comparing Çatalhöyük with the palace of knossos by matrix ... · comparing Çatalhöyük with...

15
2 CAES Vol. 4, 4 (November 2018) Comparing Çatalhöyük with the palace of Knossos by matrix-vector method Alexander Akulov independent scholar; Saint Petersburg, Russia; e-mail: [email protected] Abstract Çatalhöyük and the palace of Knossos look much alike: they both seem to be samples of the same architectural tradition. Matrix-vector method represents the plan of any building as a 3D vector and allows estimating degree of resemblance of any buildings: the higher is the degree of resemblance the more alike are plans of corresponding buildings. The degree of resemblance of Çatalhöyük and the palace of Knossos of the Protopalatial stage is 0.88; that of the palace of Knossos and the house of Myrtos is 0.57; that of the palace of Knossos and Villa Alpha is 0.73; that of the palace of Knossos and the palace of Pylos is 0.81. Thus, the palace of Knossos is closer to Çatalhöyük than to the palace of Pylos and to samples of earlier Minoan architecture. Keywords: Knossos; Anatolian Minoan connection; Çatalhöyük; Minoan architecture; topology 1. Introduction Recently an international group of geneticists has shown that genes of Minoans have Anatolian origin (Lazaridis et al. 2017). Researches on samples of Keftiw/Minoan languages found in London medical papyrus show that Keftiw/Minoan language seems to be a rather close relative of Hattic (Akulov 2017b). And thus, it is logical to suppose that Minoan material culture had certain Anatolian prefigurations. For instance, Minoan horned objects have their prefigurations in horned objects found in Anatolia and Near East (Diamant, Rutter 1969). And also it is rather logical to suppose that Minoan architectural forms also had prefigurations in Anatolia. At a superficial glance reconstruction of Çatalhöyük (pic. 1) looks rather alike that of the palace of Knossos (pic. 2). Pic. 1. A reconstruction of Çatalhöyük (image source: Çatalhöyük Nerede Hakkında Bilgi)

Upload: others

Post on 31-Jul-2020

4 views

Category:

Documents


0 download

TRANSCRIPT

Page 1: Comparing Çatalhöyük with the palace of Knossos by matrix ... · Comparing Çatalhöyük with the palace of Knossos by matrix-vector method Alexander Akulov independent scholar;

2 CAES Vol. 4, № 4 (November 2018)

Comparing Çatalhöyük with the palace of Knossos by matrix-vector method

Alexander Akulov

independent scholar; Saint Petersburg, Russia; e-mail: [email protected]

Abstract

Çatalhöyük and the palace of Knossos look much alike: they both seem to be samples of the

same architectural tradition. Matrix-vector method represents the plan of any building as a 3D

vector and allows estimating degree of resemblance of any buildings: the higher is the degree of

resemblance the more alike are plans of corresponding buildings. The degree of resemblance of

Çatalhöyük and the palace of Knossos of the Protopalatial stage is 0.88; that of the palace of

Knossos and the house of Myrtos is 0.57; that of the palace of Knossos and Villa Alpha is 0.73;

that of the palace of Knossos and the palace of Pylos is 0.81. Thus, the palace of Knossos is

closer to Çatalhöyük than to the palace of Pylos and to samples of earlier Minoan architecture.

Keywords: Knossos; Anatolian – Minoan connection; Çatalhöyük; Minoan architecture;

topology

1. Introduction

Recently an international group of geneticists has shown that genes of Minoans have Anatolian

origin (Lazaridis et al. 2017). Researches on samples of Keftiw/Minoan languages found in

London medical papyrus show that Keftiw/Minoan language seems to be a rather close relative

of Hattic (Akulov 2017b).

And thus, it is logical to suppose that Minoan material culture had certain Anatolian

prefigurations. For instance, Minoan horned objects have their prefigurations in horned objects

found in Anatolia and Near East (Diamant, Rutter 1969). And also it is rather logical to suppose

that Minoan architectural forms also had prefigurations in Anatolia.

At a superficial glance reconstruction of Çatalhöyük (pic. 1) looks rather alike that of the palace

of Knossos (pic. 2).

Pic. 1. A reconstruction of Çatalhöyük (image source: Çatalhöyük Nerede Hakkında Bilgi)

Page 2: Comparing Çatalhöyük with the palace of Knossos by matrix ... · Comparing Çatalhöyük with the palace of Knossos by matrix-vector method Alexander Akulov independent scholar;

3 CAES Vol. 4, № 4 (November 2018)

Despite between the existence of latest layers of Çatalhöyük and the existence of early layers of

Knossos palace there is a period of about 3800 years, it seems that their resemblance isn’t

accidental, but they both are samples of the same architectural tradition. In order to estimate the

degree of resemblance of Çatalhöyük and the palace of Knossos in current paper the plan of

Çatalhöyük level VI B (5986±94 – 5908±93 BCE, see: Mellaart 1976: 52) is compared with the

plan of Knossos palace of Protopalatial period (1900 – 1750 BCE, see: McEnroe 2010: 7) by

matrix-vector method.

Pic. 2. A reconstruction of the palace of Knossos (image source: Το παλάτι της Κνωσού…)

Pic. 3. Location of Çatalhöyük, Knossos, and Pylos

Page 3: Comparing Çatalhöyük with the palace of Knossos by matrix ... · Comparing Çatalhöyük with the palace of Knossos by matrix-vector method Alexander Akulov independent scholar;

4 CAES Vol. 4, № 4 (November 2018)

2. Matrix-vector method

2.1. General ideas

Plan of any building can be represented as a compound of elementary pieces (rooms); a room

can be defined as a space bordered by walls from other spaces and having no walls inside.

