Wood Pigeons and a Red Kite

I was out walking with Zoe through Reading University grounds this evening when two wood pigeons flew low across the path in front of us, and low over the adjoining field, apparently trying to keep in the cover of the occasional trees and bushes.  This seemed odd to me as pigeons usually don't seem to mind flying high, and I remarked on it to Zoe.

A few seconds later Zoe pointed to what she thought was gull silhouetted against the sunset.  It was rather large for a gull and it seemed to be flying rather to fast.  Then I noticed that its was forked and I realised that it must be a red kite.  Just a few minutes earlier someone we had met by the lake had said they had just seen one, so I take that as a sort of pre-confirmation.  I flew off over some trees and we didn't get another look at it.  The pigeons could well have known that the kite was around and were flying low to avoid attracting its attention.

Herons and Kingfishers

On Monday evening I stopped on my way home by the lake near Frimley station to watch one of the (presumably) young herons when a pair of small birds darted out of the woods behind it.  They flew low over the lake and then turned and flashed bright kingfisher blue in the sun before diving into the bushes on the far side.

Definitions and Designations

The following is from J. R. Abrial and L. Mussat  ["On Using Conditional Definitions in Formal Theories",  in D. Bert et al (Eds.), ZB2002, Lecture Notes in Computer Science. pages 242-269, Springer, 2002]:

Suppes first introduces two criteria characterizing the definition of new symbols in a formal theory: (1) the Criterion of Eliminability, and (2) the Criterion of Non-creativity. The former requires that "any definition introducing a new symbol may be used to eliminate all subsequent meaningful occurrences (of that new symbol)". The latter requires that any definition of a new symbol "(does not) make possible the derivation of some previously unprovable theorem stated wholly in terms of primitive and previously defined symbols". In other words, a proper definition must not add any extra "power" to a theory, it is just a useful, but not indispensable, extension to it.

This means that definitions are just abbreviations and therefore cannot be used to build a theory; they can only be used to express an existing theory in a different way.

Michael Jackson ["Software Requirements and Specifications", Addison Wesley, 1995, pages 51-54] has some interesting things to say on the subject of the symbols used in specifications:

One way to define a term is to give a designation. That means giving a recognition rule for recognizing some class of phenomenon that you could observe in a domain. In the domain of human relationships you might have these designations:

x is a human being (homo sapiens) = Human(x)

x is male = Male(x)

x is female = Female(x)

x is the biological (genetic) mother of y = Mother(x,y)

x is the biological (genetic) father of y = Father(x,y)

[...] You can use the designated terms in refutable descriptions that make assertions about the domain. [...]

Thus designated terms (symbols) here connect the theory with the domain that the theory describes. Jackson goes on:

Now suppose that you want to make some assertions about grandparents, and aunts and uncles, and cousins and brothers and sisters.  You don't have any designations for these terms, but it will be very inconvenient and difficult to do without them.  there are two ways of making them available for use in your descriptions.  One way is to write some more designations.  For example

x is the genetic full brother of y = Brother(x,y)

[...]

Sometimes this is the right thing  to do.  But probably it is not the right thing here.  The right thing here is to do it the other way: to give a formal definition of each of the new terms, using the terms you have already designated.  [...]

Brother(x,y)  ≙ 
  Male(x) ∧
     ∃ f . (Father(f,x) ∧ Father(f,y) ) ∧
     ∃ m . (Mother(m,x) ∧ Mother(m,y) )

This is a definition in the style of Suppes.   However, I think it is unsatisfactory to regard 'Brother' as purely a convenience to make the theory shorter.  If it was, then it wouldn't matter if you replaced 'Brother' by say 'Aunt' throughout the theory.  The choice of names is important even in strictly unnecessary definitions.  They also designate things in the domain.

In my way of specifying there is no need to introduce new symbols, as all possible symbols already exist.  Writing a specification is just a matter of defining the constraints on these already existing symbols.

(By the way, did you spot that the definition of Brother requires the extra constraint x ≠ y?  Without this I would be my own brother.)

A Common Tern

This morning at 06:40am a common tern, swallow-like and red-beaked, flew along the Kennet loop, eastwards past Reading prison.

I have occasionally seen common terns of the Kennet before. Once, I was with Zoe when one did a spectacular dive into the river and then flew up and off again.

Update on Wed 2005-07-06 by Tristram Brelstaff

On the following Sunday (June 24th) Zoe and I saw a lone common tern flying up and down the middle lake in Reading University grounds.  We saw it dive several times - the lake seems to provide better hunting than the river Kennet.  Each time it dived it did a sort of twist in the air before dropping down to the water.

A few days later I again saw the tern over the Kennet before 7am.  I suppose it is possible that all three sightings were of the same bird.

Natural Selection and Social Theory by Robert Trivers

When I first heard that this collection of papers by Robert Trivers existed I immediately wanted a copy.  I had come across Trivers' name and his ideas at second-hand many times in my reading over the past couple of decades but I had never read anything of his first-hand.  I had enjoyed William Hamilton's 'Narrow Roads of Gene Land' so much that the prospect of a similar feast from another leading evolutionary theorist was too much for me to resist, so I went out and ordered a copy.

'Natural Selection and Social Theory' contains 10 papers, each with a fairly substantial introduction.  I started by reading through the introductions and skipping the papers.   Within a week I was disappointed to find myself at the end, so then I turned back and read the  Reciprocal Altruism and Haplodiploidy papers more carefully. 

On the whole this is a lighter read than 'Narrow Roads': firstly, it is only 328 pages as opposed to 528+852 for the two volumes of 'Narrow Roads' and, secondly, Trivers' writing is less dark, intense and obsessive than Hamilton's. 

The introductions offer interesting side views on Ernst Mayr and Edward Wilson, people who, until now, I had known only through reading their books.  Trivers tells a story of how Mayr came to him in a dream and showed him the way to understand the relationship between queen and worker ants, and how Trivers later asked Mayr whether 'Personal communication' would be the way to acknowledge this 'help' in the paper!  There are tales too of Hamilton's legendary incompetence as a lecturer. 

From reading the introductions I also came to understand the significance of Hamilton's four-fold classification of social interactions into co-operative, selfish, altruistic and spiteful, something that had completely escaped me before.