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This document critically examines Guralnick's statistical studies on Greek kouroi and their relationship with the Egyptian canon. The analysis reveals limitations in her methods and procedures, casting doubt on her claims for Greek use of the Egyptian system for proportioning human figures. However, her observations about similarities among kouroi add support to conclusions formed by scholars on stylistic grounds.
Typology: Lecture notes
1 / 26
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Abstract
In a well-known series of articles,
Eleanor Guralnick
undertook statistical studies to compare
the proportions
of Greek (^) archaic kouroi with one (^) another and with the
proportions
of the Egyptian
second (^) canon; she concluded
that Greek sculptors
used the Egyptian
canon sporadically
for proportioning
kouroi during
most of the sixth century
B.C.E. (^) Here, we^ examine the results of Guralnick's analy
ses against
the backdrop
of current statistical method.
While we do not believe that her analyses convincingly
demonstrate any
Greek use of the Egyptian system,
we
agree
that the analyses
do distribute the kouroi included
in the studies into two main groups.
We argue
that this
division results from the influence of regional styles,
rather
than from the use of standardized proportional systems.
We also examine Guralnick's methodology
in (^) cluster,
principal components,^
and z-score^ analyses
and dem
onstrate that her studies do not provide statistically sig
nificant evidence for similarities among
Greek (^) kouroi or
between kouroi and the Egyptian canon,^
in part
because
of the limitations of the statistical techniques employed
and in part
because of problems
in her procedures
and
data. (^) Thus, we^ disassociate archaic Greek kouroi from a
dependence
on the Egyptian
standardized proportional
schemes and argue
instead that (^) the development
of re
gional styles
best explains
the proportional
similarities
documented by
Guralnick.*
proximate synchronism
of the earliest Greek statues in
stone and the resumption
of direct contacts between
century B.C.E.;^
and (2)
the (^) visual resemblance be
tween Greek kouroi and Egyptian
statues. Standing
Greek statues.^ Eleanor Guralnick's statistical studies of
kouroi and korai (^) are, in part,
an attempt
to demon
strate this hypothesis.
Guralnick concluded that "at
Greek sculptors
made (^) conscious use (^) of the contempo
argument
can (^) be made that in the first instance,
the
regions
in (^) the eastern Mediterranean, in^ particular
while Guralnick's articles contain much that is valuable
open
the way
for new discussion about (^) archaic Greek
statues (^) and their origins.
archaic Greek sculptors
used one or more (^) standard
ized proportioning schemes,^
and her numerous^ articles
have served to reinforce this idea. We,
on (^) the contrary,
tem of proportions.
Such proportional
similarities as
do exist among
kouroi are^ best explained,
we believe,
We are^ grateful
for the helpful
comments of the two
anonymous
reviewers for the A]A.
We would also like to thank
Kapon Editions,^
Nikolaos Kaltsas (^) (National Archaeological
Museum of Athens),
Daria Lanzuolo (DAI Rome), (^) Joachim
Heiden (DAI Athens), (^) MatthewWesterby (Metropolitan
Mu
seum of Art),
Irene B?sel (Staatliche (^) Antikensammlungen
und Glyptothek
in Munich),
and Gay
Robins for their assis
tance and permission
to use^ the images reproduced
here.
2Guralnick (^) 1985,409.
E.g.,
Osborne (1996, 209-11, (^) 371) cites^ only Guralnick
to support
his statement^ that the "size and proportions [of
kouroi] make^ it clear^ beyond
doubt that they
were directly
inspired by Egyptian
stone sculpture."
Hurwit (2007,274,
n.
as (^) evidence that the kou
ros type
was (^) invented "after Greeks had been exposed
... (^) to
Egyptian techniques";
cf. the newest edition of Pedley's (2007,
used textbook: "computer
studies have now^ con
firmed the closeness of proportions
between the earliest kou
roi and Egyptian figurines."
4Cf. Boardman 2006,12,19-24.
We have (^) not, therefore, (^) attempted
new measure
ments or pursued
fresh statistical approaches
with the
aim of^ identifying
one or more proportional
schemes
in Greek kouroi. In our^ opinion,
the evidence pub
range
of proportions
and offers an^ explanation
for
abstract proportional systems.
entirely
in two-dimensional works rather than in
three-dimensional statues.^ Egyptian
artists frequently
guidelines
show that a new^ system
came into use in the
enth century B.C.E.).^
The new^ system, (^) usually
called
cal methods. We emphasize
that these studies con
Greek kouroi and korai. At the same^ time, statistical
theory
has progressed considerably
in (^) the last quarter
century,
and important
new (^) work has been done on
what Guralnick's statistical analyses
tell us^ about kou
Fig.
male figure
with origi
nal grid
lines from Tomb 223 at Thebes, 26th^ Dy
nasty.
This illustrates the so-called second canon or
fig. 7.2).
cluster analyses,
Guralnick relied primarily
on two
Each dimension of each figure
was expressed
in terms
knee-tops
of the figure;
the ratios permitted compari
kouroi, and^ the^ average dimensions^ of Greek, Turk
5Robins (^) 1994,160.
6 Robins (^) (1994, 228, 258-59) shows^ clearly
that the guide
lines used by Egyptian
artists did not^ always
determine the
proportions
of their figures. E.g.,
the same^ grid system
was
used for the (^) taller, more^ slender figures
of the 19th and 20th
Dynasties
as had been used for the shorter and stockier fig
ures (^) of the 5th and 6th Dynasties.
Robins thus correctly rejects
the use^ of the term "canon" in reference to the Egyptian grids.
Because "canon" is generally
used for the Egyptian system,
however, for convenience^
we (^) do so here.
7Hdt. (^) 2.152-54; Boardman 1999,111-53.
8Robins (^) 1994,160-61, fig.
Guralnick 1976,1978.
10 Guralnick (^) 1978, 464, fig. 2;^ 1996a,^ 41,^ fig.
4.1. Data set A
comprised
11 dimensions: top
of head to eyes, eyes
to chin,
chin to sternal (^) notch, sternal notch to nipples, nipples^
to na
As the number of clusters is further (^) decreased, some
of the clusters must contain more and more^ objects.
three (^) clusters, cluster^ F^ contained^10 objects,
cluster
tian canon until the number of clusters was reduced
to 11,
about halfway
between the maximum number
ters?the Tenea kouros joined
cluster F. When the
clusters were reduced to 8,
the Thebes 3 kouros en
tered cluster (^) F, became again
the sole member of its
kouros and the Volomandra kouros also grouped
with
when there are many
clusters are more^ alike than
clusters is decreased. At no^ point,
however, does^ the
tered objects.
It is also necessary
to bear in mind that
have considerable consequences
in the results. For
canon much earlier,
with 16 clusters.13 In this (^) case, the
canon, these^3 kouroi, and^ the Melos^ kouros^ when
there were^11 clusters.15 Guralnick concluded that
canon.17 The analyses
have only
shown that,
in rela
tive (^) terms, these 4 kouroi seem to be more similar to
cluster. Indeed,
the cluster analyses
indicate that the
Ptoon 12, Tenea,
and Melos kouroi are more similar
cluster B when there are 17 clusters,
six stages
before
Moreover,
it is important
to (^) remember that even if
Greek kouroi,
different explanations
could be pro
Guralnick (^) 1978,465-66, figs. 3,4. 14
According
to the Panel on Discriminant Analysis,
Classi
fication,
and Clustering (1989,^ 35),^
the nature and composi
tion of the clusters "appear
to cause fundamental difficulties
for formal statistical inference and distribution theory";
see
also Punj
and Stewart (^) 1983,136; Norusis (^) 1985,183; Shennan
Guralnick (^) 1978, 466, fig.
468-69) again
used data set A^ in a^ cluster^ analysis
with a to
tal of 28 objects:
24 kouroi plus
the Egyptian
canon and the
Greek, Turkish,
and Italian men. In this (^) case, the Ptoon 12
and the New York^ kouroi^ clustered^ with^ the Egyptian
canon
when the objects
were (^) sorted into 14 and 13 clusters, (^) respec
tively.
Guralnick (^) (1978, fig. 5)^
does not show the results when
the number of clusters was^ greater
than 14. However, assum
ing
that the chart^ documents^ the highest
number of clusters
at which a kouros and the Egyptian
canon (^) clustered together,
then here, also,
the New York and Ptoon 12 kouroi joined
the
Egyptian
canon halfway
between the maximum number of 28
clusters and the minimum of 1 cluster.
Guralnick (^) 1978, 466.
17 As Guralnick (1978, 472) acknowledges,
the cluster and
principal components analyses
"cannot determine...^ how
closely
the actual measurements of the statues conform to the
proportional
schemes."
2010] KOUROI^ AND^ STATISTICS^
'4*
"
a b c^ d
Fig.
Guralnick to be proportionally
close to the Egyptian
second canon: (^) a, New York (^) kouros, probably
from
Attica, Naxian^ marble,
ca. 600-590 B.C.E. (?
The Metropolitan
Museum of Art; Fletcher
Fund 1932,32.11.1); b,
Melos (^) kouros, found on
Melos in 1891, Naxian (^) marble, ca. 550 B.C.E. (^) Athens, National^ Archaeological Museum,^
inv. no. 1558 (C.
