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Dairy, November 2008



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Sunday, November 2, 2008

Going into the city

Today, the weather was nice compared to the cold that we had in the past days. And because the shops were open in the city, I decided to go to the city. I only went to De Slegte bookshop. I looked around there for a little over an hour. I looked at several books about John Lennon. Yesterday, I already saw the book Memories of John Lennon and some other book about him. Today, I saw the book John by Cynthia Lennon. But I did not buy any of these books. However, I did buy two other books at 16:50:09. The first was the book Philosophers by Steve Pyke. The second is the book Blauwe Maandagen (Blue Mondays) by Arnon Grunberg.


Wednesday, November 5, 2008

Flemish conjugates yes and no

According to this message, Flemish does conjugate yes and no. The Dutch words for yes and no are "ja" and "nee". In Flemish it is:

Joak/Nink (yes, I do / no, I don't)
Joag/Neig (yes, you do / no, you don't) singular
Joas/Joaj Nins/Neij (yes, she/he does / no, she/he doesn't)
Joat/Nint (yes, it does / no, it doesn't)
Joam/Nim (yes, we do / no, we don't)
Joag/Neig (yes, you do / no, you don't) plurar
Joas/Neis (yes, they do / no, they don't)

Playing Go

When I got into the car this evening, I was not sure whether I should go or not, because I felt quite tired. In the end I decided to go to the university and try to play Go. When I arrived, Taco was already waiting, and not much later Rudi arrived. We soon decided that Rudi would play against us. I was given an eight stone advance. I did not expect that I would win, and at points during the game I was sure of it, but when we counted, it turned out I won with 57 against 50 points. Not bad at all.


Thursday, November 6, 2008

Metamath

Yesterday, I had a look at the language of Metamath, a computer-assisted proof checker. I now also understand how the proof system works. It is actually quite simple. The language defines named collections of strings. Each string consists of constants and variables. A constant is nothing else than a fixed sequence of characters. A variable is an identifier that is linked to one of the named collections. If a string does contain variables, it can also be viewed as a function where the parameters are defined by the variables that occur in the string, where the convention is used that if a variable occurs more than once, only the first instance is taken. When such a function is applied to strings from the linked collections, it returns a new string for the collection it is linked to itself. The strings that are produced in this manner are always getting larger and larger, which is not always helpful. For this reason another type of "function" can be specified in the language which is a kind of reduction rule, which states that if certain strings are present in a named collection, another string can be derived. The most elementary reduction rule is the modus ponens rule. In Metamath this can be represented by a number of matching strings and a production string. The matching strings may contain variables. The production string may only contain variables that also occur in one of the matching strings. If it is possible to supply strings for the variables from the collections such that the matching strings occur in the collection, than the production string can be added to the collection. If an expression of functions and arguments results in a string, that expression can be considered as the proof of that expression (under the condition, of course, that the string itself is not used directly or indirectly). In Metamath all strings in the named collection can be given an identifier and because each string has fixed number of arguments, an expression can be described by simply giving the reverse polish notation of the identifiers of the strings.

tags: Metamath (previous, next)

Burgers' Zoo

Annabel went to Burgers' Zoo with her school. She took many pictures, both most appeared to be unsharp, probably because she made the wrong selection on the main settings wheel. But some pictures turned out great, such as a picture of a deer and one of some flamingoes.


Wednesday, November 12, 2008

Playing Go

When I arrived at the university to play Go, Rudi and Taco already had started a game. I asked Rudi, if he could play against me as well. We decided on a seven stone handicap for him, because I won last week. After the nineteenth move, Huub arrived. I decided to continue my game with Rudi. Around my fortieth move, I made a big mistake and some more mistakes. After that, I continued fairly normal. The end result was that I lost with 32 points, which did not really surprise me. When I came home I tried to recollect the moves of the game. My best guess, which definitely contains errors, is found in this SGF file.


Thursday, November 13, 2008

Game record

Today, I made a second attempt to reconstruct the game record of the game I played yesterday. This SGF file contains the result so far. It feels much better than my first attempt, but there are still things that don't feel good.


