Darwin-L Message Log 6:48 (February 1994)

Academic Discussion on the History and Theory of the Historical Sciences

This is one message from the Archives of Darwin-L (1993–1997), a professional discussion group on the history and theory of the historical sciences.

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<6:48>From p_stevens@nocmsmgw.harvard.edu  Thu Feb 10 07:57:16 1994

Date: 10 Feb 1994 08:56:50 U
From: "p stevens" <p_stevens@nocmsmgw.harvard.edu>
Subject: Groups, grouping and numeralogy.
To: darwin-l@ukanaix.cc.ukans.edu

To say that "the magic number seven" says it all is indeed an overstatement, as
Bob Richardson rightly points out.  But it is impressive to see how 'classical"
systematists like Antoine Laurent de Jussieu and George Bentham are explicitly
breaking the botanical universe up into pieces of "convenient" size.
Interestingly, the two had rather different ideas as to what they thought these
groups represented.  Similarly, the size distribution of taxa in Adanson's and
Jussieu's classifications are almost identical, although the two deal with
different numbers of genera.  Also, while we are thinking about numbers, folk
classifications of plants and animals generally include 500 or so members (see
Brent Berlin, for example), or so the mythology goes, and this would agree with
the upper limits of places in the folk landscape...

I don't think that any of this necessarily bears on the "reality" of the groups
recognised by systematists.  Thus if a late 18th-early 19th C. systematist
(like Bentham) believes that nature consists of discrete groups of various
sizes, a large genus is simply a genus with a large number of species, and the
divisions bounding the small genera into which somebody else divides that genus
represent the limits of the "natural" subgroupings found within that genus.  On
the other hand, if I believe that nature is continuous (rather like Jussieu),
then any taxon will have limits that are not found in nature - but a large
genus is no more or less "unnatural" than the smaller genera into which it is
subdivided.  But such considerations do, as I mentioned, bear very directly on
the interpretations of comparisons betwen members of the same hierarchical
level.  As far as I can see, it is not an interesting biologically to examine
the size distributions of genera across flowering plants, or mollusca, or to
compare such distributions between floras.

Jeremy Ahouse's comments on protein folding are very interesting.  Systematics
is -full- of examples where continuity has been arbitrarily subdivided - and
then these subdivisions taken as being examples or dfiscrete bounded groupings.
Jussieu's families and genera are but one example; botanical terms are another
(pray tell, is an acute tip of a leaf different in other than degree from an
acuminate tip? there are literally hundreds of examples here), and also
character states used in a number of botanical cladistic analyses, especially,
but by no means only, those dealing with relationships between species. (No, I
do not understand why systematists carry out such studies if the variation they
are subdividing is continuous and they provide no justification for subdivision
at point x - rather than somewhere else.)

Again, subdivision of a continuum may have its uses.  Is the classification of
stars in sequences, and as red giants, white dwarfs[/dwarves], etc, perhaps an
example of an arbitrarily subdivided continuum that has its uses?  Red
dwarfs/dwarves will indeed have similar properties - temperature, size, etc -
just like the members of Jussieu's families, and so they refer to an
identifiable part of the sequence.  However, I do not really know what is going
on here - are they perhaps members of a discrete group, i.e. bounded by
discontinuiities in these properties from other stars?

Peter Stevens

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