Transcript Document

Symmetry and roughness in archaeology
Archaeological evidences from the Lower
Paleolithic for the development of the human
capability to produce symmetric and smoothedged shapes
David Avnir, Na’ama Goren-Inbar, Avshalom Karasik,
Idit Saragusti, Ilan Sharon, Uzy Smilansky
Financial support: National Foundation for Joint Research Projects between Natural
Sciences and Archaeology
The Weizmann Institute of Science
Why symmetry and roughness?
The Lower Paleolithic:
- A very long, nearly stagnant period, highly
homogeneous, both chronologically and
geographically.
- The changes over time and the variations
over space during this period, minor as
these may be, are highly significant and
informative for studies of past human
behaviors and their cognitive abilities.
A handaxe
Handaxes first appear
in the archaeological
record ca. 1.6-1.7 mya.
in East African sites
assigned to the
Acheulian and
Developed Oldowan
Techno-Complexes
Homo erectus (or Homo ergaster)
Homo heidelbergensis
Archaic Homo sapiens
 Handaxes can be found over a vast
geographical area.
 Handaxes were produced during a very
long period of time.
 Handaxes were produced by various
hominid types.
The working hypotheses
The degree of symmetry of handaxe
shapes increased over time
The degree of roughness of handaxe
shapes decreased over time
These chronological changes emerged from, and
are thus manifestations of, developments in the
technical and cognitive abilities of those who
produced the handaxes

B1
B1
W1
L
B2
L1
0.8
T2
0.5
T1
T
0.2
L2
W
Mirror symmetry/ bilateral symmetry/ reflection
symmetry:
A configuration is bilaterally symmetric, if one
side of it is the exact reflection of the other
side, with respect to a plane (in three-dimensional
configurations) or an axis (in two-dimensional
configurations), which are therefore termed the
‘reflection plane’ or the ‘reflection axis’,
respectively.
The Continuous Symmetry Measurement:
Find the minimal distances that the vertices of a shape
have to undergo, in order for the shape to attain the
desired symmetry.
Given n vertices of the original configuration,
located at Pi, the symmetry value, S(σ), of this
configuration is its distance from the nearest
bilateral-symmetric configuration:
n
100
ˆ
S(σ) =
Pi  P

i
n i 1
2
where Pˆ i are the corresponding points in the nearest
bilateral-symmetric configuration.
P0
Pˆ0
P '0
Size normalization
P2
Symmetry transform
P '2
P1
(a)
Pˆ2
P '1
(b)
(c)
Pˆ1
Pˆ0
P '0
P '2
(d)
Pˆ2
P '1
Pˆ1
The basic features of the Continuous Symmetry Measure (CSM): In
order to evaluate how much bilaterality (mirror symmetry) is there
in the triangle (a), its size is normalized (b), and the mirror
symmetric structure (c) which is nearest to (b) is found. (d): The
S(s) value is calculated from the minimal distance between (b) and
(c). In this case, S(s) =0.32
(a)
S(s)=0.18
(b)
S(s)=0.77
(c)
S(s)=0.31
(d)
S(s)=0.39
P2
P2
~
P2
P1
~
P1  P1
Pˆ2
~
P2
Pˆ1
~
P1
Pˆ1
‘Ubeidiya
S(s)=0.46
Gesher Benot Ya’aqov
S(s)=0.06
Ma’ayan Barukh
S(s)=0.0067
Symmetry measurement based on the
curvature function
-The curvature is a periodic function on the
contour.
-In order to measure the degree of symmetry
of the contour, we seek the point on the
contour in which the difference between the
curvature function to its right and to its left
is the minimal one.
- The symmetry value, S(σ), is calculated as the
distance between the rightward and the
leftward functions.
Symmetry measurement based on the curvature function
Roughness measurement
Roughness:

a measure of the variations in corners,
edges and faces.

