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.
Powers continuedYesterday evening, I had a look at how the expressions of the powers of (a2 + b2) are related to each other and I arrived at this figure:
1 - + 2 1 \ + - 1 2 - + - + 2 1 3 \ + - + - 1 2 3 - + - + - + 2 1 3 4 \ + - + - + - 1 2 3 4 - + - + - + - + 2 1 3 4 5 \ + - + - + - + - 1 2 3 4 5The numbers in each line, stand for the equations and the '+' and the '-' symbols stand for the variant of the Brahmagupta-Fibonacci identity that has been choosen. The '\' is used when both '+' and '-' return the same result. This happens when one of the squares is zero. If seems that twice taking the same variant, leads to the same result. Lets see if this is generally the case:
(r2 + s2)(a2 + b2) = (rb + sa)2 + (ra - sb)2
(r2 + s2)(a2 + b2) = (rb - sa)2 + (ra + sb)2
Now, it seems that the results are not the same.Sickhouse in Enschede. First Patrick Jonkman gave a presentation about the history of electronic instruments. This was followed by a live performance by Dennis van Tilburg (on SoundCloud). Nicolas from soundforce told something about the Eurorack modules he is developing. It was mostly about a DCO (digital voltage controlled oscilator). After a short break, there were some five minute jam sessions with pairs of people. The jam was hosted by Gijs van Ouwerkerk with Ingmar Kops, Gregor Beyerle, Nicolas Toussaint, and Jasper Schütz. I listened to the first jam, but left the room when it became a little too hot for my tasted. I joined the Live Hex workshop held by Ole Nieling, which was about building a simple oscilator with the CD40106BE, also known as the Hex Schmitt Trigger (with inverter) IC. I build the basic circuit with a LDR and 10nF capacitor. I went on to experiment a little and put two oscilators in series using another 10nF capacitor. There were three more performances:
Outdoor artI first went to Kunst in het Volkspark (Art in the people's park). I found the following things interesting:
Next, I went to KunstenLandschap. At Tetem art space, I met with Willemijn Calis, who was there to show the augmented reality project she had been working on. I left my coat at Tetem, because it had got too warm outside for wearing a coat. I found the following artist worth mentioning (in the order I saw their works):
first chestnut that I found last year and placed in a pot. It started to grow and I noticed that the chestnut had become hollow. I do wonder how the hollow chestnut ended up on the path and suspect that some animal was involved.
BookAt 16:54, I bought the book Kunst werkt | Art works with an introduction by Renilde Hannacher-van den Brande, in Dutch and translated to English, published by Peter Stuyvesant Stichting in 1992 from charity shop Het Goed for € 2.50.
First hot dayToday, the temperature reached more than 30°C in the Netherlands. In De Bilt it reached 30.4°C, which is the highest temperature ever measured on this day of the year, and at Airport Twente it reached 30.9°C, which might as well also be the highest temperature ever measured at that location.
PowersI wrote a program to calculate in how many ways the powers (a2 + b2) can be written as the sum of two squares. The program does this by taking the results from the previous power and apply the Brahmagupta-Fibonacci identity with (a2 + b2). I noted that all the expressions involved are polynomials on a and b where the joint powers are equal, meaning that they can be represented by a list of coefficients. The program makes use of this property, which means that some results are written like long polynomials, like for example, a4 + 2a2b2 + b4 that could be shortened to, in this case, (a2 + b2)2. It seems that the number of ways a power can be written as the sum of two squares, is one more than the number of ways that power can be written as the product of two numbers. I have not found a proof why this is the case and also I have not proven that for all cases where (a2 + b2) equals a Pythagorean prime the pairs are all actually different. It could already be the case if a and b are relative prime. Below the results are given for the powers up to and including six.
