Jane's concerned that the enclosing plate is bigger than the heated plate.
I know I said I wouldn't respond, but STOP TRYING TO TELL OTHERS WHAT *I* AM CONCERNED ABOUT. YOU DO NOT KNOW, SO YOU HAVE NO PLACE CLAIMING YOU DO.
I am not "concerned" about any of it. Though you seem to be. And I don't know why, because your analysis above actually verifies what I stated earlier. I've been wasting my time with (my opinion) an idiot.
But Earth's mean radius is 6371 km, and the effective radiating level is ~7 km higher, so these surface areas are only ~0.2% different.
0.2% is not zero. Therefore T0 (if that is the outward extent of earth system) has a surface area of T * 1.002, and its temperature will be measurably lower than that of heat source T. Therefore we have a net heat transfer proportional to T - T0, which is a non-zero quantity.
You've proved nothing here except to verify my point. But let's finish it...
Of course, in a thought experiment this difference can be made arbitrarily smaller. Despite Jane's protests, this doesn't change the fact that enclosing the heated plate makes it warmer.
This argument is HILARIOUS. The only way you can make it "arbitrarily small" is by making Spencer's (and your) whole argument "arbitrarily small" at the same time. I tried to tell you this before, but you just don't get it. That's too bad, because in reality you can't have it both ways.
If the dimensions (and therefore mass) of your "enclosing plate" approaches zero, then any absorption and re-rediation will also approach zero, and any supposed effect it will have on the temperature of the heat source will also approach zero. Even if your argument were correct, you're arguing yourself out of an argument.
So no, this argument is NOT valid with an "arbitrarily small" enclosing mass. It has to have enough to make a measurable difference on the temperature of the source (your argument, not mine) or the whole argument is empty.
You are trying to say you can make the dimensions larger by an "arbitrarily small" amount, without reducing the effect you are arguing for to an equally "arbitrarily small" amount. But the whole argument was about tangible and measurable effects. So you can't have it that way, man.
You sure know how to argue yourself into corners. Your assumptions are pure shit.
Now, I am done arguing. You can repeat the same BULLSHIT over and over all you want, but that won't make it any more valid. If you had the courage of your convictions, you would argue with the proper people about this, rather than trying to pick on (and losing to) a layman who is actually just laughing at your antics. Not laughing at your insults and attempts at ad-hominem and character assassination, no. But your antics, and your arguments about "physics", yes.