And then the plan of any building can be represented as two matrixes: the matrix of adjacency

and the matrix of direct passability.

Adjacency means that two rooms have at least one common wall. Adjacency is irreflexive

relation, i.e.: a room isn’t adjacent to itself.

Direct passability means the existence of direct passages between certain rooms. Direct

passability is reflexive, i.e.: a room is in the relation of passability with itself.

2.2. Consideration of some sample plans for the purpose of illustration

For the purpose of illustration let’s consider some simple plans; first, let’s consider building X

(pic. 4) consisting of four elements/rooms.

Pic. 4. Plan of building X

The adjacency matrix of X:

1 2 3 4

1 0 1 1 0

2 0 1 1

3 0 1

4 0

If rooms are adjacent then 1 is placed in the corresponding cell, if rooms aren’t adjacent then 0

is placed in the corresponding cell. Repetitive cells intentionally left blank.

The direct passability matrix of X:

1 2 3 4

1 1 1 0 0

2 1 1 1

3 1 0

4 1

Page 4: Comparing Çatalhöyük with the palace of Knossos by matrix ... · Comparing Çatalhöyük with the palace of Knossos by matrix-vector method Alexander Akulov independent scholar;

5 CAES Vol. 4, № 4 (November 2018)

If there is direct passability between certain two rooms then the value of the corresponding cell

is 1, if there is no direct passability the value of the corresponding cell is 0. For instance, despite

it is possible to pass from 1 room to 4 through 2, but since 1 and 4 aren’t connected by a direct

passage so direct passability in the current case is 0.

It is important to note that in current context only general possibility to pass from one room to

another is taken into account, i.e.: it doesn’t matter whether there are 1 or 2 passages/doors

between certain two rooms, if there is at least 1 direct passage the value of passability for the

corresponding pair of rooms is 1.

Thus, it is possible to speak about adjacency index (AI) and direct passability index (DPI).

AI is the ratio of the number of really existing pairs (cells with 1) to the total number of

potential pairs of rooms connected by adjacency relation. In the case of X there are 9 cells with

1 and the total number of potential pairs of rooms connected by the relation of adjacency is

calculated according to the formula of the number of combinations:

Direct passability index (DPI) is the ratio of the number of really existing pairs (cells with 1) to

the total number of potential pairs. The formula of the total number of potential pairs of rooms

connected by direct passability is the following:

In the case of X total number of potential pairs connected by the relation of adjacency is 6 while

the real number of pairs connected by the relation of adjacency is 5. And the total number of

potential pairs connected by the relation of passability is 10 while the number of really existing

pairs is 7. Thus AIX = 5/6 ≈ 0.83; DPIX = 7/10 = 0.7.

And thus X can be represented as the following 3D vector (4; 0.83; 0.7) where the first

component is the number of rooms, the second component is AI and the last one is DPI.

Now let’s consider building Y (pic. 4) which structure is more primitive than that of X.

Pic. 5. Plan of building Y

Adjacency matrix of Y:

)!(!

!

knk

nC

k

n

nknk

n

)!(!

!

Page 5: Comparing Çatalhöyük with the palace of Knossos by matrix ... · Comparing Çatalhöyük with the palace of Knossos by matrix-vector method Alexander Akulov independent scholar;

6 CAES Vol. 4, № 4 (November 2018)

1 2 3

1 0 1 1

2 0 1

3 0

Direct passability matrix of Y:

1 2 3

1 1 1 0

2 1 1

3 1

The total number of potential pairs connected by the relation of adjacency is 3; the number of

really existing pairs is 3. The total number of potential pairs connected by the relation of

passability is 6; the number of really existing pairs is 5.

AIY = 3/3 = 1;

DPIY = 5/6 ≈ 0.83.

The 3D vector of Y is the following: (3; 1; 0.83)

Now let’s consider building Z (pic. 6) that differs from X more than Y.

Pic. 6. Plan of building Z

The adjacency matrix of Z:

1 2

1 0 1

2 0

The direct passability matrix of Z:

1 2

1 1 1

2 1

Page 6: Comparing Çatalhöyük with the palace of Knossos by matrix ... · Comparing Çatalhöyük with the palace of Knossos by matrix-vector method Alexander Akulov independent scholar;

7 CAES Vol. 4, № 4 (November 2018)

The total number of potential pairs connected by the relation of adjacency is 1; the number of

really existing pairs is 1. The total number of potential pairs connected by the relation of

passability is 3; the number of really existing pairs is 3.

AIZ = 1/1 = 1;

DPIZ = 3/3 = 1.

The 3D vector of Z is the following: (2; 1; 1).

2.3. The procedure of estimation of the degree of resemblance

We have the following 3D vectors:

X (4; 0.83; 0.7);

Y (3; 1; 0.83);

Z (2; 1; 1).

The more resembling are plans of buildings the more resembling are corresponding vectors.

To estimate the degree of resemblance of two plans of buildings should be estimated the degree

of resemblance of two corresponding vectors, i.e.: to estimate the degree of correlation of each

component of vectors and take arithmetical mean of received indexes of correlation.

