The Look

Every so often it happens, someone asks how unschooling is working while giving me the ‘surely they’re done with that by now’ look. Sometimes the look gets to me, and gives me pause to think about whether what we’re doing really does work or not. Then, I remember where the kids really are academically, almost universally ahead in my opinion, and I relax a bit.

Annoying as it is the ‘look’ winds up being a positive force in general. It makes me re-evaluate my goals for unschooling in the first place. I just have two of them.  The first is  for the kids learn in a natural easy way that echoes the way I learned things growing up.   The second is for them to get out into the world to experience it, and to build the skills necessary to work with it.

Sometimes when I review, I realize we could focus more on one or the other of those goals, and try to amplify my efforts accordingly.  For example,

• “No. 1 mentioned she wanted to learn to solder, we need to take time to make that actually happen.” or
• “No. 2 is starting to bounce off the walls in the afternoon. He’s really good at action oriented activities like hikes and sports. I need to make dinners that we can take with us so we can walk out the door in the afternoon and hang out in our forested park or the playground instead of our house.” or
• “I noticed the kids are saying bye without making eye contact while leaving places we visit. We should start practicing role-play about greeting people when we’re out and about again.”

The look reminds me to do little things that make our unschooling life more effective and more fun, so, I’ll take it. Little reminders always help.

About the Antelope: Last summer when we went eclipse spotting, we met this guy.  He gave us a different sort of look.  As we ignored him, he then followed us, (always about 50 yards away), bleating his disapproval.  Apparently, we'd invaded his space.

Cool Math Tricks: Deriving the Divergence, (Del or Nabla) into New (Cylindrical) Coordinate Systems

The following is a pretty lengthy procedure, but converting the divergence, (nabla, del) operator between coordinate systems comes up pretty often. While there are tables for converting between common coordinate systems, there seem to be fewer explanations of the procedure for deriving the conversion, so here goes!

What do we actually want?

To convert the Cartesian nabla

to the nabla for another coordinate system, say… cylindrical coordinates.

What we’ll need:

1. The Cartesian Nabla:

2. A set of equations relating the Cartesian coordinates to cylindrical coordinates:

3. A set of equations relating the Cartesian basis vectors to the basis vectors of the new coordinate system:

How to do it:

Use the chain rule for differentiation to convert the derivatives with respect to the Cartesian variables to derivatives with respect to the cylindrical variables.

The chain rule can be used to convert a differential operator in terms of one variable into a series of differential operators in terms of othe…

The Valentine's Day Magnetic Monopole

There's an assymetry to the form of the two Maxwell's equations shown in picture 1.  While the divergence of the electric field is proportional to the electric charge density at a given point, the divergence of the magnetic field is equal to zero.  This is typically explained in the following way.  While we know that electrons, the fundamental electric charge carriers exist, evidence seems to indicate that magnetic monopoles, the particles that would carry magnetic 'charge', either don't exist, or, the energies required to create them are so high that they are exceedingly rare.  That doesn't stop us from looking for them though!

Keeping with the theme of Fairbank[1] and his academic progeny over the semester break, today's post is about the discovery of a magnetic monopole candidate event by one of the Fairbank's graduate students, Blas Cabrera[2].  Cabrera was utilizing a loop type of magnetic monopole detector.  Its operation is in concept very simpl…