### Respectful Parenting, Electronics System Theory, and Faith

Inspired by the Sara’s recent post about respectful parenting +Happiness is here vis-à-vis Minecraft screen time.  The end analysis there?  Trust your kids, and parent respectfully.

In electrical systems theory, we divide circuits up into two categories, differentiators and integrators.  Differentiators make circuits more sensitive to every little change.  The circuit doesn't miss much, but it might flail around quickly.  Integrators on the other hand cause the system as a whole to be less sensitive to small changes.  Systems with integrators won't respond to a small change, they simply add it to a total response, and wait for more information.  If the changes continue to happen in the same way, ultimately the system will respond, but it takes time and consistency.

This is how I view Sara’s description of handling video game screen time.  I would have been inclined to shutdown all the screens after two days spent exclusively on a video game.  If I'd done this, I wouldn't have given the 'system' of our kids the time to organically respond to their new environment.  By taking a more integrated approach like Sara did, it's easier to see what the system wanted to do for itself, and how it normally behaves without outside influences.

I like the integrating approach better, though it's occasionally difficult to remember to use it when I'm caught up in the moment.  I find myself thinking, 'something's changed, change it back.'  I might also phrase the whole thing with integrators and differentiators in a different way—in terms of faith.  It’s sometimes difficult, but it’s always been helpful for me to have faith that the kids are competent, and are going to figure things out for themselves in a healthy way.  Sure, I can offer advice if they want it, (and I do), but they get the best results, and grow the most, I think, when I’m not involved.

### 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…

### Kids R Kapable

Just a little note to concerned ‘grownups’ everywhere.  If you look at a kid—and I mean really look—I don’t mean notice a person shorter than you, I mean make eye contact, notice their facial expression and observe their body language—If you look at a kid, don’t assume they need your help unless they’re obviously distressed, or ask for it.  You might think this is difficult call to make.  You might think, not having kids of your own, that you’re unable to make this determination.  You are.  You do in fact, already have the skills even if you’ve never been around kids  It’s a remarkably simple call to make, just use the exact same criteria you would for determining if an adult was in distress.  Because, guess what, kids and adults are in fact the same species of animal and communicate in the same way.  Honest.  If someone—adult or child—doesn’t need your help, feel free to say hello, give a wave, give a smile, but don’t—do not—try to force help on anyone that doesn’t want or need it.

Y…