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Into The Labyrinth



            This is what Arthur Evans, archaeologists Sinclair Hood and Mark Cameron, and Oxford’s Ashmolean Museum judged to be the most accurate restoration of the “Toreador Fresco” (a.k.a. the Bull-Leap Fresco), whose original fragments Evans and workers uncovered in the east wing of Knossos Labyrinth in 1901. Ahead, to gain more perspective for analyses, we’ll compare the restoration that stands today in Crete’s Heraklion Museum.

Complementarities, color patterns and anomalies in both versions intrigued American scholar Dr. Charles F. Herberger to investigate the Bull-Leap Fresco in the 1960s. In those years just before the computer age, Herberger studied the Heraklion Version closely, and then in Oxford took precise measurements of the Ashmolean Version to examine the fresco’s features in scale (the verticals and horizontals, colored crescents, the layered orange/blue rows of black “ticks” or “tracks,” and more).

He knew the assumption about the Fresco’s uniquely-elaborate border: no one from Evans onward saw more in it than “decoration.” Immerwahr’s 1990 Aegean Painting compared its many-textured colored crescents, and its “tooth or dentil” pattern of black tracks, to “the old [Minoan] treatment of the background as a rocky surround” (92), which in later Mycenaean frescoes had become an “abstract” pattern.

While Evans remarked that the border seemed to anticipate Mycenaean designs, Immerwahr judged it “formative rather than derivative” (109). Born of its own Minoan past, this border’s form has more in common with earlier “curiously inscribed” objects than with later examples of its use on Mycenaean walls, and those are the ages likely to illuminate it.

The border may be only a decorative design. But no other Minoan “rocky surround” or fresco border compares to this one in its layered, complicated and yet consistent features—or in its anomalies, as Herberger noticed, and will appear.

A calendar tracks time by counting. Herberger perceived that each black track of the “tooth or dentil” pattern was identical with a Minoan “1” (Evans’ chart below from Palace of Minos 1: 279). Also below, you can see that for Evans, a crescent convex to the left in both Linear A and B signified “moon” or “crescent moon” (Palace 1: 643, 4: 685). That reference and meaning seems as clear among the signs on Minoan seals.






It seems clear that half the symbol at the center of the throne is a moon, and crescents are visually half the fresco border. As Kyriakidis notes about stellar referents in Minoan art, “It is very illuminating that when Minoans devised a writing system, they used symbols (pictographic script) similar to the ones with which they divided the sky” (2005: 153). Devising a calendar in visual terms, they could in the same way adapt a known symbol for the moon into a major feature of the border. In the New Palace period of the fresco, “artists were sharing a common iconography and transferring it among different media” (Rehak 1995c: 217). For all searching further on, we find very few crescents elsewhere with comparable investments in their individual featuring.


Exploring the implications of small clues, Herberger found the same kinds of evidences in the fresco’s border that lead other scholars to investigate objects for astronomical patterns (noted in Chapter 1: more on these Canary Island pintadera stones from Belmonte/Betancourt in Chapter 4). Features that seemed to correspond with aspects and cycles of the moon and sun—for example, their numbers and arrangements, patterns and irregularities—became the subject of Herberger’s 1972 Thread of Ariadne.

His finding was that the border of the Bull-Leap Fresco may be a calendric register of the actual 8½-year lunar/solar cycle called a Minoan Great Year in Chapter 1. The aim of this work is to test that possible discovery in new critical ways. So let us return to where the Bull-Leap Fresco was found, its dating and likely location in Knossos Labyrinth; its two versions, its elements and its immediate problems.



            In this detail from a large insert-map of Knossos from Evans’ Palace of Minos, the left end of the Labyrinth’s central court rectangle points roughly north. Just to the east beyond the Kairatos River, the sun rises on the Labyrinth over the long steep slope of the hill called Aelias. Up there, a Minoan road (as shown) led to “good Minoan houses,” a spring, and “monumental structures,” all within a fair view from the Labyrinth’s east wing (detail left, below) with its “loggia” or pillared open porches, as in the detail from a Mallia example, below right. According to Banou’s survey of evidences and Goodison’s discovery (and, if other ancient culture-centers around the world are indications), there were timely and precise alignments between sunrise and parts of the Labyrinth, with “monumental structures” between.




