Daniel Dockery

animî nostrî dêbent interdum âlûcinâri

Home of published musician, recording artist, mathematician, programmer, translator, artist, classicist, and general polymath.

When the Stars were Right

October 11th, 2017

—or, “Fun with Coincidence”. (All Hallows Read, pt. 6.)

Occasionally, my various interest areas overlap in unexpected ways; last night was one such time. Researching earlier in the evening in Greek Horoscopes (an academic survey of surviving astrological charts from the first five centuries of the current era; ed. Otto Neugebauer & H.B. van Hoesen, vol. 48 of the Memoirs of the American Philosophical Society, 1959), I was still thinking of my Lovecraft reading from the previous evening and earlier yesterday as part of my All Hallows Read, where among others I’d reread “The Call of Cthulhu”. In that story, HPL gives latitude and longitude for locations around and of R’lyeh, and he gives the date for its rising (1 March), sinking (2 April), and the crew’s landing and Cthulhu’s awakening (23 March), all 1925. While, true, he doesn’t give explicit times of day, which we’d ordinarily need for reliable chart calculation, in this instance we’re looking more at a period of time—the month of March—than a single specific instance, so we can still calculate the pertinent positions: we can find out, in other words, just which “stars were right”.

Unsurprisingly, perhaps, since Lovecraft wasn’t, after all, thinking of astrology when he wrote those dates and locations (at least, I assume he wasn’t), on its surface the chart revealed didn’t seem so special. The bits that might be symbolically significant, in relation to the story—using the more negative traditional meanings of the signs, the malefics, etc.—would be the “great malefic” Saturn, retrograde, in Scorpio, ruled by the other malefic Mars, and both malefics in opposition. Using the “modern” planets, Neptune, governing dreams and hallucinations, obsessions and madness (a Cthulhian planet if ever there were one) was also retrograde and in Leo, adding intensity, visibility: compare the remarks in the story on how people around the world were suddenly having dreams, visions, and so forth, in that period: “March 1st [… f]rom Dunedin the Alert and her noisome crew had darted eagerly forth as if imperiously summoned, and on the other side of the earth poets and artists had begun to dream of a strange, dank Cyclopean city whilst a young sculptor had moulded in his sleep the form of the dreaded Cthulhu. March 23rd […] the dreams of sensitive men assumed a heightened vividness and darkened with dread of a giant monster’s malign pursuit, whilst an architect had gone mad and a sculptor had lapsed suddenly into delirium! […] April 2nd—the date on which all dreams of the dank city ceased”. Further, the modern great malefic, Pluto (Yuggoth on the rim?) stands out even more. That is, while Pluto was retrograde when R’lyeh rose, it had just gone back to direct/normal/non-retrograde motion as R’lyeh sank again. What makes it stand out more, though, is related to a planet’s retrograde cycle. Briefly, planets are considered astrologically to have three basic states of relative motion: direct, or normal motion; retrograde, or reverse direction; and a station, or stationary position where it’s transitioning between the two. While most who have read or heard much of astrology are familiar with at least the term “retrograde”, fewer are familiar with stations, though astrologically they are significant events, times when a planet appears to “stand still” in the sky. While they couldn’t see these outer planets, the ancients ascribed a great deal of significance to planetary stations and read them as omens. The reason I digress on the topic here is that Pluto went stationary above R’lyeh on the day the crew landed and Cthulhu awoke. When it began moving again, R’lyeh returned to the depths.

If we inspect the “quality” or condition of the planets, we find a few additional surprises. When R’lyeh rose, we find that Mercury was in its worst possible condition, being both in its detriment and fall simultaneously, suggesting a time when reason, rational/critical thinking would be significantly hindered in some way, making it all the easier for those earlier cited Neptunian influences to take and hold sway. Likewise, the malefic Mars was in detriment, “increasing its power for evil” as the ancients would say. We find Jupiter, the great benefic, was fallen, decreasing or impeding the presence/action of “good”/happiness/joy. Seems dreadfully apt. We also find that around noon of that day, Mercury, already in such poor condition, was conjunct the Arabic part of Suicide. Perhaps just as interesting or suitable are the changed qualities in action when R’lyeh sank again: there we find the Sun had come into its exaltation, a position of great strength, a return of light to the world; at the same time, the Moon reached its strongest position, being in domicile (its own sign), which by sign also meant it had become the ruler of newly direct Pluto to which it was also then conjunct, astrologically suggesting the reflected light of the sun dominating or overcoming Pluto’s influence. Before this change, consider the remarks in the story about the Sun: “The very sun of heaven seemed distorted when viewed through the polarizing miasma welling out from this sea-soaked perversion”; “That tenebrousness was indeed a positive quality; for it obscured such parts of the inner walls as ought to have been revealed, and actually burst forth like smoke from its aeon-long imprisonment, visibly darkening the sun”. When the sun reappeared, R’lyeh sank. Maybe Lovecraft considered astrology after all.

Considering the emphasis on the times when the stars are right, I decided to bring in another of my subject areas, and wrote a bit of code to search for these same positions in other times. Employing the Swiss ephemeris, based on NASA’s JPL’s ephemerides, offering accurate planetary positional data spanning some 30,000 years, I wrote a program that would search from 13000 bce to 17000 ce, looking for any time where the same planetary positions held or shall hold sway. In those thirty thousand years, that same combination of stellar influences occurs only the once, in March of 1925. Considering Lovecraft remarked that R’lyeh had been there since the sun was young, and our sun’s been around roughly 5 billion years and our planet around 4.6 billion, and HPL wrote that after “vigintillions of years great Cthulhu was loose again” (no, he doesn’t bother to say how Cthulhu was trapped there for 999 undevigintillion years or so longer than the earth and sun had existed) maybe that’s not so surprising, but unfortunately we have no reliable way of calculating or even estimating planetary positions at such remote times, so we can’t tell if the same planetary conditions obtained then. On the positive side (well, at least for us, if not for poor Cthulhu), if those are the necessary conditions for the stars to be right, the planet should be safe from Cthulhu’s wake-up call for at least another fifteen thousand years!

