I used to teach basic electronics at a Vo-tech. I feel a need to clarify the bi-wire issue because I believe that some do not understand the electrical circuit. As Sean describes above a true bi-wireable speaker has a electrically separate crossover for each driver. Most speakers have separate crossovers for each driver but they are not electrically separate because the input to both of the crossovers (in a two-way speaker; one a high pass to tweeter, the other a low pass to the woofer) are tied together to the single pair of input jacks on the back of the speaker. In a bi-wireable speaker, if the jumper is removed between the two pairs of inputs and only one of the pairs has hooked up, then only one speaker will produce sound. This is a sure fire way to see if the crossover sections are independent.
Sdcampbell you are partially correct that you are feeding the same VOLTAGE to both sections of the crossover. Both pairs of wires connect to the same + & - terminals on the amp and then each pair of wires is connected to the drivers thru the crossovers. This is like connecting two toy DC motors to a single battery, both motors will 'see' the voltage and both motors will turn.
A speaker is a current driven device. The current flowing thru the voice coil reacts with the magnet to produce movement of the cone. (yes, I am sure you all know this but I am only trying to be complete) It is the job of the crossover to direct the appropriate audio current into each driver. This is done by what is called the voltage divider principle. This principle is based on Ohm's law that states the current flowing thru a circuit is proportional to the voltage applied and inversely proportional to the resistance. If you were to take two 6 ohm resistors and connect them in series and place them across a 12 volt battery, 1 amp of current would flow. (ohm's law) If the resistors were doubled in value then the current would be cut in half. Now, lets look at the voltage. The voltage across one of the resistors is determined by taking the current thru it (1 amp) and multiplying it by it's resistance (6 ohms) to arrive at a voltage of 6 volts. The 12 volt battery has been 'divided' down to six volts. The crossover in series with the speaker works the same way, only it is frequency selective. In the case of the woofer crossover, it only 'passes' the low frequency voltage to the woofer and blocks the high frequencies.
The major advantage to stretching separate wires to the woofer and tweeter is the separation of the audio frequency currents in the wires. Even though the voltage is the same on both pair of wires, the currents are not. If speaker cables were perfect, then we would hear no differences in cables. If they were perfect, it would not make any difference if both high and low frequency currents flow in the wires. It is the separation of the currents in the cables that does the most to affect the sound. Does it not seem possible that the large woofer currents could affect the small tweeter current while it traveled down the wire? It is the fact that the currents are different that makes me think one could 'tune' their speakers by using different cables on the top and bottom.
A manufacturer might not recommend bi-wire because he has voiced his speaker to take into account the interaction inside the single cable. (I am not sure how this could be done, but it always possible) If everyone were to follow recommendations, why would anyone try a different cable than the one recommended. I believe the answer is found within the context of taste. I like my 'sound' to be a certain way. I position my speakers and use 'xyz' brand equipment to make them sound the way I want. Just because a manufacturer doesn't recommend bi-wiring, does that automatically mean that I won't like it that way? It is a personal choice and I feel strongly about the option to make that choice! If I feel a speaker sounds better upside down, what is wrong with me using it that way?
I want to thank all of the Audiogon posters for their comments about the sound of equipment in this and other posts. I reside in the middle of no audio land. I really like to read the opinions of others on equipment. I believe our motives for saying something good or bad about a piece of gear is at least NOT ruled by our paychecks!
I really hope this dissertation sheds light on the bi-wire topic and will help guide all in the pursuit of good sound.