Iosifidis and G. Moutevellis;
Kaltsas (^) 2002, cat. no.^ 48); c,Tenea (^) kouros, found in cemetery
of ancientTenea in 1846, Parian^ marble, ca. 550 B.C.E.^ Munich, Staadiche
Antikensammlungen
und Glyptothek,
inv. no.^ GL (^168) (H. Koppermann;
? Staatliche Antikensammlungen
und Glyptothek,
M?nchen); d, Ptoon
12 kouros, from the Sanctuary
of Apollo
at Ptoon in Boeotia, island^ marble,
ca. (^) 530-520 B.C.E. Athens,
National Archaeological
Museum, inv. no.^12 (G. Fafalis; Kaltsas^ 2002,
cat. no. 80).
certain Greek kouroi.
?New York, Melos, Tenea,
and Ptoon 12 (see (^) fig.
(kouroi,
second (^) canon, and Greek, Turkish,
and Ital
around the points
that seem^ to^ form^ groups.
Gur
alnick found agreement
between the^ cluster^ analyses
conclusions";
in particular,
she claims^ that^ the^ prin
roi?Florence, Ptoon^ 10, and^ Volomandra?are^ also
nents analyses.
nents analyses
do not appear
to support
these claims.
In fact,
there are a number of striking
anomalies
Guralnick (^) 1978,469.
19 Guralnick (^) 1978, 470, fig.
(using
all the variables in
her data set A); 471, fig.
(using
the seven^ variables in data
set A that were most alike in the 24 kouroi and the Egyptian
canon).
20Guralnickl978,469.
them to do.26 (^) Instead, the five statues span
most (^) of
clusters (see
table l).
under a master would apply
it."29 This explanation
ample,
kouroi that are from the same region
and ap
proximately contemporary^
are (^) also visually
similar.
share technical and aesthetic preferences.
Guralnick
argues
that similar treatments of the surfaces of statues
revealed by
her statistical studies.30 (^) However, there is
derlying proportions
and surface treatment. If visually
tors (^) did not use a (^) standardized proportional system.
have contained "copies
of or adaptations
from" the
know of no (^) treatise or (^) technical work about statues
fifth century B.C.E.,^
and a book by
one sculptor
about
visually
and proportionally,
to appear contemporane
ously
in various regions.
Instead, regional sculptural
sixth century.
sculptors
nor pattern
books (^) convince, how can^ we
and the Strangford
kouros consistently
form one group
for
all the stages represented
in the graph?
clusters down to
5 clusters (^) (Guralnick 1978, 467, fig. 5).^
The (^) Greeks, Turks,
and Italians only group^
with the Egyptian
canon in the cluster
analysis using
data set B and only
when the number of clusters
is reduced to 3 (Guralnick 1978,^ 466,^ fig. 4).
26 Guralnick (^) 1978, 470. Illustrations and extensive bibliog
raphy
for these kouroi can be found as follows. New York (Met
ropolitan
Museum of Art,
inv. no. 32.11.1,
ht. 1. m):
Richter
no. 1, figs. 25-32, 60-2;
Boardman 1978, (^) fig. 63;
Floren 1987, 252
n. 6; Stewart^ 1990, 108-9, 111-12, (^) figs. 49
55; Vorster^ 2002,120-22,304, (^) fig. 190a-e.^ Thera^ (Athens, Na
tional Archaeological
Museum, inv. no. 8, preserved ht. 1.
m):
Richter 1970,69-70,
no. 49, figs. 178-83; Boardman^ 1978,
fig. 218a-d;^
Kaltsas 2002,41,
no. (^) 22. Melos (Ath
ens, National^ Archaeological Museum,^
inv. no. 1558,
ht. (^) 2.
m): Richter^ 1970,96-7,
no. 86, figs. 273-79; Boardman^ 1978,
fig.
102; Floren^ 1987,178 n.^ 5, pi. 13.3;^
Stewart 1990,119, (^) fig.
Karanastassis 2002,180-81,312, (^) fig. 253a, b;
Kaltsas 2002,
no. 48. Tenea (Munich, Staatliche^ Antikensammlungen
und Glyptothek,
inv. no.^ 168, ht. 1. m):
Richter 1970,84-5,
no. 73, figs. 245-50;
Boardman^ 1978, fig.
121; Stewart^ 1986;
Floren 1987,
n. 12, pis. 14.2,15.1; Karanastassis^ 2002,
85,313, (^) fig. 262a-d.^ Ptoon^12 (Athens, National^ Archaeologi
cal Museum, inv. no.^ 12, preserved ht. 1. m):
Richter 1970,
122-23, no.^ 145, figs.
425-29, (^) 437; Ducat^ 1971, 346-51, no.
197, pis. 112-14;
Boardman 1978, (^) fig. 179;
Floren 1987,
n.
Stewart 1990,126, (^) fig. 170; Maderna-Lauter 2002, 230-32,
319, (^) fig. 309a-d;
Kaltsas 2002,62,
no. 80.
For the sake of consistency,
dates of statues^ are^ taken
from Boardman (1978) whenever^ possible.
28 Data set A: Guralnick (^) 1978, 465, fig.
fig.
data set B, 9 out of 17 kouroi, including
the New York and the
Sounion (^) kouroi, did cluster with the Egyptian
canon when
the number of clusters was reduced to 3 (Guralnick 1978,466,
fig. 4). 29 Guralnick 1978,471.
