Report and analysis of Phaistos disc circa 1600 BCE.

Presented by Bruce C. Friedman

Prepared November 27, 2003.

Last modified: November 28, 2003.

 

Introduction: I have chosen to review the undeciphered content of the Minoan/Cretan Phaistos disc.  It is a clay tablet about 16cm in diameter. This tablet is written [imprinted] in Linear A hieroglyphs of obscure and unknown origin and meaning. It was excavated in 1908 at the Minoan palace [of Phaistos] at Hagia Triada in Crete. This disc is reasonably dated to 1600 BCE or prior. It is now in the holdings of the Archaeological Museum of Herakleion; [Inv. no.]: EP 1358

 

I endeavor to identify any likely mathematical content in the inscription and familiarize myself with the layout and analyze the patterns that can be found within all symbol strings [words].

 

Largely by instinct, I have identified one word that seems more likely to refer to a numerical quantity than the others. I believe many of the other words may refer to personal names or titles. As I do not know how to verify this, all we can do is look closely at emerging patterns.

 

Refer to my images of the obverse and reverse of this tablet:

OBVERSE: http://www.mathorigins.com/image grid/PHAISTOS_001.htm

REVERSE: http://www.mathorigins.com/image grid/PHAISTOS_002.htm

 

Obverse: [Clockwise from the outer edge from the start to the center:]

Symbols are arbitrarily assigned numbers as shown on this link:

http://www.mathorigins.com/image grid/PHAISTOS_003.htm

 

Underlined symbols represent word breaks.

 

Red symbols refer to the tail [a vowel or accent or pluralization?] on some words’ last symbol.

Words will be referred to by their assigned origin,

ex. O102 refers to the word A1-E6-B7-A2 on the obverse beginning at position 102.

These word assignments include a word length, ex. *4 for a length of 4 symbols.

If I find that I am able to identify mirrored symbols, signifying a die that was pressed upside down, these too will be colored.

To date, I have not securely identified that this does occur on the tablet.

 

O1*5

A1

26

A8

O51*6

A1

O76*6

A1

101

E6

 

E6

O27*5

A1

 

D3

 

D3

O102*4

A1

 

B7

 

E6

 

C4

 

C4

 

E6

 

A2

 

A4

 

E3

 

E3

 

B7

 

E7v

 

E7

 

F7

 

F7

 

A2

O6*3

C1

 

?F_

 

E7

 

E7

O106*3

C8

 

F4

O32*3

D7

O57*2

D2

O82*2

D2

 

E8

 

E6

 

D1

 

A2v

 

A2?v

 

E1

O9*3

D6

 

E1

O59*4

A1

O84*4

A1

O109*3

E3

 

C6

O35*5

A1

 

E6

 

E6

 

A7

 

A5v

 

E6

 

D7

 

D7

 

E4

O12*3

D6

 

F5

 

D1v

 

D1v

O112*7

A1

 

D6

 

E8

O63*7

A1

O88*7

A1

 

E6

 

C2

 

E1

 

E6

 

E6

 

D3

O15*5

A1

O40*4

A2

 

D3

 

D3

 

D3

 

E6

 

F5

 

D3

 

B2

 

E1

 

A3

 

F4

 

E1

 

D8

 

C8

 

F4

 

A5

 

C8

 

E7

 

B8

 

C3

O44*5

A1

 

B8

 

D3

O119*2

B7

O20*4

D3

 

E6

O70*2

C3

O95*4

A4

 

A2

 

C6

 

D8

 

F7

 

E7

O121*3

E3

 

A5

 

F7

O72*4

A1

 

B6

 

D7

 

E6

 

E4

 

E6

 

E8

 

E4

O24*3

D3

O49*2

C7

 

D7

O99*3

D7

 

 

 

F3

 

B4

 

D1v

 

D1

 

 

 

 

 

 

 

 

This chart OF THE OBVERSE above gives identification to 123 symbols which make up word strings of the following lengths [by columns above]:

5 – 3 – 3 – 3 – 5 – 4 – 3 –

5 – 3 – 5 – 4 – 5 – 2 –      

6 – 2 – 4 – 7 – 2 – 4 –      

6 – 2 – 4 – 7 – 4 – 3 –      

4 – 3 – 3 – 7 – 2 – 3.        

