.  As Ifrah shows from page 232 to page 239, the Hebrews didn’t adopt the Greek system of Alpha-numerals until Late Hebrew at the start of the COMMON ERA.  Before the Common Era, all the archaeological evidence shows that other systems of numerals were among them.  This presents a huge problem for those that adhere to the theory of the cabalists that try to derive meaning from the very ancient Hebrew text of the Torah by way of Gematria (the symbolic use of numbers as symbols in the Hebrew scriptures).  In other words, those trying to read Gematria into the Hebrew Bible are actually reading their own later system into it, searching for meaning in it.  It is true that the later Hebrews in the time of the Book of Revelation used the conventional alpha-numbers of the day.  That much is true.  Nevertheless, the the Alpha-numeral system was not in use by those who wrote the Hebrew Bible AT ALL, and any attempt to read this into it is either iconotropic, or flawed!  As Ifrah writes:

. . . [I]n Palestine Hebrew letters were only just beginning to be used as numerals at the start of the Common Era.
This is confirmed by the discovery, in the same caves at Qumran, of several economic documents belonging to the Essene sect and dating from the first century BCE.  One of them, a brass cylinder-scroll . . ., uses number-signs that are quite different from Hebrew alphabetic numerals.
Further confirmation is provided by the many papyri from the firth century BCE left by the Jewish military colony at Elephantine (near Aswan and the first cataract of the Nile).  These consiste of deeds of sale, marriage contracts, wills and loan agreements, and they use numerals that are identical to those of the Essene scroll . . .  (pp. 234-235)

And Ifrah goes on and on with more and more archaeological evidence.  He shows a table of the accounting system of the Kings of Israel on p. 237 from the archaeological evidence, and the numerals are actually just Egyptian hieratic number symbols!   The earliest evidence for use of alpha-numerals among the Jews is the coins from the first Jewish Revoilt in 66-73 CE (see Ifrah, p. 233).

So, Ifrah destroys the myth of Alpha-numerals among the Semites up until the Common Era.  But with Egyptian numerics, we aren’t even really talking about a system of Jews or Semites, even those in the Greco-Roman era.

However, since we are dealing with literate Egyptians (the “Ahmestrahans” of the Kirtland Egyptian Papers) of the Greco-Roman era that dealt with all the number systems and languages of the day.  None of this presents a problem for our current theory, that groups of Egyptians in the Greco-Roman era adopted the number-system of the Greeks for their own “letters.”  The only problem would arise if someone supposes that these Egyptians got said system from the Jews.  It was the Jews, as we saw here, that later got their particular system from the Greeks.

There are two systems of Greek Alpha-Numerals.  The oldest is the Greek system from the Sixth century BCE, the numbering system that was used in the Iliad and the Odyssey.  This is, according to Ifrah, “a simple substitution of letters for numbers, not a proper alphabetic number system . . .” (See Ifrah, p. 214):

Alpha =1
Beta = 2
Gamma = 3
Delta = 4
Epsilon = 5
Zeta = 6
Eta = 7
Theta = 8
Iota = 9
Kappa = 10
Lamda = 11
Mu = 12
Nu = 13
Xi = 14
Omicron = 15
Pi = 16
Rho = 17
Sigma = 18
Tau = 19
Upsilon = 20
Phi = 21
Chi = 22
Psi = 23
Omega = 24

It was later in the Greco-Roman era where the Greeks started to use a system that was a true alpha-number system that was more elaborate.  The earliest evidence of this could be a “Greek papyrus from Elephantine” which has a “marriage contract that states that it was drawn up in the seventh year of the reign of Alexander IV (323-311 BCE), that is to say in 317-316 BCE . . .” (Ifrah, p. 233). This more “true” alpha-numbering system differs from the previous and goes like this:

Alpha = 1
Beta = 2
Gamma = 3
Delta = 4
Epsilon = 5
Digamma = 6
Zeta = 7
Eta = 8
Theta = 9
Iota = 10
Kappa = 20
Lambda = 30
Mu = 40
Nu = 50
Ksi = 60
Omicron = 70
Pi = 80
Koppa = 90
Rho = 100
Sigma = 200
Tau = 300
Upsilon = 400
Phi = 500
Chi = 600
Psi = 700
Omega = 800
San (Sampi) = 900

This more elaborate and advanced system was the system that was adopted by the Jews, spoken of earlier.  As you can see, only the first five numbers are the same as those from the previous system of the Greeks.
Now, what about the “Egyptian Alphabet”?  How can this work for the Egyptians?  Well, part of the problem with that has to do with how to match up the Egyptian hieroglyphics with Greek/Semitic letters.  The Egyptians have symbols that represent one, two and three consonants (uniliterals, biliterals and triliterals respectively), and others that represent context, called determinatives or determiners.

