JamesCronen.com

No, really… this is a private message to my students. Y’all can stop reading now if you’re not taking my course.

Okay guys, looks like the project testing date will be on Wednesday as planned. In fact, the weather will be absolutely gorgeous. As settled in class, I’ll be at school from 9:30am to 2:00pm on Wednesday. If you bring a few dollars perhaps we can get pizza for lunch.

Happy building!

As my blog begins to mature, I’ve been spending more time pondering the act and nature of writing itself.

The ever-insightful Seth Godin today gives some hints on how to write like a blogger. In particular, Seth encourages writers to think more like bloggers — get and keep attention, provide insight, write often.

What really struck me about this article, however, is not his list of tips. Seth asks (rhetorically), “What if every high school student had a blog?”

He doesn’t mean an elementary web presence like MySpace or Facebook. How about a regular ol’ honest-to-God weblog?

When I was studying literacy for my teaching certification, I learned that to improve students’ writing most effectively, emphasize publication. Students shouldn’t write essays for their teachers: they should write for the world.

“Everything in life is writable about if you have the outgoing guts to do it, and the imagination to improvise. The worst enemy to creativity is self-doubt.” — Sylvia Plath

Society pokes fun at high school students for their emotion, their naïveté, and their need to be different.

In an artist, we call those exact same traits passion, imagination, and voice.

I know what you’re thinking — “Aren’t high schoolers vapid? Who would want to read what a teenager would have to say?”

Have you ever actually listened?

This is a test post to see if I’m still having Daylight Saving Time-related issues.

Nothing to see here…

As a student recently wrote on one of my chalkboards after school:

Physics 101

• Mass, energy, momentum, and charge are conserved.
• Anything you think is easy at first will quickly become complicated.

When I’m writing a blog post that I try to keep under 1,000 words, how much room is there for explaining everything about a particular topic?

Even in class, when I have 43 minutes of uninterrupted class time, I still have to gloss over ideas that are either too esoteric, too advanced for the students’ knowledge, or too insignificant to mention. If I don’t prune the material, a simple lecture on electric current becomes a twelve-hour marathon.

I even admit “lying” to my students on some occasions when I need to go back and add in a small effect later. Before you crucify me for being a horrible teacher, let me explain that most physics classes do this. First you study motion, then you add the effects of friction or air resistance on that motion, then you discuss what happens at high speed — relativistic effects.

Physics, and many other sciences, are built on basic phenomena that can be layered to obtain the required level of precision.

So, for an example, did you catch the “error” in my student’s conservation laws? If you noticed while reading that conservation of mass is really just a special case of conservation of energy, you’re right. But in Newtonian physics, mass is conserved — only in the quantum realm do we need to worry about mass-energy equivalence. My students don’t need to know that (yet), so why complicate matters? In a few weeks I’ll discuss E = mc², and then I’ll break it to them that their beloved mass conservation is no more.

Back to writing.

Science is tough enough for the public to digest. So how can we attract a greater readership? Include ridiculous detail to present an immaculate picture, withstanding the critique of the most knowledgeable reader? Or should articles be written to be intentionally vague (and arguably inaccurate), sacrificing detail for clarity?

I’m torn on this one.

Is this phenomenon unique to science writing?

Space.com reported yesterday that NASA astronomers have found the smallest black hole yet. The little guy has a mass of only 3.8 times the mass of the Sun and is only about 15 miles in diameter.

Gravity is the force that causes masses to be attracted to one another. On Earth, our gravity causes objects to fall towards the center of our planet at an acceleration of 9.8 m/s². That is, for every second an object falls, its downward speed increases by 9.8 meters per second. This means that if I throw something up in the air at 9.8 m/s, it will take one second before its velocity is zero again. After two seconds, the object is traveling downwards at 9.8 m/s.

There are two ways to increase the rate at which objects fall on a planet’s surface. They’re both related to the geometry of the planet.

The first approach is to increase the mass of the planet. The more mass, the greater the pull. Makes sense. The other approach is to keep the mass of the planet the same, but compress it into a smaller ball.

The “shell theorem” states that you can treat a uniformly-distributed sphere of mass as if all of the mass were located at a single point at the sphere’s center. Since we’re on the surface of the Earth, we’re exactly one Earth radius away from that single point where all the mass would be compressed:

The force of gravity experienced by both of the little scientists in this picture would be the same. However, one cannot stand on nothingness, and so this isn’t exactly a tenable situation for our little guy.

If we were to keep the mass the same but shorten the distance between us and the center of the Earth, the force would be greater since we’d be closer.

The only way to keep the mass the same but compress it all into a smaller ball is to increase the average density.

A black hole is formed when a large star dies. The star has burned through most of its fuel, and its furnace isn’t producing enough energy to maintain its own structure. Gravity causes the star to collapse in on itself until all the mass is concentrated in a very small volume.

Black holes have such an intense gravitational pull that nothing can ever escape from their clutches. Their “escape velocity”, the speed required to completely escape a planet’s or star’s gravity, is greater than the speed of light. Even though light has no mass, it is still (effectively) subjected to gravitational forces. At least that’s what Professor Einstein has had us believing since he published his theory of general relativity in 1916.

Just for fun, let’s figure out how dense this black hole is. The mass of the Sun is approximately 2.0 × 10³⁰ kilograms. That’s 2,000,000 trillion trillion kilograms for those of you that don’t like scientific notation. The mass of the black hole is 3.8 times this, or 7,600,000 trillion trillion kilograms.

Compress all of this into a sphere 15 miles across (so the radius is 7.5 miles). To find the volume of a sphere, multiply 4/3 times π times the radius cubed. This gives us a volume of 1,770 cubic miles. Or, if you like bigger numbers and smaller units, 7.3 trillion cubic meters. Then divide the mass by the volume to find the density.

This newly-discovered black hole has a density of one million trillion times that of water. For comparison, lead, the densest commonly-occurring material on Earth, has a density of about eleven times that of water.

A spoonful of this black hole would have a mass of fifteen billion tons! If my mass were compressed into a cube of this density, the sphere would be approximately six microns across. This is about one-twentieth the width of a human hair!

Physicists can usually learn a great deal from these extreme conditions. But, since light can’t escape from a black hole, no information can escape either. We have no way of observing the interior of a black hole. We only know of black holes’ existence because of their influence on the stars and nebulæ around them.

What we have learned is a new lower-limit for the size of star that will become a black hole at its death. Astronomers can now look for known dying stars of about this size and perhaps learn something about how stars die and how black holes are formed.