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.
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)
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.
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)
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.
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.
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.
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.)
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.
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.
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)
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.
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.
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.
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).
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.
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.
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.
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.
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.
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
Home
| October 2008
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| Random memories
Burgers' Zoo
Wednesday, November 12, 2008
Tuesday, November 18, 2008
Sunday, November 23, 2008
Sunday, November 30, 2008