Let’s imagine that there are two vectors:

M (m1, m2, m3) and N (n1, n2, n3),

where: m1 < n1, m2 < n2, m3 < n3; then degree of resemblance (DR) is calculated according to the

following formula (sign “ ~ ” is the sign of correlation):

The closer are plans of buildings the more resembling are corresponding vectors, and the higher

is the value of the corresponding degree of resemblance.

X ~ Y = ((3/3 + 3/4)/2 + (0.83/0.83 + 0.83/1)/2 + (0.7/0.7 + 0.7/0.83)/2)/3 ≈ (0.85 + 0.915 +

0.92)/3 = 0.895;

X ~ Z = ((2/2 + 2/3)/2 + (0.83/0.83 + 0.83/1)/2 + (0.7/0.7 + 0.7/1)/2)/3 ≈ (0.83 + 0.915 + 0.85)/3

= 0.865

Y ~ Z = ((2/2 + 2/3)/2 + (1/1 + 1/1)/2 + (0.83/0.83 + 0.83/1)/2)/3 ≈ (0.83 + 1 + 0.915)/3 = 0.915

Henceforth conclusions about the resemblance of plans cease to be speculative (for more details

about the method see: Nonno, Akulov 2017).

3

1

2

1

2

1

2

1

3/))~()~()~((~

3

3

3

3

2

2

2

2

1

1

1

1

332211

n

m

m

m

n

m

m

m

n

m

m

m

nmnmnmNMDR

Page 7: Comparing Çatalhöyük with the palace of Knossos by matrix ... · Comparing Çatalhöyük with the palace of Knossos by matrix-vector method Alexander Akulov independent scholar;

8 CAES Vol. 4, № 4 (November 2018)

3. Comparing Çatalhöyük and the palace of Knossos

3.1. Vector of Çatalhöyük

Çatalhöyük has 94 rooms; the total number of potential pairs of rooms connected by adjacency

is 4371; total number of rooms connected by direct passability is 4465.

Pic. 7. Plan of Çatalhöyük (source of the original image: Mellaart 1967: 59, fig. 9)

3.1.1. AI of Çatalhöyük

As far as matrixes for the plan of Çatalhöyük and for that of the palace of Knossos would be

very large and inconvenient items so in current text sets of really existing pairs are represented

as lists. Sign “∙|∙” is the sign of adjacency.

The list of really existing pairs of rooms connected by adjacency:

1) 1 ∙|∙ 3

1) 2 ∙|∙ 3

2) 2 ∙|∙ 4

3) 3 ∙|∙ 4

4) 3 ∙|∙ 6

5) 4 ∙|∙ 6

6) 4 ∙|∙ 7

7) 8 ∙|∙ 9

8) 8 ∙|∙ 16

9) 9 ∙|∙ 10

10) 9 ∙|∙ 22

11) 9 ∙|∙ 21

12) 10 ∙|∙ 11

13) 10 ∙|∙ 22

14) 10 ∙|∙ 23

15) 11 ∙|∙ 12

16) 11 ∙|∙ 13

17) 11 ∙|∙ 23

18) 11 ∙|∙ 93

19) 12 ∙|∙ 13

20) 12 ∙|∙ 14

21) 13 ∙|∙ 14

22) 13 ∙|∙ 32

23) 14 ∙|∙ 15

Page 8: Comparing Çatalhöyük with the palace of Knossos by matrix ... · Comparing Çatalhöyük with the palace of Knossos by matrix-vector method Alexander Akulov independent scholar;

