Monday, 9 September 2013

Street Addresses

Often, when I'm on long (or short) car trips, I think a great deal. Naturally, as there are a lot of them along the side of roads, I end up thinking about address signs. Where I live, they tend to be four digits long, which are nice even numbers which you can rearrange in all sorts of brilliant ways. There's always the simple palindrome, such as 1221. Another satisfying one is where all the numbers are the same except one. For example, 9939. My favourites, though, are consecutive numbers.
But not normal consecutive numbers. Not like 5678 or 4321.
They have to be out of order. For example, if you took the sequence 6789...
and scrambled it up, giving you something like 9687.

A game I like to play with myself while driving along a road is to predict when the next one will be. For example, if the address numbers are going up and I see 3109, then I have to find the lowest one which is drawn from the set 1234, that is higher than 3109. The answer, then, is 3124.

But here's a question: How many possible four digit non-sequential consecutive permutations are there (that's a long name; I need to come up with a better one)?
Well, first we need to figure out how many possible permutations there are of any given four digits.
If we take the simple 1234, then this, I think, is the total of all possible arrangements:
1234 1243 1324 1342 1423 1432
2134 2143 2314 2341 2413 2431
3124 3142 3214 3241 3412 3421
4123 4132 4213 4231 4312 4321
That gives me 24 possible arrangements, and since I don't consider 1234 or 4321 to be good, then I think I can just go ahead and cross those out, giving me a grand total of 22.

But that's not all. In a base ten system, these are all the possible consecutive four digit combinations, each of which have 22 "valid" permutations:
1234 2345
3456 4567
5678 6789

There are six. And that multiplied by 22 is 132. 132 "good" street addresses in the four digit range.

But I'm not done yet - I'd like to look at the relationships between these numbers - including sequential ones, like 1234.
To find a full list of numbers, I will take the list of permutations of "1234" from further up, then change them to 2345, 3456, etc. by placing them in a text document, and find-and-replacing 1s with 2s, 2s with 3s, etc.
Before I do that, though, it's worth mentioning that the total of numbers with consecutive digits from 1000 to 9999, is 144. Interesting.

Now that I've done that, the first thing that I did was put all the numbers into numerical difference, and looked at the difference between each number, and the one next to it. It doesn't make a lot of sense.

Anyway, enough of that. Let's make a graph.


This is very curious. There's definitely a pattern, but what is it?
My theory is that what we're looking at is a fractal, so to speak. By that I mean, I think that every time the data points pass a power of ten and a digit returns to zero, there's a little jump in the graph. Also, I think that the larger the power of ten, the larger the jump in the line. In fact, if you will direct your attention towards the edges of the graph, I would assume that those are even larger "jumps", associated with 10,000. If you kept zooming out, I believe that there would continue to be larger and larger jumps with each new digit, on to infinity. And who knows what might happen there.

Saturday, 15 June 2013

Using Computer Audio as Microphone on Macintosh

Have you ever wanted to record a file of an online audio stream or something? Perhaps you don't like using youtube-mp3.org but still want to rip music off YouTube. Whatever your motive is, I do frequently record my computer audio. The process was unfortunately quite obscure and involved a lot of internet searches. And now I'm going to tell you how.

Step one: Download and install SoundFlower.

Once done, you should see it as a device in your sound menu.

But you can't stop here; there's one more crucial step for it to work properly. So...

Step Two: Open Audio Midi Setup

Step Three: Press the plus button in the bottom left to create a multi-output device.
In the list in the bottom, select only Soundflower (2ch),
(although I believe 16ch works as well), and Built-in Output.


Step Four: To record computer audio, you will need to do two things. First, go to audio settings, and under Output, select Multi-Output Device.

Then, go to Input and select either Soundflower (2ch) or (16ch), whichever one you chose for your Multi-Output device. If you're using stereo headphones, I don't think it makes a difference.
Note the registering audio input. I was listening to Nixon in China.

This worked very well for me. There doesn't seem to be any loss in audio quality. As a matter of fact, I used this system to obtain the album Naqoyqatsi (which isn't available for purchase online) from some chap who uploaded it to YouTube.

