Cognitive Sandbox » Musings

One-to-many mapping on the hammered dulcimer

Brad Beattie — Wed, 15 Sep 2010 16:32:12 +0000

Consider the opening phrase of Oh Susanna. Consider how you’d play this on your instrument of choice. When presented with a specific note, where on your instrument do you play it? The question doesn’t make sense for some instruments (e.g. the piano) as there’s only one way to produce each sound. On others (e.g. the guitar) it depends largely on where your hands are at the moment.

I’m having a difficult time applying that concept to the hammered dulcimer. Like the guitar, many notes can be played in different locations. However, some have only one string for their respective octaves. Take G# for example. That note has only one location for each of the three octaves, whereas an octave of A is represented three times.

So when learning a new piece of music, I’m left wondering where the best place to play it is. This one-to-many mapping across a wide space is inhibiting muscle memory. Grumble grumble.

Paragon vs Renegade

Brad Beattie — Fri, 10 Sep 2010 07:12:11 +0000

Take a few minutes and watch Extra Credits’ discussion on the morality system embedded into Mass Effect 2.

One of the points raised is that assigning an arbitrary “paragon” or “renegade” label to a moral dilemma cheapens the introspection that it otherwise carries. Perhaps we could expand the one-dimensional character barometer such that there’s no clear good and evil, just as pen and paper RPGs have been doing for decades with alignment.

Instead of paragon and renegade, we could have three new meters: Individualist vs Collectivist, Violent vs Peaceful, Chaotic vs Orderly. I don’t mean for these to be the best options, just to illustrate the idea of opposing viewpoints. I’m not even sure what meter one would use to cover the example given in the above video; How does one enumerate the preference for genocide over the elimination of free will? Would that count as +1 to individualist, +1 to violent and no change to chaos/order? It might not be possible to categorize solutions to moral dilemmas (a la Donnie Darko’s lifeline exercise).

At the end of the day, the designers for Mass Effect might have opted for the simplicity of a single meter as an explicit design choice; Littering a screen with 20 character dimensions would be overkill. Still, 2 or 3 might do just fine and provide a little more depth to character choices and consequences.

Increased streetview coverage

Brad Beattie — Tue, 04 May 2010 01:39:45 +0000

Back in 2009, Google’s coverage of Canadian streets was limited to major cities.

Seems as though there was an update in the meantime.

Misinterpreting problem spaces

Brad Beattie — Sun, 14 Feb 2010 04:41:31 +0000

Polls and elections aren’t the same type of thing. The former asks for descriptive data, the latter for prescriptive preferences. To illustrate the hazards of this common misunderstanding, let’s go over some other ways data can partitioned and the problems that arise from confusing them.

Ordered data vs unordered data

Ordered data has an innate linear ordering, whereas unordered data doesn’t.

Ordered: How many apples can you eat in one sitting? (0, 1, 2…)
Unordered: What was the last type of apple you ate? (Granny smith, red delicious…)

When unordered data is confused as ordered data, a relationship is erroneously implied between the items.

When ordered data is confused as unordered, data trends are buried.

Ordered discrete vs ordered continuous

With discrete data, there exist two values for which there is no valid value in between, whereas continuous data can always be broken down into more detail.

Discrete: How many thermostats do you have in your house? (0, 1, 2…)
Continuous: What is the average temperature in your house? (22.1°C, 20.3°C…)

When discrete data is confused as continuous, inappropriate conclusions can be reached (chances are you have 2.3 thermostats in your house).

When continuous data is confused as discrete, granularity is lost. We can’t tell from the graph below whether there’s a large portion of 0.0km entries, if only odd decimal entries exist (0.1, 0.3, 0.5…), or any other detail hidden by these brackets.

Simple data vs compound data

Compound data have multiple values that bear some relation to each other.

Simple: How big is your television diagonally (24″, 32″, 34″…)
Compound: What are the dimensions of your television (20″x18″, 24″x20″…)

Compound data can be misrepresented as multiple simple data axes by ignoring the coupling between the two values, whereby the conditional probabilities are lost. Worse, it can be restricted down to a single simple data axis, whereby relevant data is entirely discarded (e.g. do sampled televisions only exist at certain aspect ratios?).

Descriptive data vs prescriptive preferences

Descriptive: What did you have for dinner last night?
Prescriptive: What should we have for dinner tonight?