9 CAES Vol. 4, № 4 (November 2018)

24) 14 ∙|∙ 32

25) 14 ∙|∙ 33

26) 14 ∙|∙ 34

27) 14 ∙|∙ 35

28) 15 ∙|∙ 35

29) 16 ∙|∙ 17

30) 16 ∙|∙ 18

31) 16 ∙|∙ 20

32) 17 ∙|∙ 18

33) 17 ∙|∙ 19

34) 18 ∙|∙ 19

35) 18 ∙|∙ 20

36) 19 ∙|∙ 20

37) 20 ∙|∙ 21

38) 21 ∙|∙ 25

39) 22 ∙|∙ 23

40) 22 ∙|∙ 24

41) 22 ∙|∙ 25

42) 22 ∙|∙ 26

43) 23 ∙|∙ 24

44) 24 ∙|∙ 27

45) 24 ∙|∙ 93

46) 25 ∙|∙ 26

47) 25 ∙|∙ 36

48) 25 ∙|∙ 37

49) 26 ∙|∙ 27

50) 26 ∙|∙ 38

51) 27 ∙|∙ 28

52) 27 ∙|∙ 30

53) 27 ∙|∙ 38

54) 27 ∙|∙ 39

55) 28 ∙|∙ 29

56) 28 ∙|∙ 30

57) 28 ∙|∙ 93

58) 29 ∙|∙ 31

59) 29 ∙|∙ 32

60) 29 ∙|∙ 93

61) 30 ∙|∙ 39

62) 30 ∙|∙ 31

63) 30 ∙|∙ 43

64) 31 ∙|∙32

65) 31 ∙|∙ 43

66) 32 ∙|∙ 33

67) 32 ∙|∙ 46

68) 32 ∙|∙ 94

69) 33 ∙|∙ 34

70) 33 ∙|∙ 94

71) 34 ∙|∙ 35

72) 34 ∙|∙ 94

73) 35 ∙|∙ 54

74) 35 ∙|∙ 94

75) 36 ∙|∙ 37

76) 36 ∙|∙ 40

77) 37 ∙|∙ 38

78) 37 ∙|∙ 41

79) 38 ∙|∙ 39

80) 38 ∙|∙ 41

81) 39 ∙|∙ 43

82) 40 ∙|∙ 41

83) 40 ∙|∙ 55

84) 40 ∙|∙ 58

85) 41 ∙|∙ 42

86) 41 ∙|∙ 43

87) 41 ∙|∙ 58

88) 42 ∙|∙ 43

89) 42 ∙|∙ 45

90) 42 ∙|∙ 59

91) 42 ∙|∙ 60

92) 43 ∙|∙ 44

93) 43 ∙|∙ 45

94) 43 ∙|∙ 46

95) 43 ∙|∙ 47

96) 44 ∙|∙ 45

97) 44 ∙|∙ 47

98) 45 ∙|∙ 47

99) 45 ∙|∙ 48

100) 45 ∙|∙ 60

101) 45 ∙|∙ 71

102) 45 ∙|∙ 72

103) 45 ∙|∙ 74

104) 46 ∙|∙ 47

105) 46 ∙|∙ 94

106) 47 ∙|∙ 48

107) 47 ∙|∙ 49

108) 47 ∙|∙ 50

109) 47 ∙|∙ 94

110) 48 ∙|∙ 49

111) 48 ∙|∙ 74

112) 49 ∙|∙ 74

113) 49 ∙|∙ 79

114) 50 ∙|∙ 51

115) 50 ∙|∙ 79

116) 50 ∙|∙ 94

117) 51 ∙|∙ 52

118) 51 ∙|∙ 53

119) 51 ∙|∙ 79

120) 51 ∙|∙ 94

121) 52 ∙|∙ 53

122) 52 ∙|∙ 94

123) 53 ∙|∙ 80

124) 54 ∙|∙ 94

125) 55 ∙|∙ 56

126) 55 ∙|∙ 58

127) 56 ∙|∙ 57

128) 56 ∙|∙ 58

129) 56 ∙|∙ 61

130) 57 ∙|∙ 61

131) 57 ∙|∙ 63

132) 57 ∙|∙ 68

133) 58 ∙|∙ 59

134) 58 ∙|∙ 61

135) 59 ∙|∙ 60

136) 59 ∙|∙ 61

137) 60 ∙|∙ 62

138) 61 ∙|∙ 52

139) 61 ∙|∙ 62

140) 61 ∙|∙ 63

141) 61 ∙|∙ 65

142) 62 ∙|∙ 66

143) 62 ∙|∙ 71

144) 63 ∙|∙ 64

145) 63 ∙|∙ 68

146) 64 ∙|∙ 65

147) 64 ∙|∙ 69

148) 65 ∙|∙ 66

149) 65 ∙|∙ 67

150) 65 ∙|∙ 69

151) 65 ∙|∙ 70

152) 66 ∙|∙ 67

153) 66 ∙|∙ 73

154) 67 ∙|∙ 70

155) 67 ∙|∙ 73

156) 68 ∙|∙ 69

157) 69 ∙|∙ 70

158) 71 ∙|∙ 72

159) 71 ∙|∙ 73

160) 72 ∙|∙ 73

161) 72 ∙|∙ 74

162) 72 ∙|∙ 75

163) 73 ∙|∙ 76

164) 74 ∙|∙ 75

165) 74 ∙|∙ 79

166) 74 ∙|∙ 82

167) 75 ∙|∙ 76

168) 75 ∙|∙ 77

169) 75 ∙|∙ 78

170) 75 ∙|∙ 84

171) 76 ∙|∙ 77

172) 77 ∙|∙ 84

173) 78 ∙|∙ 82

Page 9: Comparing Çatalhöyük with the palace of Knossos by matrix ... · Comparing Çatalhöyük with the palace of Knossos by matrix-vector method Alexander Akulov independent scholar;

10 CAES Vol. 4, № 4 (November 2018)

174) 78 ∙|∙ 84 175) 79 ∙|∙ 80 176) 79 ∙|∙ 81

177) 79 ∙|∙ 82

178) 80 ∙|∙ 81

179) 81 ∙|∙ 83

180) 82 ∙|∙ 83

181) 82 ∙|∙ 84

182) 82 ∙|∙ 85

183) 83 ∙|∙ 85

184) 83 ∙|∙ 87

185) 84 ∙|∙ 85

186) 85 ∙|∙ 86

187) 85 ∙|∙ 87

188) 85 ∙|∙ 88

189) 86 ∙|∙ 88

190) 86 ∙|∙ 89

191) 87 ∙|∙ 88

192) 87 ∙|∙ 90

193) 88 ∙|∙ 89

194) 88 ∙|∙ 90

195) 88 ∙|∙ 92

196) 90 ∙|∙ 91

197) 90 ∙|∙ 92

198) 91 ∙|∙ 92

The number of really existing pairs of rooms connected by adjacency is 198, the total number of

potential pairs connected by adjacency is 4371, so AIÇ = 198/4371 ≈ 0.045

3.1.2. DPI of Çatalhöyük

The list of really existing pairs of rooms connected by direct passability (sign “↔” is the sign of

passability):