30 Guralnick 1978,469.
31 Guralnick (^) 1978,471.
32 Gal. DeplacitisHippocratisetPlatonisb;
Plin. iW34.55. Sim
ilarly, according
toVitruvius (De
arch. 7, pref. 12),
in the sixth
century B.C.E.,^
the architects Rhoikos and Theodoros wrote a
book about their Temple
of Hera on Samos,
and Chersiphron
and Metagenes
likewise wrote (^) about their Temple
of Artemis
at Ephesos.
results of the (^) cluster and principal components^ analy
reason for this.
roi. What the z-scores offer, and^
the (^) other methods
sions. Using
the (^) z-scores, we^ are^ able to suggest
what
factors caused the earlier analyses
to produce
the
Z-scores show how an object
relates to^ the average
object
from the mean, measured in standard devia
straight
horizontal (^) axis, centered at^ zero, represents
man,
and the vertical y-axis
of the chart is marked
average
man. If human males represent
a statistically
"normal" (^) distribution, as^ is assumed, then the propor
tions for the average
man as computed by
Guralnick
the kouroi (see below,
under "Z-Score Profiles").
How
ever, the^ average
man used by
Guralnick does^ provide
statues (^) and the Egyptian canon)^
are compared,
and
relate to one another.
pared
to the average
man (^) are located at fixed points
ered the measurements^ as^ ratios (each
dimension of
for that dimension on (^) the x-axis and at a point
on (^) the
vertical y-axis showing
its distance from the average
man. (^) The distance on the vertical axis ismeasured in
than +1^ SD from the average
man. Thus,
for that pro
charted points
are then connected, creating
the ir
those of^ the average
man (^) and very
slim waists. Three
vertical dimensions?knee to navel,
knee to nipples,
and knee to sternum?in both kouroi and (^) the Egyp
tian canon (^) are, proportionally, quite
similar to^ those
less than those of an^ average
man (^) and are within less
kouros), (^) very
narrow waists,
narrow hips,
and vertical
dimensions from knee to^ sternum^ that are^ quite
close
to be greater
than the average
man's.
In (^) fact, as^ Guralnick's z-score^ profiles show,^
most
one another and to those of the average
man. (^) Since all
kouroi seem^ to have average (^) proportions
from knee to
sternum that are close to the proportions
of an aver
the 4 kouroi grouped
with the Egyptian
canon when the clus
ters were reduced to 8, about
two-thirds of the way (^) through
the analysis (Guralnick^ 1978,^ 465,^ fig. 3).
With data set^ A and
canon (^) until the analysis
was (^) extended by extrapolation
to 5
clusters (Guralnick 1978,467, (^) fig. 5). Using
data set B with (^21)
Egyptian
canon when the clusters were (^) reduced from 21 to 11
(Guralnick 1978,466, (^) fig. 4).
34 Guralnick's z-score^ charts place
the anatomical dimen
sions on^ the vertical axis and the standard deviations on the
horizontal axis;
the orientation is reversed here.
Guralnick 1982,
n. 7; 1985,400.
age man,^
it is primarily
the non^ average (^) proportions
in grouping
certain kouroi as proportionally
similar.
One important
non average
factor is the (^) difference
dimensions for the average
man. (^) In these five kouroi,
than average.
Other kouroi show a^ strong proportional
narrow (^) waists (-2.04 SD^ for^ both) ,36In
a group
of (^) late
proportionally
broader (^) than average
and waists that
are narrower (^) than average
but with less exaggeration
greater-than-average proportional
difference between
and close-to-average
vertical proportions
between
knees and sternum. In addition,
most (^) kouroi have pro
example,
the Munich and Anavyssos
kouroi?which
the sixth century
B.C.E.?are associated by
multivari
This pattern, indeed,^
caused Guralnick to wonder
namely,
that the same basic proportional
ideal occurs
ralistic kouroi (^) toward the end of the series.40 She con
cluded that "the proportional patterns
most likely
if not in basic lines."41 This seems entirely
reasonable.
use of the same proportional
scheme. She suggests,
analyses
because both conform to^ a^ (non-Egyptian)
canon "infrequently
used but long
known." We, (^) by
the generally preferred idealization,^
are a better ex
Measured from Guralnick 1985, 400, (^) fig. 1; 406, (^) fig.
The main proportional
difference between these two kouroi
is the width of the hips (Sounion:^
-0.75 (^) SD; Munich: +0.
SD). Sounion^ (Athens, National^ Archaeological Museum, inv.
no. 2720, ht.^ 3.05 m,
ca. (^) 590- B.C.E.):
Richter (^) 1970,42-4,
no. 2, figs. 33-9; Boardman^ 1978, fig. 64;
Floren^ 1987, 252
n.