According to Evans (Palace 3: 209-10; 4: 892), Brown (1983: 74) and Immerwahr’s Aegean Painting (1990: 84, 175), the Bull-Leap Fresco that we know was one of “several panels [or frescoes] within decorative frames” painted along the wall(s) of “some kind of loggia” or “open area” along the upper east wing, on one of the levels above the area today called the Court of the Stone Spout (or, Oil Spout).



            This Court “was probably originally an open space” (Brown 74). Below, in the detail from Evans’ first plan of his east wing discoveries, you see where he recorded finding “Toreador” fragments in 1901.



Evans’ next plan (below, Palace 3: 270) located more fragments a few steps away in the Court’s adjacent School Room, found “when the later rubble walls were cleared in 1902” (Brown 74: noted with a red circle).


Evans (3: 209-10) dated the Bull Leap frescoes “to a fairly advanced phase of the restored [New] Palace,” meaning “shortly preceding 1500”—based in part on their “delicate delineation” and “fine enameled surface” (211). Cameron and Hood, in their 1967 Atlas, saw a rather wider window for their creation, from the last Middle period (III B) to perhaps Late I B, or 1630-1425. Macdonald’s dating of New Palace developments in the Stone Spout area almost agreed with the latter (2002: 46).

Complicating all this was the fact that the frescoes seemed “to have fallen into contexts that were considerably later” than their likely creation (Immerwahr 84). As Hood wrote (1978: 60), the Bull Leap fragments had been “incorporated in debris piled behind the wall forming the western side of the Court,” and when that wall eventually collapsed, they fell “on top of the later walls and floors below.” Sometime after at least 1340 (Late Minoan III B), the frescoes fell among remains already thoroughly mixed with 120 earlier years: LM I, Marine Style, and LM II-III sherds of pottery.

Despite the above earlier datings, M. C. Shaw’s study (1996: 181) concluded that these frescoes had been painted fairly late (roughly 1425-1360, or Late Minoan II-III A), because the Knossos bull-leaping figures were almost twice the size of those in a similar fresco at the “Ramp House” at Mycenae. Shaw wondered if the Mycenae example had in fact been painted before Knossos’, because 1600-1425 (LM I) had been the “heyday” of Minoan “miniature” frescoes, while many larger Cretan figures belonged to later periods (179, 182).

Hood’s 1978 survey, however, noting (53) “a number of large figures” in Minoan frescoes before 1450, judged that the Bull Leap panels were “unlikely” (62) to have been painted after 1425. This was Hood’s second view favoring earlier rather than later. If we combine this, Evans’ view above of a “shortly before 1500” dating, and Immerwahr’s dating of a “derivative” Tiryns bull-leap fresco (175) to around 1510, we might best-date these Knossos panels to a generation or two after 1600, or “mature” LM I A—a mid-to-late 1500s time well after the 1600 earthquake, but not long before or after the Thera volcanic eruption. That is to agree with Hood’s 2005 judgment (80). Ahead in Chapters 5, 6 and 8 we return to these issues.

Evidently the frescoes’ colonnade ran north-south, facing east and sunrise; a fair location for calendric activities. Given “several” panels, how did they interrelate?


            In archaeologist Mark Cameron’s “Last Notes” (1987), he published this “relational conception” of the several Bull-Leap panels along their loggia. While it does not show all original evidence, it shows his idea of several contiguous panels, each a Bull-Leaping episode separated and bordered by rows of tracks and crescents. Where perhaps a support-column broke the pattern (at right), the bordering pattern resumed—first perhaps, as Cameron shows, with a small space of blue background-field between two slightly extended horizontals.

            These unequal fields lie outside both the left and right verticals in the Ashmolean Version below. The main horizontals of the border each extend by a few more “tracks” or “1’s” beyond the verticals, as if broken out. “The Toreador Fresco” may be consistent with a little bit more than one full panel in the series: or, these unequal side-borders represent the fresco’s intended form. Can we tell which is the case? Why does it matter? Ahead, the Heraklion Museum fresco agrees on these uneven spaces at each side. Both versions also agree that other “seemingly extra” tracks belong where they are, aligned with blank space at the top of each vertical row. We need to know exactly what we have as we begin, and the significance of these features will appear.



