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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.
GOGBOT café
This evening, I went to the GOGBOT
café event at Tetem art space.
There were presentations by:
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
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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.
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.
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.
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 times 1).
- : 1, 2, and 3. (3 times 2)
- : 1, 2, 4, 5, and 6. (3 times 6)
- : 1, 2, 3, 4, 5, 6, 7, and 8 or 2, 3, 4, 5, 6, 7, and 9. (3 times 12)
- : 1, 2, 3, 4, 5, 7, 8, 9, 10, and 11. (1 times 60)
- : 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.
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, 3
- : 1, .., 6 except for 3
- : 1, .., 8
- : 1, .., 11 except for 6
- : 1, .., 15
- : 1, .., 29 except for 15
- : 1, .., 41 except for 21
- : 1, .., 71 except for 36
- : 1, .., 71 except for 36
- : 1, .., 235 except for 10
- : 1, .., 235 except for 10
- : 1, .., 849 except for 465
- : 1, .., 849 except for 465
- : 1, .., 849 except for 465
- : 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 3
- : 1 2 4 5 6
- : 2 3 4 5 6 7 9
- : 2 3 4 5 7 8 9 10 12
- : 3 4 5 7 9 11 13 15 16 17 20
- : 16 17 19 21 26 27 29 31 33 34 39 41 43 44
- : 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.
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.
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:
- Pyke Koch, De schiettent, 1931
- Salvador Dalí, Couple aux têtes pleines de nuages, 1936
- Salvador Dalí, Table Solaire, 1936
- René Magritte, La reproduction interdite
- Piet Mondriaan, Componsition no II, 1929
- Piet Mondriaan, Composition with colour fields, 1917
- Kees van Dongen, Le doigt sur la joue, 1910
- Charley Toorop, Drie generaties, 1941-1950
- David Salle, The Greenish Brown Uniform, 1984
- Keith Haring, Untitled, 1982
- Cindy Sherman, Untitled #258, 1992
- David Salle, The Desert Wind of De Construction has not Touched a Hair
on My Friend Julian's Head, 1980
- Odilon Redon, Les rochers (Rochers en Bretagne), about 1875
- Odilon Redon, Rue de village about 1875
- Camille Pissarro, Les Coteaux d'Auvers, 1882
- Claude Monet,
La maison du pêcheur, Varengeville, 1982
- Claude Monet, Printemps à Vétheuil, 1880
- Vincent van Gogh, Poplars near Nuenen, 1885
- Anton Mauve, In de Moestuin, 1887
- Peter Struycken, Komputerstrukturen 4a, 1969
- Armando, Zesmaal rood, 1963
- Sol LeWitt, Floor piece no. 1, 1976
- Karel Apple, Paysan avec âne et seau, 1950
- Jean René, Bazame Grand arbre au paysage d'hiver, 1948
- Geer van Velde, Compositie, 1948
- Pierre Soulages, 12 Janvier, 1952
- Mark Rothko, Grey, Orange on Maroon, No. 8, 1960
- Kees van Bohemen, Paysage japonais, 1962
- Woody van Amen, Red, White and Blue, 1968
- Stanley Brown, 100 km, 1976
- On Kawara, 30 JUL. 68, 1968
- Jan Dibbets, Perspective Correction, 4 Horizontal Lines, 1968
- Jeroen Eisinga, Springtime, 2010-2011
- Raphael Hefti, Sensory Spaces II
- Richard Serra, Drawings 2015-2017
- Bruce Nauman, Suck Cuts, 1972
- Joseph Beuys, Grond, 1980-1981
- The Magnetic North & The idea of Freedom
- Paul Gabriel, Polderlandschap met Visser, about 1880-1900
- Albert Marquet, Pont-Neuf au Soleil, 1906
- Edgar Fernhout, Zelfportret, 1953-1954
- Salvo, Senza titalo, 1987
- Ad Dekkers, Houtgrafiek no. XIX
- Albert Cuyp, Riviergezicht, about 1650
- Pieter Jansz. Saenredam, Gezicht op de Mariaplaats en de Mariakerk te
Utrecht, 1662
- Pieter Jansz. Saenredam, interieur van de Sint Janskerk te Utrecht
about 1650
- Constant Troyan, Boslandschap, 1850
- Johannes Hendrik Weissenbruch, Strandgezicht met schelpenvissers,
1981
- Anne Marie Blaupot ten Cate, Zelfportret, 1930
- Carel Willink, Late bezoekers van Pompeï, 1931
- Ted Noten, Train Necklage, 2006
- Bertjan Pot, Random Light, 1999
- Atelier van Lieshout, Orgono Studie-Skull, 1996
- Yayoi Kusama,
Infinite
Mirror Room - Phallis Field (Floor show), 1965.
(I took two picture inside: with
flash light and with
zoom.)
- Yayoi Kusama, Photograph of collage (circa 1966) by Yayoi Kusama, with the artist
reclining on 'Accumulation No. 2', after 1965.
- Rembrandt van Rijn, Titus aan de lezenaar, 1655
- Gunnel Wåhlstrand,
Magasin III, with:
Tore, 2007,
Sydhälsö, 2003,
Uppsala, 2003,
Instön, 2003,
Lookin at Painting, 2008,
Mother Blue, 2008-2009,
Institutet, 2005,
White Peackoks, 2007-2009,
Walk, 2011,
Hällkaret, 2012-2013,
Sandstranden, 2016,
Sluttning, 2014,
Wave, 2015,
Lupris, 2015,
I stugan, 2012-2013,
Mother Profile, 2009,
Den sista ön, 2012,
Vinen, 2013,
ID, 2011,
Biblioteket, 2010,
Nyårsdagen, 2005,
Långedrag, 2004, and
Vid fönstret, 2003
- Pablo Picasso, Femme assise à la terrasse d'un café,
1901
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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