123 symbols form 31 words on the obverse for an average word length of about 4 symbols.

 

Reverse: [Clockwise from the outer edge from the start to the center:]

 

R1*5

A1

26

A2

51

C1

76

B7

101

E2

 

E6

 

C7

 

C1

R77*3

D6

 

A5

 

F6

 

C3

 

F8

 

C6

 

A8v

 

F4

R29*5

B3

 

E1

 

A5v

R104*5

B1

 

A5

 

A5

R55*3

B5

R80*5

F6

 

?F4

R6*4

D3

 

B7

 

B2

 

D6

 

C7

 

C6

 

A2

 

E7

 

E2

 

E7

 

A5

 

E7

R58*3

D6

 

A5

 

A5

 

E1

R34*4

F6

 

C3

 

A8v

R109*5

A1

R10*4

A1

 

C8

 

A2

R85*4

D3

 

A4

 

C8

 

F2

R61*5

A4

 

C2

 

E1

 

F7

 

C4

 

E1

 

E7

 

F7

 

A6v

R38*4

A5

 

D8

 

C4

 

A5

R14*3

F6

 

C1

 

C7

R89*3

A5

R114*4

D6

 

C4

 

F4

 

C3

 

E7

 

C2

 

D3

 

E1

R6*4

A1

 

E1

 

F7

R17*4

C3

R42*4

A1

 

B1

R92*3

A5

 

C4

 

C1

 

D1

 

D3

 

C6

R118*2

C6

 

F8

 

E2

 

A2

 

A5v

 

A5v

 

E6

 

F4

R70*4

D6

R95*4

A5

 

 

R21*4

B5

R46*4

D3

 

E2

 

F7

 

 

 

F7

 

C4

 

A5

 

E7

 

 

 

E7

 

E4

 

A8v

 

C1

 

 

 

F1v

 

A2

R74*3

D6

R99*5

F6

 

 

R25*4

B7

R50*5

D6

 

A8

 

D6

 

 

 

 

This chart OF THE REVERSE above gives identification to 119 symbols which make up word strings of the following lengths [by columns above]:

5 – 4 – 4 – 3 – 4 – 4 – 4 –

5 – 4 – 4 – 4 – 4 – 5 –      

3 – 3 – 5 – 4 – 4 – 3 –      

3 – 5 – 4 – 3 – 3 – 4 – 5 –      

5 – 5 – 4 – 2.                     

119 symbols form 30 words on the reverse for an average word length of about 4 symbols.

 

The combined total of 123+119 symbols [242] make 61 words varying in length from two to seven symbols.

 

Master word lists by lengths:

 

[Words with] Two symbols in order of occurrence:

Obverse

Reverse

With v?

Without v?

Times occuring as shown total

Symbols

O49

 

 

1

1

C7-B4

O57+O82

 

2

 

2

D2-A2v

O70

 

 

1

1

C3-F7

O119

 

 

1

1

B7-A2

 

R118

1

 

1

C6-A5v

TOTAL OF UNIQUE TWO SYMBOL WORDS without vowels

3

 

TOTAL OF UNIQUE TWO SYMBOL WORDS with vowels

2

 

GRAND TOTAL OF UNIQUE TWO SYMBOL WORDS

5

 

 

Three symbols in order of occurrence:

Obverse

Reverse

With v?

Without v?

Times occuring as shown total

Symbols

O6

 

 

1

1

C1-F4-E6

O9

R77

2

 

2

D6-C6-A5v

O12

 

 

1

1

D6-D6-C2

O24

 

 

1

1

D3-F3-A8

O32

 

 

1

1

D7-D1-E1

O99

 

 

1

1

D7-D1-E6

O106

 

 

1

1

C8-E8-E1

O109

 

 

1

1

E3-A7-E4

O121

 

 

1

1

E3-D7-E4
 

R14

 

1

1

F6-C4-D3

 

R55 

 

1

1

B5-B2-E7
 

R58 

 

1

1

D6-C3-A2
 

R74 

 

1

1

D6-A8-B7
 

R89 

 

1

1

A5-E7-E1
 

R92 

1

 

1

A5-C6-A5v

TOTAL OF UNIQUE THREE SYMBOL WORDS without vowels

13

 

TOTAL OF UNIQUE THREE SYMBOL WORDS with vowels

2

 

GRAND TOTAL OF UNIQUE THREE SYMBOL WORDS

15

 

 

Four symbols in order of occurrence:

Obverse

Reverse

With v?

