V987 7 November 1998


The Calendar on the Phaestos Disk (The Philosopher's Disk)


by
Ole Hagen
Independent Scholar


Introductory remarks

It is fascinating, when the opportunity occurs to make oneself familiar with a message, passed on by a fellow human being, who was in existence some 3500 years ago in a now extinct civilization. This prospect was realized once again by the find of the Phaistos-disc on Crete in 1908. The famous object is described brilliantly several times (1).

Consequently I shall come straight to the point: How can we penetrate into the secret, that is hidden behind the seal imprints on the disc? Do we have any other methods to approach the contents, than to ascribe phonetic or numerical values to the signs? Making experiments by inserting syllables for the signs, have resulted in scores of equilibristic translations; that is why the prevailing opinion is that linguistic interpretations are to be regarded with doubts, as only more and similar findings will certify a correct linguistic solution, if any (2). Conversely, how would a complex ideographic system be capable of confirming itself? The setter of the signs has taken the trouble to divide the 244 signs into groups by 60 cross-dividers. My question is by now: Are any further subdivision of the 61 sign groups to be performed? To attempt this question, I avail myself to a quite simple method, as I introduce a stem concept for the inscription, as two signs in regular order recurring together in minimum one more sign group, and then I proceed to enumerate the functions, that follows in the wake of this definition. This shows to be a promising method of investigation, that so to speak provides a fixed framework for the inscription; conceivably even a calendar. Only the succession of the sign groups remains frustrated, when the stems are defined (3).

The 22 defined stems are at the same time introductory and conclusive, as they are not consolidated before the accordance that they bring about, finally turn up as an answer to enumerations. When the signs outside the stems are redoubled (in a way like the stems themselves), it is almost impossible not to see the calendar perspectives.

Briefly and to the point, I have designed 12 figures, these illustrations, together with the legends to match, are the principal part of my investigation. Having introduced the stems, the 12 figures profitably can be studied in themselves. After all I have tried my hand at a subordinated text.

No matter what difficulties have preceded, the solution of a genuine riddle must be capable of being entrusted by the instrumentality of very few and extricating theses, so too the key to this old Cretan inscription (4) ...


Some designations related to signs and sign groups

Stem definition: A stem is a sequence of two signs, repeated in minimum one more sign group. The stem is not allowed to overlap any other stem, which can be confirmed with further significance (6).

Elements
1) The inscription is in my opinion constructed of elements, of which the stem is the essential element, it consist of two visible signs, and has the value of two units.
Shortened elements,- reduced elements-. This elements only hold the one sign of the stem, the other sign is omitted (by the constructor of the disc), but the shortened element still keep the value of two units, on par with the stem, in enumerations.
The shortened elements are subgrouped into two sorts: Shortened stems, as opposed to elements that possess signs not known from the infrastructure of the stems, I call those last units 'remainder signs'. The two dividers (g) ahead of A01 and B01, [Figure 1] initializing both side of the disc, are dotted lines, those two different cross-dividers, and this is new, have the potential as remainder signs too, and are therefore to be regarded as two shortened elements.
3) Thorn. The third element (7), 'the thorn' is a final mark only with the value of one unit, that is to say: Not a shortened, but rather a diminished element.
Signs,-days-.
Units are applied as a joint designation for signs, absent signs and thorns, all counts as singles.
Stem signs: The signs that enter into the compositions of the stems. The designation is general for units in shortened stems too. It gives thirty different stem signs, and so they are recorded alphabetically with the capital letters (8).
Remainder signs: The remaining signs, that obviously do not enter into the constructions of the definable stems, are called remainder signs, they are only present as shortened elements ( the presumed stem forms from which they derive are not present at the disc). These signs are recorded with small letters from a-p.
Absent unit: The absent sign of a short form element.
Sign groups, -weeks-.
The signs around the spiral are separated into 61 groups [Figure 2] by cross line-dividers (9). The groups contain from 2 to 7 signs, and the average amount is exactly 4 signs per sign group.
Stem sign groups: A designation used for the 50 sign groups, [Figure 3] which contain one or more stems, simultaneous presence of shortened elements or thorns do not change the designation.
Reduced sign groups: Sign groups in lack of stems; they fully consist of shortened elements, and (as an exception) a single thorn in B03 (10).
Expansion forms, -seasons-.
As the elements are given values (with influence to enumerations), the sign groups can now be conceived in different ways. Basically these two:
) The actual inscription is counting 244 units, which in a way is expanded with 70 units because of its 70 stems.
) Conversely you can say, that the actual inscription is reduced by 121 units in comparison with the full expanded inscription on 365 units. The fully expanded inscription have an average amount of 6 signs per sign group (less a thorn).
The insertion of plus or minus to the expansion forms determine, whether the thorns are to be included as units in enumerations or not.