Things from Sappho to call your girlfriend

June 10th, 2017

thoodleoo wrote:

  • ἀστέρων πάντων ὀ κάλλιστος (of all the stars, the fairest)
  • πόλυ πάκτιδος ἀδυμελεστέρα, χρύσω χρυσοτέρα (far sweeter-sounding than the lyre, far more golden than gold)
  • τὰν ἰόκολπον (violet-tressed, one with violets in her lap)
  • ὦ κάλα, ὦ χαρίεσσα κόρα (o beautiful, graceful girl)
  • ἦρος ἄγγελος ἰμερόφωνος ἀήδων (nightingale, sweet-voiced messenger of spring)

“Violet-tressed”? How do they get “tressed” out of that word? “Violets in her lap” also won’t work; the best there would be violet-lapped or having a violet lap, and if that makes no sense, it’s because it’s a mistake. More common is seeing it translated as “circled/girdled in violets”, but that comes from replacing the actual word ἰόκολπον with ἰόζωνον as emendation as if they were the same. It’s a compound word, ἴον + κόλπος, “purple breasts”; swapping out ἰόκολπον with ἰόζωνον allowed them to change it to “girdled with violets”, a trend that seems to’ve gotten its start in the Victorian translation era where they were afraid to to suggest anything vaguely “improper”, like, you know, breasts.

In earlier dictionaries, like the Lexicon Græco-Prosodiacum of Thomas Morell (London, 1824), they were more direct, so that on page 415 of said work,  Ἴοκυλπος is defined as pulchrum pectus habens. That is, “having beautiful breasts.” In support, it cites a fragment of Alcæus, ἄεισον ἄμμι τὰν ἰόκολπον: “I sing of beautiful breasts.” It gives a footnote to the word, for any confused by how a prefix that literally means “purple” is being read as “beautiful”:

Uocem ἴον in hoc composito pro pulchro quodam ac lucido colore accipio: sicuti purpureus apud Latinos fulgentem simul atque albam cycnorum speciem denotat. Tenendum porro in memoria, uiolarum quasdam esse candidas.

That is, “I take the expression ἴον in this compound for something beautiful as well as of a white, as in clear or unblemished, complexion: in the same way purpureus (i.e. ‘purple’) in Latin writings indicates a kind of white swan, and further remembering that uiolarum quasdam (‘something violet’) means to be clear/spotless/white.” A modern Greek etymological work gives [ΕΤΥΜΟΛ. < ἴον + κόλπος «μπούστο»]—where μπούστο is modern Greek for “bust”.

Now, all that said, it’s still a nice thing to say, just remember, your flowery language is actually complimenting her boobs. Compliment away! As the monk Adso of Melk once said, Pulchra sunt ubera!

Ex Bibliotheca

February 21st, 2012

On Tumblr, earlier, I saw this:

Here is a site that offers digital renderings of some of the books in the unimaginably vast universe of information (and un-formation) described in Jorge Luis Borges’ story the Library of Babel

Explore, but remember that the possibility of discovering your Vindication within the Universal Library “can be computed as zero.”

An interesting idea, but given Borges’ kabbalistic leanings, his remark that there is no form of capital lettering, no digits, and his insistence on the twenty-two letters and their fixed, symmetrical forms, it is most likely that he meant for the Library’s volumes to be expressed in the block Hebrew script, which he has admired in other places, though any language might be encyphered in that alphabet in the Library’s vast holdings, such as his “Samoyed-Lithuanian dialect of Guarani, with classical Arabic inflections” (“un dialecto samoyedo-lituano del guaraní, con inflexiones de árabe clásico“) mentioned in the story.

Other possibilities do present themselves, however, for clues suggest the language of the southern hemisphere of Tlön. How so? In “The Library of Babel,” Borges gives us explicit “titles” for three volumes: “trueno peinado,” “el calambre de yeso,” and “axaxaxas mlö“. The first could be the “Combed Thunder,” the second “The Plaster Cramp,” but what of the third? If one were to read “Tlön, Uqbar, Orbis Tertius,” from the same 1944 collection (Ficciones [Spanish, English]) in which “The Library of Babel” appeared, one would encounter a passage reading, “Surgió la luna sobre el río se dice hlör u fang axaxaxas mlö,” “‘The moon rose over the river’ would be said hlör u fang axaxaxas mlö.” In the additional text, he indicates all words are verbs in that language, and that “axaxaxas” would mean something resembling “flowing like a river,” while “mlö” would be “shining (or perhaps rising) like the moon”. Translate it however we will, there remains the point that at least one book in the Library is titled by one of the Tlönistas. Or by coincidence would appear to be.

This provides much of a proposed alphabet: in addition to the three titles, Borges also wrote that the combination of letters “dhcmrlchtdj” would appear in the Library and that there is one volume that consists of endlessly repeated “mcv”s. Taken together, sorted alphabetically with duplicate letters removed, this leaves us with 20 or perhaps 21 letters: a, b, c, d, e, h, i, j, l, m, n, o, p, r, s, t, u, v, x, y—and, as he does distinguish it, possibly ö. The alphabet in use on the above linked site adds f, g and q but omits the u needed for “trueno” and doesn’t distinguish the ö from o. If we accept that the line from the story of Tlön is of the same language or alphabet, as at least the title seems to be, then we also see evidence of the f and g in use. If we adapt those, but hesitantly combine the o and ö, we will have another set of twenty-two letters.

It likely doesn’t matter:

Un número n de lenguajes posibles usa el mismo vocabulario; en algunos, el símbolo biblioteca admite la correcta definición ubicuo y perdurable sistema de galerías hexagonales, pero biblioteca es pan o pirámide o cualquier otra cosa, y las siete palabras que la definen tienen otro valor. Tú, que me lees, ¿estás seguro de entender mi lenguaje? (Borges, “La biblioteca de Babel”)

An n number of possible languages use the same vocabulary: in some, the symbol “library” admits the correct definition: “an enduring, ubiquitous system of hexagonal galleries,” but “library” is “bread” or “pyramid” or anything else [in others], and the seven words that define it have other meanings. You who are reading me, are you certain you understand my language?

Many years ago (2003) my fascination with the idea of this library, from Kurd Laßwitz’s much earlier story (“Die Universalbibliothek,” 1904) on through Borges’ (whose 1941 variant of the tale I prefer by far) and similar themes (e.g., Arthur C. Clarke’s “The Nine Billion Names of God,” 1954), etc., had me working out the elaborate mathematics of the whole and being in awe at the staggering numbers. For instance, given that Borges explicitly defined the volumes of the library as containing 410 pages, each page containing 40 rows of text with 80 characters per line (including punctuation and spaces), defined there to be exactly 25 possible characters, and said that the library contained exhaustively everything it is possible to express with them and that no two books were identical, we can calculate that the library must have exactly 25^(80*40*410), or 25 to the 1,312,000th power volumes. To put that in perspective, that is 1.956 x 10^1834097 books, a number 1,834,098 digits long. If you were to write out five digits a second, it would take you more than four days of non-stop writing just to transcribe the whole number.

One of the most enchanting things about the library is, of course, that in its seemingly endless volumes you may find everything that it is possible to write down—including your own life story (your “vindication”), perhaps spanning multiple volumes in elaborate detail, as well as countless millions of erroneous copies whether differing by a single letter or missing entire events or with events that end otherwise than reality’s version, the answer to every mystery or riddle that it’s possible to answer, truly everything. The damning part is that these volumes can be scattered anywhere throughout the universal library and your chance of finding the one you seek is only 1 in 25^1312000, which is so incredibly small it is for all practical senses zero. Should you by luck find one good volume of a multivolume set, you have again those vast odds against your ever finding the next.

Yet perhaps the most damning, or tantalizing, aspect of it all is that you could calculate any or all of these volumes and discern the universal order of the whole by a task no more arduous than counting by ones.

In Tlön, etc., Borges mentioned in passing various numerical bases, touching on the base 12 system (duodecimal) of one of the Tlönistas and the base 60 system (sexagesimal) of ancient Sumeria and Babylon (and in its way even today in our system of minutes and seconds). This is the essential clue. While base 10 (decimal) seems to have conquered all others today, other bases have been in use elsewhere: the now infamous Mayan calendar system, for instance, uses base 20; and in computing, we sometimes use base 16 (hexadecimal), base 8 (octal) or at the lowest possible level base 2 (binary). We can conceive of the Library as being expressed in base 25 (quinquevigesimal) notation, but instead of mixed case, such as with base 16 (where the “digits” are 0 through 9, then A through F, such that the decimal number 190 is expressed as BE in hexadecimal), we can define our 25 digits to be the twenty-five symbols set out by Borges, the twenty-two letters of the alphabet, the comma, the period and the space. Each volume in the library then is merely a number, and the order of their seemingly entropic arrangement is numerical. Which is also suggested in the story when he writes how some have asserted that while the books are written in the “natural symbols” of written language, any appearance of meaning is coincidental, a side effect of using those symbols. To demonstrate, we can see the same thing in hexadecimal, such as above when I pointed out that the number 190 is “BE” which could be interpreted as an English verb; or the number 57,005 is DEAD in hexadecimal, again a “word” in appearance though a number in intent, like the dreadful notion of DECAF, which represents the number 912,559. Treating the volumes as natural numbers also explains the Library’s first axiom, that it exists “ab æterno,” just as the numbers.

An example, to demonstrate. If we take the numerical order of the characters to be that in which Borges gave them in his text—to wit, “the space, the period, the comma, the twenty-two letters of the alphabet”—and set them, in the natural arrangement, as being equal to our base 10 values of 0 through 24, then our first book, corresponding to 0 would be an entirely blank volume. The second, corresponding to 1, would be entirely blank but for a single final period. The next would be the same, but with a comma. Then an “a”, a “b” and so on for the first twenty-five books, one for each symbol. The twenty-sixth would be blank but for the last two symbols which would be a period followed by another space. The sequence would continue, almost forever. In the 9,752nd volume we’d find it blank but for the last letters “mm.”; the next would be “mm,”; the next, “mma” then “mmb” and so on again. At the end of the 19,370,996,558th volume, we would find “abula‘fia”, the name of the 13th century kabbalist renowned for his combinatorial ability. The numbers have grown enormous by the time we even get beyond single sentences. And it continues, letter combining with letter, line with line, page with page, growing and growing, as the early kabbalist text, the Sefer Yetzirah, has it (IV:16, dealing with permutations):

מכאן ואילך צא וחשוב מה שאין הפה יכול לדבר ואין האוזן יכולה לשמוע׃

“From here on go out and calculate that which the mouth cannot speak and the ear cannot hear.”

Unfortunately, even with the fastest computing systems in operation today, our sun would burn out before we could generate a fraction of the library, which is moot anyway since with even the best possible compression available today, the library would require more storage space than currently exists or will exist for likely ages to come, if ever. The most recent figures I’ve seen suggest that as of 2011, the global data storage demands for all digital media of any kind covers “only” about 940 exabytes (for those of you playing along at home, that’s roughly 985,661,440 terabytes), with that number essentially doubling every two years—and with it generally pushing the limits of the amount of storage capacity we actually have available globally. Another way to look at data amounts, if every one of the 6,995,685,817 people of the current estimated world population had a full terabyte of data, the total would be roughly 6.5 zettabytes, a vast number far, far beyond current global capacity (there are 1024 exabytes in a zettabyte). At the expected rate of growth, it should take us almost six years to reach that capacity. Yet a complete digital copy of the Library of Babel, at ideal, maximum compression, would require something to the effect of 4.24562416107 x 10^1,834,075 yottabytes—where a single yottabyte is 1024 zettabytes or 1,125,899,906,842,624 gigabytes! At that projected growth rate, it should take a measly 12 million years for us to reach that capacity.

For a countering thought, Seth Lloyd, in an article (“Computational Capacity of the Universe”) in the science journal Physical Review Letters, in 2002, asserted that the total information capacity of the observable universe is only 10^92: the capacity necessary for the complete Library is over 10^1,834,099. Borges equated the Library with the Universe, yet it seems the Library is greater in scope. By far.

So it seems very possible that while the mind can conceive of the Library, can understand it, can know how to create it, its actual creation is beyond the scope not just of human ability but also beyond the scope of universal capacity, beyond the time scale of our solar system. We have to be satisfied with only knowing that these things “exist” in some abstract sense, our vindication, the answer to every pressing problem, to every question that’s ever passed our mind or anyone’s, every great novel (and every awful one!), even this post I’m writing now, exist, waiting for someone to discover them, yet outside the possibility of truly being able to search or find them in any clear or orderly fashion.

