Closing the Circle

An economist’s “new approach recapitulates long-extant modes (Creator Styles, Part 3)

Continuing through David Galenson’s Old Masters and Young Geniuses: The Two Life Cycles of Artistic Creativity, he goes over what he sees as a continuation of the pattern he theorizes through more media apart from the one he started with, painting. While interesting, it’s also something of a dry read, filled out as it is with charts and statistics. Specifically, he covers poetry, literature, and film direction. And this last one provides a much closer corollary to the medium I work in, videogames (he also touches briefly on architects and economists, and posits that these same types might apply to all fields of intellectual activities).

In order to discuss film he conveniently skips over the fact that he accepts auteurism wholesale. This value system was popularized in the ’40s and ’50s by Cahiers du cinéma and in particular, François Truffaut, who wrote for the film journal. Since then it has found application in both film and in games. Wikipedia defines it as positing:

[A] singular artist who controls all aspects of a collaborative creative work, a person equivalent to the author of a novel or a play.

What Galenson utterly omits to mention is that there is significant criticism of this idea in both media. Indeed few people today, especially in games, accept the notion that all the achievements in this type of work are attributable to one individual. And I say this is as a game designer—a role that typically benefits from auteur theory.

I don’t think it’s either fair or true. I have always tried to promote my coworkers when interviews have attempted to focus on my role. My belief has always been that the whole at least should be greater than the sum of its parts, and that working with smart, creative people who can improve on one another’s ideas is one of the dynamics that continues to attract me to this field of endeavor. If holism is not occurring, that’s a red flag for me. Additionally, as many in this business have, I have had my name struck from credits, and indeed, have worked at companies in which individual credits were never given. These practices simply suck; if nothing else, games should learn from the standardized and guaranteed credits in Hollywood.

Furthermore, Galenson has focused all along on artists’ critical reception and, in the case of film directors, monetary success in evaluating them and which category they belong to. But not only is criticism inherently subjective, it can also be fickle, so these criteria are flawed ones. Just take a look at the ratings for some of your favorite movies on Rotten Tomatoes if you want to see that 1. audiences and critics don’t always agree, and 2. That you are likely to not agree with either of them.

As I have learned through the hard knocks of my own career, there’s many a slip twixt the cup and the lip—lots of factors are beyond a creator’s control even if they are somehow the auteur of a work: patronage, changing audience tastes, and in our modern era marketing, UA costs, and a dozen other things.

Just one such factor in the timing of a creator’s success in their field, which Galenson himself points out, is the complexity involved in an activity:

[The] Abstract Expressionists dominated the advanced art world of the late 1940s and early ’50s with visual works that were highly complex, and generally required long periods of apprenticeship from important contributors.

However, he notes that conceptual dudes come along and change things:

Within a brief span of time, however, in the late 1950s Jasper Johns and Robert Rauschenberg created new conceptual forms of art that were much less complex, and could be assimilated much more quickly, with very brief required apprenticeships. Thus the contributions of Frank Stella, Andy Warhol, Roy Lichtenstein, and many others who followed Johns and Rauschenberg were highly conceptual, and were generally made much earlier in their careers than those of Jackson Pollock, Willem de Kooning, Mark Rothko, and the other important Abstract Expressionists.

And with this, he expands his taxonomy of his two types, to include:

Aesthetic Experimenter

  • Inductive
  • Empirical
  • Discover methods during process
  • Continue to improve over a long career
  • Anti-intellectual
  • Value audience reception (commercial success)
  • They do not show themselves in a work
  • Add content to media

Conceptual Innovator

  • Deductive
  • Theoretical
  • Plan everything then execute
  • Peak young (run out of things to say)
  • Intellectual
  • Self-pleasing (about their own ideas, not the audience)
  • Autobiographical
  • Change and simplify media

And here, some of the ideas he ascribes to his types begin to sound familiar. The types of translations of poetry expounded by Jorge Luis Borges in his “Two Ways to Translate” (“Las dos maneras de traducir”), that I’ve previously covered, we recall were Classical:

The classical way of thinking is interested only in the work of art, never the artist. The classics believe in absolute perfection and seek it out. They despise localisms, oddities, contingencies.

And Romantic:

Romantics never seek the work of art, but rather the man himself. […] That reverence for the I, for the irreplaceable human difference that is any I, justifies literal translations.