a measure of directional changes in the
object’s surface (in three dimensions)
or contour (in two dimensions).
The smoothest curves are convex.
Any further structure of the curve is associated
with the appearance of concave sections; the
more there are, the more complex and rough the
curve is.
Roughness can be determined by the
frequency and amplitude of the
transitions between convex and concave
sections along the contour (inflection
points).
-
-The relative direction of the tangent
vectors at successive inflection points
is a measure of the local roughness –
the larger the mismatch angle, the
deeper the section under consideration.
S3
 2,3
S2
 1,2
S1
Inflection points (S1, S2, S3), in a convex section (S1, S2)
and in a concave section (S2, S3).
The concavity is defined as the sum of mismatch
angles over all the concave sections of the
contour:
1
concavity  
k (s )1  sign k (s ) ds

2
Roughness is a scale-dependent
concept — a contour can be smooth on
the visible scale, but very rough on the
scale of mineral granularity.
Thus, the first step in roughness
analysis consists of an
archaeologically-motivated assessment
of the scale (or scales) of interest.
Roughness measuring:
-The contour under study is numerically
smoothed, by filtering all structures,
which are smaller than the prescribed
scale.
- The concavity of the smoothed shape
is measured.
Roughness measuring
Con. = 0.121
Con. = 0.003
Data Acquisition:
All the methods require that the contour to be
analyzed be represented by a set of coordinate
points. These sets are achieved by the
following process:
1. The objects to be analyzed (handaxes) are laid
on a light box, either on one of their faces (for
their plan-view contours) or on their side (for the
side-view contours).
2. The handaxes are photographed from a
fixed distance of 30 cm. using a digital
camera, at a resolution of 300 dots per inch.
The results are dark shadows of the
handaxes on a light background.
3. The photographs are transferred to a PC, and traced
to generate bit-map (BMP) files containing only the
contour lines (as black pixels on a white background).
4. The BMP files are analyzed by a Matlab program
which automatically vectorizes the BMP data and
smooth it, resulting in sets of X,Y coordinates.
The studied samples in chronological
order, from the earliest to the latest:
‘Ubediya (UB) (n=45) => Gesher Benot
Ya’aqov (GBY) (n=96)=> Ma’ayan
Barukh (MB) (n=50)=> Tabun bed 90
(T90) (n=45) => Tabun Layer E (Te)
(n=79).

