ed to perfectly convey the distance information. However, as it is hard for the human mind to cope with more than three spatial dimensions at once, it is necessary to settle for a three-dimensional representation:
 The proportion of variance figure for this analysis is 0.42, meaning that three dimensions explain 42% of the distance information contained in the matrix. This map is optimal in the sense that it is the best representation of the distance information that can be achieved with only three dimensions.
 Chatfield and Collins describe cluster analysis as follows:
The basic aim of cluster analysis is to find the “natural groupings,” if any, of a set of individuals (or objects, or points, or units, or whatever)... More formally, cluster analysis aims to allocate a set of individuals to a set of mutually exclusive, exhaustive, groups such that individuals within a group are similar to one another while individuals in different groups are dissimilar. This set of groups is usually called a partition.
 This mode of analysis needs to be used with discretion. Even if the data set does not have a natural group structure, clustering techniques will still divide its members into groups. As Chatfield and Collins say, “The ability of clustering methods to detect non-existent clusters is well established.” There are numerous clustering techniques, each liable to produce its own set of clusters when applied to the same data. Subjecting the distance matrix for Australian cities to a mode called “divisive clustering” produces the following result:
 According to this chart, called a “dendrogram,” Australian cities can be partitioned in a number of ways. In order to define a partition, the tree is “chopped” at some vertical level to produce a series of clusters. For example, cutting across at a height of about 3500 km produces two clusters: one comprised of Adelaide, Hobart, Melbourne, Brisbane, and Sydney; the other containing Alice Springs, Darwin, and Perth. Other numbers of clusters can be produced by chopping the tree at other heights.
 Applying divisive clustering to the distance matrix for Hebrews produces this dendrogram:
 An attempt will now be made to describe the broad outlines of what might be called the “textual space” occupied by the witnesses of Hebrews. Being based on so few variation units, sampling errors are relatively large. All observations made from these analysis results are therefore provisional.
 The MDS map reveals a structure in which some regions have a higher density of witnesses than others. There is a general correspondence between these regions of higher density and clusters found in the dendrogram but it is hard to say how many clusters there are. Indeed, this dendrogram is similar to one concerning which Chatfield and Collins say, “there appears to be no natural partition.” It seems, therefore, that there is no clear number of clusters for the Hebrews data.
 To make an arbitrary choice, the dendrogram can be chopped at a height of just under 0.5 to produce six clusters:
UBS (i.e. the eclectic text preferred by the UBS editors), P46, B
01 (Sinaiticus), A, C, 33, 81, 436, 2464, cop-sa (Sahidic Coptic), arm (Armenian)
it-ar, it-b, it-comp (i.e. Old Latins); vg-cl, vg-st, vg-ww (i.e. editions of the Vulgate); cop-bo (Bohairic Coptic), geo-1 (First Georgian)
K, L, P, 044, 075, 0150, 104, 256, 263, 365, 424, 459, 1241, 1319, 1573, 1852, 1912, 1962, 2127, 2200, Byz (Byzantine majority), Lect (majority of lectionaries), syr-h (Harclean Syriac), eth-pp, eth-TH (i.e. editions of the Ethiopic), geo-2 (Second Georgian), slav (Slavonic), Chrysostom
6, 1739, 1881, syr-p (Peshitta Syriac)
 A number of these clusters are evocative of conventional “text-types” often used to describe New Testament witnesses, namely “primary Alexandrian” (P46, B), “secondary Alexandrian” (e.g. A, C, 33, 81), “Western” (e.g. Old Latins it-ar, it-b, it-comp), and “Byzantine” (K, L, ..., Chrysostom). At the same time, the dendrogram has a number of unexpected features: the cluster associated with “primary Alexandrian” witnesses is quite 