1) 1↔ 1

2) 2 ↔ 2

3) 3 ↔ 3

4) 4 ↔ 4

5) 5 ↔ 5

6) 6 ↔ 6

7) 7 ↔ 7

8) 8 ↔ 8

9) 8 ↔ 9

10) 9 ↔ 9

11) 10 ↔ 10

12) 11 ↔ 11

13) 12 ↔ 12

14) 12 ↔ 13

15) 13 ↔ 13

16) 13 ↔ 14

17) 14 ↔ 14

18) 15 ↔ 15

19) 16 ↔ 16

20) 17 ↔ 17

21) 18 ↔ 18

22) 19 ↔ 19

23) 20 ↔ 20

24) 20 ↔ 21

25) 22 ↔ 22

26) 23 ↔ 23

27) 24 ↔ 24

28) 24 ↔ 27

29) 25 ↔ 25

30) 25 ↔ 26

31) 26 ↔ 26

32) 27 ↔ 27

33) 28 ↔ 28

34) 29 ↔ 29

35) 30 ↔ 30

36) 30 ↔ 31

37) 31 ↔ 31

38) 32 ↔ 32

39) 33 ↔ 33

40) 34 ↔ 34

41) 35 ↔ 35

42) 36 ↔ 36

43) 37 ↔ 37

44) 38 ↔ 38

45) 39 ↔ 39

46) 40 ↔ 40

47) 41 ↔ 41

48) 41 ↔ 42

49) 42 ↔ 42

50) 43 ↔ 43

51) 43 ↔ 44

52) 43 ↔ 45

53) 44 ↔ 44

54) 45 ↔ 45

55) 46 ↔ 46

56) 46 ↔ 47

57) 47 ↔ 47

58) 48 ↔ 48

59) 49 ↔ 49

60) 50 ↔ 50

61) 51 ↔ 51

62) 51 ↔ 53

63) 52 ↔ 52

64) 53 ↔ 53

65) 54 ↔ 54

66) 55 ↔ 55

67) 56 ↔ 56

68) 57 ↔ 57

69) 58 ↔ 58

70) 58 ↔ 59

71) 59 ↔ 59

72) 60 ↔ 60

73) 61 ↔ 61

74) 62 ↔ 62

75) 63 ↔ 63

76) 64 ↔ 64

77) 65 ↔ 65

78) 66 ↔ 66

79) 67 ↔ 67

80) 68 ↔ 68

81) 68 ↔ 69

82) 69 ↔ 69

83) 70 ↔ 70

84) 71 ↔ 71

85) 71 ↔ 72

86) 72 ↔ 72

87) 73 ↔ 73

88) 73 ↔ 75

89) 75 ↔ 75

90) 75 ↔ 84

91) 76 ↔ 76

92) 77 ↔ 77

93) 78 ↔ 78

Page 10: Comparing Çatalhöyük with the palace of Knossos by matrix ... · Comparing Çatalhöyük with the palace of Knossos by matrix-vector method Alexander Akulov independent scholar;

11 CAES Vol. 4, № 4 (November 2018)

94) 78 ↔ 82

95) 79 ↔ 79

96) 79 ↔ 80

97) 80 ↔ 80

98) 80 ↔ 81

99) 81 ↔ 81

100) 82 ↔ 82

101) 83 ↔ 83

102) 84 ↔ 84

103) 85 ↔ 85

104) 85 ↔ 86

105) 86 ↔ 86

106) 87 ↔ 87

107) 87 ↔ 88

108) 88 ↔ 88

109) 88 ↔ 89

110) 89 ↔ 89

111) 90 ↔ 90

112) 91 ↔ 91

113) 92 ↔ 92

114) 93 ↔ 93

115) 94 ↔ 94

The number of really existing pairs of rooms connected by direct passability is 115, the total

number of potential pairs connected by direct passability is 4465, so DPIÇ = 115/4465 ≈ 0.026.

The 3D vector of Çatalhöyük is the following: (94; 0.045; 0.026).

3.2. The vector of the palace of Knossos of Protopalatial stage

The palace of Knossos has 82 rooms in it. The total number of potential pairs connected by

adjacency is 3321; the total number of potential pairs connected by direct passability is 3403.

Pic. 8. Plan of the palace of Knossos of the Protopalatial stage (source of the original image

McEnroe 2010: 51, fig 5.7.)

Page 11: Comparing Çatalhöyük with the palace of Knossos by matrix ... · Comparing Çatalhöyük with the palace of Knossos by matrix-vector method Alexander Akulov independent scholar;

12 CAES Vol. 4, № 4 (November 2018)

3.2.1. AI of the palace of Knossos

The list of really existing pairs of rooms connected by adjacency:

1) 1∙|∙ 2

2) 1 ∙|∙ 3

3) 1∙|∙ 6

4) 1 ∙|∙ 7

5) 1 ∙|∙ 8

6) 1 ∙|∙ 9

7) 1 ∙|∙ 10

8) 2 ∙|∙ 3

9) 2 ∙|∙ 4

10) 3 ∙|∙ 4

11) 3 ∙|∙ 10

12) 3 ∙|∙ 11

13) 3∙|∙ 12

14) 4 ∙|∙ 6

15) 5 ∙|∙ 6

16) 5 ∙|∙ 82

17) 6 ∙|∙ 7

18) 6 ∙|∙ 9

19) 6 ∙|∙ 10

20) 6 ∙|∙ 11

21) 6 ∙|∙ 12

22) 6 ∙|∙ 13

23) 6 ∙|∙ 14

24) 6 ∙|∙ 15

25) 6 ∙|∙ 18

26) 6 ∙|∙ 61

27) 6 ∙|∙ 63

28) 6 ∙|∙ 64

29) 6 ∙|∙ 65

30) 6 ∙|∙ 66

31) 6 ∙|∙ 67

32) 6 ∙|∙ 68

33) 6 ∙|∙ 69

34) 6 ∙|∙ 73

35) 6 ∙|∙ 76

36) 6 ∙|∙ 77

37) 6 ∙|∙ 78

38) 6 ∙|∙ 79

39) 6 ∙|∙ 80

40) 6 ∙|∙ 81

41) 6 ∙|∙ 82

42) 7 ∙|∙ 8

43) 7 ∙|∙ 14

44) 8 ∙|∙ 9

45) 9 ∙|∙ 10

46) 9 ∙|∙ 14

47) 10 ∙|∙ 11

48) 11 ∙|∙ 12

49) 11 ∙|∙ 13

50) 12 ∙|∙ 13

51) 15 ∙|∙ 16

52) 15 ∙|∙ 18

53) 17 ∙|∙ 18

54) 18 ∙|∙ 19

55) 18 ∙|∙ 37

56) 18 ∙|∙ 38

57) 18 ∙|∙ 39

58) 18 ∙|∙ 40

59) 18 ∙|∙ 42

60) 18 ∙|∙ 43

61) 18 ∙|∙ 44

62) 18 ∙|∙ 50

63) 18 ∙|∙ 53

64) 18 ∙|∙ 54

65) 18 ∙|∙ 56

66) 18 ∙|∙ 57

67) 18 ∙|∙ 58

68) 18 ∙|∙ 59

69) 18 ∙|∙ 60

70) 18 ∙|∙ 61

71) 18 ∙|∙ 62

72) 18 ∙|∙ 69

73) 18 ∙|∙ 70

74) 18 ∙|∙ 71

75) 18 ∙|∙ 72

76) 18 ∙|∙ 73

77) 18 ∙|∙ 74

78) 18 ∙|∙ 75

79) 19 ∙|∙ 20

80) 19 ∙|∙ 31

81) 19 ∙|∙ 32

82) 19 ∙|∙ 33

83) 19 ∙|∙ 34

84) 19 ∙|∙ 41

85) 20 ∙|∙ 21

86) 20 ∙|∙ 22

87) 20 ∙|∙ 24

88) 20 ∙|∙ 30

89) 20 ∙|∙ 31

90) 21 ∙|∙ 30

91) 22 ∙|∙ 23

92) 22 ∙|∙ 30

93) 23 ∙|∙ 30

94) 24 ∙|∙ 25

95) 24 ∙|∙ 30

96) 25 ∙|∙ 26

97) 25 ∙|∙ 27

98) 25 ∙|∙ 30

99) 25 ∙|∙ 31

100) 26 ∙|∙ 27

101) 26 ∙|∙ 28

102) 26 ∙|∙ 31

103) 27 ∙|∙ 29

104) 27 ∙|∙ 30

105) 28 ∙|∙ 29

106) 28 ∙|∙ 30

107) 28 ∙|∙ 31

108) 29 ∙|∙ 30

109) 30 ∙|∙ 31

110) 30 ∙|∙ 32

111) 30 ∙|∙ 33

112) 30 ∙|∙ 34

113) 30 ∙|∙ 35

114) 30 ∙|∙ 36

115) 31 ∙|∙ 32

116) 32 ∙|∙ 33

117) 34 ∙|∙ 35

118) 35 ∙|∙ 36

119) 37 ∙|∙ 38

120) 38 ∙|∙ 39

121) 38 ∙|∙ 40

122) 39 ∙|∙ 40

123) 40 ∙|∙ 41

124) 40 ∙|∙ 42

125) 40 ∙|∙ 45

126) 40 ∙|∙ 46

127) 40 ∙|∙ 47

128) 41 ∙|∙ 48

129) 42 ∙|∙ 43

130) 42 ∙|∙ 45

131) 43 ∙|∙ 44

132) 43 ∙|∙ 45

133) 44 ∙|∙ 45

134) 45 ∙|∙ 46

135) 46 ∙|∙ 47

136) 47 ∙|∙ 48

137) 47 ∙|∙ 49

138) 48 ∙|∙ 49

Page 12: Comparing Çatalhöyük with the palace of Knossos by matrix ... · Comparing Çatalhöyük with the palace of Knossos by matrix-vector method Alexander Akulov independent scholar;

13 CAES Vol. 4, № 4 (November 2018)

139) 50 ∙|∙ 51

140) 50 ∙|∙ 53

141) 51 ∙|∙ 52

142) 51 ∙|∙ 53

143) 53 ∙|∙ 54

144) 54 ∙|∙ 55

145) 54 ∙|∙ 56

146) 55 ∙|∙ 56

147) 56 ∙|∙ 57

148) 57 ∙|∙ 58

149) 58 ∙|∙ 59

150) 59 ∙|∙ 60

151) 60 ∙|∙ 61

152) 61 ∙|∙ 62

153) 62 ∙|∙ 63

154) 63 ∙|∙ 64

155) 64 ∙|∙ 65

156) 65 ∙|∙ 66

157) 66 ∙|∙ 67

158) 67 ∙|∙ 68

159) 68 ∙|∙ 76

160) 69 ∙|∙ 70

161) 70 ∙|∙ 71

162) 71 ∙|∙ 72

163) 73 ∙|∙ 74

164) 74 ∙|∙ 75

165) 76 ∙|∙ 77

166) 77 ∙|∙ 78

167) 78 ∙|∙ 79

168) 79 ∙|∙ 80

169) 80 ∙|∙ 81

170) 80 ∙|∙ 82

The number of really existing pairs of rooms connected by adjacency is 170, the total number of

potential pairs connected by adjacency is 3321, so AIK = 170/3321 ≈ 0.05.

