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Dairy, September 2015



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Thursday, September 3, 2015

PARR: slicing method

After writing about PARR, I realized that the slicing method could be used, that I also used for counting Hamiltonian cycles in product graphs and generalized to finding all kinds of subgraphs in product graphs. The idea is to take the PARR and slice it up into four by five points of the PARR configuration up into four slices each containing two columns of four points, and devise the rules for which the different configurations that can occur in each slice connect. With this it is possible to construct a transition matrix, and once this matrix is known, it is relatively easy to calculate the number of PARR configurations with certain properties. I thought about modifying the count.c program, but decided that it was faster to implement it from scratch than try to fit it in. A drawback is that I cannot calculate the recurrence equation for the PARR's on four by n points, which would go beyond the original four by five configurations. (I might decided to do this at a later point in time.) I first used the program to verify the results that I calculated before, and after this, I went on to calculate the number of connected PARR configurations with the various conditions. The total numbers of the results are presented in the table below. Each cell in the table contains the number of total number of PARR configurations and below it the number of connected configurations (in which all points are connected to one of more connection). The first column gives the PARR configurations where not all neighbour points have a connection. In the second column the are always connected. The first row gives the PARR configurations where crossing diagonals are allowed and the second column gives the results for when they are not allowed. The bold number, is the number of connected PARR configurations with no crossing diagonals and where not all neighbour points need to have a connection. I assume that this the type of PARR configurations that the original authors had in mind.
neighbours optionalneighbours connected
crossing diagonals84,024,935,266,353,181
31,904,643,741,844,306
1,048,576
517,646
no crossing diagonals4,147,603,839,035,069
847,157,460,556,451
2,976,416
2,041,600
The above count contain many configurations that are similar, except for being translated, rotated, and/or mirror with the four by five points. Next I will try to investigate the numbers of 'unique' PARR configurations.

(On September 16, I discovered that numbers marked with red, are incorrect.)


Friday, September 4, 2015

Amsterdam

I went to Amsterdam with a friend. We visited the Stedelijk Museum Amsterdam. We first looked at some from before 1960, including: Next we watched the videos by Tromarama, a group of three artist from Indonesia. Then we looked at the design exhibition in the reverse order. There we saw: Next we walked through the second floor of the museum, where we saw, among many others for which I cannot find the titles: In one of the rooms we also encountered: A year at the stedelijk: Tino Sehgal. Finally, we went downstairs to visit the exhibition: ZERO: Let us explore the stars about the ZERO movement. This contains works by Jan Schoonhoven. My friend bought the catalogue for me. We saw the Condensation Cube by Hans Haacke. I took a picture of Sphèr-Trames by François Morellet showing a hexagon shape. I also took a picture of Lichtrooster in de ruimte (light grid in space) by Heinz Mack, which for some magical reason reflected images rotated by about 90 degrees.

We also went to bookshop Scheltema, which moved to Rokin 9. We mostly stayed at the top floor looking at second hand and cheaply priced books. At 16:10, I purchased a black, hardback Moleskine Daily Diary / Planner of 2016 (ISBN:8052204400010) for € 17.50.


Thurday, September 10, 2015

Book

At 11:47:21, I bought the book De Aanslag (The Assault) by Harry Mulisch, ISBN:20150910114721, from bookshop Broekhuis for € 5.00.

Gogbot

In the evening, I visited The Gogbot festival with a good friend. We first went to look at the exhibition at Concordia. We found NOVA EDEN by Rob van der Burg the most interesting. Next we looked inside the 'Oude Kerk' and the sqaure around it. We found PHOTOTROPE by Pauline van Dongen most interesting. We did also look at a quick look in the TkkrLab dome, where it was rather quiet. This year year lacked any very exciting instalations. Maybe this is due to the theme: "The Internet of Things" with its focus on small, often hidden, devices.