Stem determinations

Let me by means of an example introduce the reader into, how a deduction of a stem is carried out in practice. I choose a sign group at random "B13" [Figure 4], and then I intend to investigate its contents of stems, if any. A stem is a construction of two and only two signs. By this means, there are given three compositions for a sign group with five signs as B13: 1) S RR F. 2) S R RF. 3) SR RF.

Taking the potential stems in the first composition, beginning with RR, this combination of signs are to be searched for in all 61 sign groups. - It is not found. The search are proceeded with S. - The result is still negative. Only the combination SR in the third composition has a repetition; namely in the sign group B05. B05 consist of four signs, and by that it has two compositions: B SR K and BS RK. The stem SR is yet not guaranteed before both compositions of B05 have been tested. The first one SR was tried with a positive result. The potential stems in the second composition cannot be recovered. The stem SR is by now determined. On the other hand, if the possible second compositions BS or RK were recovered, but only at one location, just as SR, then the contents of stems in B13 and B05 would have been evasive, cf. B22, B29 and A04. There is thus demanded a majority in favor of the deduced stem, before certainty is attained. In A17, A29 and A23 the combination WB emerges, but it is overlapping the stem BA, which is present thirteen times in all, by means of which WB is not to be a stem.

The two identical sign groups A17 and A29 must besides BA, of necessity hold two more pair of stems, but a search determines, that none of the compositions available are found in other sign groups, with which the stems cannot be deduced with certainty. At this point the outcome must be based on an estimate: That the position for a sign in a stem is to be respected, when it is known from a definable stem, due to that the definable stems observe these position rules among themselves, eg.:

	B28, B16              B29, B22  XY
	A17, A29  W            A14, A20  ZY
	A14, A20  XW            A08, A24  Z

In which represents the defined stem in the sign groups B28, B16, and XW in A14, A20, while W is a (evasive) stem in A17, A29. The positions for the two signs of the stems appear moreover to form the basis of a valid subdivision of the stems into three groups (11).

Eventually I have to comment on the inaccessible stem in A23 and B14. This stem form positively compromises my definition, for the fact that the two signs in the stem of A23 are not sequential connected. As it is, I simply have to take the standpoint, that the sign c in A23 is a parenthetic addition, as the enumeration results, enabled by this conception, for me are beyond any doubt. -The exemption proves the rule-. The twenty-two stem forms turn out to be an efficient tool during a structural analysis of the inscription.

Other writers as well have directed their efforts to identify stems (12); however, as far as I see, without fully realizing the momentous request for the absolute amount, which proved to be 70 stems. This, and the conclusion that a stem consists of two and only two signs, has the novelty.

What succeeds the definition of the stems is on my part an attempt to bring about some quantitative possibilities, which are positively self-contradictory or immaterial amongst; but one have to remember, that the premises of this riddle are lost, there are no preceding statements accessible such as: Cut the Gordian knot or find the quadrate of the (calendar) circle, as normally known from riddles, the initiatives must at this stage be hypothetical, until the numbers finally will be able to confirm itself.

The consequences of the stems

I have by now isolated the total amount of 70 stems, and have by that process obtained a bisection of the inscription into stems towards the sign material left over. Thereby all 244 signs (261 visible units) are given various functions as stem signs, stem group-signs, remainder signs etc. A new method of investigation has hereby emerged, in which to compare the signs and sign groups effectively.

First, the already mentioned, differentiation can be made between stem signs versus remainder signs. Another immediate distinction, which is now possible, is the one between stem signs from within the stems towards stem signs without (shortened stems). The stems in themselves are easily classified with a convincing result: The three stem groups have 11 stem chains, 22 stem forms and the stems make up 33 stem pairs, as visualized on figure 3; but with the 70 stems there is an excess of 4 unpaired stems, these 4 stems are influential in relation to the stem sign groups too, as they are hold neutral, in the same way as the 11 reduced sign groups (without any stem contents) sometimes are kept apart from the 50 stem sign groups in enumerations.

Likewise the stems, the sign groups make up pairs and unpaired as well. In connection with 22 pairs of stem sign groups, it gives 6 unpaired sign groups, which I name 'pendants', i. e. they make up a third link with 6 of the stem sign group pairs. These pendants are besides B07, B21 and A19; probably A05, A12 and B22, probably because it is not sufficiently clarified, which sign groups are components and which are pendants to the pairs. It is after all not crucial to the enumerations.