3.2.2. DPI of the palace of Knossos

The list of really existing pairs of rooms connected by direct passability:

1) 1 ↔ 1

2) 1↔ 3

3) 2 ↔ 2

4) 2 ↔ 4

5) 3 ↔ 3

6) 3 ↔ 4

7) 4 ↔ 4

8) 4 ↔ 6

9) 5 ↔ 5

10) 5 ↔ 6

11) 5 ↔ 82

12) 6 ↔ 6

13) 6 ↔ 7

14) 6 ↔ 14

15) 6 ↔ 15

16) 6 ↔ 18

17) 6 ↔ 79

18) 6 ↔ 78

19) 6 ↔ 77

20) 6 ↔ 76

21) 6 ↔ 68

22) 6 ↔ 67

23) 6 ↔ 66

24) 6 ↔ 65

25) 6 ↔ 64

26) 6 ↔ 63

27) 7 ↔ 7

28) 7 ↔ 8 (?)

29) 8 ↔ 8

30) 9 ↔ 9

31) 9 ↔ 10 (?)

32) 9 ↔ 14

33) 10 ↔ 10

34) 10 ↔ 10

35) 10 ↔ 11

36) 11 ↔ 11

37) 11 ↔ 12

38) 11 ↔ 13

39) 12 ↔ 12

40) 13 ↔ 13

41) 14 ↔ 14

42) 15 ↔ 15

43) 15 ↔ 16

44) 15 ↔ 18

45) 17 ↔ 17

46) 17 ↔ 18 (?)

47) 18 ↔ 18

48) 18 ↔ 19

49) 18 ↔ 37

50) 18 ↔ 39

51) 18 ↔ 40 (?)

52) 18 ↔ 50 (?)

53) 18 ↔ 51

54) 18 ↔ 53

55) 18 ↔ 54

56) 18 ↔ 56

57) 18 ↔ 57

58) 18 ↔ 58

59) 18 ↔ 59

60) 18 ↔ 60

61) 18 ↔ 61

62) 18 ↔ 62

63) 18 ↔ 71

64) 18 ↔ 72

65) 18 ↔ 73

66) 18 ↔ 74

67) 18 ↔ 75

68) 19 ↔ 19

69) 19 ↔ 30

70) 19 ↔ 31 (?)

71) 20 ↔ 20

72) 20 ↔ 21

73) 20 ↔ 22

74) 20 ↔ 24

75) 20 ↔ 30

76) 21 ↔ 21

77) 22 ↔ 22

78) 22 ↔ 23

79) 23 ↔ 23

80) 24 ↔ 24

81) 24 ↔ 25 (?)

82) 25 ↔ 25

83) 25 ↔ 26

84) 26 ↔ 26

85) 26 ↔ 27

86) 26 ↔ 28 (?)

87) 27 ↔ 27

88) 27 ↔ 30

89) 28 ↔ 28

90) 28 ↔ 29

91) 29 ↔ 29

92) 29 ↔ 30

93) 30 ↔ 30

94) 30 ↔ 33

95) 30 ↔ 34

96) 30 ↔ 35

Page 13: Comparing Çatalhöyük with the palace of Knossos by matrix ... · Comparing Çatalhöyük with the palace of Knossos by matrix-vector method Alexander Akulov independent scholar;

14 CAES Vol. 4, № 4 (November 2018)

97) 30 ↔ 36

98) 31 ↔ 31

99) 31 ↔ 32

100) 32 ↔ 32

101) 32 ↔ 33 (?)

102) 33 ↔ 33

103) 34 ↔ 34

104) 35 ↔ 35

105) 36 ↔ 36

106) 37 ↔ 37

107) 38 ↔ 38

108) 38 ↔ 39

109) 39 ↔ 39

110) 40 ↔ 40

111) 40 ↔ 41

112) 40 ↔ 42

113) 40 ↔ 45

114) 40 ↔ 46

115) 40 ↔ 47

116) 41 ↔ 41

117) 41 ↔ 48 (?)

118) 42 ↔ 42

119) 42 ↔ 43

120) 43 ↔ 43

121) 43 ↔ 44

122) 44 ↔ 44

123) 45 ↔ 45

124) 46 ↔ 46

125) 47 ↔ 47

126) 47 ↔ 48 (?)

127) 47 ↔ 49 (?)

128) 48 ↔ 48

129) 48 ↔ 49 (?)

130) 49 ↔ 49

131) 50 ↔ 50

132) 50 ↔ 51

133) 51 ↔ 51

134) 51 ↔ 52

135) 51 ↔ 53

136) 52 ↔ 52

137) 53 ↔ 53

138) 53 ↔ 54

139) 54 ↔ 54

140) 55 ↔ 55

141) 55 ↔ 56

142) 56 ↔ 56

143) 57 ↔ 57

144) 58 ↔ 58

145) 59 ↔ 59

146) 60 ↔ 60

147) 61 ↔ 61

148) 62 ↔ 62

149) 63 ↔ 63

150) 64 ↔ 64

151) 65 ↔ 65

152) 66 ↔ 66

153) 67 ↔ 67

154) 68 ↔ 68

155) 69 ↔ 69

156) 69 ↔ 70

157) 70 ↔ 70

158) 71 ↔ 71

159) 72 ↔ 72

160) 73 ↔ 73

161) 74 ↔ 74

162) 75 ↔ 75

163) 76 ↔ 76

164) 77 ↔ 77

165) 78 ↔ 78

166) 79 ↔ 79

167) 80 ↔ 80

168) 80 ↔ 82

169) 81 ↔ 81

170) 81 ↔ 82

171) 82 ↔ 82

The sign of question means that the existence of the corresponding pair is doubtful.

