It seems to me that many (perhaps most) teachers look favorably on methods that do not require of them any creative output. One of the favorite methods in an average teacher's repertoire is the principle of systematic work.

Systematic work is based on the old adage of practice makes perfect. This is what you say to little kids who want to be in the Olympics: you work hard and you can get there. And there is no reason to doubt that. The fact is that to be successful in sports requires an enormous amount of systematic work. However, there is one caveat that they don't mention - it only works if there is a limited amount of people doing this. If we all started working systematically, no matter how good we'd be, the Olympics wouldn't have space for 7 billion of us anyway. But I digress.

But if you look at it from a structural point of view, systematic work means brute force. So basically you work at it for as long as it takes, until it cracks. And sometimes this works. But it assumes that your understanding of the problem has some sort of linear behavior, so the more you work on it the more you understand. And that is by no means a law of nature.

It's much worse when the behavior is asymptotic. You can work on it forever and you still won't get it. To illustrate this, imagine there is a tree in your yard that is blocking your otherwise excellent view. You want that tree out of there. So you grab a rope and tie it to the tree. You take the other end and tie it to your bike. Now if the tree is a certain size, you can try all you want to pull it out of the ground, and the tree won't budge. Apparently, this simple fact is lost on some teachers. (For more on this read The Truth About Homework.)

Brute force often works, but it's the last resort and it's not the smartest way of solving a problem. To be able to work systematically in any sort of productive way you need to know more than just to work systematically, which is basically a synonym to the word repeat. If you find yourself in the middle of a lake, in a rowing boat, systematic work is no doubt your best strategy. But even then you have to set a course first. This is a question some teachers don't have an answer to. If they explain something and you don't understand it, then there must be something wrong with you and you need to "work harder". Since everything can be solved through systematic work, well there you go. You just need to help yourself.

What is worse is that sometimes you need to deliver creative solutions, either because the problem cannot be solved otherwise, or because that is the only way you can score a high grade. Now, creativity is the opposite of systematic work. I can easily imagine that systematic work originates from an earlier time when schools thought "teaching discipline" was an integral part of their business, and therefore if you're very disciplined you're going to be working systematically, it fits like a glove.

Now try combining that with creativity. Here I am working at something systematically and all of a sudden I have an idea "what if I tried to... no! I will not allow myself to be distracted, I have self discipline!" But it is interesting that teachers expect creativity when they themselves have no obligation to muster any. It's precisely those cases where something is hard to explain that you so desperately need the ability to think creatively and come up with a different description of the same thing. The best teacher I've ever had (high school, English) was also the most creative one I've seen.

It's been a while now since I found out about Magnatune, the record company that doesn't hate the world (and doesn't peddle muscular rappers and skimpy clad teenage girls). In this time I've listened to a bunch of albums with amarok, and here are the best ones I found. I've listened to many more, but these are the ones I liked enough to secure permanently.

Amarok has the nice property that you can browse the collection right in the program. If you buy using amarok, it remembers the albums you got, so you can redownload and stuff like that, very handy. If you only stream, you get the same music, but you also get a short commercial at the end of every track.

Rob Costlow - Woods of chaos

It's always difficult to determine genres. Magnatune calls this New Age music. Another description given is melodic piano pieces, which is dead on. It's a suite of greatly soothing pieces I would say. One thing it perhaps lacks is enough complexity to last a long time, so after a while the pieces become too familiar and appear a bit dull.

Costlow has one other album on Magnatune, Sophomore Jinx, which I didn't find as good.

Johannesburg Philharmonic - Coleridge-Taylor/Dvorak Violin Concertos

I found this album while browsing the classical section (which seems to be the best one on Magnatune).

Coleridge-Taylor is an interesting find. His concerto opens with an irresistably virtuosic voilin solo delivered by Philippe Graffin, and from that point on I knew I was listening to something I would like.

And then there is the Dvorak, one of the underrated Romantic composers I'd say, sure to catch my eye every time. The concerto in a minor is not his most well known work, and I think not as good as his cello concerto in a major, but still offers quite enough to satisfy.

Ehren Starks - The Depths of a Year/Lines Build Walls

Ehren Starks is more of a jazz piano act. These two albums are declared New Age and Classical respectively, although I'm not sure if I would stick them in separate categories. The difference is that The Depths of a Year also has a cello part, played by Kate Gurba. This offers a powerful dimension to an otherwise piano dominated offering.

Each album has a dozen discrete pieces, and they happen to be quite varied. Some are more calm and melodic while others are more busy and engaging. The mixed bag is tough to pull off, but when done right it produces an album that offers much more than a series of performances in much the same style.

I've always been inclined to think of dreams by trying to relate them to the time I spent asleep. Especially when I wake up remembering several dreams and they all seem quite "long" I start thinking about how long I might have been dreaming out of the whole time I was asleep. (Is it me or does sleep when dreaming seem like "you get more out of it"? :D )

Of course, dreaming doesn't happen the whole time being asleep, only in certain periods (that's all I know about it), so you will never have a night's sleep where you dream from beginning to end.

But that got me thinking. Why do we assume that the "speed" of dreams is the same as the speed of consciousness? What we do in our conscious state is a constant sort of data processing function, we perceive things and respond to them. But while asleep there is no perception happening. And so there is no need to respond to anything either. Which means.. there is no reason to assume that dreams "happen" at the same speed, is there?

In fact, dreams are supposed to be spawned by the brain as a way to keep you asleep while detecting that you are about to wakeup. But it stands to reason that this reaction must be rather quick, it doesn't seem likely that you start waking up and then the dream kicks in and you sort of teeter on the brink of waking up but still sleep another two hours. What seems more likely to me is that this is a quick response, so you start waking up, you start dreaming, but that only keeps you asleep for a short period of time.

How short? Well, since there is no perception involved, you're not actually responding to sensory perception at all, it's just a (pre-calculated?) simulation. So dreams could actually be extremely short, and you wouldn't know it, because it's just a representation of things in the brain.

So when people say things like "my life flashed before my eyes", we think that is silly, because how could you relive so much "real time" of life in such a short period of time? But if you think about it in the terms stated so far, it makes perfect sense. It doesn't take much time to experience fragments from your whole life, because you aren't responding to perception, you are just replaying it in your head. And you don't need any time to think about it either, you aren't thinking about it, just feeling it.

So how fast? Well, considering how fast you brain can respond to sensory perception that you aren't thinking about consciously, like recognize faces, voices, associate images with each other, recognize patterns and so on, this could actually be pretty damn fast.

Having been a student for something like two decades I have come across many bad teachers, lots of broken approaches, numerous stupid ideas and several people who should not be teaching at all. One thing that continues to surface, which I thought I was done with after junior high, is questions of this format:

Give three reasons for the collapse of the Roman Empire.

It's one of those things that seems so stupid, and so obvious, that noone would possibly be doing it, right? Wrong, they persist with this.

Let me answer the question. I open my Roman Empire box. In there I have various smaller boxes, one is called reasons for downfall. This one contains files. So let's see, there are 8 files in here, but I only need three. Okay, now I can transcribe the reasons one by one onto the answer sheet.

Newsflash. Human knowledge is not stored in file cabinets which enumerate causes and effects. I have *never* found myself in a real life situation where enumerating three reasons helped me get something done. Why three? How about two and a half? How about three and a half?

To anyone who actually wants to know something one well-argumented reason is worth far more than three snippets, and it probably touches on several other effects in play. This is a far more natural way of expressing thought than to compartmentalize and enumerate little slices of knowledge.

What are we actually doing here? Are we learning or are we doing brain teasers? If you ask people to enumerate 50 colors that would also be challenging, because most can't think of that many. But what would be the point?

So it is obviously futile, but it's also harmful. If you have *ever* thought deeply about *anything*, then you know how complicated cause and effect scenarios are. There can be so many factors, so many causes than are predicated upon other causes and so on, which means that decomposing the entire problem in terms of this causes this is very difficult. We love to ask ourselves why? but we rarely find good answers to those questions, because the answers are too hard to understand.

What you are doing when asking for three reasons is tremendously trivializing the problem. You are creating the appearance that one could actually give three reasons and that would explain the whole thing. Can we not have more honesty than this? Explaining the collapse of the Roman Empire is actually a hugely difficult undertaking, considering how many people affected and were affected by it. And each of those had their reasons and interests at stake, and adding up all of this is not something you can explain in three paragraphs each stating one reason. Or put it this way. If you *do*, it's a completely meaningless answer.

So why do people do this? Since it's common practice, you don't have to give three reasons for giving a question like this on a test. But how did this start? Face it, it's a really easy thing to do for a teacher. They put very little thought into it and they move on. It's much more difficult to phrase a more complicated question spanning (say) two lines that entices an intelligent response.

Instead of focusing on the problem students are thinking:

• Goodie, I remember those three paragraphs in the textbook almost word for word. I haven't really thought about what they mean, I only read them, but luckily they came up on the test.
• Damn, I can only think of two reasons.
• I have two good reasons and a third one, but I'm not sure if I can give the last one on its own, because it's not "enough" of a reason by itself, I think.
• I have three reasons, but two of them are triggered by the first one, so does that qualify as three or just one?
• I have five reasons, but I'm not going to get any more credit for that, because I can only give three.

I have found myself in all of these situations at one time or another. Particularly the first one used to happen a lot in junior high.

How do you fix it? Just as easy:

Give a reason for the collapse of the Roman Empire.

Or if you want to make it clear that you encourage "more than one" reason (however it is you distinguish reasons from each other), you can say.

Give a reason (or more than one) for the collapse of the Roman Empire.

If you don't want to be so obvious that you are obsessed with quantifying reasons, rephrase it:

Why did the Roman Empire collapse?

Congratulations. Your students are now thinking about the problem rather than about your idiotic requirements for the answer.

How does this change the question? It doesn't. Students know how many points they get for this question, so they can estimate how long a response has to be, whatever the format of the question. Meanwhile,

• those who have extensive knowledge are more likely to go beyond what you expect and they may get more credit, and
• those who don't know anything are less likely to cook up something on the spot based on three keywords they remember from the textbook, because it's much harder to incorporate those fragments into a sound argument than into three short paragraphs that are complete clichés.

Okay, it's an old issue and a well known issue that has been systematically raised for decades and I'm not going to replay the usual rhetoric.

However,