Dutch / Nederlands
Site map

I write, therefore I am

With this variation on a famous statement by the philosopher Descartes, I would like to express that the act of writing about what happens in my life is important to me.

Friday, July 14, 2017


Tuesday, July 11, 2017


Sunday, July 9, 2017

Gerrit Rietveld Academie

I went to Amsterdam, where I arrived at the central station at eleven. I took some metro's and after I short walk, I arrived around a quarter to noon at the Gerrit Rietveld Academie to look at the finals exhibition of this year. I stayed there till four in the afternoon. I found the following students with their work worth mentioning (in the order that I encountered them):

Afterwards, I visited bookshop Het Martyrium for about a quarter of an hour before closing and Scheltema, where I looked around for about one and half hour without buying anything.

On the way how, I saw two sun dogs with a rainbow pattern. I took a picture. When I biked home from the railway station, the sky turned red and I stopped to take some pictures of which the last turned out to be the best.

Wednesday, July 5, 2017


At 17:56, I bought the book The Game: Undercover in the Secret Society of Pickup Artists written by Neil Strauss in English and published by Canongate in 2007, ISBN:9781847672377, from charity shop Het Goed for € 1.95.

Tuesday, July 4, 2017


Monday, July 3, 2017


When at charity shop Het Goed, one of the people working there, when I was looking at the art book section, pointed out that there was half a shelve of catalogues (all rather thin, more like large flyers) from Stedelijk Museum Amsterdam. As it was close to closing time, I was not able to scan all of them. I found three catalogues related to Peter Struycken. I found one of which I was sure that I already have and two that I was not sure about. At home it appeared that the one that I thought I might have, I did not have, and the one that I thought that I might not have, I did have. At 17:52, I bought the following two 'catalogues':
  • p. struycken published by Stedelijk Museum Amsterdam in 1967 for € 0.95.
  • Nederlandse inzending Biennale Sao Paulo written by Edy de Wilde and published by Stedelijk Museum Amsterdam in 1968 for € 1.50.


Sunday, July 2, 2017


Thursday, June 29, 2017


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).

  6=  =

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

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

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:
  • 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

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.

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 (of 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.

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.


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.

© Rudi Verhagen

Saturday, June 10, 2017


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.

Friday, June 9, 2017


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.

Thursday, June 8, 2017


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

Tuesday, June 6, 2017


Thursday, June 1, 2017


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.


Monday, May 29, 2017


Sunday, May 28, 2017

Bookshops in Utrecht

From the railway station, I walked through the streets Voor Clarenburg and Mariastraat to bookshop De Wijze Kater. I just paid a short visit and only looked at some singing bowls. Next I went to bookshop Steven Sterk and spend some time looking around. At last, I visited Broese Boekverkopers. There again, I only looked around.

Saturday, May 27, 2017


July 2017
Juni 2017
May 2017
April 2017
March 2017
Alzheimer's Disease
Trip to China 2010
-- contact --



Kabuki Syndroom


Useless lists


My life as a hacker
Signature programs
Software enginering
The Art of Programming
eXtreme Programming Programs


Hamilton cycles
cutting sticks
Califlower fractal


Volcano Blog


The email address below, may only be used for private communications. This email address may not be put on any mailing list. I do not want to receive emails with advertisements of any kind. My email address is:

Site statistics

If I did not count wrong, this site consists of 931 HTML-files with a total size of 21,619,743 characters, having 44731 internal links and 9657 external links. (About 729 of the external links are broken.) Furthermore, it contains 184 C/C++ program files with a total size of 4,235,129 characters, and 3 PASCAL program files with a total size of 35,259 characters. There are 71 text files with a total size of 770,426 characters. With respect to images, this site containts 1212 JPEG images (total size 52,863,168 bytes), 146 GIF images (total size 3,765,046 bytes), 89 PNG images (total size 2,114,941 bytes), and 2 BMP images (total size 3,727 bytes). With respect to sounds, it contains 14 WAV files with a total size of 389,002 bytes and 1 MP3 files with a total size of 70,182 bytes. It also contains 43 PostScript files (total size 308,387 bytes), 2 LaTeX files (total size 132,020 characters), 8 PDF files (total size 640,573 characters), 22 zip files (total size 2,487,335 bytes), 3 gzipped tar files (total size 52,345 bytes), 45 SGF files with a total size of 85,019 bytes, 101 KML files with a total size of 4,325,445 bytes, and 2 EXE files with a total size of 38,340 bytes. It also uses 15 JavaScript files with a total size of 621,667 bytes, This leads to a total size of 97,897,062 bytes.


Creative Commons License

I, Frans hold the copyrights of this and all other pages on this website. For this website a Creative Commons License is applicable. You may not use this work for commercial purposes. I consider all computer programs to be copyrighted by me under the GNU General Public License, unless stated explicitly otherwise. All quotes (text and program fragments) from other sources are excluded from this, and should be considered as copyrighted by their authors.

(This space is intentionially left empty)