9, pi. 20.1; Stewart^ 1990,111-12, figs. 44,
45; Kaltsas^ 2002, 39,
no. 17; Vorster
fig.
193a-e. Munich (Mu
nich, (^) Glyptothek,
inv. no. (^) 169, ht. (^) 2.08 m, ca. 540- B.C.E.):
Richter 1970,118,
no. 135, figs. 391-94;
Boardman 1978, (^) fig.
Floren 1987, 256
n. 22, pi. 20.4;
Karanastassis 2002,
77,312, (^) fig. 251a-d.
37 The information in table 2 ismeasured from Guralnick
1985, 407, (^) fig. 8;
dates are from Boardman 1978, (^) figs. 180,
182, 145, 147.^ Ptoon^20 (Athens, National^ Archaeological
Museum, inv. no. 20,
ht. 1.03 m, ca.^ 510- B.C.E.):
Richter
no. 155, figs. 450-57;
Ducat 1971, 355-62,
no. 202,
pis.
117-19; Boardman^ 1978, fig.
180; Floren^ 1987, 315
n. 41;
Stewart 1990, 126, (^) fig. 180;
Kaltsas 2002, 71-2,
no. 102;
Mad
erna-Lauter 2002, 232, 319, (^) fig.
310a-c. Attic style
of Ptoon
20: Boardman (^) 1978, 88; Stewart (^) 1990, 124; Maderna-Lauter
2002, 232. Aristodikos^ (Athens, National^ Archaeological
Mu
seum, inv. no. 3938, ht.^ 1.95 m,
ca. (^) 510- B.C.E.):
Richter
no. 165, (^) figs. 492, 493;
Boardman 1978, (^) fig. 145;
Floren 1987, 258
n. 31, (^) pi. 20.5;
Stewart 1990, 133, (^) fig. 218;
Kaltsas (^) 2002, 66, no.^ 94; Maderna-Lauter (^) 2002, 227-29, 319,
fig.
307a-e. Strangford (London,^
British Museum, inv. no.
475, ht.^ 1.01 m,^
ca. (^) 510- B.C.E.):
Richter (^) 1970, 136, no.
159, figs. 461-63; Boardman^ 1978, fig.
ens, (^) Acropolis Museum, inv. no. 698, ht.^ 0.86, ca.^ 490-
Richter 1970, 149,^
no. 190, figs. 564-69;^
Boardman
fig.
147; Stewart^ 1990, 133-35, figs. 219,^ 220;^
Kaltsas
2002, 58, no.^ 69.
38 Of the 23 statues charted in z-scores (Guralnick 1985),
19 have heads that are proportionally greater
in height
than
the head of an average
man by
more than +1 SD. Of the 11
complete
kouroi charted in z-scores by
Guralnick (1985),
are proportionally
taller by
more (^) than +1 SD from baseline
to knee-top
than is an^ average man,^
and 9 are proportionally
taller in total height
than an^ average
man (though only
3 are
taller by
more (^) than + SD). 39 See also the z-scores^ for these two statues (Guralnick
1985, 406, (^) fig. 7).
Both statues (^) have wide shoulders,
narrow
waists, and^ wider-than-average hips.
Kroisos from Anavyssos
(Athens,
National Archaeological Museum,^
inv. no. 3851,
ht.
1.94 m, ca. 530 B.C.E.):
Richter 1970, 118-19,
no. 136, (^) figs.
395-98; Boardman^ 1978, (^) fig. 107; Floren^ 1987, 255
n. 21, pi.
20.3; Stewart^ 1990,122, (^) figs. 132,134; Kaltsas^ 2002,58,
no. 69;
Karanastassis 2002,177-79, 312,^ fig.
252a-d.
Guralnick 1985,404-7.
41 Guralnick 1985,407.
42 Guralnick (^) 1978,467, fig. 5; 469.
2010] KOUROI^
Table 2. Proportioned
Dimensions of^ Four^ Late^ Archaic^ Kouroi^ in Standard^ Deviations^ from^
an Average
Human
a Guralnick presents
this information as^ a^ z-score^ chart; the values shown here were^ obtained by measuring
the distances on
Guralnick's chart and converting
the distances to standard deviations. Each dimension was considered as^ a proportion
of the
statue's height
from the top
of the knee^ to the^ top
of (^) the head.
exist among
kouroi than are^ standardized propor
different times.
wider-than-average shoulders,^ very^
narrow waists,
and
close-to-average heights
from sternum to knee-top.
