Reinventing Zero (the hard way)

In a recent paper, Eric Hehner gives the following beautiful example of people reinventing the concept of zero the hard way:

In the 1991 Toronto phone book, there is a page that helpfully gives the time difference to various places in the world; to the U.K. it says "+5", and to Costa Rica it says "-1". But to Cuba it says "NA", and the legenda explains "time difference not applicable". By 1996 they tried to correct it; for Cuba it says "=", with the same explanation. In 1997 they discovered the number 0 , but they felt the need then, and still do today, to explain that 0 means "no time difference".

Not Part of the Conversation

Paul Graham is really a very good writer: he has interesting things to say and he says them clearly.  Here is an example I came across today:

On the web, articles you have to pay for might as well not exist. Even if you were willing to pay to read them yourself, you can't link to them. They're not part of the conversation.

 Exactly.

Watership Down by Richard Adams

I finished reading this to my 10-year old daughter a couple of weeks ago.  It is a wonderful read - much deeper and more detailed than the film.  The writing is beautiful and the characters  are convincing and varied.  Adams creates a believable rabbit culture with its own mythology, rather like Tolkien did but on a smaller scale.  I particularly like the way that most of the rabbits have great difficulty in understanding some things which humans find obvious, like the idea that a piece of wood can be used to float across a stream.

Next spring, one sunny morning, I am going to wake Zoe up early and together we will catch a train to Newbury. From there we will take the Basingstoke bus as far as Kingsclere, and then we will walk up onto Watership Down and there I will point out to her the places mentioned in the book.  We will walk on along the ridge to Ladle Hill and, if there is time,  cross the valley to Beacon Hill on the opposite side and then look down on Highclere Castle.

Cormorants

On Sunday afternoon there were at least 7 cormorants on and around the large Reading University lake.  Zoe and I first saw 3 of them on the water surface, occasionally diving, then they took off, flew round the lake a few times and then up to the tops of the trees on the north shore, where 4 other ones were already hanging out their wings to dry.

There were also a few shoveller ducks, most of them just sunning themselves under the trees on the north side, but 3 or 4 of them were out in the middle circling together.

Logic for Computer Science

Today, in my reading,  I came across the following:

The only kind of logic necessary in computer science is the predicate calculus, used in the rigorous yet "informal" way of the working mathematician, but perhaps reformulated and extended by useful theorems in the direction presently being investigated by Dijkstra. Formalisms requiring a separate "proof system" or bearing the "formal logician's trademark" should be viewed rather critically.

R. T. Boute, On the Shortcomings of the Axiomatic Approach as presently used in Computer Science, Proc. IEEE COMPEURO 88, System Design: concepts, methods and tools, pp. 184-193, April 1988.

[By the "formal logician's trademark" Boute means the turnstile symbol.]