The expression (a2 + b2)2 is equal to:
Maker Festival TwenteYesterday and today, I went to Maker Festival Twente where Annabel was present with the jigsaw puzzles she made. She started to develop the puzzles as part of a minor in creative entrepreneurship. She designed the concept, selected the materials, developed the package material, instructions, and marketing materials. Before arriving at the final design, she did a lot of experimentation and made several samples, some of which she tested on her fellow students. A record of her progress can be found on her instagram account. For the production of the puzzles, she used of the laser cutter of Twenspace, a local maker space, which was also present at the maker festival, just next to her. This allowed people to have their puzzles engraved with a personal message. It was quite and interesting experience to present the puzzles at the maker festival and see how the people, mostly parent with their children, responded.
There were some other intersting things at the maker festival:
Big Data is watching youI went to the Gogbot Café number 8: Big data is watching you, which was held at Tetem art space. The topic of the coming GOGBOT festival will be about machines and artificial intelligence.
The first talk was by Arthur Boer and Boris Smeenk. Their first joined project was the Screen Shot project in 2016. They repeatedly took screen shots from an image. In 2017 they did the Epoch project, a machine learning project. They also did a visual experience with 'blending' all the mac OS wallpapers. They also used this for the Dutch Design Week 2018. In 2018 they did the Make Believe project to use AI algorithm implemented in smart phones They developed the Phony camera which removes people from the image being taken. The final project is OBJ: Object Behaviour Jam (2019), a camera which recognizes objects and replace them with the closest object in the database. So it shows what the algorithm sees.
The seond talk was by Sander Veenhof, which is a condenses verion of the talk Be Your Own Robot he gave last month. He adds the idea of Open Source DIY AI instead of sharing data with the big cloud companies. Then there was a break.
The third talk was by the artist Elise Marcus. We receive so much information and often we do not know what to trust. So, lets assume you have some extra sense to know the environment directly. How would this affect our behaviour if every one would have this sense. She is creating the Mother Earth Network. They are creating sensors that you can build yourself and use these, with the idea of combining all this sensor data. An introductory video.
The last talk is by professor Ciano Aydin from the University of Twente about Extimate
technology. Self-formation: out post-modern era's promise. Self-formation
as anti-essentialism. Transhumanists/techno-optimits: from self-formation to
self-enhancement. NBIC-technology. Our posthuman future. Ray Kurzweil: The
prediction of the singularity. Two problems with this: no univocal criteria
for 'improvement' and technology is becoming 'extimate'. About the first:
Technology are not neutral but bring about new and different standards for
what is normal, healthy and enhanced. He talks about the example of the
coachilar implants affecting the sign-language culture. About the second:
Uncanny valley as a robot or other artifact becomes more human-like. What
about machine like humans. The inverse Turin test: in what ways are humans
becoming more machine like. Is there an uncanny valley in machine-like humans:
extreme forms of plastic surgery. It seems that the goal of big data is now to
automate us. We are autonimos: There is an inside and an outside. There is
something about identity: what identifies us are things that we have no chosen
ourself: our name, our sex, our skin, and so on. Technology is more and more
determining who we are. Maybe the uncanny value is caused by the fact that we
know what it means to be human. The example of a young child swipping the cover
of a book.
BookAt 17:47, I bought the book Horken & Heksen written by Jeffrey Wijnberg in Dutch and published by Scriptum Psychologie in March 2011, ISBN:9789055947560, from charity shop Het Goed for € 2.95.
Square WaveI went to the Square Wave - Modular Synt Improv Meet in Deventer, which was organized by Voltmeister. Eight people had shown up with their (modular) synthesizer. During every round, they were paired up by a draw for doing a synthesizer improvisation given a BPM selected at random. I am thinking about starting with modular synthesizers myself. Around 2003, I played with various software synthesizers. For example: SynFactory. In the past weeks, I did some investigation with respect to the various formats and directions there are with respect to modular synthesizers. I getting more and more excited about the Eurorack format.
Friday, May 17, 2019
PlanetArt reopeningI went to the reopening of PlanetArt in Enschede. They are, besides many other things, the organizers of the GogBot festival. I met various people that I know to different degrees. There were also a lot of people that I do not know. I had some interesting conversations and decided to write this while being there. I decided not to stay too long.