The red lines above (in this detail from Cameron’s conception) approximate the edges where the Bull Leap fresco may have broken from its series, or, from a separate position along the loggia. Odds are high against the chance that it detached from the wall in the same way at each pair of corners. Yet, in both independent Museum Versions, we find 3 tracks or “1’s” extending beyond both of the left side’s horizontals; and 7 tracks or “1’s” beyond both horizontals at right.

Does this represent an optimally-accurate “rounding off” of 4 rough corners by both Museums? If so, it is not apparent why they agree in just these ways about unequal details. Going by the Ashmolean Version (in color just above)—with its darker colors indicating strictly-original fragments—there was slight original evidence to extend the horizontal borders in these asymmetrical ways. We might assume they were left this way, twice independently, to simulate a broken-out fresco-panel; to show that what we have came from within a contiguous series.

Evans’ colleague “Mr. Noel Heaton” added his observations to The Palace of Minos on these matters (3: 211, note 3). “[T]he horizontal border at the top and bottom apparently ran straight on, the vertical border dividing the wall into panels.” Heaton remarked “the exceptional absence of the joints usually found in the borders of the plaster in the case of either its horizontal or vertical divisions. The plaster in this case runs without a break from one panel to another,” and it “was not divided up into areas of sufficient size for the [entire loggia’s] decoration to be completed before the process of setting became too advanced.”

If all the Bull Leap panels were created at once, multiple painters would be needed to finish before the plaster set. A group of painters appointed to the border might not be expected to vary it to individual taste. And yet (below), there are differences among fragments of this bordering from different panels.

What seems most unclear is how Heaton could conclude from fragments that the plaster ran “without a break…one panel to another.” Perhaps no surviving fragment happened to bridge or straddle a “joint” between two panels. In Cameron’s conception, at least one panel stood separately. We cannot ignore any of these reasons to be skeptical about how “the” Bull Leap fresco took its present asymmetrical form.

Notably, when artist E. Gillieron produced a first image of it for Evans’ Palace (3: Fig. 144), Evans responded with “many comments and corrections” toward a corrected version—with special attention to the unequal borders omitted by Gillieron. As Herberger found, following Cameron and Hood by directly examining the fragments and Evans’ handwritten notes, Evans had insisted on their replacement, to “avoid doing violence to the evidence provided by the extant fragments,” Thread 53).

So, Cameron and Hood restored the shown border-extensions when they produced their “Plate IX, Second Version,” presented first above and again below. In Cameron’s judgment, the Second Version resulted in a fresco “much more accurate and sensitive” to the original fragments. It seems remarkable that two independent groups of experts showed the “broken out” or separate panel in just the same way.

Herberger, then, relied most on Evans’ eyewitness-based standards as he took his research forward. Something, too, compelled the Heraklion restoration experts to include the unequal extensions at left and right, in just the same way as the later Ashmolean. Only ahead can we see why this matters fundamentally, but it belongs among the first main things to notice.

 Was the Bull-Leap fresco that we have broken out by chance from between two other connected panels? Or was it set apart along the loggia with exactly these unequal extensions at each side? In Cameron’s conception, both scenarios are possible, and an “as is” set-apart location is at least as likely. The original-design structures in both Versions show that one full circuit of this single panel’s border requires the use of 4 rows of tracks. The complete border (16 rows) includes tracks for 4 circuits, each along a different path of orange and/or blue rows; and 4 was a noteworthy number in Chapter 1’s lunar/solar observation charts. Chapter 5 presents more evidence that this is a “self-contained” border, connected to the others by the realities of astronomy.

Let us observe more of the Heraklion and Ashmolean Versions, and see what definite features they present. Here is the Heraklion Museum Version:

As in the Ashmolean fresco, we find 8 pairs of blue-and-orange rows of tracks distributed outside and inside the crescents in the pattern. One unique pair, just below Bull, presents orange-over-blue: the other horizontal pairs match, with blue-over-orange. Was this a casual variation, an aesthetic one? Necessary? Careless?

