Wishful Coding

While everyone was making new years resolutions for themselves, I was making new years resolutions for the world. Or rather, thinking how change happens.

It seems people are hardly able to change themselves, even if they set out to do so. So how can we even begin to think about changing humanity as a whole? It seems we just keep doing whatever is easiest/best/most comfortable, and change only happens when something easier/better/more comfortable comes around.

Sometimes you read about these civilizations that seemed to be really advanced for their time, but then just sort of died out. Looking back it is often obvious why, and you wonder if they did not see it coming. But what if they saw it coming all along, but were unable to change their ways?

The only mechanism we have for global change is governance. But as Douglas Adams explains

One of the many major problems with governing people is that of whom you get to do it; or rather of who manages to get people to let them do it to them: It is a well known fact, that those people who most want to rule people are, ipso facto, those least suited to do it. Anyone who is capable of getting themselves into a position of power should on no account be allowed to do the job.

Often times I have an idea to make something somewhere a little better. No grand plans to solve world hunger, just small things. Often by means of sharing or exchanging information or goods. Without exception, these ideas include the sentence “If everyone would just…” and you quickly learn about the Network Effect.

I’m just back from 32c3, where I saw a number of interesting art projects. Many of these projects used technology not to provide utility, but to convey a message. Thinking about all the above, I built The World Improvement Server; a caricature of global change.

Th World Improvement Server runs a program that speaks the SUN-RPC rwall protocol, listening for your world improvement ideas. These ideas are then broadcast over the QOTD protocol to anyone who cares to listen.

To start improving the world, simply run rwall 37.247.53.27 and type your idea, followed by EOF.

To learn more about ways to improve the world, simply telnet 37.247.53.27 17, which as of 2 January 2016 returns

$ telnet 37.247.53.27 17
Trying 37.247.53.27...
Connected to 37.247.53.27.
Escape character is '^]'.

If everyone would just [...]
the world would be a much better place!

Submit global world improvement using rwall.

Remote Broadcast Message from pepijn@pepijn-Latitude-E6420
	(/dev/pts/0) at 18:19 ...

If everyone would just use this service to make the world a better place
the world would be a better place.


Connection closed by foreign host.

I’m building a simple synth on a breadboard, where the frequency is defined as \(f=\frac{1}{RC}\), so by using different resistors with a row of buttons, different tones can be made. But what if you press two buttons simultaneously? You get 2 parallel resistors, giving:

I stumbled on this while playing with it, and the combined tones seem to be nice intervals sometimes. So I started to wonder if there was a connection.

In 12-tone equal temperament, the ratio of the frequency between two notes is \(\sqrt[12]{2}\), so we could just plug it in and see what comes out. Take a series of notes:

And a series of a combined frequencies:

Plotting these in Matlab gives the following result

base = 220;
bp = 1/base;

tones = base.*(nthroot(2,12).^(0:12));
periods = 1./tones;
r = (bp.*periods)./(bp+periods);
duotones = 1./r;


plot(0:12, tones.*2, 'o', 0:12, duotones,'o');
grid on
grid minor

As can be seen, some combined tones are indeed quite close, but most not exactly. But then equal temperament does not have exact harmonics either. So we still do not know if we are generating actual harmonics, or just frequencies that happen to be close.

So what if instead of starting with \(\sqrt[12]{2}\), we start with integer multiples of the base frequency and fold then back into one octave. This gives:

Plugging that into the parallel resistance equation, we can begin to search for exact harmonics giving exact harmonics.

harm = 1:31;
harm_cap = zeros();

for i = harm
  j = i;
  while j>2
      j= j/2;
  end
  harm_cap(i) = j;
end

period = 1./harm_cap;

par = (1.*period)./(1+period);

freq = 1./par;
freq_cap = zeros();

for i = harm
  j = freq(i);
  while j>2
      j= j/2;
  end
  freq_cap(i) = j;
end

[C,ia,ib] = intersect(harm_cap, freq_cap)

And we can indeed verify that two resistors with a 2:1 ratio give a fifth (3:2):

Likewise a resistor ratio for a fifth gives a major third (5:3)

Math, music, physics. So beautiful.

Update:

As pointed out by Darius Bacon, this might not be a complete surprise, as there is a striking similarity between parallel resistance and the harmonic mean.

Wikipedia also has the following to say about the harmonic series:

Its name derives from the concept of overtones, or harmonics in music: the wavelengths of the overtones of a vibrating string are 1/2, 1/3, 1/4, etc., of the string’s fundamental wavelength. Every term of the series after the first is the harmonic mean of the neighbouring terms; the phrase harmonic mean likewise derives from music.

I wanted to invite someone over to watch a movie, but realised that my energy saving light bulb isn’t the most cozy environment ever. The light they give of always feels a bit cold.

To remedy this I went to the store to buy some candles (and forgot to buy matches). But just plain candles seemed so boring, so I wanted to do something special with them.

I remembered from years back this Tai Chi practice where you put glasses of water or candles on your hands and rotate them over and under your shoulder. It creates this beautiful spiral movement. So I thought it would be nice to make a robot that moves my candles around.

The robot is done. Now to wait for the movie.

https://youtu.be/jTTEXhUBSRs