h=2
Figure 4: The simplest binary tree for “Alf must jump high”
ity discussion is limited to active voice sentences with only determiners, nouns,
transitive verbs, adjectives, and prepositions. Inclusion of case theory, COMP,
INFL,.. might be of interest but would complicate matters. In section 4 the
singular matrix F for features is given. F is not an ultrametric matrix and
there appears to be no relation to U. In section 5 it is shown that the no-
tion of c-command is equivalent to an ultrametric minimum distance. This
allows a new definition of government to be given. In appendix 7 other lin-
guistic hierarchies are discussed; in particular there appears to be at least two
separate occurrences of culturally determined partial ordered hierarchies - the
accessibility hierarchy for relative clauses and the universal colour ordering. For
completion in appendix 7 there is a very briefly account of what these hierar-
chies are, a comparison and contrasting of them, and the speculation that they
are specific examples of a grand cultural hierarchy. The question arises of why
such hierarchies should exist, and it might be because they reduce the amount
of memory needed to process information by clumping information together in
the style of Miller (1956) [25]. For a more recent reference see Cowan (2001) [9].
A hierarchy is an example of a representation as discussed by Roberts (2005)
[33].
2 XX Structure Implies No Equilateral Triangles
2.1 Binary and N-ary Branching for simple sentences
X structure implies binary branching Haegeman (1994) p.139 [13], and the
figure 8. To see what this implies for ultrametric distances consider all five
species of binary branched tree. The fixed word order in ’Alf must jump
high’ reduces the total number of possible matrices form 15 to 8. The first
has diagram Figure 4 (compare Haegeman (1994) p.141 [13] diagram 84a) and
corresponding matrix: