Flies and Trains

The “flies and trains” problem is an interesting one. The problem itself is rather complex on the surface: Say you have a train traveling at 30 mph (or km/h if you want. The units don’t really matter). There’s a wall 30 miles (or km) ahead. A fly takes off from the front of the train toward the wall at 60mph (or km/h). When it reaches the wall, it instantly turns around and flies back to the train. When it reaches the train it instantly turns around and flies back to the wall. This continues until the train reaches the wall. How far does the fly travel?

You may start by saying that it takes 30 minutes for the fly to travel the 30 miles to the wall. In the meantime, the train has traveled 15 miles. That part’s easy. But when the fly starts heading back to the train it gets tricky. How far does the train travel before the fly reaches it?

Eventually you end up with a convergent geometric sequence to solve. At that point you can figure out that the fly has traveled 60 miles.

But there’s a far simpler way to approach the problem. If you haven’t spotted it already you’ll likely facepalm when I explain it.

Let’s start with just the train. It’s traveling 30mph and it’s 30 miles to the wall. That means it will take the train an hour to get there. Since the fly is traveling at 60mph and will also travel for an hour, it will travel 60 miles.

Yeah, that’s how simple this problem really is.

Sometimes it takes just a simple change in perpsective to turn something complicated into something really simple.

How to Think Backwards

The past few weeks I’ve been learning a new piano piece: The 3rd movement to Beethoven’s “Tempest” Sonata. It’s a fairly long piece at 7 minutes and is 10 pages of sheet music; 2 of which are played twice. That’s about 30 seconds of music per page played.

Now normally when you learn a piece of music, you start at the beginning. You learn the notes of the first few measures and get those down. Then you move to the next few measures, learn those, then continue.

Then somewhere about 2-3 pages in you’re at the point where it takes a while to play the stuff you’ve learned. Then you hit the stuff you haven’t learned yet and it’s like crashing your car into a brick wall. It’s also discouraging.

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ADHD is Awesome!

It’s awesome except for the fact that it took me nearly two weeks to really get going on this article.

So why is ADHD awesome? It’s a bit of a story.

In my case, I love my ADHD. Normally, when someone has ADHD, they struggle to fit in with what society considers “normal” for attentiveness. They expect you to sit still and do the same thing for hours at a time and be happy with it. When you have ADHD though, that’s just not happening.

Inevitably you’re labelled as a troublemaker and get yelled at for not focusing or not sitting still. That was me from about age 3 until I realized that I didn’t need to fit in – which was about age 15 or so. Read More

Creativity Is Not What You Think

What do you think of when you think of someone who’s creative? You probably pictured a painter, musician, or something else in the artistic realm. You probably didn’t think of someone searching for the cure for cancer or writing software to beat the stock market. Yet both of those are highly creative tasks.

Definition of create:
  1. To cause to come into being, as something unique that would not ordinarily evolve or that is not made by ordinary processes
  2. To evolve from one’s own thought or imagination, as a work of art or an invention.

It’s true that when many people think of creative work, they think of artistic professions – painters, sculptors, musical composers, and the like. Basically if you have to buy a ticket to see it, it’s a creative endeavor.

But is that really the case?

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