Based on Galenson’s expanded descriptions of his two types, it seems clear that Aesthetic Experimenter and Classicist are synonymous, as are Conceptual Innovator and Romanticist.

Furthermore the dyad of artistic values that Borges refers to, just like the one Galenson proposes, permeates all creative endeavors. And indeed, as Galenson suggests of his categories, these might apply across intellectual activities. So ultimately, his categories don’t appear to be new ones at all, but simply a restatement of these already long extant ones. Arguably, the categories Borges uses are both too value laden with respect to the terminology employed, and overlooked in modernity. The only value Galenson seems to add then, is a discussion of the relative ages of creators belonging to one or the other group as related to their successes in their chosen field. And, as related previously, a great deal of statistical data intended to prove out these categorizations.

But again, I think this boils down to a commonplace: there is a certain brash reductiveness that is required of the Romantic point of view that nearly directly implies youth—or at least makes this approach appealing to younger creators.

In the end, Galenson concludes that to be successful, ambition and aptitude are more important than the concerns of method. Here we finally agree, and indeed, being aware of these styles, and changing one’s approach as needed might be still more important.

Read Previous Articles in this Series

Part 1: Passing on Picasso

Part 2: The Role of the Ear-Lopper

And the Rotas Go ’Round

The intricate solution to an ancient enigma (The Mysterious Square, Part 2)

Once the Christian origins of the “Sator Square” came into question, other notions as to how it could be solved did come forward, which were more or less far-fetched, involving overlaying a Templar cross on the figure, as well as several other patterns. Other religious resonances were also suggested, including Mithraism, a Graeco-Roman mystery religion based on the Persian worship of the god Mithra, but altered significantly.

But the one that seems best thought out and satisfying is one that says the Square is Judaic in origin. There is significant evidence of a Jewish presence in Pompeii, and while this community was not large, it gets past the test where any supposed Christian origin falls down. Indeed, there being a small community—one that was expelled from the Roman nation on two separate occasions—also makes sense to the necessity of this coded message.

Dr. Nicolas Vinel, if not the originator of the Judaic interpretation of the Square, certainly appears to have tied it up with a bow, and his work is the main source of what I’m relating here.¹ I’ll note also that what convinces me is that this is not a single solution, but a kind of web of correspondences that so completely covers every aspect of the Square that even if some part of it weren’t true, there would still be a lot right.

The first such element relates to the size and shape of the Square, which corresponds to that of the bronze altar Moses is instructed to build in Exodus 27:1–2:

And you shall make the altar of acacia wood, five cubits long and five cubits wide; the altar shall be square, and its height [shall be] three cubits. And you shall make its horns on its four corners; its horns shall be from it, and you shall overlay it with bronze.

In Joshua 22:34, the important symbolic function of this altar is described thus:

[The altar is] a witness among us that YHWH is God.

Thus simply by its 5×5 size and shape, the Square is a representation of this altar in plan, itself a symbol of the Jewish Diaspora and faith in their God.

The next part of the solution involves a transformation of the square based on its underlying numbers. This moves the 5×5 of numbers in order into a new configuration thus:

Essentially two rotations are performed: the central cross is rotated to the right 45 degrees, and the diagonal cross is also rotated, but the numbers alternate rather than maintaining their positions, with the other numbers falling fairly easily into place after that.

As I’ve implied in the title to this article, the fact that a rotation is performed, and the solution uses the proper rotas-first form of the square allows the first line to give a clue to its solution.

Now we are looking at a figure known as a magic square: In a magic square, a figure whose discovery easily predates the Square, the numbers in each row and column, as well as the diagonals add up to the same number. In the 5×5 version, this number is 65, the center remains 13, and in each of the two concentric squares adding a number with the one across from it adds up to 26.

The numbers 13, 26, and 65 are numerical representations of the divine name in the gematria, a system that assigns numerical values to words. Though it was originally AssyroBabylonian-Greek, its use in Jewish mysticism has a long and well known history. Using this system, 13 is ehad “One”, and indeed, there is but one one N, in the center where all things begin. 26 is the numerical value of the Tetragrammaton, the four letters transliterating the name of God, i.e. YHWH. At some point, people decided that saying YHWH aloud was not cool (think the stonings in Monty Python’s Life of Brian), and Adonai was used in its place. 65 is its written form, Adonai. Now while it is true that there are many, many names of God, these, particularly the last two, are very important ones. 13 also corresponds to N, in yet another way, as it is the 13th letter of both the Greek and Latin alphabets. Note that it is not contended that the letters simply correspond to the numerical values of the magic square, but the magic square is important to transforming the square.

