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Dutch / Nederlands

Dairy, October 2013



Sun Mon Tue Wed Thu Fri Sat
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 13  14  15  16  17  18  19
 20  21  22  23  24  25  26
 27  28  29  30  31


Wednesday, October 2, 2013

Chestnut

Around half past nine, I picked-up a small chestnut at Wilminkweg, just outside of Enschede. It looked shinny dark brown when I picked it up, but in the afternoon, when I put it on my desk, it had turned light brown.

The food hourglass

At 11:02, I bought the book De Voedselzandloper (The food hourglass) by Kris Verburgh (ISBN:9789035137585) from bookshop Polare for € 17.95. In the evening, I paged through it a little.


Thursday, October 3, 2013

Palindrome date

Today is a palindrome date when written according to the (D)D-(M)M-(YYY)Y format: 3-10-2013. The previous such date was October 2, 2012 and the next will be ctober 4, 2014.


Saturday, October 5, 2013

GPS game

Today we had our 'summer' outing of our company. We went to Deventer and in the afternoon we played a GPS game, where we were given a GSP tracker with 24 marked locations. We were also given a sheet with 24 photo's taken at those locations and given the task to pair them up. During the game some extra assignments where given. There also was a challenge area where you could earn extra points by doing some games in the categories: think, dare, or do. For the think game, I solved three tangrams and for the dare game, I comsumed one fried locust. Our team became thirds from the eight teams. In the evening at home, I reconstructed the route we took bases on my memories with Google Earth: KML file or in Google Maps.


Tuesday, October 8, 2013

Second visit to Peter Struycken

I went to visit Peter Struycken again. He allowed me to investigate his personal archive with respect to his (non-commisioned) work. I even could take a part of his archive home to continue my work on compiling a list of his works. (See this page for the results of my ongoing research.) He also gave my a USB stick with all the digitized images of his works he has collected. (He has given me permission to publish these images in the context of my research.) In the past weeks he spend some effort to digitize the many slides he has. He has become quite interested about my research, and after I showed him some of the information that the Groninger Museum has online about him, we thought it would be a good idea to make an appointed to visit the depot and investigate all the information they have about him. They have a large collection of his work and he also donated some of his studies to the museum. I could also take some books (invitations) home. These are:


Saturday, October 12, 2013

Books

At 9:35, I bought two books from bookshop Polare. Yesterday morning, I already decided to buy these books, but I did not have a suitable bag with me. The two books are:

Mathematical Vistas

This afternoon, I finished reading the book Mathematical Vistas: From a Room With Many Windows by Peter Hilton, Derek Holton, and Jean Pedersen, which I started reading on September 14 the day I bought it from bookshop Polare. I have to admit that I did not read every letter of it, and many times, I did not really try to grasp what it said. I book like this would require many hours of serious study to complete understand every part of it. Still, I found it an interesting read. It surely did made me think about the Four colour theorem for many hours, and it still does.


Wednesday, October 16, 2013

Grafiek+

This morning, I discovered that some prints by Peter Struycken were on display at the Grafiek+ exhibition at the university. These are works owned by Rijksmuseum Twenthe. They were on display in the building "De Spiegel". Around one o'clock I went there and saw the following prints:


Friday, October 18, 2013

Gravity

This evening, I went to see the movie Gravity together with a colleague. To me the experience of this movie was spoilt by some of the great physics errors that you do expect in a SF movie like "Star Trek" but not in a movie like this, which attempts to be realistic. For some explaination read: Bad Astronomy Movie Review: Gravity.


Saturday, October 19, 2013

Warm day

This morning, I went walking with Li-Xia (in a wheelchair) in the Eco park. I played with the marble track on the artwork Haakse Haas, I found a green marble while searching for one of my own marbles (which I did find later). I decided to keep it and carry with me.

At 13:23, I took a picture of the sundail on the Old Church at the city center, which at noon, can show the approximate date. Unfortunately, the sun was not so bright, so the shadow of the sundial is not really sharp.

In bookshop Broekhuis, I looked at the exhibition on the third floor, which was part of the month of the print. I did not see anything interesting. At 13:44, I purchased a black, hardback Moleskine Daily Diary / Planner of 2014 (ISBN:9788866135647) for € 16.95.

At Galerie Objektief, I met with Wil Westerweel, whoes pictures were on display. I gave me a free CD with many of his pictures. Hence, I went to Rijksmuseum Twenthe to see the exhibition Paths to Paradise because I discovered that it included four works by Peter Struycken. It took me some time to locate the four works, because the works were ordered by theme and works for very different ages and thus from very different styles, where combined. I found it a little odd to find the highly abstract works by Struycken between figurative works. I also looked at the "Please do not touch. Even clean hands can damage." installation by Annelies Doom. It consisted of the small shelfs attachted on the wall. The first had two white cloves to handle valuable objects, and the remained shelves had one book for evey word, where the thickness of the book seems to be related to the emphasis given to the word. The book for "not" was the thickest. From the fact that some of the soft covers had curled-up, it seems that the books had been touched. (Later, at home, I discovered that the nine books had an ISBN, namely: 9789461902405, and were published by Uitgever Digitalis. but it's not available.

I also looked at the exhibitions Bart Hess. A Hunt for High Tech, which I did not find interesting, and Renie Spoelstra. Het dode punt van de schommel, that I found intriguing after I understood the idea and process by which the works were made.