The foundation of the stems is in other words confirmed by the favorable numbers, that it causes, as the product (or the complementary product) of almost every enumeration turns out to be a multiple of eleven. Surprisingly many of the fundamental enumerations gives figures, which are fragments of a table over 5 and 6 by turns: (5+6+5+...n) and (6+5+6+...n) = {5, 6, 11, 16, 17, 22, 27, 28, 33, 38, 39, 44, 49, 50, 55, 60, 61...} This was an exposition of some of the obvious functions of the stem definition. The schedule contains more details.

The result of this initial enumerations recounts, that the inscription may prove to be a calculation of some kind with an otherwise and more coherent classification, than to be expected in a text based on phonology; in this connection one has to take into consideration, the immediately disorganized impression that side B in particular leaves, I would have expected a very opposite impression, if the systematics was really caused by a linguistic text. Any agreement on the length of the lines has even not been reached (13).

The great question is subsequently, what is due to the foreshadowed system, is it by any means a manifestation of a concealed prosodic text?, or is the search for quite otherwise interpretations. What is accounting for the widespread presence of the number eleven in the counting, both in the totals as well as in the amounts of species of signs and sign groups? Is the disc some sort of a quadratic table? (14) It is certainly tempting to hesitate for figures with relations to the calendar year in the inscription.

Some data of the disc

The statements are divided about the numbers of characters on the disc. I have come across the totals: 241, 242 and 243, of which 242 (face A:123, face B:119) signs are the most frequent opinion. (15) 242 is written as 11 + 11. As something new I contemplate the two dotted dividers ahead of A01 and B01 as true signs, and the total amounts are in my view 242 + 2 = 244 signs or 10 + 12. As it happens 244 is a multiple of 61, which is of statistical significance, because the disc is divided into exactly 61 (5 + 6) sign groups ( as well as 61 dissimilar elements). Accordingly each sign group holds on the average of 4 signs. After this, the calendar prospect get into the picture, as 6 multiplied with 61 is equal to 366, corresponding to a leap year, and 365 - 244 = 121, thus the inscription is missing 11 signs. 10 + (11) + 12 = 365 or 366 / 3 = 122 signs This missing third part has no substantial presence in the inscription, but stands implicit, (except for the 17 thorns, which are included in this third part).

The visible inscription (), with its 244 signs, corresponds to two thirds of a year or eight months (16) in which side A's 124 signs will make up four months on 31 days each, and side B's 120 are equal to four months on 30 days.

Postscript

Now when the probability has been made, that the sign groups are not inevitably words, but rather ideographic records of weekly functions (17), then new prospects of investigations emerge in relation to rituals drawn from murals and seals from Crete and Egypt, as contrast to the thoroughly tested standard of references to the linear inscriptions; but rites in conjunction with annual occurrences in nature, form a whole study in itself, far outside the scope of this essay. To put an interpretation on pictures from the edge of historic times is very interesting, but also continually reflected by the imperfect documentation, though perhaps there will also show to be an analogy to something of common historical property, what concerns the pictorial contents of the signs. (18) Or it will show, that the pictorial message of the signs is a sealed chapter in an even higher extent, than e.g. the symbols of the never doubted Mayan-calendar.

Let me emphasize, that my superior objective with this investigation was to attain insight in the regularities, from which the sequences of signs were composed. In other words, I was not occupied with interpretations of the signs in themselves, but with an investigation of the interrelations and the frequency of the signs; this proved to be the right angel of incidence.

The accomplishment of my conception of the inscription implied a good number of disciplines (19), yet I am still not an adept on calendar mathematics, and the continued refining of this calendar, I shall leave to the reader, when the publication is effected in a way proportional to the importance of my discovery, that everyone, who has tried his hand at this enigmatic disc, amateurs as well as scholars, in this way shall get admission to my discovery. It is my trust, that someone among the readers will take inspiration from my method of investigation and its results to place the last intricate pieces in this extraordinary calendar.

Mare liberum
- - -

The Author's home page with more information on his theory

Supplementary Notes

This paper is a revised and expanded version of a little preprint, which I issued about ten years back, but as I feel that my method of investigation and its results deserve some more attention, I have against my objectives, used furthermore time to demonstrate some more perspectives of my discovery. This paper is pieced together from several unpublished essays on the topic.