Perhaps we should, after the fashion of the site at the beginning, pick up our own “forbidden dice cup”…

“A blasphemous sect suggested that” [rather than searching for meaningful volumes] “all men should juggle letters and symbols until they constructed, by an improbable gift of chance, these canonical books.” […] “The sect disappeared, but in my childhood I have seen old men who, for long periods of time, would hide in the latrines with some metal discs in a forbidden dice cup and feebly mimic the divine disorder.”

The non-Mayan “Mayan” Prophecy

December 26th, 2011
The Mayan Prophecy

The most annoying thing about the “Mayan Prophecy” is that it isn’t Mayan. It’s a “prophecy” made by moderns about the Mayans, made by people who either misunderstand or willfully misrepresent their numerical and calendrical system. Some more reasonably minded folk have suggested the Dec 21st, 2012 date is nothing more than a Mayan equivalent to our own modern Y2K bug of a decade ago, but in reality it’s not even that. The Mayan long count calendar is perfectly capable as it stands of representing another 2,365 and a half years before it runs out of digits and has to reset the way our digital calendars rolled over from 99 to 00 without a column to indicate the century.

To understand what the date does represent, it’s first necessary to gain a very basic understanding of how the long count calendar (used by much of Mesoamerica and not just the Maya) notates dates. First, the Mayan numbers were written in a base-20 not in the base-10 number system we know in most of the western world today). That is, whereas with our numbers each column of digits indicates a number from 0 to 9 before rolling over into the next column to its left, a Mayan number has symbols from 0 to 19. A further complexity is that in their calendrical system, the second column from the bottom (their dates are written vertically) only goes from 0 to 17, then the remaining three columns return to the 0 to 19 count (this allowed a full run of the second and first row to indicate 360 days, the equivalent to their year). In most modern transcriptions of the dates, we use a simple notation of where the leftmost position correlates to the one traditionally on top and the right to the bottom. So we have a possible range of 0 days ( to 2,879,999 days, or about 7,885 years (

All December 21, 2012 corresponds to is the date, a period of 1,872,000 days, 5,125 years, since what the Maya held to be the date of “creation” of the current cycle in 3114 BCE, which is simply the last time they indicated the date to be (which leads to one of the speculations that the topmost rung of the calendar may only go from 0 to 13 in the same way that the second rung only goes from 0 to 17 rather than the full 0 to 19).

This whole “prophecy” mess got started with the discovery of what’s now known as the Bernal tablet during some roadwork back in the 1960s. It’s a large Mayan stele which originally held a great deal of text, including a passage identifying, the Dec 21st, 2012 date. However, the tablet is badly damaged with missing portions and more than a few passages on the surviving parts eroded or otherwise illegible including the part about just what it is that’s supposed to take place on that date. There remain only some vague remarks about the little known Mayan god “Bolon Yokte”, apparently associated in some way with “creation”, however just what his association is with the date is obliterated from the tablet. While you can find many of the 2012-world-ending sort today claiming it says Bolon Yokte will “descend from the sky” or whatever (which is anyone’s guess as to what that supposedly means), the archaeologist Bernal, who did the original translation, made it explicitly clear that the passage was speculation on his part and not at all visible on the tablet. It is just as reasonable, perhaps more so, to assume a reference to a god of creation is only in observation of the calendrical date being the same as that assigned to the original “creation” myth.

Given that other Mayan inscriptions list dates far in the future of 2012, it’s very obvious that they themselves didn’t believe 2012 would be an apocalyptic end of the world. For instance, an inscription to commemorate the (future) anniversary of the 80th calendar round of K’inich Janaab’ Pakal’s coming to the throne projects to a date of October 21st, 4772 c.e. And despite the typical representation of long count dates as having only five parts, as detailed above, there are texts that add several more. The stele known as Quiringua F shows and subtracts a “distance date” of producing a final date over 90 million years in the past. On stele D from the same site, there’s a date of that adds a distance date of which would be more than 400 million years in the future from the time the stele was erected (circa February, 766 c.e.). Rather dwarfs 2012, doesn’t it?

As for the association of the Mayan god to the date, if one considers comparative religion in general and not just a Mayan focus, the association of deities or supernatural entities generally, to calendrical cycles isn’t at all unusual or even overly significant. The Hindu system of yugas is particularly similar, citing the world to currently be in the Kali yuga (कलियुग), which they say began 3102 b.c.—only 12 years after the beginning of the current Mayan cycle. Curiously, they indicate the Kali yuga as the 4th cycle, while the Mayan text, the Popol Vuh, claims the current cycle is also the 4th. But don’t read too much into it: these kinds of coincidences happen all the time if you read broadly enough in comparative studies.

In the end, the point is simply this: there is no prophecy by the Mayans that the world or anything else—other than a calendrical cycle!—ends in 2012.

The Redemption of Lucifer

May 30th, 2011

AKA Mistranslated Bibles and Errant Theology

[This ramble brought to you by seeing one too many misrepresentations of the Isaian passage, sparked by this morning seeing an anon—ostensibly Christian—troll* citing it while haranguing a [now deleted] Tumblr with farcical “arguments” about the beliefs of anon’s patchwork theopoeia. Hat-tip, Renée. (*Which is just another mangled myth, since traditionally trolls are supposed to eat Christians!)]

As a translator, I am accustomed to encountering passages where someone has slipped in our craft, and I have been as culpable as any; these are sometimes embarrassing, sometimes amusing, but sometimes a translator so misses the mark as to change the entire meaning of a passage and confound those who, unacquainted with the original material, rely on that translation. Perhaps the most pernicious example of this can be found in the “translations” of the Christian editions of the Tanakh‘s book of Isaiah, cap. 14, verse 12, which has endured so long as to become part of their theology.

איך נפלת משמים הילל בן־שחר

How you are fallen from heaven, Hêlēl ben-Šāḥar!