0.80
UB
%
0.70
90
70
UB
60
GBY
MB
50
T90
40
Te
30
20
10
0
0.60
0.50
Symmetry value
80
Degree of symmetry
%
GBY
0.40
Te
0.30
T90
MB
0.20
0.10
Symmetry value
Degree of symmetry
Frequency distribution of the
symmetry values, plan-view
contours.
0.71- 0.75
0.65- 0.70
0.60- 0.65
0.55- 0.60
0.50- 0.55
0.45- 0.50
0.40- 0.45
0.35- 0.40
0.30- 0.35
0.25- 0.30
0.20- 0.25
0.15- 0.20
0.10- 0.15
0.05- 0.10
to 0.05
0.00
UB
GBY
MB
T90
Te
Time
Means and ranges of the symmetry values,
plan-view contours.
One-way analysis of variance for the degree of symmetry of
the plan-view contours: F = 18.045;  < 0.01% i.e. statistically
significant (at the 0.05 level) differences between the five
studied samples.
Results of pair-wise multiple comparisons test between the five
samples (Tamhane’s T2 post-hoc test). Mean differences (column
minus row).
UB
UB
GBY
MB
T90
Te
-
-0.090*
-0.107*
-0.084*
GBY
0.090*
-
-0.017*
0.006
0.019
MB
0.107*
0.017*
-
0.023*
0.036*
T90
0.084*
-0.006
-0.023*
-
0.013
Te
0.071*
-0.019
-0.036*
-0.013
-
* The mean difference is significant at the 0.05 level.
-0.071*
%
45
UB
0.25
UB
GBY
40
MB
35
T90
Te
T 90
Te
GBY
0.20
T90
Te
Degree of roughness
30
25
20
0.15
MB
0.10
15
10
0.05
5
0
0.22-0.24
0.20-0.22
0.18-0.20
0.16-0.18
0.14-0.16
0.12-0.14
0.10-0.12
0.08-0.10
0.06-0.08
0.04-0.06
0.02-0.04
0.00
to 0.02
%
Degree of roughness
Degree of roughness
Frequency distribution of the
degree of roughness, plan-view
contours.
UB
GBY
MB
Time
Means and ranges of the degree of
roughness, plan-view contours.
One-way analysis of variance for the degree of roughness of the
plan-view contours: F = 23.206;  < 0.001 i.e. statistically
significant (at the 0.05 level) differences between the five studied
samples.
Results of pair-wise multiple comparisons test between the five
samples (Tamhane’s T2 post-hoc test). Mean differences (column
minus row).
UB
GBY
-0.037*
MB
T90
Te
UB
-
-0.065*
-0.019
-0.020
GBY
0.037*
-
-0.028*
0.018
0.017
MB
0.065*
0.028*
-
0.046*
0.045*
T90
0.019
-0.018
-0.046*
-
-0.001
Te
0.020
-0.017
-0.045*
0.001
-
*The mean difference is significant at the 0.05 level.
- The symmetry and roughness values generally
tend to decrease over time, i.e. handaxes
generally become more symmetric and less
rough.
- These trends are seen only among the UB,
GBY and MB samples, while the two Tabun
samples, exhibiting higher values than could be
expected, considering their assumed ages,
deviate from these general trends.
- The spread of the values generally
decreases over time. Here again, the two
Tabun samples deviate from this general
trend.
Why is it interesting at all?
- What factors can account for these
phenomena?
-What changed through this period of time,
that might explain the observed trends?
-How can those cases that deviate from these
trends be explained?
- Why increasing symmetry and decreasing
roughness?
What is the evolutionary meaning of these
changes?
‘Low level’ factors:
- Raw material: type, size, shape
- Blank type
- Intensity of flaking (amount of scars)
- Type of percussor (hard hammer vs. soft hammer)
- Function and functioning
‘High level’ factors:
- Cognitive abilities
- Factors emerging from the social context (social
norms…)
Site
Tested variables
UB (N=43)
Pearson’s correlation
coefficient
Sig.
(2-tailed)
-0.008
0.958
GBY (N=94)
Quantity of retouch
0.060
0.566
MB (N=50)
to
-0.217
0.130
T90 (N=45)
Symmetry plan-view
-0.020
0.897
0.077
0.497
Te (N=79)
Entire sample (N=311)
-0.027
0.636
Conclusions:
- None of the tested ‘low level’ factors can be clearly
pinpointed as a necessary or sufficient condition for
producing highly symmetric and smoothed-edges
handaxes.
- None of these variables can be used to explain the
observed variability in the degrees of symmetry and
roughness.
- Although some of the tested variables must have
imposed some constraints on the shapes of the handaxes,
in most cases the producers of these artifacts could
potentially overcome these constraints or avoid them
altogether. Occasionally, this might have required
additional investment of time and energy.
- Had highly symmetric and smoothed-edges handaxes
been equally desired, and the cognitive and technical
abilities of imposing these properties been the same,
the ‘low-level’ factors did not present any severe,
unavoidable restrictions.
ThereforeThe final shapes of the studied handaxes represent,
above all, their producers’ priorities and mental
abilities.
Artifacts have long been considered as a highly
valuable source of information for studying the
evolution, and thus the construction, of the modern
mind.
-The ability to perceive bilateral symmetry is
not uniquely human (mate selection…).
- Some animals are known to construct
complex and symmetric patterns, like
the honeycomb. These, however, do not
require an idea, or a concept of
symmetry, because they are
considered a direct consequence of
rules followed in a rote fashion or of a
motor pattern.
Non-human primates do not produce symmetry (in
nature) and are probably incapable of doing so, as
evidenced by studies of ape art in captivity.
The ability to consciously produce symmetry is
uniquely human.
When did this ability evolved, and what kind of
abilities are required to consciously produce
symmetric shape?
