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Diary, June 2017


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Thursday, June 1, 2017

Book

At 17:54, I bought the book AKI Eindexamencatalogus studiejaar 1987/1988 written in Dutch and published by Instituut voor Hoger Beeldend Kunstonderwijs in 1988 from charity shop Het Goed for € 3.95.

Thursday, June 8, 2017

GOGBOT café

This evening, I went to the GOGBOT café event at Tetem art space. There were presentations by:

Friday, June 9, 2017

Kraggehuis

At the end of the afternoon, I arrived in Giethoorn. I had wait some time before the boat arrived to bring me to the Kraggehuis, a group accomodation in the middle of the lake. When the boat arrived, I had to wait a little more, because there were some last minute shoppings to be done. The boat had no engine, so we needed to used long poles to push is forward, because the water is less than a meter deep. Some people were playing Go outside when we arrived at the island. Dinner was served around eight in the evening, just after a couple arrived peddling on 13'2 Explorer boards. I looked at several Go games being played by others.


© Rudi Verhagen

Saturday, June 10, 2017

Peddling

This morning, three others and I spend about two hours traveling through Giethoorn by boat and using poles to push the boat forward. I did some reading and also slept for an hour. In the afternoon, the couple who arrived peddling was teaching others to peddle on their boards. I also gave it a try, being a little nervous because I did not have a spare pair of trousers in case I would fall in the water. At my first attempt to stand up-right, I dropped to my knees immediately as I felt unstable. I was instructed to place my feet a little further apart. On the second try, it worked a little better. I had to take a few deep breaths to calm my hardrate and stop my legs from trembling. When I started peddling, I noticed that the trembling returned, but slowly it got a little better. When a speedboat was approaching, I dropped to my knees before the waves arrived. I guess, I would need another hour to become comfortable enough to go on a longer trip.

The Boxer and the Goal Keeper

In the evening, I finished reading the book The Boxer and the Goal Keeper: Sartre Versus Camus by Andy Martin, which I started reading on May 19. I bought the book on Wednesday, March 9, 2016. I found this a well written and interesting to read book. The only problem I had with it, and which I have encountered with other biographic books, is the in some places thematic approach. The book definitely made me interested in reading more from and about both Sartre and Camus.

Sunday, June 11, 2017

Swimming and sailing

This morning, I swam around the lake together with some other people. After having taken a shower, I went sailing with four others. We managed to return to the island with only a little use of the poles. The boats have an almost flat bottom and no keel, which makes them drift very easily, especially when there is not enough wind to make some speed. In the afternoon, I went sailing with two others. One of them jumped into the lake several times and pulled the boat while walking on the bottom of the lake. This weekend, I only played one game of Go, when Pepijn asked me to play against him. I lost with 50 against 16 points where I got nine stones ahead. But even then it is not too bad, because he is a Dan player and I also did not really concentrate a lot on the game. I did look at games being played. We also replayed the first of the 50 AlphaGo vs AlphaGo games till the start of the end game. It is a pitty that DeepMind/Google is going to decommission AlphaGo and not making it available anymore to be played against.

Thursday, June 15, 2017

Irregular chocolate bar

Yesterday, I saw a photo strip by Ype & Ionica about an irregular chocolate bar, inspired by bar from Tony's Chocolonely, that could nevertheless be equally shared by 1, 2, 3, 4, 5, and 6 persons. I noticed that in their design there were two pairs of pieces with the same surface area and I wondered if there was also a solution with all different numbers. I also wondered, if the more generic mathematical puzzle: find the 'smallest' set of natural numbers such it can be divided in all manners up to a given n, had been addressed by someone. On a Dutch blog by Ionica Smeets, she reports that someone named Dic Sonneveld found a solution with all different numbers, namely: 8,10,11,12,13,14,16, 17, 18, 19, 20, and 22. She also mentioned that several people concluded that there is no solution with eleven pieces. I started to do some puzzling myself and also told a colleague about the puzzle. It is obvious that the numbers for a given n should be equal to or be a multiple of the Least common multiple (or LCM) of intergers upto and including n. My colleague and I found the following solutions:
  1. : 1. (1 times 1).
  2. : 1, 2, and 3. (3 times 2)
  3. : 1, 2, 4, 5, and 6. (3 times 6)
  4. : 1, 2, 3, 4, 5, 6, 7, and 8 or 2, 3, 4, 5, 6, 7, and 9. (3 times 12)
  5. : 1, 2, 3, 4, 5, 7, 8, 9, 10, and 11. (1 times 60)
  6. : 1, 4, 5, 7, 8, 9, 11, 12, 13, 15, 16, 19. (2 times 60)
He found the last solution, the others are mine, but he did find another alternative for 4. I report two solutions for that case, depending on the definition of 'smallest' set of natural numbers. The first solution contains eight numbers with 8 as the lowest value, while the second solution contains seven numbers, but with 9 as the lowest. He found another solution with seven numbers, meaning that even between solutions with the same number of numbers, we have to define some kind of relationship to define which is the smallest set. A (finite) set of (finite) natural numbers can be represented by a single natural number using a binary representation.