The problem lies in that single bolded phrase, the name Hêlēl ben-Šāḥar. The figure as a whole is most likely a survival from Canaanite myth, and scholars have found parallels in the larger story in that Isaian passage to some of the texts uncovered at Ugarit, such as that of Athtar attempting to usurp the Most High Baal. But the first name, Hêlēl, meaning “bright” or “shining”, was an epithet of the planet Venus rising as the morning star. This was still understood by the translators of the LXX (working between the 3rd and 2nd centuries BCE in Alexandria):

πῶς ἐξέπεσεν ἐκ τοῦ οὐρανοῦ ὁ ἑωσφόρος ὁ πρωὶ ἀνατέλλων

They rendered the name as Heosphoros, the morning star, also classically understood to be Venus, and was discussed as such from Homer to Plato and Hesiod among others, called Ἀφροδίτης ἀστήρ, the star of Aphrodite (whom the Romans called Venus). But nearly 500 years later, when Jerome was commissioned by the 37th pope, Damascus I, to produce the Vulgate Latin “translation” of the canonical Biblical texts, the error arises. For הילל and ἑωσφόρος, he chose to use the Latin lucifer. While הילל is an hapax legomenon and we cannot compare the translations of it in other parts of the text, the more accurate Greek translation appears in six other places in the Tanakh passages of the LXX.

In the first of these, I Samuel 30:17, the Hebrew is מהנשׁף ועד־הערב—”from before sunrise to after sunset”—rendered correctly in the LXX as ἀπὸ ἑωσφόρου ἕως δείλης, but mistakenly rendered by Jerome as a uespere usque ad uesperam, “from evening to evening”.

In Psalm 109:3, “from the dawn” is in Hebrew משׁחר, which the LXX gave as “before dawn”, πρὸ ἑωσφόρου and Jerome gave as “before the morning star”, ante luciferum.

In Job, where we find the largest concentration of this term, the first, in 3:9, is simply dawn, שׁחר in Hebrew, ἑωσφόρον in the LXX, but this time Jerome opted for auroræ, which still means dawn (or the goddess of the dawn). In 11:17, “like the morning” is in Hebrew כבקר, ὥσπερ ἑωσφόρος in the LXX, but here Jerome went back to his other term, with ut lucifer, “as the morning star”. In 38:12, we have dawn again, the Hebrew שׁחר, the LXX‘s ἑωσφόρος, and Jerome vacillates back to aurorae. Finally in 41:10, the Hebrew once more offers שׁחר for dawn, the LXX sticks to ἑωσφόρου and Jerome… came up with yet another word, diluculi. It can still mean dawn, though usually meant the earliest or first rays of sun in the morning.

We can see that the most common term here in the Hebrew is שׁחר, yet for that single term, Jerome offered lucifer, aurora and diluculum (and elsewhere in his text used mane to translate the same word), and is inconsistent even in the use of those. For instance, in Psalm 109:3 he used lucifer for שׁחר, yet in Isaiah 14:12, it is הילל that he translated as lucifer while rendering שׁחר as qui mane oriebaris, “who rose early in the morning”. In Job 11:17, he used lucifer for another term altogether (בקר); in Job 38:32, he “translated” מזרות as lucifer, which seems to be intended for מזלות—the constellations—as used in II Kings 23:5, which Jerome there translated as duodecim signis, the “twelve signs”! The LXX gave the transliterated μαζουρωθ in both places. In Job 38:12, he used both diluculum and aurora in the same passage, writing diluculo for בקר, “morning” (which word he translated as lucifer in Job 11:17) and auroræ for שׁחר. In Job 24:17, he decided בקר could then be… aurora. Elsewhere (Psalm 73:16) he also used aurora to translate the Hebrew word אור (light). Diluculum is easily his favorite of these, however, as it occurs some 41 times in his text, as translations of these Hebrew terms and some others as you might have come to expect.

These are not examples of translating a text’s meaning idiomatically into another language as he varies these terms haphazardly even when the meaning and context remains the same; it’s just bad translation. But the point of this article is to focus more particularly on the consequences of his bad translation, especially as concerns Isaiah 14:12. There, despite having used lucifer in five places in his text, he chose to treat the word in only that one place as a proper name—despite that the context in which he’d used it in every other passage should also make it a proper name in Latin. That is, if not a name, the word only means “light-bringing” and was used in Latin to refer to everything from lightning (lucifera lampade) and meteors (luciferas faces) to the moon, and sometimes, as a feminine adjective, referring to the goddess of the moon, Diana (as Cicero writes in de Natura Deorum, 2.68). But when used in Latin to refer to the morning star, it is a masculine proper noun, the name of a mythological figure who appears in the works of Ovid, Lucretius, Pliny, Propertius, Cicero and many others. Awkwardly, for Jerome, Lucifer the Morning Star was mythologically the son of Aurora, though he seems to use the two synonymously. Lucifer, the Roman god’s myth, was well enough established to root him firmly in the Greek and Roman genealogies. In Ovid’s Metamorphoses, XI, 266, we meet Ceyx, king and son of Lucifer, who tells the story of his brother Dædalion. Dædalion had a daughter, Chione, who gave birth to a son, Autolycus, by the god Mercury. In Homer’s Odyssey, we find Odysseus the son of Anticleia, the daughter of that same Autolycus, making the hero Odysseus the great-great-great grandson of Lucifer. Which is simply to say, each time Jerome used Lucifer as a translation of the morning star, it should have been a personification, and not just in the one place.

The problem is not just one of vocabulary but interpretation, as it seems clear Jerome, if not the whole early (and subsequent) church, misunderstood the meaning of the entire passage. The original is an allegorical reference to the predicted fall of the King of Babylon, casting him in the role of the mythological figure of Hêlēl, and yet, for some reason, Jerome and the early church fathers, perhaps, particularly Tertullian and Origen, have tried to make the passage out to be about their imaginary devil, and Jerome’s choice to personify this one reference has had the consequence of creating the immense error that “Lucifer” is the name of “the devil”! They seem to choose to ignore the significance of the other occurrences of “lucifer” in the text, including, singificantly, in Jerome’s version of the Christian “New Testament” books, for he uses it in II Peter 1:19, where they talk of the time when the morning star will rise in their hearts as if it’s a good thing—yet Jerome, correctly for once, translates the Greek φωσφόρος as lucifer: donec dies inlucescat et lucifer oriatur in cordibus uestris, “until the day dawns and Lucifer rises in your hearts”. (Ἑωσφόρος and φωσφόρος were synonymous, both being translated as lucifer by the Romans; e.g., in Apollodorus’ Library, I.7.4, “Ἀλκυόνην δὲ Κῆυξ ἔγημεν Ἑωσφόρου παῖς“—Alcyone was married by Ceyx, son of Lucifer—Ἑωσφόρος was used, while in Cicero, de Natura Deorum, 2.53, we find stella Ueneris, quæ Φωσφόρος Græce Lucifer Latine dicitur, “the star of Venus, which is called by the Greeks Phosphorus is Lucifer in Latin”.)