Finally, I went to Tetem kunstruimte, where I looked at Hybrid Skins and 100 jaar grafiek uit ene particuliere collectie (100 years of prints from a private collection).


Wednesday, October 23, 2013

Sequence A056353

I wrote a program that produces the sequence A056353. The program calculates the number of sequences consisting of 0, 1, and 2, such that the sum is a multiple of 3. Furthermore, sequences that are rotated, reversed, or have 1 and 2 exchanged, are considered the same. The sequences for the first number of length are:
  1. 0
  2. 00 12
  3. 000 012 111
  4. 0000 0012 0102 0111 1122 1212
  5. 00000 00012 00102 00111 01011 01122 01212 01221 11112
These sequences are related to the Four colour theorem.


Friday, October 25, 2013

Two more sequences

I continued working on the program working on sequences of 0, 1, and 2. I suspected that the sequences can be divided in two groups, namely those that can be generated from the sequence 00 and those that can be generated from the sequence 12. By generating, I mean a process of replacing two digits of a sequence by three, by inserting 0 in the middle and either adding 1 or 2 to all three digits (modulo 3). For example, given the sequence 0012 we can generate another sequence by taking 01 from this sequence, insert 0 in the middle (resulting in 001) and add 1 to each of them (resulting in 112) and replace the 01 in the original sequence with it, resulting in 01122. Sequence 01122 can thus be generated from the sequence 0012. It is clear that any sequence consisting three or more 0 cannot be generated from either 00 or 12, because in each generation step, there is always either a 1 or a 2 inserted. The program shows that it is indeed the case that the sequences that can be generated from 00 and 12 do not overlap for all sequences with length up to 14. I haven't found a mathematical proof that this is the case for all sequences. This leads to two sequences that are related to sequence A056353. It is remarkable that there are much fewer sequences that can be generated from 00 than from 12. The table below is taken from the output generated by the program
      all     00     12
 3      3      1      1
 4      6      2      3
 5      9      2      6
 6     22      8     13
 7     40     10     29
 8    100     33     66
 9    225     57    167
10    582    168    413
11   1464    366   1097
12   3960   1061   2898
13  10585   2646   7938
14  29252   7514  21737


Sunday, October 27, 2013

Even more sequences

After some puzzling, I constructed the following transition table:

   0 1 2
a  b c d
b  a e f
c  g h i
d  j k l
e  l j k
f  h i g
g  c d b
h  f a e
i  k l j
j  d b c
k  i g h
l  e f a

Given a sequence of 0, 1, and 2, the above table can be used to calculate the value for the sequence, by starting with 'a' and calculate for each element in the string another value by using the above table. Now it appears that whenever you end with 'a', that the sequence is a sequence that can be generated from 00. For sequence generated from 12, you get one of 'b', 'i', or 'k'. I guess it will not be very difficult to prove this, by the effect of rules for replacing two digits by three digits in the generation step. Below the table extended with the number of sequences ending at the given letters:

          all        00        12       'b'       'i'       'k'
  2         2         0         1         0         1         0
  3         3         1         1         0         0         1
  4         6         2         3         1         1         1
  5         9         2         6         2         3         1
  6        22         8        13         4         6         3
  7        40        10        29        12         8         9
  8       100        33        66        19        23        24
  9       225        57       167        60        56        51
 10       582       168       413       146       135       132
 11      1464       366      1097       370       361       366
 12      3960      1061      2898       951       984       963
 13     10585      2646      7938      2714      2611      2613
 14     29252      7514     21737      7226      7255      7256
 15     80819     20209     60609     20285     20189     20135
 16    226530     57233    169296     56520     56426     56350
 17    636321    159080    477240    159376    158879    158985
 18   1800562    451928   1348633    449392    449753    449488
 19   5107480   1276870   3830609   1278053   1276311   1276245

When studying the transition one can see that each column has all the letters from 'a' to 'l' exactly once, meaning that they are permutations of each other. It is well known fact that any set of permutations is related to a finite group. The table can be used to construct the following group (with 12 elements):

    *    0   12   21   22   01   10    1   11   20   02    2
    0    *   21   12   10    1   22   01   20   11    2   02
   12   21    *    0    1   10   01   22   02    2   11   20
   21   12    0    *   01   22    1   10    2   02   20   11
   22   01   10    1    2   20   11   02   12    0   21    *
   01   22    1   10   11   02    2   20    0   12    *   21
   10    1   22   01   02   11   20    2   21    *   12    0
    1   10   01   22   20    2   02   11    *   21    0   12
   11   02    2   20   21   12    0    *    1   22   10   01
   20    2   02   11   12   21    *    0   01   10   22    1
   02   11   20    2    0    *   21   12   22    1   01   10
    2   20   11   02    *    0   12   21   10   01    1   22

In this table '*' stands for the empty sequence, and it also happens to be the identiy element. This is the Alternating group A4, because it is the Von Dyck group with, for example, a is 12, b is 10, c is 02 and a2 = b3 = c3 = abc = e. (See also: Alternating group A4 (tetrahedron) Cayley graph and table.)


Monday, October 28, 2013

Transition graph

I made this drawing of graph representing the transition table I constructed over the weekend. The arrows with the red triangle are the transitions for 1, and with the blue triangle the transitions for 2. The light grey lines, connecting opposite points, represent the transitions for 0 in both directions. The green lines represent some transitions for 211 or 122 and the purple lines for 221 or 112.


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