            Another aspect is obvious. Enlarging the computer image, we study each alternating orange-or-blue row and find the tracks spaced unequally. Some tracks flank spaces twice their own size, and some crowd together. Only at times do tracks in paired orange/blue rows align. Possibly, their numbers mattered more than perfect visual regularity. If Herberger is right on how they were painted to produce these irregular results (Thread Chapter IV), we might have another clue as to why each black track is like a visual pun on the Minoan numeral 1:

Knowing how many marks were required in each track, a painter would find it easy to fill them in free-hand after determining a midpoint in each border, and then subsequent midpoints, in smaller and smaller subdivisions of each. It would be a simple calculation to determine how many marks or tracks had to be painted in each subdivision to give the total wanted for each track, and for the fresco’s grand total. Thus, the tracks could be painted in with the mathematical precision required by a calendar, even though their spacings, done free-hand, are therefore not perfectly regular.


Are there other contemporary examples of these tracks and crescents to compare? Above is a fragment (and detail at center) of a different Bull Leap fresco panel, showing these crescents and tracks together as a border. Yet, compared with “the” fresco’s crescents, these are more elongated. Their rounded ends also point the opposite way, a substantial contradiction to the view that the bordering “ran without a break…one panel to another.” We see differences in the detailing of both white and blue examples; and, this border-fragment includes figures Evans called “germinating seeds” among the crescents. Possibly the crescents are “only rocks” in the scene’s surrounding earth, the seeds splitting open with life.

If seeds germinate only in their seasons, their placement might suggest something about phases and time where they fall. (There are 9 seeds clustered round the crescent: as winter months approach beyond the 9th moon, Crete sows next year’s grain.) Clearly, the Bull Leap panels’ borders were not all alike. We can see that the unequal and non-aligned distribution of tracks in each was a convention across the panels. And it appears below that among all examples of these tracks and crescents, only in the Bull Leap panels were they used together.

Below is the one other cousin of these crescent-forms—from the great relief of the bull and olive tree above the north entrance to Knossos Labyrinth (with an enlarged detail of a crescent below it). These upright crescents do seem to represent a “rocky surround,” and in the enlarged detail, we may see an inmost cache of possible “seeds” again. Altogether, there seems to be no example to contradict or eliminate the use of such forms elsewhere for other purposes.




What other contemporary examples of “tooth or dentil” border patterns or tracks do we find? The first fragment below (from Cameron/Hood’s Atlas) adorned the Labyrinth’s west court “Pillar Shrine,” and dates from the latter Middle into Late Minoan times, like the Bull Leap frescoes. The track-pattern here is associated with three central and sacred Minoan symbols, pillars, double axes and “horns of consecration.” The misaligned orange and blue rows match the Bull Leap fresco borders except in their tracks’ red and blue-green colors.



While we have one example (the north entrance bull relief) of crescents all but surely used as only “rocky surround,” the other examples of these rows of tracks come from likewise sacred contexts—as shown next, below, in these Atlas restorations of the “Pillar Shrine Miniature Fresco,” which is believed to show a main and actual west court shrine, perhaps during a Minoan festival.




While we see the same characteristics in these rows of tracks, note for later the 5 colored disks across the top of the shrine (lower example): orange, blue, red, black and white, the same 5 colors that repeat (in different sequence) in the Bull Leap fresco’s crescents, as we will see. The last two examples of these tracks follow.

First is a restored painted-plaster detail from below the west wing magazine’s 13th “cist,” dated by Evans to after 1700 BCE, or Middle Minoan III. Below the cist is a border (dated after 1600 or Late Minoan IA) from an east wing light-well, just south of where the Bull-Leap fragments were discovered. Are the rows of tracks allusions to the Bull Leap fresco border, or were they borrowed from here and modified for fresco use?


The varied spacings of tracks in most examples keep their paired rows out of full alignment. Although they appear in sacred contexts, none of these exampled tracks are combined with crescents. There are earlier examples of these tracks (ahead.) As for later Minoan uses, orange and blue rows do border the rosettes along the sides of the Late-period Agia Triada larnax, but with a very different “dentil” pattern.