Saturday, September 12, 2015

2 by 2 unique PARR configurations

I found a newspaper article Tussen kunst en wetenschap: Taco Stolk en de schoonheid van wiskunde on page 15 of the Leidsch Dagblad of December 5, 2001. The text is not completely visible, but I guess that PARR stands for Particle Aesthetics Relation Research. With the article there is also a picture of Taco Stolk sitting in front of laptop showing (with white on a black background) a PARR configuration on seven points and nine connections with two crossing diagonal connections. I conclude from this, that crossing diagonals are allowed in PARR configurations.

Below, a drawing of all unique PARR configurations on a two by two grid, not taking into account rotating and mirroring. I have placed them in rows and columns depending on the number of horizontal and vertical connections (rows) and the number of diagonal connections (columns). There are 31 of them:


Monday, September 14, 2015

Consciousness and the Brain

This morning, I finished reading Consciousness and the Brain by Stanislas Dehaene, which I started reading on August 15. Two months before, I bought it in Antwerp. The book is based on scientific research in the past thirty years, which is reflected in list of references covering 32 pages. Yet, the book is very readable and I enjoyed reading it. There were only a few sections where I felt that the author was kind of repeating the same statement in a different manner, probably with the aim to clarify his central ideas. The book indeed exposes some very interesting discoveries with respect to consciousness, but I doubt if those (now or in the future) address the mystery with of subjective experience. I also think that his ideas about how consciousness could (in the future) be achieve with computers, rather simplistic, probably due to a lack of understandig of how computers work.

Chapter 6 deals with the disorder of consciousness that can follow coma, such as the vegetative and minimally conscious states. I wonder how these match with de disorder of consciousness that occur in the late stages of dementia. Is it true that people progress from the minimally conscious state to the vegetative state before going into coma. I wonder if any research has been done in this area, now that relatively simple techniques for detecting conscious states have been discovered.


Tuesday, September 15, 2015

You should be here!

I finished reading the book You should be here! A book about Helsinki by Tom Bulgaria, which I started reading on August 30 after I bought if on August 21. I enjoyed reading this alternative tourist guide to Helsinki. It made me want to stay there for some months and visit all the places mentioned in the book. I stayed in Helsinki in May 1996.


Wednesday, September 16, 2015

PARR: corrections

While working on the counting algorithm for unique PARR configurations, I discovered an error in the previously published results. The current version of the program finds the results shown below in the table. The bold number is the number of connected configuration in which not all neighbour points have a connection and in which crossing diagonals are allowed.

neighbours optionalneighbours connected
crossing diagonals 84,024,935,266,353,181
3,111,175,282,862,826
1,048,576
517,646
no crossing diagonals 4,147,603,839,035,069
82,280,232,154,141
2,976,416
2,041,600

Rainbow

When I biked home, I noticed, while biking on the Lonnekerbrugstraat, that the sun behind a cloud just above the horizon was causing rays of light from above and under the cloud. At the same time it started to rain a little, and when I searched for a rainbow, I found a partial (around 19:19). It quickly grew into an almost complete, rather faint single rainbow. I waited for the sun to appear behind the cloud, hoping it would result in a bright rainbow against al already rather dark background, but that never happened. When around 19:23, I arrive at the end of the Lonnekerbrugstraat my view was obstructed by some trees, and when I could see the sky again, the rainbow was gone, and so where the rays because the sun had disappeared behing some thick clouds. Later, I realized that this rainbow was not caused by direct sunlight, which made it noteworthy.


Thursday, September 17, 2015

Blao

This evening, Carina Schüring visited us. She brought the painting, which she recently named 'Blao', with her. It is the painting that I had decided to buy after we visited her on Wednesday, July 15. After we had dinner, I read through the purchase contract, stated in German, as she is a German citizen, signed it, and transfered a sum of money to her account, thus making me the owner of the work. The contract contained a clause, giving her the right to put the work on display, whenever she has an exhibition, for which it is suitable. I am very happy to borrow it to her for that purpose.


Friday, September 18, 2015

Book

At 10:15, I bought the book POPism: The Andy Warhol '60s by Andy Warhol and Pat Hackett, from the charity shop Het Goed for € 1.50.


