Here is the situation I am trying to understand:

An 50 year old house (late knob and tube wiring). No distributed
grounds to electrical outlets or junction boxes. Everything works fine
electrically for a long time.

When doing some electrical work, a wire was cut. If you want the
details, it was supposed to be a wire to an electrical outlet that
work was to be done on. Turns out this was not the wire to that
outlet. The breaker was switched off for the outlet, but the wire was
hot. Only other info is that this was a white wire running parallel
with a red wire.

What happened was that when the wire was cut, the 110 recessed lights
in the room near by (the kitchen) went to double brightness.
Everythign was shut down, the wire was reconnected and the kitchen
lights were back to normal brightness. How is this possible??

Presumedly the house circuits are divided between the 2 phases of a
220 feed into the house. And somehow cutting that one wire put 220
across the kitchen lights, since that is the only way I can understand
the double brightness (and measuring with a voltmeter betweent the 2
cut ends, about 210V was measured). But I can't visualize how the
house wiring would be such that a 110 light circuit works fine
normally, but cutting one wire only somehow puts 220 to that circuit.

Any thoughts?

-Jim