Here, finally, are collected later Mycenaean examples of these tracks, all from Tiryns and Mycenae. In the first at left below (from Tiryns), tracks border a bull-leaping scene in a way quite reminiscent of the Knossos fresco in question. The next two examples, both from Mycenae—at right in the first row, and in the center, next row—also share track-borders, surrounding scenes of ritual and athletics including bulls. Then, in the bottom row at left, we see the tracks forming part of a shield-bearing fresco from Tiryns, and in it the tracks combine not with crescents but with running spirals. At bottom-right, finally, is a detail from Tiryns’ “Women’s Procession” fresco. It appears that on the mainland, these tracks retained the same “free-hand” alignments, and as well, their prestigious associations with bull-sports, ceremonies, and acknowledged symbols of power.




So we know that experts found the fresco’s unequal left/right borders essential, and that elements of its unique border made rare but important Minoan appearances. With each exploration of a Bull Leap fresco feature, we build a basis to know what we really have that might be consistent with a pattern of the moon and/or sun. Let us see how the grand totals of tracks and crescents, and their features, compare to astronomical facts.

Below again is the Heraklion Museum Version. The Ashmolean Version does not restore the full rows of tracks, but provides crucial evidences of their total just ahead.



If we work like the first restorers of this Fresco, using careful measurements and averages to produce substitutions for lost original fragments, we can count in any direction for a conservative estimated total of 1,436 tracks (being 1,086 horizontal ones and 350 vertical); or, 721 tracks in blue rows and 715 in orange ones. Calendric significance does not leap out; unless perhaps we divide 721 blue tracks in half to reach 360 + 1. Doing so with 715 orange tracks leaves us further from a year-like number at 357½.

            What about the border’s colored crescents? While the horizontal borders total 23 x 2 (or 46) crescents, the verticals are unequal, with 7 crescents at left and 8 at right, for a total of 61—close to the 60 lunar phases in a year of 12 Moons with 5 phases each. Evidence for a five-phase lunar cycle appears as soon as we look at the crescents’ colors.

In the comparative detail below, the top row is the Heraklion Version’s upper horizontal row of crescents; and the bottom row is the same horizontal as shown in the Ashmolean’s corrected Second Version.



They match and substantiate a 5-color pattern of orange, red, white, blue and black (or, of course, the reverse). Let us compare the color sequences in the Versions’ two vertical rows.

First, the two Versions’ left vertical borders. In Heraklion’s (shown at left below), the restorers did not follow this color-sequence. And, in comparison to the Ashmolean Version’s left vertical (below at right), Heraklion omitted a blue crescent-symbol (the third crescent from the bottom in the Ashmolean’s). No original fragments suggest that a white crescent-symbol instead falls 3rd from the bottom, where it is in the Heraklion Version. As a result, as we seek our totals, the Heraklion left vertical shows only 7 crescents, where the Ashmolean Version, “much more accurate” (Cameron), presents 8 crescents there.




Next—below—compare the two Versions’ right verticals.

Heraklion’s right vertical (shown at left below) contains a segment of the color-sequence supported by original fragments. But a black crescent, always found between blue and orange, is missing just above the bottom orange one. According to pattern, a black crescent should fall 2nd from the bottom: it does so in the Ashmolean right vertical (below at right).




So, despite small disagreements, both Versions’ vertical borders present original fragments that agree with the sequence in the horizontal rows. Most important to counting-issues, the Second Version displays two vertical rows of 8 crescents each. The most accurate Version’s total number of colored crescents is 62, for use ahead.

Are there clues that suggest which way to follow the color sequence? The crescents are all the same size. Each has curved points and a rounded edge at the other side, a form that can “face” both ways and evoke almost any lunar phase.



Nilsson (who called the moon "the first chronometer," 1920: 148) showed that where a calendar began with and “consisted of moon-months, its beginning must therefore have been a day of New Moon” (273). He found also that in most early calendars, the Moon’s New and Full phases were the most important.

To all observers, the Moon has two extremes in Full and Dark phase. Of the crescents’ 5 colors, black can reliably anchor us at Dark phase (the black crescents even contain white and red dots, like a moonless sky of bright stars and planets). White crescents correspond to its opposite, and they are speckled with dark marks, like the face of Full Moon.

We work it out. Dark Moon (black), then New and Waxing phases on its way to Full Moon (white). The pattern’s orange crescents, always between black and red ones, must be New Moon, the standard of “first visible crescent” that runs to First Quarter’s 7th day. Orange has a pocked because illuminated face like Full Moon’s.

