Wed 2005-07-06 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.
Sat 2005-07-02 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.)
Fri 2005-06-24 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.
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.
Sun 2005-06-19 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.
Tue 2005-06-14 Over the last week, I have on two occasions seen coots on the river Kennet building what appeared to be 'second nests'.
The first time I saw this was when I saw one of the pair that had brought up two chicks on the nest near Highbridge Wharf started piling up strips of greenery under the boat traffic light just east of the Duke Street bridge. The pair's two chicks seemed to be joining in, well one of them was standing on top of the pile. At first I thought they had decided to move nest but after a day or so I saw that the new nest had disintegrated and they were back at their old nest again.
Then, this morning I saw that one of the coots from the nest at the mouth of Gunter's Brook was carefully draping strips of greenery over a log that had become fixed near the river bank. It was placing the strips apparently quite deliberately, while its solitary chick looked on.
My first thought was this building of second nests could be the way that the parents teach their chicks how to build nests. Another possibility is that these piles of greenery are food stores, however, this is less likely because there seems no reason to build them away from the main nest.