- No clear evidence for the ability to impose
symmetry from the earliest industries, between
ca. 2.5 mya, and ca. 1.5 mya.
- From ca. 1.5 mya. onwards, the archaeological
evidence indicates that this ability increased.
Looking from the ‘minimum necessary competence’
perspective, i.e. the minimal cognitive abilities
required for the production of specific artifacts,
the current data certainly indicates that the
abilities for producing symmetric and smooth
shapes increased throughout the Lower
Paleolithic.
Possible explanation – the main development is in the ability of
fine motor-control.
- By the time of the earliest Oldowan Techno-Complex,
hominids already had a high ability of fine motor control as
indicated by the finely retouched flake tools.
- This implies that no constraints were imposed by this ability
on the production of Oldowan artifacts, i.e., early artifacts
are often crude because of (other) cognitive limitations, and
any subsequent developments in stone-tool production were
mainly the result of cognitive developments.
What kind of cognitive abilities are required to
produce highly symmetric artifacts, and what
can we infer from these abilities about the
evolution of the human mind in general?
Early handaxes (‘Ubeidiya)
– ‘global’ and two-dimensional symmetry: “…one
lateral edge has been trimmed to copy the other.
But the inverted copy is not a precise duplicate.
It reproduces the qualitative characteristics of
the shape, but it is not a quantitative duplicate”
(Wynn, 2000).
The spatial perception-cognition abilities
required to produce such symmetry:
the ability to reverse a configuration around a
midline. Reversal of order is a topological notion
— topologically, ABC and CBA are the same
order, only reversed, i.e. ABC/CBA is symmetry.
Late handaxes (Ma’ayan Barukh):
- Congruent symmetry - the mirrored sides are quantitative
duplicates of each other
- Three-dimensional symmetry: some of the handaxes have a
virtual infinity of symmetric cross-sections (longitudinal and
transversal).
The spatial perception-cognition abilities required to produce such
symmetries:
Visual projection, i.e. the understanding and coordination of multiple points of view.
- Mental rotation
“During trimming, the modification of the surface to regularize the
shape of the cross section from one point of view could not be allowed to
ruin other cross sections, most of which could not be directly observed.
These unobservable cross sections must have been purely mental
constructs” (Wynn, 1989).
- The concept of “Euclidean” space, i.e. a notion of spatial quantity.
Can we say something more general
about the level of intelligent of the
handaxes producers?
Two schools of mind theories:
The ‘holistic’ school:
- The mind is a holistic structure, which
constitutes, or consists of a generalpurpose intelligence.
- Although this intelligence is applied in many
different ways to various behaviors, there is an
underlying consistency across the various behaviors.
- This general intelligence may be built, according to
some models, hierarchically, from several
superimposed ‘layers’, each of which is achieved at a
different developmental stage.
- Each of these ’layers’ is composed of an entire
series of associated cognitive abilities, which are
assumed to coalesce together once that cognitive
stage is achieved
The 'modular' school:
- The mind is constructed in a modular manner, from
several distinct, domain-specific modules, faculties
or ‘intelligences’.
- Each of these modules is dedicated to a specific
kind of mental task.
Generally, the more specialized a claimed
module or intelligence is, the narrower the
range of behaviors that it will be manifested in,
hence reducing the chances of inferring it from
the archaeological record, unless it is directly
related to tool behavior.
And vice versa – the more generalized an
intelligence is claimed to be the wider the
range of behaviors it will be manifested in,
some of which may leave identifiable traces in
the record.
Therefore cognitive inferences drawn on artifacts
are heavily dependent upon the specific
mind theory adopted in such studies
?
What can we conclude from the results?
-The data presented in the current study
suggests a gradual development of the
ability to produce symmetric shapes (and
not a ‘punctuated-equilibrium’ process).
- Whatever cognitive abilities are inferred
from the archaeological data, these have
probably evolved gradually throughout a
very long period of time.
The timing of such cognitive developments is a crucial
question, mainly due to its possible implications as for
the identity of the relevant hominid species
participating in such a process:
- Late development - archaic Homo sapiens and/or
Homo heidelbergensis .
- Early development (at least ca. 750,000 years ago,
the age of GBY) - Homo erectus (or Homo ergaster)
as the probable candidate.
- In any case, it implies that these abilities were
shared among all the species to have diverged from
whoever the candidate is to have possessed such
cognitive abilities.
The evolutionary meaning
The ‘handicap principle’
Plans for the future:
Analyze additional assemblages
Quantitative study of the question of
standardization
Additional study of the cognitive questions….
The end