at first I thought it was just a big wad of masking tape on the end of the wire (bad enough, not an actual insulator, and a fire hazard), but upon peeling the masking tape I found this :
Oh, of course. You spliced on an extra 1 inch of wire, no wire nut, wrapped in masking tape - and the thing that most boggles my mind is that the wire ends are not even twisted in any kind of sane way, they are just randomly balled up around each other. Not to mention the original wires are plenty long without the splice.
Pretty impressive piece of fail.
BTW one of the hazards of old knob & tube wires is that the insulation is only rated to 60 C, but newer light fixtures are allowed to heat up to 90 C (which new Romex can handle). So you need to be careful when installing new light fixtures, and at the very least don't over-bulb (*). One way to solve this (without a ton of rewiring) is to back up the knob and tube a few feet away, put a junction box there, then run new Romex for the last few feet.
(* = I just love to over-bulb ; I can never get enough light; I used to put 100 W's in everything whenever I moved into an apartment. Here I might be a bit more careful about that, because they do generate a lot more heat (BTW I despise the gross inhumane light of CFL's, but one advantage of them with old wiring is they draw much less power (which keeps the wires cool) and they themselves are cool (which doesn't heat up the light fixture and box)). I'm not a huge fan of dimmers (fucking 75 W is already dark enough, I don't need any less than that), but if I could install an *amplifier* that let me over-drive the bulbs that would be sweet (but not in my house, which is apparently wired by paper clips and masking tape)).
It's kind of scary what kinds of disasters can be hiding inside your walls that you don't know about upon purchase (or maybe ever, until they cause water damage or a fire or whatever). I really like doing home improvement work in the garage and the basement, because the walls are unfinished so I can see where the studs are, which is so handy, I can see all the wire runs and junction boxes. It's totally superior.
Covering up your walls is super over-rated. I think if I was designing a modern house it would be all Pompidou Center style with color-coded pipes running around where I could directly access the electricity, water, etc.
If you want a more old fashioned home look, you could still do all your major wire runs around the ceiling and then cover them with a removeable wood crown molding piece. That way if you want to get into the wires, you just pop off the crown molding and you have a wooden box for access.