The good thing about this system is that if you use an application such as Audacity, then you can output it in whatever format you wish - for this particular case, I wasn't limited to not very good quality mp3 files - you can do whatever you want this way. FLACs, OGGs, AIFFs... Anything is possible!

Wednesday, 29 May 2013

The Rite of Spring

For those of you who don't know, today, May 29 is the 100th birthday of what is perhaps Igor Stravinsky's most famous work, The Rite of Spring! It apparently caused riots on its parisian opening (people hated it), but soon came to be recognized as one of the foremost developers of 20th century classical music.
I for one quite enjoy this piece (though it's not for everyone). For your convenience, here's a quite splendid animation of the piece:
Too bad there was no google doodle though. That would've been amazing.

Wednesday, 10 April 2013

A Post Whose Nouns Have Been Replaced Entirely With Dictionary Definitions

      Last period from Friday evening through Saturday evening, regarded as a time for leisure, I went for a long walk in the country or wilderness up a nearby geographical assemblage of rocks or series of strata having some common characteristic. It's a long steep slope, one at the edge of a plateau or separating areas of land at different heights, which showcases rock formations that are visible on the surface of hard sedimentary rock, composed mainly of calcium carbonate or dolomite, used as building material and in the making of cement to the surrounding part of the earth's surface that is not covered by water, as opposed to the sea or air. Walking on the beaten path through rough country such as a forest or moor along the areas next to a steep drop gives some nice sights or prospects, typically of attractive natural scenery, that can be taken in by the eye from a particular place, including my place for human habitation, one that is lived in by a family or small group of people. The only matter or situation regarded as unwelcome or harmful and needing to be dealt with or overcome was that my coverings for the foot, typically made of leather, with a sturdy sole and not reaching above the ankle were too small, so soon my lower extremities of the leg below the ankle, on which a person stands or walks began to hurt. Additionally, we forgot to bring a colourless, transparent, odourless, tasteless liquid that forms the seas, lakes, rivers, and rain and is the basis of the fluids of living organisms. So there were pleasant events or occurrences that leave an impression on someone combined with unpleasant ones.
      One interesting object that one need not, cannot, or does not wish to give a specific name to, to note is that there are slender, fast-growing trees that have thin bark (often peeling) and bear catkins along the steep rock face's area next to a steep drop which are thousands of the time taken by a planet to make one revolution around the sun old. Once the long walk in the country or wilderness was over, we returned to our thing used for transporting people or goods on land, such as a car, truck, or cart, only to find a notice telling a driver of a fine imposed for parking illegally, typically attached to a car windshield! Which was kind of annoying, since this space allocated for a specific purpose had gigantic, well paved paved strips alongside a road for stopping on, as well as several conspicuous buildings or areas used for a specified purpose or activity, of interest. But it was a no stopping area or stretch of land having a particular characteristic, purpose, or use, or subject to particular restrictions, so I guess this is just the civil force of a national or local government, responsible for the prevention and detection of crime and the maintenance of public order trying to make some current medium of exchange in the form of coins and banknotes. Oh well.

Saturday, 2 February 2013

Ambient Music

Lately, I've been listening to ambient music more frequently. I think I've developed a taste for it - at least the sort of slow moving, spacey kind. What interests me is the kind where it's essentially a set of chords which are drawn out over a long period of time. I don't mean slow like ASLSP; I just mean long enough that you can really think about what every chord sounds like.
Anyway, so I took this idea and turned it into my own piece of music. It's on my YouTube channel:
I don't want to brag here, but I really like listening to this song. But enough of that, I want to explain how it works:
The piece, in its written form, consists of 30 distinct chordal changes. What I did was I played each part, individually, on a synthesizer, extending each chord for as long as I felt sounded right. Since it is fifteen minutes long, this averages out to a change every thirty seconds.
Somehow, this kind of slow progression seems to hold my attention. Maybe it's because of the ringing reverberation between notes? I don't know. Anyway, what do you think?