I understood the mathematics quite well. It would have helped if someone had explained that the "A" stood for the amount of energy input into the heatpump, presumably the portion that is power supplied by the user to push the heat around. The thing is, you still have the Carnot equation upside-down and you don't blink an eye when it gives upside-down results. The equation in that page you linked to cannot give any result less than 1. It cannot give an output to input ratio of less than one. All of this is quite explicit. You have no call to call me "dummy." I don't know what planet you live on where you think that is appropriate.
So what we have here is "Light" telling me that you can get 4 watts of heat out of a heat pump per watt that you supply as power, and that this is because of the mathematics at
this Wikipedia page. Then he calls me a dummy because I point out what is glaringly obvious. Here is the
Carnot Equation (scan down the page) for comparison.
The mathematics describe a situation that is exactly as if a heat engine that is 25 percent efficient at producing mechanical energy will, if reversed, become 400 percent efficient at transporting heat energy uphill by applying mechanical energy. It is exactly what Light has claimed, and the entire industry claims. It satisfies a type of mathematical symmetry. It is also impossible according to the laws of thermodynamics. It is supposed to take at least as much work to push a given number of BTUs uphill as you would get out of those BTUs, no exceptions. If someone wants to challenge that, please do. It is supposed to be one of those crackpot claims that no one is ever supposed to believe, that you can use some kind of tricks to get heat to go uphill without expending a lot of excess energy. So, in theory it can't work at all. Experimental evidence shows that it does work. This is what I've been trying to get at all night.