In each red crescent between orange and white, we have a color chosen in most ancient art to signify ascendancy, potency and power. Orange/New, red/Waxing, white/Full; and beyond each blue crescent in the pattern, Dark Moon.

Blue, by this lunar logic, must denote Waning into shadow and darkness. Examples ahead show blue associated with shadow, decline, death, the underworld and Beyond. For one, in the funeral scene on the Agia Triada larnax (Chapter 7), the vessel receiving sacrificial blood for the dead is uniquely blue: so are the vestments of the pouring priestess, and a tree beside the likely-deceased man and his tomb. Another example is the blue-painted (shaved) heads of young Theran girls about to be initiated to womanhood, where blue likely denotes the impending death of their former social selves (see Marinatos, Art & Religion in Thera: a sample-image at this chapter’s end).

With a fairly obvious series of lunar phases in these 5 colors, here is how a 5-phase lunar cycle would track the actual moon in the sky:



Noting the actual average total to be 29.5 days here, we recall the reasons for intercalation of almost one half-day each month, from Chapter 1. These phases work also with its solstice observation charts. Here and first, given the clues so far and many evidences to come about the Minoan pattern of doubling, let us observe something fundamental about the Moon itself. Of all the different changing phases it presents to Earth in one typical month's cycle, the central Full Moon which typically lasts 2 days is the only visible phase that is naturally doubled—the only pair of days (excluding Dark Moon) that show exactly the same face to Earth. Perhaps this crowning unique phase of lunar power seemed worth imitation and borrowing into Minoan iconography. From here, we might experiment forward with some evidence that the fresco’s crescents can signify a year of lunar phases.

Indeed, 62 is not 60. And no clue yet directs us to follow the color-sequence in only the way above, that matches color and lunar phase. Yet, we have only begun. 

The crescents’ textures show work invested to differentiate them, while keeping them uniform in the cycle of 5 colors. We noted New and Full Moon’s faces, and Dark Moon’s stars in Black. The red and blue crescents’ wavy lines evoke “movements” or transitions as intermediate Moon-phases, waxing toward Full or waning toward Dark. The lines in red/Waxing crescents simulate radiant energy, like heat-shimmers moving air before the eye: the lines in the blue/Waning crescents logically signify a flowing-away or loss of power. These lines within the crescents keep the same orientation toward the next phase in horizontal and vertical row-positions. Functional either way, they evoke movement without leading the eye in one direction or the other. Possible calendric operations ahead may demand that neutrality—or in a sense, a doubling.

            One more observable fact suggests more than decoration in these crescents and tracks. Grant for one moment that the tracks or “1’s” signify solar days. The measurements ahead show a distribution-average of 6 tracks aligned with each crescent around the border: or, 30 solar days per 5-phase lunar cycle.

We find again that posing questions between lunar and solar indications can take us forward by letting those elements anchor and inform each other. As Marinatos notes (2010: 130), “duality is a constant and key feature” in Minoan representation. So we turn from here back to the rows of tracks or “1’s” again, in our quest for accurate totals of both these main features in the Bull Leap fresco.

Obviously, the different goals of the Heraklion and Ashmolean Versions led to different restoration results. The Heraklion Version’s more-complete look results from the mainly visual goals of its restoration, under the highest museum standards: it carefully assembles and builds on original fragments to show a conception of original magnificence. In contrast, the Ashmolean Version is more fragmentary: its purpose was to show all and only original pieces proving this Bull-Leap Fresco’s features.

What we see by comparisons, below, is that Heraklion, to visually restore a fresco without calendric aspects, brought a “thinned out” approach to re-creating stretches of the rows of tracks, for a brighter effect. Evans, Cameron and Hood worked to restore what editing had changed. The next images isolate rows of tracks from the two Versions for comparisons: each shows Heraklion’s above and the Ashmolean Version below. First, here are the paired rows of tracks from each Version’s uppermost horizontal row:


            Clearly, the two Versions present different densities in the distribution of tracks along these paired rows. The Ashmolean (lower pair) restores a higher density of tracks along the row, in strict keeping with their density in the original fragments.