Sunday, November 16, 2008

Qua Art Qua Science

This afternoon, I attended a meeting organized by Qua Art Qua Science where Professor Bob van Eijk gave talk about elementairy particles and where the latest paintings and drawing by Billy Foley were presented. This happened to be the thirteenth meeting organized by Qua Art Qua Science, which happened to have the same persons involved as the first on September 14, 2004. Before the talk, I greeted Billy Foley, when he was taking some pictures of his works on display. He even remembered meeting with me before. After the meeting I had some chance to talk with him again. I had listened to him explaining about how his paintings came into being. It is a process of drawing (painting) lines and observing the effect they have on the composition of the drawing (painting). It seems as each new line he adds (or removes by fading) provokes some new idea. I asked him if he afterwards he could recall the order in which he made his work, and he told me that he couldn't. Then I told him a little about the game of Go and how there seems to be a certain resemblance between his manner of painting and the way his works come into being. I also explained how concepts such as form and flavour (taste) are used by Go players. He found it an interesting idea. There are two works that I find interesting. I also bought two leaflets printed by Qua Art Qua Science, namely: The Quark and the Jaguar (about this meeting) and Connected Holes about the work of Rinus Roelofs. (During the talk, the basketweave tiling on the floor also gave me some ideas.)


Tuesday, November 18, 2008

L-tiles

Last Sunday, I got some ideas about tiling a basketweave tiling with L-tiles. Each L-tiles consists of four unit squares. I discovered that it is rather easy to make such a L-tiling (of which an example is shown on the right). The basketweave is created with starting with a square grid of unit size two and alternating dividing each square in half either vertical or horizontal. Each L-shape is made by combining two halfs from two adjacent squares. I wondered if every rectangle of a basketweave contains an L-tiling, and if so, how many. Then I made the observation that each L-shape connects two squares and that because each square contains two L-shapes, it is linked with two other squares. That means that an L-tiling of a rectangle defines a collection of cycles. Now the question is whether each collection of cycles defines an L-tiling, because if that is the case, then the answer to the question of all possible L-tilings for a certain rectangle can be answered relatively easy. After some puzzling, I concluded that this is indeed the case. It also means that L-tiles is equivalent with a set of Wang tiles with two colours and and the six tiles that have two sides of each colour.


Wednesday, November 19, 2008

L-tiles: correction

The statements I made before with respect to the number of L-tilings are incorrect, because any sufficiently long straight segments in a cycle can be filled in more than one way by L-tiles. That means that the number of L-tilings with a given set of cycles is a multiple of a power of two.

Playing Go

This evening, I went to the university to play Go. I arrived at the same time as Taco and we decided to play against each other where he got a seven stone handicap. Well into the middle game, Huub came and watched us play. At the end of the game, I made some big mistakes with respect to playing a ko, and I lost at least ten points. This was enough for Taco to win with 56 against 53. Afterwards we discussed the game and replayed the game. At home, I tried to replay the game, which resulted in this game record.

(follow-up)


Friday, November 21, 2008

Wet snow

At 11:54, we noticed that big snow flakes were falling from the sky, but they are not staying on the ground. Immediately, we started to talk about Friday, November 25, 2005, which started in a similar way. The snowing only lasted for about fifteen minutes. After some sunshine, it started to snow again at two o'clock. It snowed for about half an hour, which left some snow on the grass and cars, but not on the pavement.


Saturday, November 22, 2008

Snow

This morning, there was a thin layer of snow on the roofs and the cars. During the afternoon, there was some wet snow. 5 cm (2 inches) of snow has been predicted for tomorrow.

Collected works of Gerard Reve

This afternoon, I went into the city. First I looked for a dairy at Broekhuis, which I would look to use to make some notes about every day, I custom that I have started earlier this year. Next I walked to bookshop De Slegte. Outside I saw the collected works of Gerard Reve sealed in plastic for just € 14,95. Earlier this year, on July 6, I already consider buying it at some sale. Inside I asked how the sale of it was going, and they told me that it was going very good. I looked around the shop, but just kept thinking about buying it. In the end I could not resist the tempation, and bought it. I took it with me to Camel where I met with Annabel and Li-Xia for dinner. At home, I counted the pages of the collected works and found that it was 4354 pages. That is 0,34 € cents per page, which must be one of the cheapest 'books' I ever bought.


