how desparate you must be to be reduced to arguing that rearranging terms in a formula is making a case.
Ian, talking to you is like talking to a slightly retarded child. You have to have every single thing explained to you in detail and even after you get the explanation, you still don't get it.
You might start by showing me in the physics literature where it is permissable to randomly apply the distributive property (or any property for that matter) of algebra for phisics problems. To the best of my knowledge, in physics, if you are going to apply an algebraic property then the property must be assigned a physical meaning. In this case it hasn't or if it has, then feel free to point me to the text in the physics literature in which it has. If you had ever taken physics, you would know that you can't simply apply random mathematical properties to equations dealing with physical laws and then say look, they get the same answer so they must be the same. It doesn't work that way in physics.
When you apply the distributive property to the SB law, you describe an entirely different set of physics. The SB law is expressed as p=sigma (T^4 - T^4) which describes an emitter at one temperature emitting into a background at a lower temperature.
When you apply the distributive property to the equation, you are applying the SB law twice which describes a very different thing. By using the distributive property you are describing (sigma T^4) the emitter at its temperature radiating into a background at a lower temperature minus the background (sigma T^4) which, according to SB is also radiating into a background at a lower temperature. Obviously this isn't what is happening. It is a violation of the 2nd law of thermodynamics. You have the background which is at the lower temperature radiating back to the emitter but to do so you must apply the SB law a second time and claim that now the emitter is at the lower temperature even though we both know that the emitter is at a higher temperature. The answer is the same but one is describing a phyisical process which is observable and repeatable and the other describes a fictional process (backradiation) invented to support AGW alarmism which is not observable and exists neither in nature nor in the laboratory.
I am sorry Ian, but you have made it more than clear that you simply don't posess the requsite math skills, analytical skills, or knowledge of the physical laws to adequately discuss this topic.
If you believe there exists observable, repeatable proof of backradiation, then present it. Failing to do that loses you the argument as my argument stands.
you still havent answered the question. if your math is correct, why do you get the same temperature for the heater whether it is radiating into a zero degree container or a 255 degree container? simple question, asked many times, always ducked.
I answered your question Ian. As I have said, you lack the requsite math and analytical skills to understand what you are being told. Did, or did not spencer state that his experiment was to represent the bars as an analog to earth sitting in space? He said:
roy spencer said:
One way to demonstrate the concept is with the following thought experiment, which I will model roughly after the Earth suspended in the cold of outer space.
Now Ian, do you think that spencer doesn't realize that space is represented at 0 K or do you think that perhaps spencer doesn't know that space isn't at 0 F? He said cold space and that being the case I am supposing that setting the temp at 0 F was an oversight on his part.
I have answered your question Ian, ad nauseum. Again, sorry that you lack the requsite skills to even realize that you have been answered, much less understand the answer you were given.
When you can show me in the physics literature that it is permissable to apply algebraic properties to physics problems without having first assigned a physical meaning to the property, or you can show observable, repeatable evidence of backradiation, we will have something to talk about. Till that time, you are wrong, and you have been proven wrong whether or not you posess the math skills necessary to realize it.
Further posts on your part will be answered with the paragraph above. You know and I know, (or maybe you really don't know) that no such carpet permission exists in physics to apply algebraic properties in physics and by now it is obvious that you know that no evidence of backradiation exists or you would have already posted a link to it.