            The next sample pairs, below—also from each Version’s upper horizontal row, but from the rows just above the bull-leaping scene—reflect the same differences produced by different restoration goals. The Ashmolean Version’s original fragments present a comparatively higher density of tracks per row than Heraklion’s.


Very similar differences inform the two Versions’ restorations of rows of tracks in their vertical rows. First below are both Versions of the fresco’s left vertical. Note that Heraklion’s, at left, show 5-6 fewer tracks in them than the Ashmolean’s at right.



            Next, below, are both Versions of the fresco’s right vertical, and these examples show a slightly greater difference; showing again that the Ashmolean Version’s higher density of tracks is closer to the fresco-rows’ original density.



            The Heraklion Version border’s total number of tracks was 1,436. We cannot, however, simply total and compare the Ashmolean Version’s total tracks, because they are not restored along the two pairs of lower horizontal rows (below).



And this was the problem faced by Herberger in trying to establish a grand total of tracks for the fresco border. His approach to a solution followed the same basic restoration process seen in the upper horizontals and two verticals of the Ashmolean’s results. Herberger measured every original fragment of the rows; calculated careful averages of the numbers of tracks in each; and then, used those averages to restore all of the border’s paired rows—thus to create a complete Schematic of the fresco border, with the aim of reaching a very reliable estimate of its total number of tracks.

The Heraklion Museum Version’s estimated total of tracks was 1,436. We will find 1,561 in Herberger’s Schematic (just below): a difference of 125 tracks, averaging 31 more per Schematic row than in the “thinned out” Heraklion Version. Let us see precisely how that Schematic total compares with both Museum Versions.

Below (left-to-right) are the Heraklion and Ashmolean Museum Versions of the fresco’s left vertical outside rows, and the corresponding segment of Herberger’s Schematic (each including the noted small extensions of the horizontals).



Next, below, is a comparison laid out in the same way for the fresco’s right verticals (outside rows) with the matching segment from Herberger’s Schematic.



A final comparison, below, can speak in numbers for the kinds of differences produced by Herberger’s measurement processes; which were guided most of all by the Ashmolean Version’s fidelity to only the original fragments. Below are the Heraklion Version’s restored lower-most horizontal rows, where most of the original tracks were missing, and the Herberger Schematic of the same.



Above, Herberger’s Schematic shows two rows with 130 tracks and two with 120: the Heraklion Version’s rows total 131, 128, 120 and 119 tracks. So, between Heraklion’s work and Herberger’s, based on the Ashmolean Version’s slightly denser tracks—one row of tracks is the same, two of them differ by 1 track, and one row differs by 2.

Below, examine Herberger’s top-to-bottom measurements of every original fragment attested by the Ashmolean Version. We do have at least one fragment from all 16 original rows. With even the smallest, he measured its length in inches, determined the average number of tracks per inch; and used that data to replicate missing stretches of the fresco’s tracks. (From Thread of Ariadne.)



            In the last two columns at right, we see what this process meant. Given the Ashmolean Version’s average numbers of original tracks, the total numbers of tracks per row restored by Herberger are exactly like them to within 1-2 tracks in any part. You see that of the 16 rows, 8 of their resulting averages are rounded down to the nearest whole number. No fraction is rounded upward by more than .5, or ½ of one possible track; so that “extra“ tracks do not creep into totals. We will not forget that 1-2 track variance.



            Hence, Herberger’s complete Schematic of the border of the Bull-Leap fresco. It was not an overwhelmingly difficult process, nor so fraught with problems that a best-possible estimate could not be reliably reached. To find our way ahead, we’ll need both this Schematic and the colors of the two Museum Versions as our guides.

            We found 62 colored crescents in the fresco—close, but not exactly the 60 phases in a year of 5-phase moons. As for the tracks, with the Schematic’s total of 1,561 tracks—arrived at by measurement, not counting—each circuit includes 390 tracks or possible solar days—plus 1 track in one of the circuits. That leaves us 25 (+1) days from the objective solar-year total, 365¼ days.

Hopefully, our results are close enough to go forward and see what becomes of these patterns and problems. We have to discover (demonstrate) how to count a guided way through this labyrinth of signs, and the risk is a dead end. The next chapter tries the way with what we know so far.





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