TensorTime has moved!

Effective immediately, this blog has moved to


so update your bookmarks and follower status. I have already ostensibly migrated all of this blog’s followers to the new blog, and it was spectacularly easy to do thanks to the WordPress tools. If anyone finds they are not still following the new blog, please let me know or just follow the new one as you see fit.

This site, hosted on WordPress.com, will not be updated and will eventually be deleted.

I made the move because I need to be able to embed GlowScript and Trinket programs and this is forbidden in blogs hosted on wordpress.com, and for understandable reasons. The blog is now hosted on a subdomain of my own website. You may find the site slower than wordpress.com and if you do, please let me know and I’ll see what I can do about it.

All LaTeX embedded in posts should render correctly on the new site. After a lot of experimentation, I have found a fantastic LaTeX plugin for WordPress that allows for using external packages and eventually I will implement it retroactively on all existing posts.

Thanks to all my readers and followers for making this project worthwhile to me, and I’ll see you at the new site!


Learning Critical Thinking Through Astronomy, Week 9

Monday, Tuesday, and Wednesday of this week constituted our fall break. Unfortunately, that means the evening section, which meets MW, did not meet at all and the two daytime sections (one of which meets MWF and the other meets TuTh) only had one full class period each.

This “week” was devoted entirely to what I call “celestial anatomy.” By that I mean learning the various parts of the Earth/sky system. Here is the list of anatomical terms students should be familiar with and should be able to operationally define:

  1. horizon
  2. north-south line
  3. east-west line
  4. celestial meridian
  5. prime vertical
  6. zenith
  7. celestial equator
  8. north celestial pole
  9. south celestial pole
  10. ecliptic
  11. equinoxes (named for the months in which Sun sits there, not seasons)
  12. solstices (named for the months in which Sun sits there, not seasons)
  13. time bumps

Allow me to elaborate on some of these. Note that items 1-6 have something very important in common, namely that they are conceptually attached to the ground. None of them make any sense otherwise. The cardinal directions (north, south, east, and west) have been previously operationally defined in terms of a shadow’s behavior, which also is “attached” to the ground. Once you leave the ground, this way of defining directions has no real meaning. Okay, you need to be very far above the ground, like in low Earth orbit. There is a way of operationally defining cardinal directions on the plane of the sky, but it obviously can’t be done with shadows. That’s an important and often overlooked conceptual point. Items 7-12 are inherently attached to the sky and have sensible meanings without referring to the ground or anything attached to the ground. Students frequently lift their celestial spheres out of their cradles (the cradle is the cardboard box the kit was shipped in) and attempt to point to the zenith or the celestial meridian without realize that those things have no meaning without the horizon or ground.

It’s important to remember that textbook astronomy has an inherent northern hemisphere bias. December is almost always called a winter month, but our friends in Australia (and everywhere else on the southern hemisphere) would certainly disagree. However, both our Aussie friends and us would agree about Sun’s postion along the ecliptic during December. One of my goals is to eliminate the northern hemisphere bias in all of my activities so they can be used anywhere in the world. At an AAPT conference, I once asked a representative from a prominent physics textbook publisher how they handle the northern hemisphere bias for their users in South America. That representative’s response was that they “just translate the books into Spanish.” I smiled politely and walked away.

Item 12, time bumps, stands by itself at this point becuase there are obviously no time bumps on the real sky. These are small dimples around the celestial equator on the kit students construct that mark hourly increments in right ascension (RA). I have students count the intervals between consecutive dimples and they correctly count twenty-four of them, and almost immediately make the connection with the concept of twenty-four hours in a day. Why twenty-four instead of some other number? It’s probably because twenty-four is divisible by 2, 3, 4, 6, 8, and 12. You’d be hard pressed to find another reasonable number with so many divisors. The next chapter is devoted entirely to the measurement of time but for now, we simply use the time bumps as a way to estimate time intervals when the sky changes. This would probably make more sense if you had one of the kits in front of you.

After I present this guided anatomy lesson, I let students go back over it and quiz each other in their groups. Then we have an assessment in class, for which the standard is

I can correctly identify parts of the Earth/sky system.

Students come to me individually with their kits and I randomly pick four of the above items (omitting time bumps) and ask each student to identify it on his/her model. Most do well, but many need further practice and will need to reassess.

In today’s (Friday’s) class, I noted at least three students who either didn’t have their kits with them or had them and had not yet complete construction of their kits. I guess I can’t win ’em all.

As usual, I’m happy to field questions and comments.