Now, as you can see, for the uniliterals (single consonantals), it is easy enough to try to line them up with the numeric values of letters from the other alphabets that they seem to correspond to.  The numeric values in this case would seem to be consistent and constant in both the Semitic and Greek alphabets.  These in general follow the “North Semitic” order, which is a fairly consistent ordering scheme for many alphabets.  It may be that the north semitic ordering was created for numerics to begin with.  Because the other significant ordering system is called the “South Semitic,” yet even in this scheme, the number values of the letters in these alphabets following it are consistent with their North Semitic counterparts.

So, for uniliteral Egyptian characters, it may be that the numeric scheme is straight-forward in this way, that we can expect that they are simply numerically equivalent to their Semitic counterparts.  As we have shown elsewhere, the people that were concerned with these types of numbers anyway in the Hypocephalus would have been the Egyptians of the Greco-Roman period.  As the research of Dr. Rozen Bailleul-LeSuer shows in his article Between Heaven and Earth:  Birds in Ancient Egypt, there is evidence that the alphabet of Egyptian uniliterals “followed, with some variations, that of the South Semitic alphabet, which originated in the Arabian Peninsula. By comparison, he deduced that the latter was apparently the older.  Note that the alphabetical order used in modern Egyptological publications was established by scholars in the nineteenth century and does not follow that of the original Egyptian alphabet.”  ( Also, it is significant that Dr. Bailleul-LeSuer wrote:

The text about which Smith and Tait came to such conclusions, namely, papyrus (hereafter P.) Saqqara 27 (fourth–third century bc), is a school text consisting of two alphabetical lists with bird names. In the first list (lines 2–7), “various birds are said to be ‘upon’ various trees or plants” with which they are paired. In each pair, the bird and plant names always begin with the same letter. For example, in line 2, the first phrase of the list reads as follows: [r] p3 hb ḥr p3hbyn “the ibis (was) upon the ebony-tree,” in which the word hb “ibis” is paired with hbyn “ebony-tree,” both beginning with the letter h. In the second list (lines 9–14), “various birds are said to ‘go away’ to various places.” In line 10, for instance, one finds the sentence šm n⸗f bnw r Bb[l] “the Benu-bird went off to Baby[lon]” in which, according to the same pattern, the word bnw “heron” is paired with Bb[l] “Baby[lon],” both names beginning with the letter b.

As you can see, these are precisely the general types of alphabetical word-game pairings that I have been speaking about the whole time in this blog, as are used in the Kirtland Egyptian Papers, where Egyptian hieroglyphics are artfully paired with things in creative ways.  Nobody would say that the Egyptian letter that corresponds to hb “translates” as ebony tree, yet here, the alphabetical Egyptian uniliteral letter is paried with Ebony tree in a pun, a word game!

P. Saqqara 27 is in fact one of the few papyri, ranging from the Late Period to Roman times, to include letter names or words listed in alphabetical order and thanks to which the sequence of letters in the Egyptian alphabet can be established, at least partially.  In some of these papyri, such as P. Berlin 8278 and its fragments, letter names could also be placed at the beginning of a line as a way of classifying different sections of the text by using letters instead of numbers.

Again, as I have noted at other times in this blog, I am specifically claiming that Egyptian letters from the Sensen Papyrus were artfully used to decorate text in the Book of Abraham as a marker system, or something akin to letters that enumerate sections of text, and that the selection of those is because they have a meaningful or artful connection to the text that they enumerate, similar to the word-game pairings above.  I’m calling on individuals to recognize that this is what we find in the Kirtland Egyptian papers is precisely these types of meaningful pairings and enumerations.  That is the whole point of this blog.

However, for the purposes of the current article, I am bringing all this up to show the evidence from Dr. Bailleul-LeSuer’s article that shows that in the Greco-Roman era, the Egyptians had the South Semitic ordering for their uniliteral characters, and therefore, this shows that they had the same concepts for these characters as the other nations had for their own alphabets.  Therefore, it is not a stretch to posit that these characters had the same number-assignments as those they correspond to in the South Semitic alphabet.  Therefore, we can expect that the uniliteral Egyptian letters above do indeed have the numeric values that we have identified above, because to these Egyptians, they were directly equivalent to the South Semitic list.  Whether it started out this way for the Uniliteral hieroglyphs in the Old Kingdom before the development of the Semitic Alphabets is entirely a different question, a question that we are not really concerned with in the current scope of this article.  The reason is that we are trying to ascertain what number scheme the Egyptians of the Greco-Roman era were applying to these characters.  The quotation above shows that, most likely, the South Semitic alphabets came first before the South Semitic ordering of the Egyptian uniliterals.  Therefore, we can expect that this is a form of iconotropic imposition of a foreign scheme on the Egyptian “alphabet,” which was imported into Egypt.  It is, nevertheless the scheme we are concerned with here, because it is the relevant one to the time period of the Egyptians that had imposed iconotropically an Abrahamic context on the Joseph Smith Papyri.  Therefore, for these reasons, I am comfortable applying these values from the Hebrew and Greek alphabetical-numeric schemes to the uniliterals above.  So this resolves only the first part of the problem.  One objection could be raised that the following uniliteral Egyptian letter is actually the conventional Egyptian number for 1000:

However, there may be a certain context that it is 1000, and some other number in an alphabetical-numeric scheme.  For example the Hebrew letter Aleph is the number 1 usually, but in a year context, it is the number 1000.  Therefore, I don’t see this type of thing as a valid criticism.
Now, with all this background above in mind, as for the Facsimile #2 of the Book of Abraham, Figure 11, here are the hieroglyphs in question are separated out, with numbers assigned to them as far as can be done, with the Greek system in mind:

  Gardiner M17, Moeller 282, the Reed symbol, or the Egyptian uniliteral letter I, corresponding to the Hebrew Yod and Greek Iota.  In both the Greek and Hebrew alphabetical-numeric scheme, it is the number 10.

 Gardiner A2, Moeller 35,man with hand in mouth.  This is a determinative in indicating eating, drinking, speaking, thinking, etc.  This doesn’t match with a Greek numeral, as it isn’t a uniliteral, so something else may be going on.

Gardiner Z3, Moeller 563, three strokes, indicating plurality in general.  In the regular Egyptian number system, the number 1 is the straight line.  This may be indicative that this can stand for the number the number 3.

Gardiner G17, Moeller 196 This is a picture of an owl, and is the uniliteral letter M.  This corresponds to the Hebrew Mem and the Greek Mu.  These letters both stand for the number 40.
Gardiner R8 , Moeller 547 Egyptian Triliteral character NTR, meaning “god.”  This is a picture of a flag.  This doesn’t match up with a Greek letter, since it is a tri-literal.
Gardiner A40 , Moeller 45 -  This is a seated god.  Same thing as above.  It is a determinative, so it doesn’t match with a Greek letter.

Gardiner O34 , Moeller 366  – door bolt - This is the uniliteral character pronounced S or Z, corresponding to the Hebrew Zayin and the Greek letter Zeta.  These both are equal to the number 7.

Gardiner A54 Moeller (not present in list) – This is a recumbent mummy on couch, meaning “sleeping” or “death.”  This is the triliteral character SDR.  Once again, this doesn’t match with a Greek letter.

Gardiner Q3 , Moeller 388  – stool - This is the uniliteral character P, corresponding to the Hebrew peh and the Greek pi.  These are both the number 80.

Gardiner O50 , Moeller (not present in list) – Threshing floor, meaning “time,” or “occasion.” This is the biliteral character SP, so it doesn’t match with a Greek letter.

You will notice that I have only assigned numerical values to the uniliterals above so far.  However, now comes a more complex problem before us for the bi-literal and tri-literal (two- and three- consonantal) characters and the determinatives which have no specific vocalization.  How do we handle those?  What type of meaningful theory ought to be applied to those?  This part of the theory will have more risk to failure, because we had a clear precedent for them the way we do with the uniliterals.

One thing is clear.  All Egyptian words can be spelled out with uniliterals, and wouldn’t change what they are.  Biliterals and Triliterals are clearly just a convenience, when it boils down to it.  This is likely an indication that a biliteral or a Triliteral would be simply something that can be swapped in for two uniliterals.   A numeric value for such a thing would be a sum of the values of the two uniliterals that make up its sound, and therefore is a shortcut, just like when it is a shortcut for spelling out multiple consonantal sounds.  Therefore, the character SP above according to the Hebrew/Greek numbering scheme would simply be an expression for 200+80=280, where S=200 and P= 80.  NTR would be 500+300+100=900.  While it is true that in the Greek system, the letter Sampi is 900, the letter doesn’t exist in the Hebrew.  The letter SDR would be 200+4+100=214.  While some letters have the same values as others because they add up to be the same, this just means that there are multiple ways to express the same value.

The last difficulty, however, is the determinatives.  On their own, these usually have no phonetic value, but just are an indicator of the type of idea at hand.  They are context-giving indicators.  The simplest context for the determinative above of the man putting his hand on or in his mouth is simply to eat or food.  WNM is the ancient Egyptian word for food, and therefore, this would be 6+50+40=96.

Keep in mind that these are just quick, off-the-cuff non-researched guesses for the biliterals, triliterals and determinatives.  My partner Vincent Coon may have a better suggestion for these, or for the mathematics involved.

So, unless there is something more elaborate at work here, with custom assignments for bilateral or trilateral letters, the scheme seems pretty straight-forward.

So, as you can see, this seems to be no more complex than just doing the math if you don’t have the value of a letter memorized.

Even if these deductions are flawed at some level, there is nothing crazy about Joseph Smith’s suggestion that alphabetical letters can stand for numbers.