Applying Phylogenetic Methods to Analyse
Ancient Chinese Oracle-Bone Characters
Related to Animals
A report on recent joint work
with ZENG Zhenbing and Stefan Grünewald
The Evolution of Regulation
Higher evolution requires more regulation:
• The Pythagorean Theorem
24 words
• The Lord’s Prayer
66 words
• Archimedes’ Principle
67 words
• The 10 Commandments
179 words
• US Declaration of Independence
1 300 words
• US Constitution
7 818 words
• EU directive on the sale of cabbage
26 911 words
60 oracle-bone characters for animals from the late
Shang Dynasty (about 3300 BP, that is, the time of
the legendary Troja war)
The English translation of the first 20 characters
01: dragon
02: phoenix
03: unicorn
04: caterpillar (perhaps also unicorn)
05: migrating bird (perhaps also just the cuckoo)
06: seashell
07: worm
08: roundworm
09: scorpion
10: fish
11: frog
12: turtle
13: crocodile
14: snake
15: python
16: mouse
17: rabbit
18: macaque
19: elephant
20: leopard
The English translation of the next 25 characters
21: bear
22: tiger
23: trapped wolf
24: fox
25: dog
26: shaggy-haired dog
27: deer
28: hornless deer 29: fawn
30: wild pig
31: pig
32: piglet
33: boar
34: barrow
35: Père David’s deer
36: pinto
37: horse
38: black horse with yellow back
39: galloping horse
40: ram
41: bison
42: ox
43: cattle
44: female
45: male
The English translation of the last 15 characters
46: cattle, penned up for sacrifice
47 & 48: bird
49: short-tailed bird
50: owl
51: kite
52: stork
53: eagle-owl
54: wild duck
55: pheasant
56: chicken
57: magpie
58: sparrow
59: swallow
60: wagtail
A distance-based cognitive network for the 60
ancient animal characters listed above
mouse
hornless deer
chinese unicorn
deer
bison
fawn
macaque
elk
tiger
100.0
horse leopard
elephant
rabbit
insect without leg
bear
bird1
frog
bird2
turtle worm
crocodile
swallow
owl
stork
magpie
chicken
phoenix
fowl
fish
scorpion
dragon
sparrow
cattle
sheep
roundworm
python
Eurasian eagle-owl
seashell
wild duck
pig,dog
boar
cuckoo
male ox
wagtail
pheasant
shaggyhaired dog
female ox
penned up ox
large ox
kite(milvus)
castrated pig
piglet
fox
varicoloured horse
snake
galloping horse
wolf
swine
yellowback black horse
How can such networkss be constructed?
This question relates to a fundamental problem coming up in many
areas of pure and, in particular, applied mathematics:
How can we analyse and represent (finite) metric spaces in a
canonical (non-approximative) and meaningful way?
More specifically: Is there an analogue to Fourier Theory for
extracting the “essential” information embedded in a distance
table?
And what could play the role of the “simple harmonics”?
Where could this be relevant?
Such a Fourier Theory for extracting the “essential” information
embedded in a distance table would be relevant for, e.g.,
• phylogenetic analysis and, in particular, the (re-)construction of
phylogenetic trees,
• similarity analysis, in particular, multidimensional scaling of
similarity data,
• classification,
• pattern recognition,
• “toponomics” (i.e., the study of the spatio-temporal distribution
of proteins),
• and the analysis of the organisation of perceptual processing
procedures.
Tight-Span and Split Decomposition Theory
Moreover, some such Fourier Theory exists: indeed, tight-span
and split-decomposition theory offer some kind of the required
Fourier Theory for metric spaces.
More specifically, they allow us to canonically decompose any
finite metric into a sum of “weakly compatible” weighted split
metrics (that play the role of the simple harmonics in
split-decomposition theory), and some (hopefully small)
split-indecomposable residue:
The NeighbourNet diagram above: a representation
of a system of “weakly compatible” weighted splits
mouse
hornless deer
chinese unicorn
deer
bison
fawn
macaque
elk
tiger
100.0
horse leopard
elephant
rabbit
insect without leg
bear
bird1
frog
bird2
turtle worm
crocodile
swallow
owl
stork
magpie
chicken
phoenix
fowl
fish
scorpion
dragon
sparrow
cattle
sheep
roundworm
python
Eurasian eagle-owl
seashell
wild duck
pig,dog
boar
cuckoo
male ox
wagtail
pheasant
shaggyhaired dog
female ox
penned up ox
large ox
kite(milvus)
castrated pig
piglet
fox
varicoloured horse
snake
galloping horse
wolf
swine
yellowback black horse
Distance measures for the ancient characters
For its construction, we need to define appropriate distance
measures for our 60 characters.