Without v?

Times occuring as shown total

Symbols

O20

See similar R6

 

1

1

D3-C6-A5-E6

O40

 

 

1

1

A2-F5-F4-A5

O59+O72+O84

 

3

 

3

A1-E6-D7-D1v

O95

 

 

1

1

A4-E7-B6-E8

O102

 

 

1

1

A1-E6-B7-A2

R6

 

1

1

D3-C6-A5-E1

 

R10

1

 

1

A1-C8-F7-A6v

 

R17 

 

1

1

C3-C1-F8-E6
 

R21 [ #?] 

1

 

1

B5-F7-E7-F1v

 

R25 

 

1

1

B7-A2-C7-C3
 

R34 

 

1

1

F6-C8-F2-C4

 

R38 

 

1

1

A5-C1-F4-E1

 

R42 

 

1

1

A1-D1-E2-F4

 

R46 

 

1

1

D3-C4-E4-A2

 

R66 

 

1

1

A1-B1-D3-A2

 

R70 

1

 

1

D6-E2-A5-A8v

 

R85 

 

1

1

D3-C2-E7-C4

 

R95 

 

1

1

A5-F7-E7-C1

 

R114 

 

1

1

D6-C2-F7-C4

TOTAL OF UNIQUE FOUR SYMBOL WORDS without vowels

15

 

TOTAL OF UNIQUE FOUR SYMBOL WORDS with vowels

4

 

GRAND TOTAL OF UNIQUE FOUR SYMBOL WORDS

19

 

 

Five symbols in order of occurrence:

Obverse

Reverse

With v?

Without v?

Times occuring as shown total

Symbols

O1

 

1

 

1

A1-E6-B7-A2-E7v

O15

 

 

1

1

A1-E6-A3-F4-C3

O27

 

 

1

1

A1-E6-A4-E7-?F_

O35

 

 

1

1

A1-E6-F5-E8-E1

O44

 

 

1

1

A1-E6-D8-F7-E4

 

R1

 

1

1

A1-E6-F6-F4-A5

 

R29 

 

1

1

B3-A5-B7-A2-E7

 

R50 

 

1

1

D6-C1-C1-F8-E1

 

R61 

 

1

1

A4-E1-D8-C7-C3

 

R80+R99 

2

 

2

F6-D6-E2-A5-A8v

 

R104 

 

1

1

B1-?F4-C7-E7-A5

 

R109 

 

1

1

A1-A4-E1-F7-A5

TOTAL OF UNIQUE FIVE SYMBOL WORDS without vowels

10

 

TOTAL OF UNIQUE FIVE SYMBOL WORDS with vowels

2

 

GRAND TOTAL OF UNIQUE FIVE SYMBOL WORDS

12

 

 

Six symbols in order of occurrence:

Obverse

Reverse

With v?

Without v?

Times occuring as shown total

Symbols

O51+O76

 

 

2

2

A1-D3-C4-E3-F7-E7

TOTAL OF UNIQUE SIX SYMBOL WORDS without vowels

1

 

TOTAL OF UNIQUE SIX SYMBOL WORDS with vowels

0

 

GRAND TOTAL OF UNIQUE SIX SYMBOL WORDS

1

 

 

Seven symbols in order of occurrence:

Obverse

Reverse

With v?

Without v?

