Until I can...buy a neg R...
I bet you've already bought a few negative resistances.

Every buy an NE2 neon bulb? They have a negative resistance region (which is why you can make a nice oscillator with one.)
Got any light-dimmers in your house? They usually contain a triac (which has a negative resistance region), and a diac (which also has a negative resistance region.)
When I was about eleven or twelve, I was trying to make my own turntable at home, and one of my biggest headaches was that the motor wouldn't maintain a constant speed. When the pickup stylus was at the outer edge of the record, there was more load on the motor, and it would slow down because of its internal resistance. When the stylus reached the center, there was less load on the motor, and it would speed up.
I started hunting for a solution, and that's when I first heard about negative resistance. At the time, there was a two-transistor circuit used in many cassette decks and turntables to maintain constant speed from a DC motor. The circuit worked by inserting a negative resistance in series with the motor: just like PRR's substation example, if you match the external negative resistance to the positive resistance already inside the motor, then the speed variation goes away, and the motor speed becomes (nearly) constant irrespective of load (within reason).
Ohm's law itself is an abstraction - you can't see, smell, touch, or hear current or voltage or resistance, after all, and you can't go out and buy a volt.

Electrons are real, but we can't see or feel them directly either. Electronics is full of invisible abstractions you can't pick up and look at. Changing the sign of the voltage from minus to plus is just one more of those little abstractions.

I think all the abstractions are actually one of the reasons I enjoy electronics - it makes it all the more magical when you strum your guitar and sound actually comes out of the loudspeaker!

-Gnobuddy