Am I 32-bit, or 64-bit?

[Ken D'Ambrosio]

Okay, because I think that Ubuntu 10.10 with Compiz, the cube, wobbly windows
and Gnome 2.x is the epitome of the Linux experience, I've given up on more
recent stuff, and installed 10.10 -- 32-bit -- on my laptop.  But I'm a total
btrfs whore, so I installed that (aside from my /boot partition).  Buuut...
btrfs on whatever 10.10's kernel is is kinda flaky; blew up the FS the first
time I tried to create a subvolume.  So I booted a (very) recent random distro,
64-bit, with a 3.2 kernel, specifically because 3.2 has some magic in it to
help with unmountable btrfs drives.  Worked like a champ.  Then, still in my
64-bit OS, I downloaded a 3.3 kernel off kernel.org.  Since my base OS --
Ubuntu 10.10, as I installed it -- is 32-bit, I *wanted* to do a
make ARCH=i386 bzImage
But... i386 seems to be missing as a possible architecture.  The closest I
could find was x86.  But this concerned me, because x86_64's bzImage is a soft
link to x86's.  Anyway, "What the hell," I thought, and compiled it.  Installed
it.  Booted it.  And it works great!  Until I went to install Chrome.  Chrome
said, "You're running a 64-bit OS; here's your 64-bit version."  I tried
installing that, and no soup.  32-bit version installed fine.  So then I
glanced at "uname -a":

Linux galadriel 3.3.0 #2 SMP Wed Apr 4 13:04:22 EDT 2012 x86_64 GNU/Linux

Am I running a 64-bit kernel on a 32-bit OS?  Bwah?

-Ken