Figure B3.1.1. Six possible arrangements of three timepieces on cladograms. Note that each pair is redundant: the order in which the objects on each "V" is presented is irrelevant. Each pair is said to be "commutatively equivalent."

that, by the definition of a cladogram, a and b for each type are identical.This is because the groups at a node share the characters listed at that node, regardless of order For this reason, we really have only three cladograms to consider (Figure B3.1.2). One might at first wish to place the digital watch in the smallest subset, in the most derived position (as in types I and II), since it is the most modern, technologically advanced, and sophisticated of the three. Remember; however; how the cladogram is established: on the basis of shared, derived characters. Cladogram types I and II say that the digital watch shares the most characters in common with either a wind-up watch (type I) or a quartz watch (type II). A look at the characters themselves suggests that this is not correct: wind-up and quartz watches are both analogue watches (have a dial with moving, mechanical hands) and their internal mechanisms consist of complex gears and cogs to drive the hands at an appropriate speed.The digital watch, on the other hand, consists of microcircuitry and a microchip, with essentially no moving parts. It is apparently something very different, and from its characters, bears little relationship to the other "watches."

What is the digital watch? In an evolutionary sense, it is really a computer masquerading (or functioning) as a timepiece.The computer has been put in a case, and a watchband has been added, but fundamentally this "watch" is really a computer In our hypothesis of relationship, the watchbands and cases of watches have evolved independently twice (once in computers and once in watches), rather than the guts of the instrument, itself, having evolved two times.That the watchbands and cases evolved twice independently is a more parsimonious hypothesis than arguing that the distinctive and complex internal mechanisms (themselves consisting of many hundreds of characters) of the watches evolved twice independently.

What, then, is a watch? If the term "watch" includes digital watches as well as the other two more conventional varieties, then it should also

(continued on p. 58)

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