All
appears
to (^) have originated
on (^) Naxos and exercised
erence for slender stature and linear surface pattern
made of Naxian marble. Boardman noted similarities
Thera kouros as a somewhat inept
imitation of Naxian
and Parian sculpture by
a local Theran carver.44 The
Melos kouros (ca.
also of Naxian marble,
Naxian sculptor
or a sculptor
under strong
Naxian
influence.45 The Tenea kouros (ca.
from
there is general agreement
about the Cycladic
connec
tions of this statue,
scholars have tended to associate
(^12) (ca. 530-520 (^) B.C.E., of^ "island^ marble"), found
the local style
came (^) under
cades between ca. 550 and 530 B.C.E.;
Naxian sculptors
became tyrant
on (^) Naxos and confiscated unfinished
works for resale ca. 540 B.C.E. (Arist. [Oec] 2.2.2,lines
appear
heavier than their Naxian counterparts,
with
B.C.E., (^) perhaps
under Parian influence,
but they
con
from the second quarter
of the sixth century.
After ca.
some Ptoon statues begin
to resemble the
International Style
of contemporary
Attic kouroi. The
43Stewart 1990, 111; Ridgway 1993,88.
44 Naxian marble: Kaltsas (^) 2002, 41, no.^ 22; see^ also Board
man 1978,71;
Kreikenbom (^) 2002,148.
45Pedley 1976,35-6;^
Boardman 1978,71;
Floren 1987,178;
Stewart 1990,119; (^) Ridgway 1993,85; Karanastassis^ 2002,181.
46Stewart (^) 1986, 61 (Paros-trained sculptor);
Floren (^) 1987,
(a
Corinthian sculptor inspired by
both Parian and
Naxian kouroi);
Martini (^) 1990, 213 (more
Parian than Nax
ian) ;Sturgeon 2006,47 (closest
to sculptures
from Paros and
Attica).
47Ridgwayl993,80,84-5. 48 Stewart (^) 1986,119.
2010] KOUROI^
Fig.
similar by
Guralnick: left,
Florence kouros (also
known as the Milani kouros), (^) prov
enance uncertain, island marble,
ca. (^560) B.C.E. Florence, Florence^ Archaeological Museum^ (H. Koppermann;?^
Rome,
neg. 1962.0001);^ right,
Ptoon 10 kouros, from the Ptoon sanctuary
in Boeotia, Naxian marble,
ca. 550 B.C.E. Athens, National
Archaeological Museum,^
inv. no.^10 (G. Fafalis; Kaltsas (^) 2002, cat.^ no.^ 44).
kouros and the three-times-life-sized statue^ of Isches
dated ca.^ 590-580 (^) B.C.E., the Isches kouros provides
he has notably
wide (^) shoulders, narrow^ waist, and verti
cal dimensions from knee to sternum that are a little
greater
than those of an^ average
man. By
contrast,
vertical dimensions.
Guralnick noted the same two basic proportional
the Egyptian
canon."57 This (^) characterization, however,
suggests
a causal relationship
that is not warranted. A
visual examination of all these statues shows immedi
parison
of the z-scores^ of Sounion and New York (^) (Guralnick
1985,401, (^) fig. 2) shows^ similar^ profiles,
but Sounion has over
all wider horizontal dimensions than New York.
55
Kyrieleis (1986,^ 38)^
first dated Isches to ca. 580-
B.C.E. but later (Kyrieleis
1996, (^) 57) revised^ the date^ to ca.
600-580 B.C.E. The statue is now^ in the Vathy
Museum on
Samos (ht.
as restored 4. m).
For bibliography,
see Kyrieleis
1986,35-41, (^) pis. 14-19; 1996; Floren^ 1987,
n. 31, pi. 30.5;
Kreikenbom (^) 2002,144,309, fig.
229a-c.
56Munich z-scores^ are measured from Guralnick (^) 1985,406,
fig. 7;
z-scores (^) of Isches are (^) taken from Guralnick 1996b, 521,
table 1.
"Guralnick (^) 1978,466.
Fig.
Isches in the Sanctuary
of
Hera on^ Samos, Samian (^) marble, ca.^ 590-580 B.C.E.
(E. Gehnen;?^ DAI^ Athens, (^) neg. 1988/363).
portions.
These resemblances are^ very (^) general; they
does not mean^ that these kouroi were^ proportioned
kouroi: ithas proportionally wider-than-average
shoul
ders,
a very
narrow (^) waist, narrower-than-average hips,
close-to-average
vertical dimensions between knees
and (^) sternum, and taller-than-average
head, lower
proportions
are common to idealized male figures
of
many
eras and cultures, (^) including
modern western
culture. The triangular
torso of male figures
on Greek
geometric
vases is an extreme case of this stylization.
elongation,
too, was^ a^ frequent
characteristic in Greek
and Roman art^ and in classicizing figures
thereafter.
thigh.
Since these exaggerated
dimensions were at
Guralnick's studies also demonstrate how the pro
portions
of kouroi evolve toward greater
naturalism.
z-score profiles,
we can see (^) how the relation between
shrinks,
the statues become more like the average
age
man (^) have the value of zero standard deviations.
Even the more^ naturalistic kouroi^ continue^ the^ gener
Guralnick's published
results and examined her^ inter
pretations
of those results. We now^ look^ at her method
Measured from Guralnick (^) 1985,403, fig.
