This year we are discussing the Book of Martial Power (BOMP) on Saturdays.
This particular principle plays a huge role in how you practice and how you perform your martial art. Basically, The Power Paradox states, that if it feels powerful then it isn't, and if it feels weak but gets a big effect then it really is powerful.
I usually think about this like this - The only way I can feel my own power is if it is reflected back from you. If I apply power to you when you are totally incapable of resistance, then you will reflect almost none of my power back to me and I will not feel my own power. But on the other hand, if I apply power to you and feel you resisting, then you are reflecting much of my power back to me.
If you can learn to skillfully manipulate synchronization, ma-ai, and kuzushi, then uke will never be in a position to resist, and he will eat all of the power you apply to him. You only ever feel the power that he doesn't eat because you mis-managed your synch, ma-ai, or kuzushi.
I think this is why the haymaker (or as we call it the Redneck Punch) is so prevalent with untrained fighters. When a haymaker hits, some power is absorbed in the receiver as damage, but a lot of power is reflected back to the puncher to be absorbed in the musculature of the chest and shoulder. So, because of the feedback, the puncher feels like the haymaker is very powerful. On the other hand, a straight punch executed correctly creates a very big effect in the receiver and does not reflect much power back to the puncher, so the puncher feels like the punch was weaker than a haymaker.
True Power feels like weakness. Power that feels powerful is weak.
[photo courtesy of Clover 1]