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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. 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 2n1 (distinct) natural number that
sum up to m, which is a multiple of n(n1), such that
there exists partition of size n and n1 sets, where the
numbers in each set of the two partition sum up to m/n and
m/(n1) 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 2n1 (distinct) natural number that sum up to
3n(n1), such that there exists partition of size n
and n1 sets, where the numbers in each set of the two partition
sum up to 3(n1) and 3n respectively.
Proof: For given n, the show the construction of the set.
First of all, it includes 3(n1). Next, 1 is added to the set and
also 3(n1)1, such that they add up to 3(n1). Now there,
must also a number that together with 3(n1)1 adds up to 3n.
This is the number 4. And that lead to the number 3(n1)4 that
needs to be included. Continueing this process, will finally lead to the
number 3(n1)(3(n2)+1), which is equal to 2. The numbers 1
and 2 together with 3(n1) add up to 3n. We also have
another n2 pairs that up to 3n. That makes a total of
n1 pairs that add up to 3n. Besides the number 3(n1)
there are also n1 pairs that add up to that number, making total
of n sets (one with only one element) that up to 3(n1). This
completes the proof. Notice that the constructed set comes down to the set
{1, 2, 4, 5, .., 3(n1)2, 3(n1)1, 3(n1)}.
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 was 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 powerup. I changed it in such a way that the sequence does not
start on powerup, 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.
This months interesting links
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 September 2017