The Order of Man: A Biomathematical Anatomy of the Primates

CHAPTER 3 Mathematical 'Dissection' of Anatomies

CHAPTER 3 Mathematical 'Dissection 5 o f Anatomie s Abstract - Introductio n - Discoverin g structura l difference s Simple observatio n - Th e concep t o f a grou p - O f dat a o r o f organism s The concep t o f severa l group s — O f dat a o r o f organism s The concep t o f interface s betwee n group s Examples fro m rea l biologica l dat a - Discoverin g structura l difference s New method s - On e metho d - Th e biometri c approximatio n A secon d metho d - Th e pictoria l approac h - Ye t othe r method s The res t o f th e spectru m - Problems , fe w measurement s versu s man y Two dimension s versu s thre e - Keepin g geometr y versu s losin g i t Special versu s genera l morphometri c point s - Tw o specimen s versu s man y - Testin g Some biologica l implication s o f th e ne w method s - Summary. Abstract. In thi s chapte r w e revie w a variet y o f method s fo r describin g structura l difference s betwee n organisms . Assessment b y the human ey e and analysi s b y the mental acuity of the observer are briefly considered , as are some of the deficit s o f thi s approach . Structura l analysi s i s considere d firs t theoreticall y an d variou s problem s noted . Th e question o f th e ver y existenc e o f such problem s i n practic e i n biolog y an d anthropolog y i s confirme d b y example s stemming fro m studie s o f th e Primates . We then move to methods that involve simplifying visua l assessment by reducing it to measurement. Such method s often involve , however, mor e complex analyse s usin g computational method s of one kind or another; one of the mos t well-developed of such analytical approaches is the multivariate statistic. Some of the deficiencies of measurement an d analysis ar e reviewed . This discussion leads us to consider method s (a s the observational) tha t depend upo n visual data, bu t which appl y methods of analysis able to obtain information fro m a picture over and above that available to the eye and mind. A few of these methods have been used to investigate real biological problems; many have so far only been used as exemplars of what ma y b e don e i n th e future . Finally, w e retur n t o th e bes t use d o f the newe r techniques , multivariat e statistica l analysis , an d discus s i n som e further detai l problems in its usage, including the importance of the testing of all methods, whether complex or simple. Introduction Understanding anatomica l fragment s i n th e evolu tionary contex t depend s upo n first obtainin g in formation abou t th e structura l difference s tha t truly exis t an d second attempting t o mak e judge ments abou t th e biologica l meanin g o f th e discov ered differences . Classically , whe n assessmen t b y the huma n ey e an d judgement b y th e huma n min d are th e mai n tool s involved , thes e tw o phase s ma y not appea r t o b e clearl y separate d fro m on e another; th e entir e procedur e ma y b e don e i n on e intuitive leap, as it were, a method tha t is nevertheless rathe r powerful . Bu t a s othe r technique s fo r describing an d discoverin g structur e ar e adde d t o the powers o f human observation , an d a s a series of different argument s a t man y differen t level s be comes par t o f th e menta l proces s o f th e biologica l judgement, s o i t become s mor e an d mor e import ant tha t th e logi c of the tw o phase s b e separate , o r where no...