My 6th grade is studying waves. Part of this involves making waves using slinkies. I know that slinkies are fun toys, so there’s a whole harangue about treating them carefully and not playing with them. Nonetheless, it didn’t take 2 days until someone turned one into abstract art.
Now, I know that slinkies aren’t expensive, but it’s the principle of the thing. Now I don’t have enough for all the groups.
How much do you know? Really? That much? Are you sure?
It turns out that there are lots of ways to think that you know more than you really do. Here’s a good scischow youtube about it. One of my favorites is the Dunning-Kruger Effect, which I see lots of. Basically, the less you know about something, the more you think you know. As a teacher I see this when students think they understand the topic, but then proceed to bomb the test. It works like this: When you have a beginners knowledge of something, you don’t know the intricacies of it. You don’t know just how much more there is to know.
I teach middle school science, so the material has been simplified—there’s a lot more to it than what I teach. Some students don’t get the simplified version, and they think that what they’ve gotten (the very simplified) is easy. Then they have to take a test on what they should know, and they have trouble with it. And when they get to a question on higher-order thinking skills … watch out!
The thing is, I think they could do much better. But when they’re studying, they think they know it, so they don’t study much. If they understood how much more they need to know, I think they’d realize that they needed to study more.
Anyway, watch the video.
Google’s autonomous cars can teach us a lot of things. This Lifehacker article gives good hints on what kinds of things we should be learning from our soon-to-be codrivers.
- Pay attention to where others are going, and how fast they are moving. This will help you to anticipate your future moves. And it doesn’t only apply to cars. If you see that a bicyclist is approaching a parked car, you know that they will be moving over. Make room for them or slow down.
- Turn signals are helpful, but don’t trust that the other driver is using them properly. I know that I’ve forgotten to cancel mine sometimes, or turn it on too soon. But it helps to anticipate what the other driver will probably do soon, including moving into your lane.
- Maintain proper following distance. You should be keeping 3 seconds of distance between you and the car in front of you, so you can react and slow down if needed. Many times other drivers will move into this space. Don’t get upset about this. Just give enough space again. Personally, I like to go a little slower than the prevailing traffic on the highway. This makes driving much less stressful. The difference in timing is minimal, and the reduced hassles more than makes up for it.
The autonomous cars will be “driving like a grandma”, that is, playing it safe. This can upset us, but it really is better to be driving this way. Life isn’t a race. If we treat it as one, we place ourselves, and others, in danger.
So, there was this cool post on AskReddit: What’s your favorite maths fact? And one of the comments was about Graham’s Number. Now you may know about the googol (10100). And if you know that one, you certainly know about the googolplex (10googol). And you’d be right in thinking that those numbers are big. And you know that those aren’t anywhere close to infinity. But if you want to think about large numbers, and kick your math up more than a few steps, read this post on going from 1,000,000 to Graham’s Number.
So, on the way to rather large numbers, you may see some mileposts:
These, and a googolplex, are pikers compared to Graham’s Number. To get there, you first have to go up the math ladder from counting, to addition, to multiplication, to exponentiation, to tetration (this is where my math migraine kicks in), to pentation, to hexation, and wayyy beyond.
If, and that’s a big if, you can wrap your mind around Graham’s Number, … well first off, you’re lying, just admit it … but this supremely large number, where there isn’t enough space in the universe to write down all the digits (the train passed that station long ago on this math journey, just read the article at the link), is not even approaching what infinity is. This isn’t anywhere close to aleph-null (ℵ0).
One thing that sometimes comes up when we’re talking about Scientific Theories, is that Science changes. It isn’t static. Some of the science that I learned about in school is different from what I teach now. Science may be wrong. Some students think this is bad: “Why learn science if it changes? Why bother if it isn’t right?”. But this is actually Science’s greatest strength.
The confusion stems from a misunderstanding of what science really is. Science is about trying to find out the best explanation for how the natural world works. Think about that. It’s not how the world works, but really is our best current explanation for how it works. As we learn more, our explanations may change.
Once we thought that the Sun rotates around the Earth. It certainly looks that way. But if everything rotates around the Earth, then there are some strange things in the sky that have to be explained. The planet’s retrograde motion. Why Venus has distinct phases, but Jupiter doesn’t. These can’t be explained by having the Earth in the center. But long ago it was the best explanation we had.
Later on, Copernicus and Kepler came up with better explanations. The Earth isn’t in the center, the Sun is. The Earth is just a regular planet orbiting the Sun. This very neatly explains retrograde motion and Venus’s phases.
But it wasn’t quite right. Careful observation showed that something was funny with Mercury’s orbit. It wasn’t quite where Newtonian Mechanics expected it to be. Clearly, something was wrong with our understanding.
Albert Einstein’s Theory of Relativity explained the change in Mercury’s orbit. Mercury is so close to the Sun’s gravity that there are relativistic effects on its orbit.
So as our understanding increased, our explanations got better. The scientific theories changed. Science doesn’t change because it’s wrong, it changes because it improves. What was wrong was our understanding at the time. But at the time it was the best explanation we had. What you learn now is our best current explanation. If it changes in the future, it will be because we learn more, which is a Very Good Thing.
Today is the Winter Solstice in the Northern Hemisphere. It is the day that a few things happen. The sun gets as far south as it gets. Today is the shortest day of the year. Tonight is the longest night of the year. Today is the first day of winter.
Since the winter solstice marks the start of the days getting longer, it was important to ancient people. There are various monuments that signal when the solstice is. These include Stonehenge, Newgrange, and even the Georgia Guidestones.
An interesting article brings up one of my favorite philosophical problems. Suppose Google’s self driving cars become common. You’re riding in one. Then something goes wrong, an oncoming car loses control and is headed right for you. The only alternative to a head on collision is to swerve into the right hand lane, where there just happens to be a full school bus. Swerving will cause the school bus to crash. What should the self driving car do? Should it protect the car’s owner at the cost of a bus full of children?
This is called the trolley problem. There are a number of interesting variants, but just how should the autonomous car react?
No, not that valedictorian story. That’s a good story, and I cry every time I read it. This is another one.
I like science fiction, and I just listened to a good podcast on EscapePod. Valedictorian is about a girl in the future where 20% of the population is regularly culled to outside the firewall. She has 3 rules:
- She will always give her best
- She will not live in fear
- She will be herself
The story is a good one that asks what it means to be human. I found it more interesting than most.
I’ve been teaching Newton’s second law to my 6th graders, and I’m really surprised at how the textbooks try to do the math. When I learned it (back before dirt), I learned f = ma (force is mass times acceleration). Our textbook says a = f/m (acceleration is force divided by mass). But I haven’t seen a textbook use this:
With this, all you do is plug in what you know, and it will show you how to get what you’re missing. For example, if you have force and acceleration, you fill them in, and you have force divided by acceleration. That gives you mass.
You can also think about like this: I want to get the force, so I cover up the f. I’m left with mass times acceleration. Or I want to get acceleration, so I cover up the a. I’m left with f over m.
Now, instead of having to remember 3 formulas (f=ma, m=f/a, a=f/m), I just have to remember this one thing that gives me the 3 formulas. All I really need to remember is that force goes on top (because multiplication is commutative).
Portal 2 is a game where you have to use portal guns to create teleportation fields to move around and survive. I’ve head about teachers using it for lessons, especially for physics, but I haven’t had the chance to look into it. There is a website teachwithportals.com which has lesson plans for use with Portal 2. Surprisingly with Language Arts lessons as well as science. I’ll have to look into this.