The number of really existing pairs of rooms connected by direct passability is 171, the total

number of potential pairs connected by direct passability is 3403, so DPIK = 171/3403 ≈ 0.05.

Thus, the 3D vector of the palace of Knossos is the following: (82; 0.05; 0.05).

3.3. Comparison of vectors

3D vector of Çatalhöyük is the following: (94; 0.045; 0.026).

3D vector of Knossos palace is the following: (82; 0.05; 0.05).

Çatalhöyük ~ Knossos = ((82/82 + 82/94)/2 + (0.045/0.045 + 0.045/0.05)/2 + (0.026/0.026 +

0.026/0.05)/2)/3 = ((1 + 0.87)/2 + (1 + 0.9)/2 + (1 + 0.52)/2)/3 = (0.935 + 0.95 + 0.76)/3 = 0.88

It is a rather noteworthy that degree of resemblance of Çatalhöyük and the palace of Knossos of

the Propopalatial period is higher than degree of resemblance of the palace of Knossos and the

central house of Myrtos (a sample of Early Prepalatial architecture 3000–2200 BC) that is 0.57

(Akulov 2017a: 14 – 15, 21), and the degree of resemblance of the palace of Knossos and Villa

Alpha (a sample of Late Prepalatial architecture from Malia 2200 – 1900 BC) that is 0.73

(Akulov 2017a: 12 – 14, 21). Also degree of resemblance of Çatalhöyük and the palace of

Knossos is higher than degree of resemblance of the palace of Knossos and the palace of Pylos

(a sample of Mycenaean architecture of about 1400 – 1190 BC; its location is shown in pic. 3)

that is 0.81 (Akulov 2017a: 18 – 21).

Page 14: Comparing Çatalhöyük with the palace of Knossos by matrix ... · Comparing Çatalhöyük with the palace of Knossos by matrix-vector method Alexander Akulov independent scholar;

15 CAES Vol. 4, № 4 (November 2018)

Thus, it is possible to conclude that the palace of Knossos of the Protopalatial stage is closer to

Çatalhöyük than to samples of earlier Minoan architecture.

Pic. 9. Location of Myrtos and Malia

References

Akulov A. 2017a. Comparison of some early Minoan and pre-Minoan buildings with the ‘palace’

of Hacilar by matrix-vector method: preliminary notes on Anatolian origin of Minoan

architecture. Cultural Anthropology and Ethnosemiotics, Vol. 3, N 4; pp.: 2 – 24

Akulov A. 2017b. The structure of verbs of Keftiw/Minoan incantation against samuna ubuqi

disease from London Medical Papyrus demonstrates close resemblance with the structure of

Hattic verb. Cultural Anthropology and Ethnosemiotics, Vol. 3, N 3; pp.: 28 – 34

Çatalhöyük Nerede Hakkında Bilgi (Information about Çatalhöyük)

http://www.bilgilisayfa.com/catalhoyuk-nerede-hakkinda-bilgi.html – accessed November 2018

Diamant S., Rutter J. 1969. Horned Objects in Anatolia and the Near East and Possible

Connexions with the Minoan “Horns of Consecration”. Anatolian Studies, Vol. 19; pp.: 147 –

177

Lazaridis I, Mittnik A., Patterson N., Mallick S., Rohland N., Pfrengle S., Furtwängler A.,

Peltzer A., Posth C., Vasilakis A., McGeorge P. J. P., Konsolaki-Yannopoulou E., Korres G.,

Martlew H., Michalodimitrakis M., Özsait M., Özsait N., Papathanasiou A., Richards M.,

Roodenberg S. A., Tzedakis Y., Arnott R., Fernandes D. M., Hughey J. R., Lotakis D. M.,

Navas P. A., Maniatis Y., Stamatoyannopoulos Jh. A., Stewardson K., Stockhammer P., Pinhasi

R., Reich D., Krause J., Stamatoyannopoulos G. 2017. Genetic origins of the Minoans and

Mycenaeans. Nature 548; pp.: 214 – 218

McEnroe Jh. C. 2010. Architecture of Minoan Crete. Constructing Identity in the Aegean

Bronze Age. University of Texas Press, Austin

Page 15: Comparing Çatalhöyük with the palace of Knossos by matrix ... · Comparing Çatalhöyük with the palace of Knossos by matrix-vector method Alexander Akulov independent scholar;

16 CAES Vol. 4, № 4 (November 2018)

Mellaart J. 1967. Çatal Hüyük: A Neolithic Town in Anatolia. Thames and Hudson, London

Nonno T., Akulov A. 2017. Estimation degree of resemblance of plans of buildings by matrix-

vector method. Cultural Anthropology and Ethnosemiotics, Vol. 3, N 4; pp.: 52 – 60

Το παλάτι της Κνωσού όπως ήταν στην ακμή του Μίνωα (The palace of Knossos as it was in the time of Minos

prosperity) http://www.timelink.gr/arthro/time-doc/to-palati-ths-knvsoy-opvs-htan-sthn-akmh-toy-minva-video – accessed

November 2018