1. Among others, objectively by Jean-Pierre Olivier, "Le disque de Phaistos", dition photographique (BCH 99 1975), 6-34. A complete treatment of the subject is found in: Christian Jeppesen, Some remarks on the Archaeological Placing of the Phaistos Disc. (KUML 1962), 180-190.

2. You cannot change the eternal circles of the celestial bodies, but the grammar of an extinct language you can easily make up.

3. My analysis is at the same time independent of typology, period of time, origin and direction of reading, whereas linguistic analyses demand an unreserved attitude to these conditions.

4. 'In any cryptanalytic problem a single sure entry solves the problem'. A quotation from Benjamin Schwartz, "The Phaistos Disc I". (JNES XVIII 1959), 108.

5. Davis, Simon, The dechiperment of the Minoan Linear A and Pictographic Scripts (Johannesburg 1967), fig.97. This actual quadripartited seal can be seen as an ibex, partial hidden behind a bush (only its horn visible), and a startled bird. The seal (impression?) has an analogy with the signgroup A09.

6. Extension of the definition: Three converse stemforms apparently occur, but only "WX" in B04 is relevant, as further appearances, besides the one in B12 (supposed pair to B04) , show in both A14 and A20. The others, not valid, converse forms are "OY" in B28, B25, which is overlapping the confirmed stemform "ZY", and "OZ" in B23, B27 is without further recurrencies.

7. The thorns are not embossed, contrary to the other signs, but scratched into the disc, before the clay did harden. The common opinon is that of seventeen thorns engraved.

8. During an examination of a subject as the Phaistos disc, it is inconvenient to refer continuously to the imagery of the characters, consequently they are numbered from 1 - 45, Sir Arthur Evans, Scripta Minoa vol. 1 (Oxford 1909), but as I am engaged with countings, it is distracting to use arbitrary numerals as notation. Among the 46 dissimilar signs, I especially work with the 30, that make up the stems, and stretching the alphabet to 29 capital letters with the Danish capitals , , (together with an ampersand) gives me a more comfortable notation. The 16 dissimilar remaining signs are recorded with the small letters from a - p with the pearl string dividers as g. I have had in view, that the two combining signs in the stems are recorded with adjoining letters.

9. As it will have appeared the stems are not indicated as enclosed structures in the inscription, contrary to the signgroups.

10. It is significiant that the tendency is towards a location of the reduced signgroups on odd signgroupnumbers (10 of 11). (An indicium for the stem "Z&", because B14 is an equal number).

11. The stemforms can be linked together, on the basis of mutual signs on mutal positions, into eleven stemchains. The chains invite to a further more classification into the three stemgroups.

12. Gnther Ibsen, "Der Diskus von Phaistos, ein Versuch zur Entzifferung". (IF 47 1929) 1-41.

13. I have been encouraged to repeat my analysis on the basis of another text written in foreknown syllabic characters. A collation of the statistic returns should then give evidence of agreements. - In accordance with facts, ancient inscriptions are most often imperfectly preserved; so if the disc had had a truncated corner, if for instance the signgroups A01 and consequently B01 were missing, then it ought not to call for any intimate knowledge of my enumerations to comprehend, that the detected system was off its balance, though still present for the intiated reader. Personally I find, that such crossanalysis is superfluous.

14. In a multiplication tabel the square numbers form pairs across the diagonal e.g.: 1*16, 2*8, 4*4, 8*2, 16*1. C.f. stems.

15. These differing opinions are all about, whether the only illegible character on the disc, the outlying sign in A08, is obliterated by design, or failing that, if two signs were in its place. I accept any sign , but I prefer a stemsign of stemgroup II, and the sign "P" is the best match in my opinion.

16. It is worth notice, that the glossary of linear B contains eight words only, which are considered to be names of months. John Chadwick, Documents in Mycenaean Greek (Cambridge 1956).

17. The established opinion insisting on the inscription to be linguistic, has its reason, I believe, in the lack of systematic in the numbers of characters showing in the signgroups (from 2 to 7), but it was not a durable argument.

18. An unmistakeable frame of reference with the so-called Chaldean tradition, as known from Babylonian zodiacs and the Egyptian Dendera ceiling , seems unlikely to me, see Leon Pomerance, The Phaistos Disc. An interpretation of Astronomical Symbols (Gtborg 1976).

19. The accomplishment of my decoding of the inscription implied a good number of disciplines, primilary the discipline of excluding disciplines not essential for the final conclusion, such as the Hittite grammar learnt by rote.




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