BooksAt 16:45, I received the book Jaarboek 09|10 written by Ina Bodde, Marion Bouwhuis, Ina Klaassen, Coen Scheen, and Petra Winkes, in Dutch and English, published by ArtEZ Art & Design in 2010, ISBN:9789075522358, which I had bought on Wednesday, May 1, 2019 at 19:22 from AKI shop for € 25.00. At 17:46, I bought the following three books from charity shop Het Goed:
Open air book market TuindorpIn the morning, I went to the open air book market Tuindorp in Hengelo. At 11:43, I bought the book Het litteken van de dood: de biografie van Jan Wolkers written by Onno Blom in Dutch and published by Bezige Bij in 2017, ISBN:9789023468721, from Ruco Pesse for € 14.59.
Saturday, May 11, 2019
Pythagorean primesI spend some time researching the conjecture, which I described on last Thursday. First of all, I discovered that the relationship that I described has been known (in a slightly different form) for centuries and is known as the Brahmagupta-Fibonacci identity. I also have discovered that it seems that numbers n are always the product of Pythagorean primes. Fermat's theorem on sums of two squares states that prime number can be written as the sum of two squares if and only if it is a Pythagorean prime (proof). Combining the two, it is also clear that there is only one way in which a Pythagorean prime can be described as the sum of two squares. If there were two (or more) ways, than you can find two numbers that are the sum of two squares, which when multiplied are equal to the prime, which would be a contradition. It seems also rather obvious that the product of two different Pythagorean primes must have two ways it can be written as the sum of two squares. Although the reverse also seems likely, the proof for it seems a little more complicated. It is clear that the product of two primes, can only written in one way as the product of two numbers (where the first is smaller or equal to the second).
ExhibitionsAt Concordia, I saw the exhibitions Le Gymnasium Sacre by Sam Samiee and Grenzeloos with works from the four Dutch artists Ronald de Bloeme, William Engelen, Jeroen Jacobs and Maarten Janssen, who (independenlty of eachother) moved to Berlin.
Sum of squaresA friend of mine pointed out that it seems that if a odd number can be written as the sum of n pairs of squares (and the greatest common divider of all these squares is one), that the number can be written as the product of n-1 different pairs of numbers. The numbers in these pairs are sums of squares as well. I do not know if this is a know fact, but it seems to be true for all such numbers up to a million (as verified with this program). Today, I proved that for any two pairs of squares that add to the same number, there exists (at least one) product of two sums of two squares that results in the same number. If the sum of squares is odd, one of the squares must be odd and the other even. In that case, match the odd and even squares of both pairs. In all other cases either both squares are even or odd. In which any matching will work. Now given: ai2 + bi2 = aj2 + bj2 = n, assume that ai is smaller than aj (and that the match with respect to oddity/evenness). There exist whole numbers c, d, e, and f such that: ai = c - d, aj = c + d, bi = e + f, and bj = e - f. Through subsitution, one can show that: c2 + d2 + e2 + f2 = n and c.d = e.f. Furthermore, one can define q, r, s, and t, as follows: q = gcd(d, f), r = gcd(c, e), s = f/q = c/r, and t = d/q = e/r. For which one can show that: (q2 + r2)(s2 + t2) = n.
Factotum - WYDSIWYGI went to the opening of the exhibition Factotum - WYDSIWYG by the photographer René Damen at B93. The exhibition was opened by Jeffrey Pardoen through a video connection from England. Factotum is Latin for Jack-of-all-traits and it does describe the exhibition well. The photographs are group together in interesting combinations, which are not always obvious on first sight. Sometimes, they resemble in colour, sometimes they resemble in shape, and sometimes they resemble in little details. This has indeed something poetical as Pardoen said during the opening speech.
Other PlacesIn the evening, I had a quick look at the exhibition Other Places at the University of Twente. I found the works by Judith Schepers most impressive.
Sunday, April 28, 2019
Saturday, April 27, 2019
Trip to China 2019
-- contact -- Frans
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