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)
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
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
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
)!(!
!
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
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
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
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
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
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.)
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
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
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).
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
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