Times occuring as shown total

Symbols

O63+O112

 

 

2

2

A1-E6-D3-D3-E1-C8-B8

O88

 

 

1

1

A1-E6-D3-B2-D8-E7-D3

TOTAL OF UNIQUE SEVEN SYMBOL WORDS without vowels

2

 

TOTAL OF UNIQUE SEVEN SYMBOL WORDS with vowels

0

 

GRAND TOTAL OF UNIQUE SEVEN SYMBOL WORDS

2

 

 

One consideration is that all [four of the unique] 2 – 3 – 4 and 5 symbol words that appear more than once, have a vowel at the end.

See:

2 symbols: O57 and O82

3 symbols: O9 and R77

4 symbols: O59 and O72 and O84

5 symbols: R80 and R99

Another consideration is that one and only one unique word of each length appears twice or more.

See:

2 symbols: O57 and O82

3 symbols: O9 and R77

4 symbols: O59 and O72 and O84

5 symbols: R80 and R99

6 symbols: O51 and O76

7 symbols: O63 and O112

 

Unique words per side – by length

Symbol length

2

3

4

5

6

7

Tally

OBVERSE

4

9

5

5

1

2

26 [of 31]

REVERSE

1

7*see below

14**

7

0

0

28 [of 30]

 

5

15

19

12

1

2

54 [of 61]

 

*This includes the one word found on both sides of the tablet, [see O9 and R77] see that the reverse total above is only indicative of 28 unique words.

**Although four symbol words are 280% more common on the reverse, this may be accidental and may not suggest the reverse is anything other than a continuation of the obverse. I am also unsure if the sides have been properly named as obverse and reverse!

Of the 12 unique 5 symbol words, 6 of them begin with A1-E6!

Of the 2 unique 7 symbol words, both of them begin with A1-E6!

The one unique 4 symbol word that begins with A1-E6 and has an end vowel, appears 3 times!

The other unique 4 symbol word that begins with A1-E6 has no vowel and appears once.

 

Of the total of 61 words [including duplicates], 13 begin with A1-E6.

Of the 54 unique words, 10 begin with A1-E6.

Of the 10 unique words that begin with A1-E6, only one is on the reverse. See R1*5.

I find this indicative of the similar likelihood of finding the word “Mister” in a list of names.

Perhaps this list refers to personnel, but surely it is some kind of LIST!

As the special tecnique of this stamped, fired clay tablet requires much more labor than writing, perhaps this is a dedicatory / prayer item and again perhaps the content is a list of prayer words / incantations.

 

Vowel accented end symbols by word length

2

3

4

5

6

7

A2v-once

A5v-thrice!

A8v-once

A8v-twice

-

-

A5v-once

 

D1v-once

E7v-once

 

 

 

 

F1v-once

 

 

 

 

 

A6v-once

 

 

 

2

3

4

3

 

 

 

Tally of ocurrences of vowel accented end symbols in unique words ignoring word length

A2v

A5v

A6v

A8v

D1v

E7v

F1v

1

3

1

2

1

1

1

10 unique words end in vowels. Of these, only two begin with A1-E6; see D1v and E7v.

 

Only one voweled word appears on both sides of the tablet: D6-C6-A5v.

 

The longest consecutive symbol string that is repeated is found at O51*6 and O76*6:

See: 3 and a half words [15 symbols]:

A1-D3-C4-E3-F7-E7-D2-A2v-A1-E6-D7-D1v-A1-E6-D3.

22 of the 45 unique symbols can be found following A1-E6 [anywhere] in the words that begin with A1-E6.

Only 7 of these occur more than once: A2; B7; D3; D8; E1; E7; F4.

 

The only 3 symbols that appear twice consecutively within a word:

D6: see D6-D6-E2 [See O12*3]

C1: see D6-C1-C1-F8-E1 [See R50*5]

D3: see A1-E6-D3-D3-E1-C8-B8 [See O63*7 and O112*7]

 

Closing statement: The content and layout are imprinted with some care in a fashion resembling the technology of movable type printing. Some references to inverted or mirrored symbols have been seen by me but I have not yet identified the symbols in question that may have been produced this way or come to understand what type of die-tool could have been used in this fashion.  Still digging and still hoping to “prove” that R21 symbol string is a quantity!

 

*NOTES ON FILE WITH [B_515]

 

 

 

 

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