Wednesday, June 21, 2017

Smallest maximum

In the past days, I worked on a program for calculating solutions to the Irregular Chocolate Bar problem. I discovered that it is not difficult to find solutions with using large sets of numbers where the maximum number is as small as possible. This results in the following solutions:
  1. : 1
  2. : 1, 2, 3
  3. : 1, .., 6 except for 3
  4. : 1, .., 8
  5. : 1, .., 11 except for 6
  6. : 1, .., 15
  7. : 1, .., 29 except for 15
  8. : 1, .., 41 except for 21
  9. : 1, .., 71 except for 36
  10. : 1, .., 71 except for 36
  11. : 1, .., 235 except for 10
  12. : 1, .., 235 except for 10
  13. : 1, .., 849 except for 465
  14. : 1, .., 849 except for 465
  15. : 1, .., 849 except for 465
  16. : 1, .., 1201 except for 1081
Note that some of the solutions are the same, for example, for 13, 14 and 15. This is because 14 is equal to 2 times 7, which are already included for a bar that can be divided in 1 up to and including 13 groups. Furthermore, 2 and 7 are coprime, which might explain why there exists a division in seven parts for which each part can be divided in two smaller parts. The same true for 15, which is equal to 3 times 5. I have no proof if this hold in general, but it seems likely.

Finding solutions with the smallest set (or possibly larger) numbers, proved to be much harder. The method of just generating all sets, proved to be too slow. I next worked on an algorithm that would generate sets that would fit the largest number of divisions. These sets contains twice as many or one less number of numbers. But this did not get me much further. So far, I have found:

  1. : 1
  2. : 1 2 3
  3. : 1 2 4 5 6
  4. : 2 3 4 5 6 7 9
  5. : 2 3 4 5 7 8 9 10 12
  6. : 3 4 5 7 9 11 13 15 16 17 20
  7. : 16 17 19 21 26 27 29 31 33 34 39 41 43 44
  8. : 17 23 25 32 37 38 47 52 53 58 67 68 73 80 82 88
It is possible that for the last two solutions, there exist even better solution, with fewer number (thirteen and fiftheen), but even larger values.

Friday, June 23, 2017

AKI finals 2017

In the afternoon, I went to the AKI finals 2016 exhibition at the AKI. This year, the exhibition was only in the school building. I ran into Wim T. Schippers and talked a little with him while standing at an installation by Ole Nieling. I found the following artist interesting: At 18:31, I bought the book provocatie | provocation | 挑衅 edited by Johan Visser, written in Dutch, English, and Chinese, published by AKI ArtEZ on Saturday, July 23, 2016, ISBN:978907552389, for € 15.00.At 18:31.

Saturday, June 24, 2017

Museum Boijmans Van Beuningen

During the afternoon, I visited Museum Boijmans Van Beuningen. I first looked at the main exhibition, curated by Carel Blotkamp with the new lightning designed by Peter Struycken, which he made in an attempt to approach daylight as good as is possible. To my surprise, I ran into Wim T. Schippers again. At two, I attended the official opening on the small sqaure in front of the entrance of the museum. The sky was grey and there was a little rain. After this, I also walked throught the other exhibtions: Sensory Space 11, Richard Serra, Drawings 2015-2017, The Magnetic North & The Idea of Freedom, and near the end of the afternoon, after having walked throught the exhibitions again, Gunnel Wåhlstrand. I listened to the talk by Carel Blotkamp about his work as a curator of the main exhibition. The list of noteworthy (to me) works I saw is:

Thursday, June 29, 2017

Necklage

I have been working on the 'necklage' solutions for the Irregular Chocolate Bar problem. The necklage solutions are the solutions with 2n-1 numbers. Let S be the sum of all numbers of a solution, than for a necklage solution the number S/n must be included and there must be n-1 pairs that add up to S/n. Furthermore, one can reason that there must be n-2 pairs and one triplet that add up to S/(n-1). All the pairs of both groups form alternating chains. One such chain connects the S/n number with the triplet and the other chain connects the two other numbers in the triplet. The could be viewed as a necklage with a 'triangle' in the front and a piece hanging down. Hence the name of these solutions. I adapted the program and it found the solutions shown below. I let it run for higher numbers as well, but it did not find any solutions that also had a division for numbers between 1 and n-1. There are good reasons to believe that these are the only necklage solutions. In the listing the minus sign is used for pairs that up to S/n and the equal sign is used for pairs and triplets that add up to S/(n-1). 

3:
    2-4
  6=  =
    1-5

4:
       4-5          5-4       1-8=4
 9=3-6=  =    9=3-6=  =     9=    -
       2-7          1-8       2-7=5

5:
        2-10=5            1-11=4       1-11=4-8
 12=3-9=     -     12=3-9=     -    12=       =
        4- 8=7            5- 7=8       2-10=5-7

6:
         3-17=7-13       1-19=5-15= 9
 20=4-16=        =    20=           -
         5-15=9-11       3-17=7-13=11

This months interesting links

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