When we move from the numbers back to the letters, the result of the transformation is a set of rows and columns each of which is its own palindrome, and the central tenet cross remains, but on a diagonal.


The fact that this transformation yields this result is compelling in itself, but there’s more: Now there appears not only the words, but a picture also of the bronze altar of the temple: now we see it in profile, where its dimensions are 5×3, and it is made up of the Latin words:


altar of bronze

The tenet’s Ts at the corners also correspond to the biblical instructions for the altar’s construction as the “horns on its four corners”, where the physical shape of the T is suggestive of this description. Furthermore, as the holiest part of the altar, there is a tradition of grabbing these horns as a sort of sanctuary, such that in the Vulgate version of 1 Kings 1:50 it says of Adonijah, a servant of Solomon fearful of being put to death:²

[…] tenuit cornu altaris.

[…] he […] took hold of the horns of the altar.

The cryptogram’s use of T to represent these horns as well as tying in the word tenet as what one does with them can only be called extremely clever—here tenuit is simply an inflected form of tenet. Also, though I am aware that the Vulgate did not yet exist, having pointed it out in the previous part, I am not engaging in an anachronism, as this is a simple one-word correspondence between the Hebrew and Latin.

Furthermore, and working off the same aerea that we’ve already seen, is a reference to the prophylactic symbol of the brazen snake created by Moses to cure those poisoned by real ones:


snake of bronze

And, as with the previously revealed words, the word serpens describes what it is with its shape, tracing a snaky path. Additionally, it is “lifted up” just as the snake it represents was on a pole. The corresponding bible passage from Numbers 21:6–9 is:

YHWH said to Moses, “Make yourself a serpent and put it on a pole, and let whoever is bitten look at it and live.” Moses made a bronze snake and put it on a pole, and whenever a snake bit a man, he would gaze upon the bronze snake and live.

Finally, both the double ara aerea and the double serpens in the square, rather than simply being palindromes, continue forever. They share their first and last letters and read in an unending circle—the opposite of the ungodly, as described in Solomonic wisdom (Wis 2:5):

After our end there is no returning: for it is fast sealed, so that no man cometh again.

There is still more evidence that is provided my the inscriptions that accompany the Pompeiian Square, but it’s beyond the scope of the cryptogram itself, so I won’t discuss it here.

Read Previous Articles in this Series

Part 1: Attempted Unravelings


  1. That is, “The Hidden Judaism of the Sator Square in Pompeii”, Revue de l’histoire des religions, 2006.
  2. My emphasis.

Sator Square Non-Starters

Failed solutions to an ancient rebus (The Mysterious Square, Part 1)

The so-called Sator Square, a palindromic grid of letters which can be read beginning at any of the four corners, has captured people’s imaginations for millennia. Early in its history, those who ostensibly understood it inscribed it widely, and it eventually came to have a cultural value similar to that of the Icelandic Rune Staves I have also written about. More recently, lacking a key to its understanding, scholars and layfolk have theorized about its meaning. So, in something of a turnabout from my posts about the Witham Sword, I wanted to evaluate some of the different solutions to this mysterious square.

The text reads:


This appears to be some type of Latin phrase, and has puzzled many since it first started appearing. And appear it did, reaching a status some have described as memelike long before the intertubes began trading in such stuff. Its earliest appearances seem to have been in the Italian Peninsula, but it has been seen in France, Portugal, and as far away as England and Syria. There is even a runic inscription that shows the square Although somehow this has been characterized and spread across the internet as being a runestone, it is (as can be seen in the image, below) carved into wood—the bottom of a bowl of some kind, partly missing, but which doubtless finished the Square.

Then, as I noted, the secret of the square seems to have been lost. The earliest known attempt at a decipherment of the Square came from a Byzantine scribe in the 14th century, but there have been many since. The 19th century saw a boom in scholarly efforts, which continued until last century when they dropped off, with codebreakers either feeling it to be unsolvable or being satisfied with the efforts already made.

