5 June 2002: Complex sentences: subordinate and coordinate clauses

The central property of complex sentences is essentially that they consist of other sentences.

This property is called recursivity, and the grammars of English which account for this property must consequently be recursive.

One kind of recursive grammar has at least two rules, and looks like this:

S'' -> S'

S'' -> S' and S''

where S'' is the dominating complex sentence S' is the included sentence

Note that the complex sentence may in principle include just one complex sentence, or it may include a simple sentence and another complex sentence.

Remember Jonathan Swift's rhyme in On Poetry, 1733:

So naturalists observe, a flea
Hath smaller fleas that on him prey;
And these have smaller still to bite 'em;
And so proceed ad infinitum.

(Explain Swift's pronunciation of ``flea'' ... !)

And the 19th century mathematician Augustus De Morgan's parody as a definition of recursivity:

Great fleas have little fleas
Upon their backs to bite 'em,
And little fleas have lesser fleas,
And so, ad infinitum.

However, Swift was obviously thinking more of his younger competitors than of recursivity - his poem continues:

Thus every poet, in his kind, Is bit by him that comes behind.

But the expression ad infinitum is to be taken literally - a recursive grammar defines an infinite number of potential sentences. Of course, not all are used in practice, but the number and variety of sentences which are actually used is so great that the assumption of infinite size is a convenient fiction. It is not only that, however: a recursive grammar (like other generalisations) is predictive, an essential property of a scientific theory: it predicts infinitely more sentences than have ever been observed, so that new sentences can be described - or not, if the grammar is not a good one.

Hints and tasks:

1. Find
   • definitions and
   • examples of the use of
   the terms subordinate clause and coordinate clause in your favourite grammar handbook.
2. How many kinds of coordinate clause are there?
3. Illustrate each kind of coordinate clause.
4. Which structures and parts of speech, apart from sentences, can be coordinated?
5. How many kinds of subordinate clause are there?
6. Illustrate each kind of subordinate clause.
7. Search on the web for definitions of the following terms and examples of their use:
   • recursive rule
   • context-free rule
   • constituent structure
   • phrase structure grammar
   and try to work out how these terms are related.
8. Select a subordinate clause and a coordinate clause from the corpus tale, and draw a tree to illustrate their structure.

A couple more remarks on the side...

The property of recursion is sometimes called ``self-similarity''.

Recursive (or inductive) definitions are common in mathematics, and fractals in mathematics, and in computer art, are often cited as an example of recursion:

(Acknowledgements and apologies to the unknown authors of these images, found ownerless on the web.)

It is sometimes said that fractals are appropriate models of certain structures in nature, such as ferns (as in the images), or snowflakes.

Task:

1. Find more examples of fractal images on the web.
2. Draw a picture of a complex sentence which looks like a fractal.
   (Hint: You will find an example in one of my earlier introductory courses.)