The difference is subtle, but it’s there. With descriptive data, respondents have no incentive to tactically misrepresent their opinions. With prescriptive preferences, respondents (aka voters) are aware that their response will influence a future that likely affects them and will vote accordingly.

When prescriptive preferences are confused as descriptive data, a few things can happen:

Continuous data can be filtered down into discrete data. Instead of allowing degrees of preference, ballots are restricted to binary expressions of support.
Compound data can be filtered down into simple data. Although multiple options exist, ballots restrict the voter to supporting a single candidate.

Both confusions are present when Plurality voting is used in lieu of a more expressive ballot, where in voters could express more than just a single binary preference for a single option. Maybe this comes from ignorance of alternative voting methods, technical restrictions from the online voting application used, or seeing everything as a nail when you’re holding a hammer; Take your pick.

When Plurality voting is used to obtain prescriptive preferences, the same type of analytical fallacy is being made as is detailed in the above examples, all of which lead to a poor understanding of the underlying reality the data represents.

Motivated hobbies

Brad Beattie — Fri, 15 Jan 2010 03:21:27 +0000

Start a project around a subject you feel passionate about. It’s surprising how quickly you can get things done when there’s internal motivation. My most recent project went from prototype to useful application in about 10 days. I have to say, there’s a bit of pride that goes along with reaching a presentable milestone.

Spinning a clocklet disc

Brad Beattie — Fri, 11 Dec 2009 08:08:36 +0000

Imagine an infinitely small particle that keeps perfect time. Let’s call this particle a clocklet. We don’t have such particles, but they’re useful for considering the following.

Make a disc of clocklets about and start it spinning. Clocklet C0 is at the centre of the disc, C2 is on the edge, and C1 is half way in between. When the disc is spinning slowly, all three clocks agree on the time. C2 moves at twice the speed of C1. C0 spins, but does not otherwise move.

As we spin our disc faster and faster, the clocklets begin to differ due to an effect known as time dilation. Furthermore, C2 can never go faster than the speed of light even if C1 is moving faster than half the speed of light.

So what happens if it does? Assume that the disc spins fast enough such that C1 moves at 51% the speed of light. If the disc stops spinning, would C1 still be half way in between C0 and C2? Furthermore, does C0 differ at all from an independent clocklet outside of this disc?

I don’t have the background to answer these questions, but it’s certainly entertaining to think about.

Easing Toronto to Vancouver culture shock

Brad Beattie — Wed, 09 Sep 2009 04:13:41 +0000

It’s not perfect, but you’d be surprised how much something as small as this helps. The lack of thunderstorms in Vancouver leaves me feeling… thirsty. It’s not the right word, but you get the idea.

Vancouver’s cloud

Brad Beattie — Thu, 22 Jan 2009 03:50:52 +0000

It’s been a strange week here in Vancouver. A cloud’s come and settled down on the city, coating it in a thin mist. It’s surprising to stand on Kits beach at night and see nothing but black. No West Van. No downtown loglo. Nothing. Just the low groans of fog horns from somewhere out in the darkness.

Soaks my skin

Brad Beattie — Sat, 20 Aug 2005 03:07:00 +0000

While at work, I noticed that it started raining mid-way through the day. The sky darkened and the street-lights flickered on one at a time. It was only when buckets of water were washing against my 9th floor window that I realized how heavily it was coming down.

I know these pictures don’t do justice to the flooded streets that followed soon after. You see, by the time I was running to my bus, the puddles had been replaced by rivers with my name on them. I wasn’t in any position to pull out my camera.

I’d like to be able to say that I kept my dignity and stayed dry, but there are some downpours that reach the point of being surreal. When you realize that you can’t get any wetter, it’s nice to stop running and just watch.

An exercise in perspective

Brad Beattie — Wed, 03 Aug 2005 01:06:00 +0000

I took the train recently; Apparently it’s full of memories. Come to think of it, all of the intercity travel I do tends to be. Maybe it’s the nature of this traveling: it’s always to visit someone and there’s not much to do but wait to arrive.

My mind tends to wander towards those I’ve taken these routes for. Go Trains eastbound from Toronto, Greyhound west along the 401. Sometimes I think of traveling just to see the places I no longer have reason to be in.