I know it is a commonplace warning not to plug in a 4 ohm speaker to an amplifier rated for 8 ohms. I am wondering what is the actual danger that is presented by doing this in an electrical sense. 

My understanding is that an amplifier changes the output voltage level in order to change the power going to the speaker. Power is determined by the formula P = V^2 / R. Therefore plugging in a 4 ohm speaker rather than an 8 ohm will essentially double the power being drawn at the output. It would therefore seem the danger is drawing more power than the speaker or the amplifier is rated for.

However, the other day upon plugging a 4 ohm 40W speaker into an 8 ohm amplifier to test this, it started smoking immediately even at the lowest volume setting. I'm not sure if this was just some kind of fluke or if there's another factor at work here, perhaps something to do with impedance. If there is please let me know, or otherwise help clarify my understanding. Thanks!