Mythologically, Lucifer’s a nice fellow; he heralds the new day, ushers the darkness away, and helps the lost find their way back home. So, Christians, you’ve been picking on and blaming the wrong guy for nearly two thousand years. Isn’t it time you leave him alone and get your own Bible right?

The silent friendship of the moon

April 21st, 2011

In Borges’ “La cifra” and the obverse of his “Poema“, both translated here earlier, the poet refers to Virgil. In the “Poem”, among the things brought with the hexameters of Virgil’s Æneid is “[l]a amistad de la luna“, “the friendship of the moon”, and “La cifra” opens with “[l]a amistad silenciosa de la luna / (cito mal a Virgilio)“, “the silent friendship of the moon / (I misquote Virgil)”.

He is making reference to line 255 in the second book of the Æneid, from the scene where the Greeks slip out from the Trojan horse to sack the city of Troy, making their way “tacitæ per amica silentia lunæ“, “unnoticed through the friendly silence of the moon”.

Borges’ interest seems only in the expression quite abstracted from the story’s context through his own fondness for the moon as evidenced in many of his other works. He returns to the expression many times. In his brief essay on Dante’s Purgatorio, I.13 (from Nueve ensayos dantescos [1982]), he refers again to “el famoso hexámetro de La Eneida: «a Tenedo, tacitæ per amica silentia lunæ»” (“the famous hexameter from The Æneid: «from Tenedos, unnoticed through the friendly silence of the moon»”), comparing to it verse 60 of canto I of Dante’s Infierno, “mi ripigneva là dove ‘l sol tace“—”pushed me there where the sun is silent”.

In Borges’ defence, though he needs none, his misquotation isn’t as severe as that perpetrated by José Lezama Lima in Paradiso: “Pero con esperada frecuencia volvíamos al ternario, a unir sol, tierra y luna, aunque yo casi siempre me inclinaba a la luna silentiæ amicæ.” (In Gregory Rabassa’s translation, this reads “But with expected frequency we returned to the ternary, to unite sun, earth and moon, although I almost always leaned toward the silent friendship of the moon”, though his translation is incorrect for the Latin.)

Insatiate Orque

April 13th, 2010

Notes on the origin and etymology of the orc in English, inspired by seeing someone slightly more than my own age recently remarking on their belief that the word was invented by Tolkien, and that it had become a “word” courtesy of Peter Jackson’s film-adaptation of his Lord of the Rings trilogy, further asserting that before the movies, no one “their age” would have understood the word!

Poor Blake! Forgotten so soon?

In thunders ends the voice. Then Albions Angel wrathful burnt
beside the Stone of Night; and like the Eternal Lions howl
in famine & war, reply’d. Art thou not Orc, who serpent-form’d
stands at the gate of Enitharmon to devour her children;
Blasphemous Demon, Antichrist, hater of Dignities;
Lover of wild rebellion and transgresser of Gods Law;
Why dost thou come to Angels eyes in this terrific form?

Blake, America: A Prophecy, 1793

His Orc, a major character in his literary mythology, derives from both the attested English meanings of orc as a noun:

orc, n. 1

Originally: any of various ferocious sea creatures. In later use: a large cetacean, esp. the killer whale, Orcinus orca. Cf. ORCA, n. Now rare.

    1590. J. Stewart, Poems II.40, “Strong ourks and phoks and monsters euerie day | From seis he send.”

    1631. P. Fletcher, Sicelides III, “That Orke mouth of thine did crumme thy porridge with my grandsires braines.”

    1794. W. Jones, Hindu Wife 42, “Some slowly through green waves advancing. E’en orcs and river-dragons felt Their iron bosoms melt.”

orc, n. 2

A devouring monster; an ogre; spec. a member of an imaginary race of subhuman creatures, small and human-like in form but having ogreish features and warlike, malevolent characters.

    1656. S. Holland, Don Zara I. i. 6, “Who at one stroke didst pare away three heads from off the shoulders of an Orke, begotten by an Incubus.

    1854. Putnam’s Monthly Magazine, Oct. 380/1, “The elves and the nickers, the orcs and the giants.”

    1865. C. Kingsley, Hereward, I. i. 71, “But beyond, things unspeakable—dragons, giants, orcs, […]”

The Oxford English Dictionary, 3rd ed., 2004.

As the citations suggest, Blake was also neither the first nor only to use the word in English. There were two distinct forms of orc in use in early, Anglo-Saxon English; one, from the Latin orca (II A), referring to a large vessel (in OE, this was generally used to refer to religious cups, chalices or other offering vessels), has not persisted into modern English, but the other, deriving from the Latin Orcus, referred more to an evil or underworld spirit, or the underworld itself, and in compound words reflected a meaning closer to what has persisted into the modern language.

