Long time no see.

[robhansen]

For the last few years I've been making life updates over at Facebook (and to a slightly lesser extent Google+), mostly because of the network effects.  There are a lot of people there; it's an easy way to reach a decently large audience.

Unfortunately, most of the social networks are for the most part ruled by people who believe reason and education are against their religious convictions.  The level of discourse is so de minimis that it staggers my imagination.  My average post there is about three paragraphs, and is longer than 99% of the stuff in my feed.  I don't know how to function in that environment, much less thrive.

So, it's back here, at least as an emergency measure.  For God's sake, won't you please make me think?

Some brief updates:

• My nephew shot himself in the foot with a shotgun in late December.  He's keeping the foot but has a long rehabilitation ahead of him.  Whether he's learned anything about the importance of proper firearms safety remains to be seen.
• I almost died in a fire in December, when my upstairs neighbors decided to extinguish hot fireplace coals by bagging them and putting them on the balcony, thinking the winter weather would quench the coals.  Needless to say the bag was paper and the balcony made of creosote-impregnated wood.
• My Uncle Lou died sometime in the night between January 5 and January 6.
• I turned 42 the morning of January 6.  The celebration was short-lived.

Anyway.  Talk to me.  Make me think.  Or if you can't make me think, just speak up and let me know you're reading what I'm writing.

Comments

[vatine]

It is well-known that if you have three solid bodies in a 3D space, you can construct a plane that cuts them in half. [ note: now that I'm trying to find reference to a proof, I can't, of course ]

This plane would be trivial to construct, if there's a point that is part of all planes that divides a body in half. Is there such a point?

[robhansen]

By "body", I assume you mean something with volume. Call them V1, V2, V3. For each V, define a center P according to some property of uniqueness -- center of mass, whatever, so that each V maps onto a P.

You now have three central points P which define a plane which bisects each V.

I maintain the bisecting plane is trivial to construct in the first place, assuming sensible choice of the function mapping V => P. :)

[vatine]

For "body", read "continuous volume", yes.

It's not really a question of constructing the bisecting plane, it is a question of "considering all points in all planes that exactly halve a body, is there, for all bodies, at least one point that is in all the halving planes".

I have not yet managed to construct a counterexample (but there are bodies for which said point is actually outside the body, like, say, a torus).

[kyrielle]

*waves* I'm reading. I'm here. I even talk here sometimes, sometimes about the same things as FB, sometimes not.

[fraupastor]

Glad you're still here, that your nephew is still here, and that your brain is still active and wanting exercise! Sorry to hear about your Uncle Lou. I know when it comes down to it that no death feels like a good death, but I hope you can in time find peace with his passing.

Also, happy birthday! I hope that the celebration was a good one.

I'm still here, still reading.

[nilasae]

*meep* Still reading, posting very infrequently. Good to have you back!