To this end, we will restrict our attention to five rather distinct and
independent categories of features that any such character may
exhibit:
The five distinct categories of character features
(i) The 6 distinct types of augmenting a compound character’s
radical by additional marks,
(ii) the 33 distinct versions of representing the shape of an
animal0 s head,
(iii) the 6 distinct versions of the body outline,
(iv) the 10 distinct combinations of specifically emphasised
attributes of the body (legs, feathers/fins/manes, tail, and/or
skin texture),
(v) and the 24 distinct marks (post-, super-, pre-, and subscripts)
that may – or may not – be attached to a character0 s radical.
From feature categories to distance measures
Classifying our 60 characters according to these five distinct
feature categories yields five distinct distance measures whose
weighted linear combinations yield a 5-parameter family of
integrated distance measures.
From distance measures to circular orderings to
groupings
And, given any such linear combination, one can
• use e.g. the NeighbourNet algorithm as proposed by David
Bryant and Vincent Moulton to construct and visualise the
associated best-fitting “circular” networks,
• consider the groupings suggested by them,
• and compare these groupings with known traditional groupings.
E.g., the diagram we saw already
mouse
hornless deer
chinese unicorn
deer
bison
fawn
macaque
elk
tiger
100.0
horse leopard
elephant
rabbit
insect without leg
bear
bird1
frog
bird2
turtle worm
crocodile
swallow
owl
stork
magpie
chicken
phoenix
fowl
fish
scorpion
dragon
sparrow
cattle
sheep
roundworm
python
Eurasian eagle-owl
seashell
wild duck
pig,dog
boar
cuckoo
male ox
wagtail
pheasant
shaggyhaired dog
female ox
castrated pig
penned up ox
large ox
kite(milvus)
piglet
fox
varicoloured horse
snake
galloping horse
wolf
swine
yellowback black horse
yields the following groupings:
Sources of traditional groupings to which this grouping could be
compared:
• the ErYa, the oldest surviving Chinese encyclopedia and, thus,
also the oldest surviving encyclopedia in the world, probably
compiled during the late Warring States period (i.e., in the 3rd
century BC) on the basis of much earlier texts going back perhaps
even to the early West Zhou Dynasty (i.e., around 1.000 BC)
• the work of Aristoteles from the 4th century BC,
• the herbal books that were, from the late 15th century (that is,
soon after book printing had been re-invented in Europe in 1439)
to the 18th century, rather popular in Europe.
• and LI Shizhen0 s fundamental treatise Compendium of
Materia Medica from 1578 AD.
The grouping a herbal book from 1557
For instance, in its third part Natur und Eigenschafft der
vierfuessigen Thiere der Erden (Nature and features of
quadrupeds and other animals living on land), a popular herbal
book from 1557 compiled by Adam Lonitzer (1528 – 1586)
presents the following list of land animals (with nice woodcuts,
representing even unicorns, basilisks, dragons, and elephants all of
which must have been equally strange to the author):
Human, ram and sheep, ox and cow, aurochs (not yet extinct at
that time), buffalo, goat and billy goat, pig, wild pig, horse,
donkey, mule, dog, cat, simian monkey and vervet monkey,
baboon, lion, panther and leopard, tiger, camel, beaver, stag, deer,
chamois, musk deer, civet cat, unicorn, rhinoceros, elefant, moose,
bear, fox, squirrel, badger, hedgehog, porcupine, hare and rabbit,
lynx, wolf, otter, weasel, marten, mouse and shrew, rat, dormouse,
hamster, marmot, mole, frog, toad, tortoise, scorpion, crocodile,
gecko (scinci officinarum or crocodili terrestres), serpent, basilisk,
dragon, spider, lizard and newt, locust, silk worm, ant, cricket,
roundworm (lumbricus), woodlouse, flea, louse, and snail.
Clearly, the chosen order is by no means random and suggests a
certain implicit view of some intrinsic animal relationships.
A colour code describing the ErYa grouping
To compare the distance-induced groupings derived using
split-decomposition theory with those given by the ErYa, we use
purple for the characters representing insects and worms (Chapter 15)
red for the 9 characters representing fishes etc. (Chapter 16)
green for the 16 characters representing birds (Chapter 17)
blue for the 16 characters representing wild beasts (Chapter 18)
black for the 16 characters representing livestock (Chapter 19)
The distribution of the ErYa groups along the circular
ordering induced by our NeighbourNet diagram
Comparing this ordering with a random circular order
Some more colour rings induced by the NeighbourNet
algorithm for other parameter settings
And more of this ...
Summary
Our ‘phylogenetic’ similarity analysis of oracle-bone characters
related to animals indicates that these pictographs are based on an
intuitive understanding of animal classification that is not too far
from the classification system of the ErYa which it predates by one
millennium which in turn predates classification systems in the
West by another millennium.