59Cf.Boardman (^) 2006,20.
,i Hollander (^) 1978,98-9.
61 For geometric
bronze male figures,
see, (^) e.g., Schweitzer
pis.
130, 131, 136-39, 164, 165, 182-84, 185.^ For^ geo
metric vases, see, e.g.,
Schweitzer 1971, (^) pis. 35,36,40,69,^
62The z-scores^ are measured from charts^ inGuralnick^ 1985;
date of the Isches kouros: Kyrieleis 1996,57;^
date of Paros kou
ros: Stewart 1990, (^) pis. 118,119;
date of Ptoon 10: Kaltsas (^) 2002,
no. 44; all other
dates: Boardman 1978.
[AJA
114
Date Z-Score for Z-Score for
Sounion
Isches
Ram-bearer
Thera
Volomandra
Florence
Melos
Paros
Keratea
Tenea
Anavyssos
Kea
ca. 600-
ca. 590-
ca. (^) 590-
ca. (^580)
ca. 580
ca. (^580)
ca. (^) 570-
ca. 570-
ca. 560
ca. (^550)
ca. (^550)
ca. (^550)
ca. 550
ca. (^550)
ca. (^550)
ca. (^) 540-
ca. (^530)
ca. 530
ca. (^) 530-
ca. (^) 510-
ca. 510-
ca. (^) 510-
ca. (^) 490-
a The z-scores are expressed
in standard deviations for average
human males. For all kouroi^ except Isches,^
Guralnick presents
this information only
in z-score (^) charts; the values shown here were obtained by measuring
the distances on^ Guralnick's charts
and converting
the distances to standard deviations.
similar to Keratea and Paros^ than to Anavyssos, Kea,
kouros groups
soon (^) and consistently
with the Anavys
sos kouros in the two other cluster analyses
and is close
charts. Thus,
one (^) should interpret
Guralnick's clusters
ters, (^) groups
of objects
are most similar as aggregates;
measure to (^) cluster the objects
rather than minimiz
algorithm
used one of several different similarity
mea
larity
measure (^) used. Studies have shown that analyses
ferent similarity
measures produce
different results.
Given a particular
set of variables,
some (^) methods per
(where
B is the between-cluster covariance matrix)
has the advantage
of accounting
for covariance in the
computer
to perform
the algorithm
was an important
today)
.69For our^ purposes,
it is important
to note that
better even^ after several methods had been used.
Another important
consideration is the robustness
were put
in a^ cluster with other kouroi,
the variance
Cluster analysis
is also sensitive to (^) the exact (^) values of
data. Small changes
in the value of a variable can move
the data point
from one^ cluster to another.72 The re
sults of Guralnick's cluster analyses
thus depend
on (^) the
for the kouroi and the Egyptian
canon. (^) Guralnick first
roi; of^ these, she^ herself^ measured^ six, and^ she^ used
took several measurements and then used the average
expects
that the greater
the number of measurements
taken and averaged,
the more accurately
and precisely
the actual dimension can be estimated. The amount of
of the measurements from their mean. Guralnick does
not provide
these deviations or the number of measure
ments taken,
so we cannot (^) estimate this uncertainty;
was (^) measurement error of unknown magnitude
in the
have affected the clustering.
serious problems
with respect
to exact values because
cluster analyses
and the z-score profiles, however,^
Gur
either used an average
value or^ selected one^ value
68Friedman and Rubin (^) 1967; Everitt et al. 2001,65-7,94-9;
Baxter (^) 2003,103-4.
Seber 1984,
for example,
that Gural
nick extrapolated
the division into five clusters in her cluster
analyses
with 28 objects
because this task exceeded the capac
70Shennanl997,254.
71
Punj
and Stewart (^) 1983, 143-44; Baxter 1994, 165-66;
Baxter (^) 2003,102. Principal components analysis
is also sensi
tive to outliers (James
and McCulloch 1990,142;
Baxter 1994,
Morrison (^) 1990, 385: "small perturbations
in the data
might
lead to very
different clusters."
73 Guralnick 1970, 3, 40. Guralnick
measured Dermys
and
Kitylos,
and the Tenea, Volomandra, Melos, (^) Anavyssos, and
Munich kouroi. She used previously published
measurements
for the New York and Aristodikos kouroi.
Guralnick 1978,461.
75 Guralnick (^) 1970,108-24, tables 1-8.
76 Guralnick 1970, 41-2,127,
table 10. Guralnick also gives
a range
of 1.75 to 2.25 units for the height
of the face.
curve (^) from which the mean (^) and standard deviation for
each proportional
ratio could be computed.