On the unsolvable front, Rose Mary Sheldon has provided us with an exhaustive 34-page bibliography of the solutions posited, titling her work, “The Sator Rebus: An Unsolved Cryptogram”.¹

Let’s turn to just a few of the solutions Sheldon considers to have failed. First there’s that of that first Byzantine scribe, who broke it down thus:

σάτορ—ὁσπεἱρων [sower]
άρέπο—ἄροτρον [plough]
τένετ—ϰραεί [holds]
ὄπερα—ἔργα [works]
ρότας—τροχούς [wheels]

There are problems, of course. Mainly these are around arepo, which would continue to bedevil would-be codebreakers as we shall see. The scribe here claims is ἄροτρον (L. arepum, of which arepo would be an inflected form) supposedly meaning “plough”, although it is found in no other source. Some have suggested a borrowing from a Gaulish or Celtic term, *arepos, which again is nullibiquitous. The asterisk in *arepos is used by linguists to mark a reconstructed word—that is, one that is unattested but conjectured to exist. Wanting arepo to mean plow or opera rotas to somehow imply it seems a clear case of confirmation bias: “it says ‘sower’ so it must say ‘plow’.” I think given the brevity of the rebus, the inclusion of such redundancies would actually be quite undesirable. Still, it lives on in many modern interpretations which hold that the phrase’s full translation, with the other words translating in order as “the sower”, “to hold”, “works”, and “wheel”, is therefore:

The sower holds the plough, the works, the wheels.

Others have decided that arepo is a proper name, again choosing to set aside the fact that it’s a hapax legomenon, and so render the phrase:

The sower Arepo holds the works, the wheels.

They somehow feel that “the works, the wheels” implies a plow even though the plows of the appropriate time in no way resembled such a description. Frustration with the word led some to dismiss it as a term like abracadabra—without meaning, but while some such terms are attested, it’s a far from satisfying conclusion. Abracadabra, rather seems to derive from ΑΒΛΑΝΑΘΑΝΑΛΒΑ (ablanathanalba), a palindromic term associated with the rooster-headed anguipede, ΑΒΡΑΣΑΞ (Abrasax). Ad repo, “I creep towards” is another interpretation that has been suggested but results in still worse nonsense. Yet another suggestion is the Latinized and shortened name of the popular god of good luck from Graeco-Roman Egypt, Harpocrates (Har-pa-khered, “Horus the Child”).

To get from Harpocrates to Arepo, elide the initial ⟨h⟩ (the Greek is Ἁρποκράτης), inject a vowel ⟨e⟩ to break up the consonant cluster rp, drop the entire second half, and Robert is your father’s brother. The meaning (in a charitable reading) thus becomes a decently apotropaic formula:

The sower Harpocrates keeps in check toils and tortures.

Never mind that the god is nowhere depicted as a “sower”, appearing in Egyptian stelae perched on a crocodile’s back, snakes clutched in his outstretched hands—an image that calls to mind Herakles…. And later, and especially in the Graeco-Roman context as a child with a finger pressed to his lips. Marcus Terentius Varro was apparently the first to describe the gesture thus:²

[…] Harpocrates digito significat, ut taceam.

[…] Harpocrates with his finger makes a sign to me to be quiet.

However it is important to note that this pose actually relates to the form of the hieroglyph for “child”, and did not have a meaning relating to silence or secrecy in its original context. This sometimes-winged figure was later conflated with Cupid—Cupid with a uraeus on his head, though later forms morphed it into a topknot. If anything, he is shown holding a cornucopia—the polar opposite of the idea of sowing.

The next major direction of exploration came from the idea that the inscription should be read boustrophedonically. The term means “as (plowing) oxen-turn”, therefore referring to a reading that alternates directions, so:


The image of plowing oxen probably was a temptation to employ this type of reading, but it’s just more fruit of the poison arepo tree. And again applying a generous amount of imagination to the reading, we can interpret this as the New Testament dictum:

As ye sow, so shall ye reap.

This solution also has its share of issues: first, inscriptions in boustrophedon appeared only in the prehellenic Greek (until 510 BC) and archaic Etruscan [link] (until 480 BC) periods, coinciding with the advent of the Phoenician-based alphabet into those cultures, before they had settled on a single reading direction; left-right for Greek and right-left for Etruscan. So these predate the first known appearance of the square by just about 500 years.

