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Dairy, October 2017



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Tuesday, October 3, 2017

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.


Wednesday, October 4, 2017

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.


Thursday, October 5, 2017

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, the 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 lead 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)}.


Sunday, October 8, 2017

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.


Tuesday, October 10, 2017

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 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.


Wednesday, October 11, 2017

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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