Þanon untydras     ealle onwocon,
eotenas ond ylfe     ond orc-neas,
swylce gigantas,     þa wið Gode wunnon

Then all the evil brood were born, ettins and elves and hell-fiends, even the giants, who strove with God

Beowulf, ll. 111–113

The usage evolving in later English however was modified, or reinforced perhaps, by the influence of the word as it had passed through other languages which had derived their own usage via the Latin Orcus, such as the Italian orco, a sort of man-eating giant relating to the similar Spanish ogro (and English kin ogre), etc. The description of the sea-monster orc of cantos CI–CX of Ludovico Ariosto‘s Orlando furioso (1516–1532) combines a mixture of the two meanings, applying the tusks and other monstrous features of the typical humanoid orc to the sea-monster orca, as can be seen in many of the illustrations of the scene of Ruggiero rescuing Angelica, such as those of Doré. The encounter was summarized in 1863,

Rogero, lance in rest, spurred his Hippogriff toward the Orc, and gave him a thrust. The horrible monster was like nothing that nature produces. It was but one mass of tossing and twisting body, with nothing of the animal but head, eyes and mouth, the last furnished with tusks like those of the wild boar. Rogero’s lance had struck him between the eyes, but rock and iron are not more impenetrable than were his scales. The knight, seeing the fruitlessness of the first blow, prepared to give a second. The animal, beholding upon the water the shadow of the great wings of the Hippogriff, abandoned his prey, and turned to seize what seemed nearer. Rogero took the opportunity, and dealt him furious blows on various parts of his body, taking care to keep clear of his murderous teeth; but the scales resisted every attack. The Orc beat the water with his tail till he raised a foam which enveloped Rogero and his steed, so that the knight hardly knew whether he was in the water or the air. He began to fear that the wings of the Hippogriff would be so drenched with water that they would cease to sustain him. At that moment Rogero bethought him of the magic shield which hung at his saddle-bow; but the fear that Angelica would also be blinded by its glare discouraged him from employing it. Then he remembered the ring which Melissa had given him, the power of which he had so lately proved. He hastened to Angelica and placed it on her finger. Then, uncovering the buckler, he turned its bright disk full in the face of the detestable Orc. The effect was instantaneous. The monster, deprived of sense and motion, rolled over on the sea, and lay floating on his back.

Thomas Bulfinch, Legends of Charlemagne, “The Orc”

Only a few years later, Robert Browning’s work, The Ring and the Book was published in 1869,

Methinks I view some ancient bas-relief.
There stands Hesione thrust out by Troy,
her father’s hand has chained her to a crag,
her mother’s from the virgin plucked the vest,
at a safe distance both distressful watch,
while near and nearer comes the snorting orc.
I look that, white and perfect to the end,
she wait till Jove despatch some demigod;
not that,—impatient of celestial club
Alcmena’s son should brandish at the beast,—
she daub, disguise her dainty limbs with pitch,
and so elude the purblind monster!

ibid., ix, Juris Doctor Johannes-Baptista Bottinius—
Fisci et Rev. Cam. Apostol. Advocatus

When Joshua Sylvester in 1604 published his translation of one of King James’ favorite poets Guillaume de Salluste Du Bartas’ La Sepmaine; ou Création du monde of 1581, he described Hunger thus,

Here first comes Dearth, the lively form of death,
still yawning wide with loathsome, sickening breath,
with hollow eyes, with meager cheeks and chin,
with sharp, lean bones piercing her sable skin,
her empty bowels may be plainly spied
clean through the wrinkles of her withered hide.
She hath no belly but the belly’s seat,
her knees and knuckles swelling hugely great,
insatiate Orque that, even at one repast,
almost all creatures in the world would waste;
whose greedy gorge dish after dish doth draw,
seeks meat in meat. For still her monstrous maw
voids in devouring, and sometimes she eats
her own dear babes for lack of other meats.
Nay, more; sometimes, O strangest gluttony,
she eats herself, herself to satisfy,
lessening herself, herself so to enlarge,
and cruel thus she doth our grandsire charge;
and brings besides from Limbo to assist her
Rage, feebleness and thirst, her ruthless sister.

Du Bartas His Devine Weekes and Workes Translated,
II, The Story of Adam, iii, “The Furies”

If the nouns aren’t enough orc for you, it’s also attested as a verb; e.g., “I Orkt you once, and Ile fit you for a Cupid.” And, no, Tolkien had nothing to do with it—it’s from Fletcher’s Sicelides of 1631.

Oration on the “Dignity” of Man—no, not that one

December 19th, 2007

Inspired by an old post of the Laudator temporis acti which I ran across today, I thought I’d take a moment to share a bit of hope and cheerful optimism from the ancient world concerning the role and state of man.

Palladas, ever a charmer, left a bit of verse that’s come down to us in the Greek Anthology (X, 45), known generally as “The Descent of Man”. Frustrated by the vain puffings of fellow humans of his own time on the topic of the majesty of man, he sought to recall to mind a few details so often forgotten by them, or seemingly so:

Ἄν μνήμην, ἄνθρωπε, λάβῃς ὁ πατήρ σε τί ποιῶν
    ἔσπειρεν, παύσῃ τῆς μεγαοφροσύνης.
ἀλλ᾽ ὁ Πλάτων σοὶ τῦφον ὀνειρώσσων ἐνέφυσεν,
    ἀθάνατόν σε λέγων καὶ φυτὸν οὐράνιον.
ἐκ πηλοῦ γέγονας· τί φρονεῖς μέγα; τοῦτο μὲν οὕτως
    εἶπ’ ἄν τις, κοσμῶν πλάσματι σεμνοτέρῳ.
εἰ δὲ λόγον ζητεῖς τὸν ἀληθινόν, ἐξ ἀκολάστου
    λαγνείας γέγονας καὶ μιαρᾶς ῥανίδος.


If you would recall, o man,
just how your father sowed you,
you’d bridle your vain pride.

Yet the dreamer Plato’s deception
has taken root in you,
calling you immortal,
a heavenly plant.

“You come from dirt;
how are you proud?”
So one might ask,
arranging the figure more pompously.

But if you seek the truth,
you were begotten
of unbridled lust
and an unclean drop.

But he was hardly the first to say or think it. A couple of centuries or so before him, Aurelius (Τὰ εἰς ἑαυτόν, βιβλίον δʹ, μηʹ, δʹ; c. 174/180) quipped,

ἀεὶ τὰ ἀνθρώπινα ὡς ἐφήμερα καὶ εὐτελῆ καὶ ἐχθὲς μὲν μυξάριον, αὔριον δὲ τάριχος ἢ τέφρα.

Human (lives) are always cheap and ephemeral: yesterday, a little ejaculate; tomorrow, embalming or ashes.

In roughly the same time period, a passage of similar nature appeared in the Mishnah tractate, Pirké Avot,

עקביא בן מהללאל אומר, “הסתכל בשלשה דברים ואין אתה בא לידי עברה.” (א) דע מאין באת, (ב) ולאן אתה הולך, (ג) ולפני מי אתה עתיד לתן דין וחשבון.