Second, in boustrophedon inscriptions the letters themselves are typically reversed to show the reading direction. Such inscriptions also invariably begin left to right, while this solution requires a right-to-left start. That is, this solution would require the versions beginning with sator to be the older, original form, which contradicts all evidence. Indeed, the desire to read the cryptogram boustrophedonically may have actually prompted the current dominance of the sator-first form.

Finally, the symmetry of the square is a major element of its magic, or at any rate, aesthetics. The 5×5=25 form is destroyed by the 30-letter reading required for the boustrophedon to work. Furthermore, the words arepo and rotas are omitted entirely in this solution, which seems like taking the easy way out.

As you may have also noticed, we have now entered a realm where interpretations are based on the idea that the inscription is a Christian one. And the locations it has been found in suggest such an association, as they include Benedictine and Cistercian abbeys, a cathedral, an Anglican church, and a private chapel.

And many other seeming links to Christian tradition have been noted in potential solutions: An old Cappadocian tradition gave the shepherds of the Nativity the names Sator, Arepon, and Teneton. An old Byzantine biblical tradition calls the Three Magi Ator, Sator, and Peratoras. And the Ethiopians and Abyssinians invoke the Savior by enumerating the five nails of the Cross: Sador, Alador, Danet, Adera, and Rodas.

Attempts were also made to read the opening lines of the square as a set of abbreviations, similar to those I used in my solution for the Witham Sword:

SAlvaTOR A REx Pontifex O


SATOR A Rerum Extremarum Principio Omni

Of the two the first is execrable and the second only somewhat less so but again nowhere apart from this posited solution to the Square are these words found together—a fairly clear sign that there was no such phrase to code into a rebus.

One solution that seems to satisfy many interprets the Square as an anagram for Pater Noster, the opening words of the Lord’s Prayer, with a leftover pair of ⟨A⟩s and ⟨O⟩s as Alpha and Omega, representing God’s omnipresence.

Some aver that this could not possibly be a coincidence, that this must be the solution. However, when it comes to anagrams, quite a few attractive ones are possible—and some even manage to use all the letters—including:

  • Oro te, oro te, pater, sanas.
  • O pater, ores pro aetate nostra.
  • Ora, operare, ostenta te pastor.
  • Retro, Satana, toto opere asper.
  • Satan, oro te pro arte, a te spero.
  • Satan, ter oro te, opera praesto.

However all of these Christian associations are easily swept aside by the fact that the earliest known versions of the Square are graffiti from Pompeii. Two such were found in the city in separate locations and written in different hands and were buried in the ash of an exploding Vesuvius, giving a clear and irrefutable terminus ante quem of 79 AD. Not only was there no known Christian population in the city by that time, 1. It is not known how long before 79 AD the inscriptions were made—one of them has at least one responding graffito, so it had to have stood there for at least a while, and 2. If this were a Christian cryptogram it would likely have had to have been formulated and dispersed from other larger communities and there is zero evidence for this.

On top of this, the language of the early New Testament was either Aramaic or Greek—some debate remains as to whether Greek was originally used or if there was an Aramaic urtext—with the earliest possible date for the Gospels in any form being around 40 AD. That accomplished, a Latin translation would have to have been undertaken—for which, I might add, there is also no evidence until the Vetus Latina, a hodgepodge of translated sections from the 2nd century at the earliest. Then a cryptogram relating to such a text would need to be created and disseminated even to places with a negligible Christian community community, all within a maximum of 39 years. The whole hypothesis is pretty sketchy—even accepting the several unproven bits, the timeline just doesn’t work.

In fact, the discovery of the first of the Pompeiian Squares in 1936 was more likely the cause of the decline of scholarship on the issue more specifically than the cases I mentioned earlier—nearly everything had to be simply thrown away. The second, while actually found in 1925, was in much worse shape, coming from a ruined house, and was only able to be identified via the model of the other graffito. In Part 2, I’ll get to a theory I do credit, and why.

Read Subsequent Articles in this Series

Part 2: And the Rotas Go ‘Round


  1. In Cryptologia, 2003.
  2. Marcus Terentius Varro, De Lingua Latina, 5.10.