Sunday, November 23, 2008

Swapping L-tiles

Some time ago, I already realized that there are several ways in swapping two tiles, as shown on the image on the right. I wondered, if by means of this kind of swapping one could change any L-tiling inside a square into another L-tiling. The top swap, as shown on the right, involves a change of the matching patterns of cycles. So, the real question is whether a pattern of cycles inside a rectangle, can be changed into any other pattern by the pairwise swapping of two parallel horizontal connections into two parallel vertical connections between four points (or vice versa). It is sufficient to show that it all patterns of cycles can be transformed into a one given pattern. I looks like that this is possible. The method is as follows. You start with a rectangle and try to make a cycle that connects all points on the border. And after you have done this, you procede with the inside rectangle where the border has been removed. The points in the corner are already connected correctly. If you encounter two adjacent points on the border that are not connected, it seems as if this is always possible. You might have to perform some swappings from further away, possibly to the other side of the rectangle, but it is a rather straight forward process. You can stop if you arrive at a rectangle if the shortest side is three or less. For rectangles with the sortest side being equal to two, it is obvious that they can be turned in a single cycle over the border. If the shortest side is equal to three, this is not possible. But if one restricts the procedure to one of the longest sides, it is possible to make one unique cycle. Which ends the proof (if I have not made any mistakes).


Monday, November 24, 2008

Snow

This morning, there was snow (almost) everywhere. It already started to snow yesterday around three o'clock, but it was only after seven o'clock that the snow stayed on some parts of the ground. Now the ground has been covered almost completely. And it is still snowing a little (around a quarter to eight in the morning). Yesterday evening we heard on the news that some other areas have been hit by a thick layer of snow, almost like three years ago. I took two pictures. The sad thing is that this weekend nine people died from traffic accidents. Because the temperatures remained around the freezing point, the snow remained for the rest of the day.

Game record

Some days ago, Huub send me two pictures he took during the game of Go Taco and I played last Wednesday. Today, he send me the game record according to his recollections and his pictures. This did not fit completely with some of the moves that I remembered clearly. After some further thinking, I arrived at this game record.


Tuesday, November 25, 2008

Thin layer of snow

This morning, there was a thin layer of fresh show on the streets together with all the snow that was left over from yesterday. During the night the temperature jump up and down between zero and five degrees below Celsius. Temperatures are expected to rise today, and probably most of the snow will melt away.


Wednesday, November 26, 2008

Playing Go

When I arrived at the Theater café to play Go, I found Rudi and Taco playing at one of the round tables in the centre of the café. Rudi immediately offered to play against me simultaneously. We agreed on a handicap of seven stones. I decided to make notes about the progress of the game, hoping that this would help in recalling the game. But soon I found it to be too distracting and affecting my game play. I lost with 27 points. While he was still playing against Taco we replayed our game for about two thirds, and he made some remarks about my (and his) game play. It seems that he plays quite loosely as long as he knows that he is ahead in the game. From a strategic point of view, having to play two games, this is actually quite good and a sign of a good Go player. I don't see much Go players record their games while they play. The best time to do it is, when you replay a game, or when you are on your own, as I am doing now. Because if you are not able to recall your games, it is probably also not worth recording them, because you haven't reach the right maturity for it being useful. At home I spend some time to recall the game, which resulted in this SGF file.


Sunday, November 30, 2008

Swapping L-tiles

Earlier this week, I realized that there might be a problem with the proof I presented last Sunday with respect to swapping L-tilings. I thought about the case shown on the right, where you have to make a swap starting from the top, to make the line at the bottom. But once you do this, the line on the top is gone. I wondered if this situation could occur and tried to complete the diagram on the right, but whatever I tried, I could not find a solution. It took me some thinking to come up with a solution. Finally, I noted that there are two kinds of nodes, labeled with 'a' and 'b'. The right side needs to contain two paths to connect the open ends. Because these paths start and end with a node marked with 'b', two more nodes with a 'b' are used than with an 'a'. Any other cycles on the right side will make use of an equal number of nodes marked with 'a' and 'b'. However, no matter how wide the grid on the right side is made, the number of nodes marked with 'b' is never two more than the number of nodes marked with 'a'. Because this leads to a contradition, we can conclude that this situation can never occur. If the grid would be higher, the situation only gets worse, because more and more nodes marked with a 'b' are needed. Only if the height is three, it is possible, but that is a case we already dealt with.

A little wet snow

This afternoon, we had a little snow, but it did not stay on the ground. So, it has to be qualified as wet snow.


This months interesting links


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