מאין באת? מטפה סרוחה

ולאן אתה הולך? למקום עפר רמה ותולעה

ולפני מי אתה עתיד לתן דין וחשבון? לפני מלך מלכי המלכים הקדוש ברוך הוא

פרקי אבות, ג׃א


Akavya ben Mahalal’el used to say, “Reflect on three things and you will escape the hand of sin.” (1) Know where you came from; (2) know where you are going; and (3) know in whose presence you will have to make an accounting.

Where do you come from? An unclean drop.

Where are you going? To dust, worms and maggots.

To whom shall you make a reckoning? To the King of the King of Kings, the Holy One, Blessed be He.

Pirké Avot, 3:1

Biblical numbers

August 30th, 2003

Dr. Pickover asked, “What kinds of numbers did Jesus use (or someone of his era)?”

Since it’s claimed he spoke Aramaic, I expect he’d have used the Aramaic/Hebrew number system where their alphabetic characters also served as their numbers. (The languages, of course, also had names for the numbers, just as we have “1” and “one”, etc.; I’m just referring to how numbers were written.) Since some of the apocryphal and pseudepigraphic infancy gospels tell tales of his having discoursed on the symbolism of the Greek & related alphabets, one might also argue that he could have written using the Greek number system, which likewise used its alphabet for numerical digits. If you consider the text of the “New Testament” as definitive, all numbers that appear in passages with references to Jesus in the four gospels are written out in Greek (e.g., εἷς/μία/ἕν [one], δύο or δύω [two], τρεῖς/τρία [three], τέσσαρες/τέσσαρα [four], ἕξ [six], ἑπτά [seven], ὀκτώ [eight], ἑπτάκις [seven times], ἐννέα [nine], δέκα [ten], εἴκοσι πέντε [twenty five], τριάκοντα [thirty], ἑκατόν [one hundred], ἑβδομηκοντάκις ἑπτά [seventy times seven], δισχίλιοι [two thousand], πεντακισχίλιοι [five thousand], etc.) Most numbers in the text tend to be written out, though there are a few exceptions: e.g., the infamous “666” of the Apocalypse is written with the three Greek letters chi (χ), xi (ξ) and the antiquated stigma (Ϛ); in the Greek numeral system, the letter χ has a value of 600, ξ 60 and Ϛ/Ϝ a value of 6, so that the three letters appearing together as a number have the combined value of 666. (See also the article, “Arithmology in the Bible” ).

Further, he asked, “Do you think he could multiply?”

It would be hard to say, but perhaps the text can be taken in support with passages such as:

λέγει αὐτῷ ὁ Ἰησοῦς· οὐ λέγω σοι ἕως ἑπτάκις ἀλλὰ ἕως ἑβδομηκοντάκις ἑπτά.

dicit illi Iesus non dico tibi usque septies sed usque septuagies septies

Said Jesus: To you I say not ’til seven times,’ but ‘until seventy times seven.’

Matthew 18:22

While both seven & seventy can have symbolic meanings, the passage may not be literal, but nevertheless it is an example of the idea of multiplication—though I don’t think it really makes it clear whether he or his listeners would have been able to give the answer.

Having also asked why 0 wouldn’t have been used: neither the Hebrew, Aramaic nor Greek number systems had a character representing the number 0, as it wasn’t needed by non-positional number systems. There’s a whole section on the emergence of zero in Ifrah’s The Universal History of Numbers: From Prehistory to the Invention of the Computer, if I recall correctly.


June 23rd, 2003

In the preceding post, “Polygorials”, I mentioned the class of numbers I’d discovered and written about in a small paper; here, I thought I’d offer a general description.

Figuring more prominently in antiquity than in modern mathematics—though there are exceptions from Gauss to Euler to Cauchy, et al.—the subject of polygonal numbers is one that has long intrigued me. A subset of the more general figurate numbers, they consist of integer sequences defined by numbers that can be represented as geometric figures, regular polygons in this case. For example, the triangular numbers are those for which a number of pebbles can be arranged in the shape of a triangle; the squares, represented as squares; the pentagonal as a pentagon; and so on for the rest.

Image: Polygonal numbers: triangular through heptagonal
Fig. 1. 2nd–6th polygonal numbers: triangular through heptagonal

Nicomachus noted that for a k-sided polygon, the nth polygonal number is formed by taking the sum of every (k-2)th number from 1 to n. That is, for the triangular numbers, k=3, thus they arise from summing every number from 1 to n: 3 (1+2), 6 (1+2+3), 10 (1+2+3+4), 15 (1+2+3+4+5), etc. For the squares, k=4, you take the sum of every second number, thus the sum of odd numbers: 4 (1+3), 9 (1+3+5), 16 (1+3+5+7), 25 (1+3+5+7+9). For any k, the nth number to add to the sum is (k-2)n-(k-3), so we can define:

polygonal function
Fig. 2. Closed form for generating the nth k-gonal number

The traditional factorial function, designated n!, gives the product of the natural or counting numbers from 1 to n. Out of curiosity, I decided to explore a generalization of this function where we’re taking the product of polygonal numbers from 1 to n for some k; for p(n,2) we’ll still yield the traditional factorial, but for k>2, we will produce new integer sequences of the product of the triangular, square, pentagonal, hexagonal, etc., numbers. With a bit of exploration and work, I discovered that these can be generated via the closed form:

polygorial function
Fig. 3. Polygorial function

where (m)n represents the Pochhammer symbol.

A few of these sequences have already been studied in other contexts—e.g., the product of the triangulars is sequence A006472; the squares are sequence A001044; the hexagonals are sequence A000680, etc.—but most are novel. Of perhaps more or equal interest are the interrelationships discovered between some of these sequences. The ratio of the hexagorials to the trigorials, for instance, produces the Catalan numbers (proof). The infinite sum of the ratio of the tetragorials to the hexagorials can yield π:

Fig. 4. π

Daniel Dockery

animî nostrî dêbent interdum âlûcinâri

Home of published musician, recording artist, mathematician, programmer, translator, artist, classicist, and general polymath.