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 66 words • The Lord’s Prayer • Archimedes’ Principle 67 words • The 10 Commandments 179 words • US Declaration of Independence 1 300 words 7 818 words • US Constitution • 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 bison fawn tiger deer macaque 100.0 leopard horse elk elephant rabbit insect without leg bear bird1 frog bird2 turtle worm crocodile owl stork swallow magpie fowl chicken fish phoenix scorpion dragon sparrow cattle sheep roundworm python seashell Eurasian eagle-owl wild duck pig,dog cuckoo boar male ox wagtail pheasant shaggyhaired dog female ox kite(milvus) castrated pig penned up ox large ox piglet fox varicoloured horse snake galloping horse wolf yellowback black horse swine
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 bison fawn tiger deer macaque 100.0 leopard horse elk elephant rabbit insect without leg bear bird1 frog bird2 turtle worm crocodile owl stork swallow magpie fowl chicken fish phoenix scorpion dragon sparrow cattle sheep roundworm python seashell Eurasian eagle-owl wild duck pig,dog cuckoo boar male ox wagtail pheasant shaggyhaired dog female ox kite(milvus) castrated pig penned up ox large ox piglet fox varicoloured horse snake galloping horse wolf yellowback black horse swine
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 animal ′ 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 character ′ 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 bison fawn tiger deer macaque 100.0 leopard horse elk elephant rabbit insect without leg bear bird1 frog bird2 turtle worm crocodile owl stork swallow magpie fowl chicken fish phoenix scorpion dragon sparrow cattle sheep roundworm python Eurasian eagle-owl seashell wild duck pig,dog boar cuckoo male ox wagtail pheasant shaggyhaired dog kite(milvus) female ox castrated pig penned up ox large ox piglet fox varicoloured horse snake galloping horse wolf yellowback black horse swine
yields the following groupings:
Sources of traditional groupings to which this grouping could be compared: • the ErY a , 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 Shizhen ′ 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 ErY a grouping To compare the distance-induced groupings derived using split-decomposition theory with those given by the ErY a , 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 ErY a 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 ...
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