However, Guralnick^ could^ not^ have^ plotted
a bell
dimension of the men. The authors were interested
in actual dimensions of real men, not proportional
re
representations
of human figures,
some (^) life-sized and
some larger
or smaller than life-sized. She therefore
actual (^) dimensions, and this means^ that she needed the
mean (^) and standard deviation for each proportional
ratio of real (^) men, rather than for each dimension,
to
compare
with the kouroi.
pose
we (^) wanted to compute
the "perfectly average"
university
nationwide with respect
to student-faculty
average student-faculty
ratio for^ a U.S. university.
This
expressing
the dimensions of each man^ as^ a^ ratio, and
then computing
the average
value of all the ratios.
of universities to get
the average
number of students
that Guralnick (^) used, does not^ give
the average
student
ratio of two averages,
S and F.
second method does not^ produce
a (^) random variable
puted
from the number of students and faculty
at (^) each
chart the z-scores of kouroi and korai in her articles
reconstruction of her procedure. Here,^
in addition
to a z-score profile
that compares (^) proportions
of the
Isches kouros with those of an^ average
Greek (^) man,
create the z-score profile;
the information is given
in
head-top
as (^) the proportioning
base. The standard de
viations for Greek men are given
in centimeters,
indi
the dimensions of Greek men.^ However, Guralnick's
data do not include the measures of interest for com
of measurement).
height
from knee-top
to head-top
as (^) the average
Greek
man.89 Then the difference between each converted
the (^) ratio of (^) shoulder width to knee-top-to-head-top
Suppose
one (^) school has 300 students and 50 faculty
mem
bers,
another has 600 students and (^20) faculty,
another has 700
students and 100 faculty,
and another has 300 students and 40
faculty. Using
the first procedure,
the average
value of the stu
dent-teacher ratio is 12.6 students per faculty
member. Using
the alternative procedure,
the average
number of (^) students
per
school (475 students) is^ divided^ by the average number^ of
faculty per
school (52.5 (^) faculty),
and the overall ratio is com
puted
as 9.0 students per (^) faculty
member.
87Guralnick 1996b, 512, (^) fig.
(z-score (^) profile); 521, table^
(data
used for the profile).
88Herzbergetal.
1963, (^153) (shoulderwdth.), 154 (chest
num), 129 (ht.
of nipples),
(ht.
of navel),
(ht.
of knee
top).
89E.g.,
letx
the shoulder width of Isches if the statue were
the same^ height
as an average
man. Then x/knee-top
to head
top
distance of the average
man
shoulder width of (^) Isches/
knee-top
to head-top
distance of Isches.
[AJA
114
Table 4. Dimensions of Isches (^) Kouros, Average
Dimensions and Standard Deviations of Greek Men,
and Z-Scores
Average
Greek
Standard Deviation
Z-Score of Isches for
Knee-Top
to Head-Top
Ht. knee-top
to navel 149.4 51.
(44.69 cm). (^) Expressed
as a z-score (i.e.,
in terms of
(i.e., 3.85/2.25).
Guralnick uses^ the z-scores
computed
in this way
to create z-score profiles
of the
Isches kouros.
the computed
mean and SD of this proportional
value
sions of each man^ measured, only
the average
value
and standard deviation for each dimension. (^) Guralnick,
therefore,
could not have produced
a (^) random vari
the proportional
values of the statue. (^) Hence, we^ must
conclude that the z-score^ profiles
in which the dimen
sions of the Isches kouros are compared
to the average
same must (^) be true (^) of the z-score profiles
in Guralnick's
charted with z-scores for proportional
values.
Guralnick (^) seems, for^ the most^ part,
to (^) consider the
Egyptian
second canon^ as^ an^ invariable and compre
hensive proportional system.
The surviving
evidence
neither as fixed nor as comprehensive
as her studies
contains several errors. The height
from top
of knee to ster
num is given
as (^) 240.7 in tables 1, 3a, 3b, 4,^ 5,
and 6 but ap
pears
as (^) 243.7 cm in table 2. The value of 243. produces
the
z-scores of 0.24 and -0. given
in table 1. For height
from top
of knee to navel,
the top-of-head
to top-of-knee
z-score (^) is given
as -1.13 in the (^) table. This should be +1.13,
and it is charted as
a plus
value in the z-score^ chart^ created^ from^ this data^ (Gur
alnick (^) 1996b, 512, fig.
1). For^ depth of chest, the base^
to top
of-head z-score is given
as -0.49; this should^ be^ -1.49.^ For^ base
to navel, the base to top-of-head
z-score is given
as 0.00;
this
should be+1.33.
Guralnick (^) 1996b, 512-15, figs.
The Egyptian
canon is treated as a single
set of values in
the cluster analyses
and the z-score^ analyses. Eight examples
of the Egyptian
canon are (^) charted in the principal compo
nents analyses (Guralnick^
figs.
6, (^) 7), and^ the
article on Boeotian kouroi mentions two sets of values for the
Egyptian
canon included in cluster analyses,
as if they
were
two additional statues (Guralnick 1996a, 39).