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.
The 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:
I the evening, I went to the second edition of Sonic DIY at
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:
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):
Rinus Roelofs: Had about a hunderd
polyhedra on display.
Judith Schepers and
Danielle Spoelman with their
Lab of Secrets. I joined in and wrote a secret on a piece of paper, put it
into a test tube, added some water and hung it on a line. I was allowed to
get a stamp and placed it in my diary.
At location number 25, the farm "de Vèger", I found a copy of the
book Stilte, ruimte, duisternis: Verkenning in de natuur (Silence,
space, darkness: Exploration in nature) by Kester Freriks. I noted it, because
I had just seen an art work with three wooden boxes with the words silence,
space and darkness on them. Then someone told me that the book had served as
the theme for this year. Somewhere along the route, I took a picture of a wild orchid and a
picture of the sky.
When I came home, I kicked against a hollow chestnut, while walking in the
garden. It was the 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.
Links
Pattern Radio: Whale Songs. Use AI to explore thousands of hours of
humpback whale songs and make your own discoveries.
At 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.
Today, 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.
I wrote a program to calculate in how many
ways the powers (a^{2} + b^{2}) 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 (a^{2} +
b^{2}). 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, a^{4} + 2a^{2}b^{2} +
b^{4} that could be shortened to, in this case,
(a^{2} + b^{2})^{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 (a^{2} + b^{2}) 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.
Yesterday 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:
I 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.
At 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.
I 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.
I 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.
At 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:
FastFurniture, Multiples and Other Productions written by
P.J.H. Kockelkoren in English and Dutch, published by Uitgeverij
AKI/ArtEZ in January 2007,
ISBN:9789073025103, for € 1.50. (Later, I discovered, that I
already have this book.)
Fluid Fascinations - Visualisatie written by Martha J. Haveman,
Onno Bokhove, and Valerie Zwart, written in Dutch and English and
published by Qua Art - Qua Science in April 2010.
Art is therapy written by Alain De Botton and John Armstrong,
written in Dutch and English and published by Rijksmuseum in 2014,
ISBN:9789491714382.
In 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.
I 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).
At Concordia, I saw the exhibitionsLe
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.
A 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:
a_{i}^{2} + b_{i}^{2} = a_{j}^{2} + b_{j}^{2} = n,
assume that a_{i} is smaller than a_{j} (and that the match
with respect to oddity/evenness). There exist whole numbers c, d, e, and f such
that: a_{i} = c - d, a_{j} = c + d, b_{i} = e + f, and
b_{j} = e - f. Through subsitution, one can show that:
c^{2} + d^{2} + e^{2} + f^{2} = 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: (q^{2} + r^{2})(s^{2} + t^{2}) = n.
I went to the opening of the exhibitionFactotum - 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.
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