Monday, September 21, 2015

Node.js

I uploaded a new version of the webiste about Peter Struycken. This version has both static and dynamic parts. The dynamic part is based on the JavaScript code, I already had. The static part is generated with Node.js using the same data but with some additional files. Becaues it seems that Node.js does not support a include mechanism, I wrote a batch file, which just copies some files together. Because the website has both an English and a Dutch part, and I basically need to run the same generation for two languages, I came up with the idea to just include the generation part twice. To reduce space, I already developed a small program to strip JavaScript from useless information (spaces and comments) and remove all data from 'src' fields in records. This is how the batch file looks
Iparse.exe -s PS_js.gr dataSrc.js >errors.txt
StripJS.exe <dataSrc.js >data.js
StripJS.exe <enSrc.js >en.js
StripJS.exe <nlSrc.js >nl.js
StripJS.exe <contSrc.js >cont.js
StripJS.exe <dynSrc.js >dyn.js
more <data.js >temp.js
more <contSrc.js >>temp.js
more <enSrc.js >>temp.js
more <genSite.js >>temp.js
more <nlSrc.js >>temp.js
more <genSite.js >>temp.js
Node temp.js 2>>errors.txt
mysample.exe errors.txt


Saturday, September 26, 2015

Unique PARR configurations

I completed the algorithm for finding unique PARR configurations. The algorithm makes use of the transition table that is generated by the slicing method. It took me some time to get all the rotations and mirrorings correct. The algorithm simply generates all the configurations (up to a certain number of points) and then rotates, mirrors the configuration in all directions seeing if it would result in a 'smaller' configuration. If it does not, it is counted, and also written to a binary file for later processing. With smaller, I mean that a binary vector is made out of all the points and connections and if this vector is smaller than the configuration in it original orientation. It appreared that for the restriction that all pairs of neighbour points should have connection, either with or without crossing diagonals, it is possible to calculate all unique configurations within reasonable time. For the configurations where not all neighbour points are connected, this is not feasable, simply because the number connected configurations is more than a million times larger. Only all unique configurations on nine or less points where counted and written to file. The calculation for those configurations took almost six hours on johan. I guess that for ten or less points the time will more than fourty hours. The current version of the program finds the results shown in the table below. The numbers between brackets are for all configurations with nine or less points.

neighbours optionalneighbours connected
crossing diagonals 84,024,935,266,353,181
3,111,175,282,862,826
(17,682,852)
1,048,576
517,646
113,346
no crossing diagonals 4,147,603,839,035,069
82,280,232,154,141
(10,215,753)
2,976,416
2,041,600
466,446

The image shown with the 'PARR' bar on WLFR shows the PARR 7|11 Reference Guide about PARR configurations with seven points and eleven connections. The calculation show that there are a total of 802 connected PARR 7|11 configurations. The program PARRan_7_11.cpp when given the PARR_con_o_9.data file as input produces the list of all solution (as ASCII art): PARR_7_11.txt.

I just noticed that the image also shows a disconnected PARR on the left page of the book that is layed open at the bottom half. Both PARR configuration shown in that book have five points and four connections. I guess this is the PARR 5|4 Reference Guide. Maybe I should also calculate the number of unique configurations on disconnected PARR configurations.


Wednesday, September 30, 2015

PARR: maximal connections

When I was working on the PARR configurations, I noticed that there were two unique configurations on five points with eight connections. Because I could only imagine one such configuration, I first thought that there must have been a bug in the program, but when I looked at the print of the configurations, I found that five points in the shape of a cross also have eight connections. Then, I began to look at the other configurations with a maximal number of connections. I expected that there would be a simple pattern in those, but that appeared not to be the case. I found the following sequences of maximal number of connections for the number of points starting with one: 1, 3, 6, 8, 11, 14, 17, 20, 23, 26, 30, 33, 36, 39, 43. I did check for this sequence in the The On-Line Encyclopedia of Integer Sequences®, but did not find it. I made a drawing of all the maximal configurations on four to sixteen points, in which red lines connect configurations of different sizes that can be embedded without translation and a blue line for two configurations that require mirroring:

Remark: The second configuration on the second last row does not fit in a 4 by 5 PARR configuration


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