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Wiring brain machine
This evening at TkkrLab, I continued
working on the brain machine. I drilled holes in the box for the jacks, the
potmeter and the reset button. I wired these to the PCB. On the right
a picture of the inside.
Conjecture
I propose the following conjecture: For each natural number n (larger
than three) there exists a set of 2n-1 (distinct) natural number that
sum up to m, which is a multiple of n(n-1), such that
there exists partition of size n and n-1 sets, where the
numbers in each set of the two partition sum up to m/n and
m/(n-1) respectively.
Proof
I found a simple proof for yesterdays conjecture, which
is related to the Irregular Chocolate Bar
problem.
Theorem: For each natural number n (larger than three) there
exists a set of 2n-1 (distinct) natural number that sum up to
3n(n-1), such that there exists partition of size n
and n-1 sets, where the numbers in each set of the two partition
sum up to 3(n-1) and 3n respectively.
Proof: For given n, we show the construction of the set.
First of all, it includes 3(n-1). Next, 1 is added to the set and
also 3(n-1)-1, such that they add up to 3(n-1). Now there,
must also a number that together with 3(n-1)-1 adds up to 3n.
This is the number 4. And that led to the number 3(n-1)-4 that
needs to be included. Continueing this process, will finally lead to the
number 3(n-1)-(3(n-2)+1), which is equal to 2. The numbers 1
and 2 together with 3(n-1) add up to 3n. We also have
another n-2 pairs that up to 3n. That makes a total of
n-1 pairs that add up to 3n. Besides the number 3(n-1)
there are also n-1 pairs that add up to that number, making total
of n sets (one with only one element) that up to 3(n-1). This
completes the proof. Notice that the constructed set comes down to the set
{1, 2, 4, 5, .., 3(n-1)-2, 3(n-1)-1, 3(n-1)}.
Finishing brain machine
Last Friday, I installed Arduino on netbook, downloaded the Tone library and
compiled the Arduino_Brain_Machine.pde file and uploaded it to the brain machine. The
day before, I already had realized that the volume control might not going to
work as designed and that I might have to add two diodes to fix that. And
indeed the volume control did not work. I noticed that it immediately started
to make sounds after I had plugged in the power and that the reset button did
not work. I also verified that the LED part was working. Today, I finished the
glasses with the LEDs and tested the device. I noticed that the LEDs were less
bright than the brain machine from Ada Fruit, but that it did not really
change the experience once you have adjusted to it. I also noticed that the
potmeter did influence the quality of the sound. So now I doubt if I should
fix it. On the right a picture of the finished
box and glasses, which I decorated with the paper from the Ada Fruit brain
machine.
Reprogramming brain machine
This evening at TkkrLab, I looked at the code
(based on Arduino_Brain_Machine.pde) of the brain machine. I had noticed that at
the end the LEDs where left switched on. I discovered that the schematics had
the LEDs connected to the positive voltage, where I had connected them to the
ground. I asked someone about whether this gives a problem and I understood that
connecting the LEDs to positive voltage may make them brighter. I also modified
the sequence of blinking frequences, removing the gamma was that interleaved
the delta was in the middle. I discovered that the reset button does work, but
that it was only used to restart the sequence after it had completed after it
had started on power-up. I changed it in such a way that the sequence does not
start on power-up, but that the button has to be used to start the sequence
and that the button can also be used to stop the sequence once it is running.
This resulted in the following BrainMachine.ino.
Book
At 17:35:03, I bought the book Walk Through Walls: A
Memoir written by Marina Abramović in English and published by Penguin UK in 2016,
ISBN:9780241974513, from bookshop Broekhuis
for € 14.99.
Girl in a Band
This morning, I finished reading the memoir
Girl in a Band by Kim Gordon, which I started reading on the first of the month. I bought
the book on Saturday, July 22 when I was in The
Hague. I had never heard from her before nor heard any of her music, and I also
did not follow the music scene and all that is related to it, so I could not
really appreciate all the details with respect to her music and the people she
worked with, although some of the names are familiary to me. (I am often
surprised that so many famous people have met and know eachother.)
Nevertheless, I found it an interesting book to read, because she seems to talk
very open and honestly about her life, as if she could have been a woman with
a normal job.
HEMA puzzle
In the evening, I went to the Overkill festival and there I found a little
wooden puzzle sold by the Dutch shop HEMA. Of course, I wanted to know the
number of solutions. I wrote the following geometric puzzle representation for the puzzle:
2 0
64
0 0 0 1 0 2 0 3 0 4 0 5 0 6 0 7
1 0 1 1 1 2 1 3 1 4 1 5 1 6 1 7
2 0 2 1 2 2 2 3 2 4 2 5 2 6 2 7
3 0 3 1 3 2 3 3 3 4 3 5 3 6 3 7
4 0 4 1 4 2 4 3 4 4 4 5 4 6 4 7
5 0 5 1 5 2 5 3 5 4 5 5 5 6 5 7
6 0 6 1 6 2 6 3 6 4 6 5 6 6 6 7
7 0 7 1 7 2 7 3 7 4 7 5 7 6 7 7
11
8 1 0 0 0 1 0 2 0 3 1 0 1 1 1 3 2 3
7 3 0 0 0 1 0 2 1 0 1 1 2 0 2 1
7 3 0 0 0 1 1 0 1 1 1 2 2 1 2 2
6 3 0 0 0 2 1 0 1 1 1 2 2 2
6 3 0 0 0 1 0 2 0 3 1 0 1 3
5 3 0 0 0 1 0 2 1 0 2 0
5 3 0 0 0 1 0 2 0 3 1 0
5 3 0 0 0 1 0 2 1 0 1 1
5 3 0 1 1 0 1 1 1 2 2 1
5 3 0 1 0 2 1 0 1 1 2 0
5 3 0 0 0 1 0 2 1 1 2 1
I piped this through gen_dpfp and dpfp2ec into my
Exact Cover solver. It found 89 solutions,
which can be viewed below:
Overkill Festival
This weekend, I attended the Overkill
Festival held in Enschede. I would like to mention the following art works
and games which I liked:
I spend most of my time with the people organizing the Alzheimer GameJam,
who are from Conceptlicious Games and
Breath Audio.
This months interesting links
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