Only One Way to Test
Although my output on the greenhouse topic has been greatly reduced, the reason is because I have settled at the end-point of the approaches for analysis. There is a single way to test for a radiative greenhouse effect, and it is a direct test which can be performed either with fundamental mathematics, or empirically. Actually the question of the empirical vs. purely mathematical approach becomes totally paramount here, and my preference is to say that a purely mathematical proof is possible.
That’s a good question, right? Are purely mathematical tests of the behaviour of reality possible? All scientists would of course say no, that empiricism actually drives and is the heart and core of any possible knowledge we may have about reality, and that mathematics only serves our empirical probings, not proves them. However, then you have that pesky case of Dirac, who discovered antimatter purely by a mathematical proof…albeit a mathematical proof which came from earlier empiricism-based science, so perhaps that’s not a good example after-all. Then again, empirical tests are proposed based on testing what the mathematics says about the way reality should behave.
The radiative greenhouse effect schematics like we see below of course do use mathematics, but they can’t be said to necessarily use ontological mathematics. Non-ontological, abstract mathematics can be used to make statements which totally contradict empirical reality.
If one were to replace the “input” radiative fluxes in the above diagram with their corresponding temperatures, then the above diagram (from climate science alarm) would say that when you add one object at -18°C to another abject at -18°C, then you get +30°C. That is, if you take one ice-cube, and combine it with another ice-cube of equal temperature, then you get a higher temperature object in that combination. With abstract mathematics you can do that just fine, but it is total garbage ontologically because empiricism tells us that reality does not behave that way. Ontological mathematics also tells us that reality won’t behave that way, but this requires a much, much more advanced form of mathematics that is typically only seen in advanced courses in statistical theory in university physics.
So, it is typically much easier for empiricism to tell us what the ontological properties and behaviour of reality is, than it is for the correct mathematics to tell us. That being said, although empiricism tells us what happens, it doesn’t tell us why it happens. In the final analysis, you only get the why from ontological mathematics, in this case from fundamental statistical theory, otherwise called the Laws of Thermodynamics.
The only “why’s” whose answer we are capable of being certain about, in fact the only why’s which provide absolute fundamental knowledge in their answer, are based in mathematics. Why? Because when you can reduce some problem, some behaviour, some feature, etc., to the equivalent of 1 + 1 = 1 + 1 = 2, then you have demonstrated something indisputably true, a tautology which is incapable of ever being wrong. Your feelings can be wrong, your instincts can be wrong, your senses can be wrong, your intuition can be wrong, etc., but 1 + 1 = 1 + 1 = 2 does not partake of a possibility of wrongness – it is permanently true. Advanced statistical theory, although quite complex, still reduces to such mathematical tautology of 1 + 1 = 2, and we find that reality behaves according to such ontological mathematics in the situations where it applies.
This opens up an interesting new question: How to distinguish between what would be ontological mathematics, vs. merely abstract or “practical” mathematics? That question requires its own analysis and it won’t be covered here so that we can get back on topic.
The Way to Test
The way to test the radiative greenhouse postulate is with what I have come to label a “de-Saussure device”, after the fellow Horace-Bénédict de Saussure, who with Joseph Fourier of Fourier-transform fame, constructed a device to trap solar radiative thermal energy inside internal cavities for the purpose of exploring how high of temperature could be achieved within the entrapment. I wrote about their results in this paper.
Such a device is simple enough to construct for the empirical test, but it is also simple enough to model with the fundamental heat transfer equations that Joseph Fourier developed with his Fourier transform. And for anyone who has read Mike Hockney and the foundations of ontological mathematics, you will know that when it comes to questions of utilization of the Fourier transform, we are most assuredly dealing with a question of ontological mathematics. (And further, if it is a question of ontological mathematics, then whatever the application in question is it must also have something to say about the nature of the soul; the spiritual consequences of the results of the application of the Fourier transform to a de Saussure device and the implications for the greenhouse effect will not be discussed here.)
Very simply, we have short-wave radiation coming into a device, whence the subsequent long-wave radiation is absorbed layer-by-layer. As in the following diagram:
The layers act as a sort of one-way filter, allowing solar radiation to pass within the device while absorbing the long-wave radiation generated inside. There would be a transmission cut-off at the frequency where the solar spectrum crosses the expected generated thermal response spectrum, as for example in the case of the solar and terrestrial spectra in the figure below between 104 and 105 Angstroms.
One of the boundary conditions of the device is that the innermost short-wave absorbing surface is insulated on its backside, which thus provides the mathematical boundary condition required in the numerical computation of the diffusion equation for the backside of that short-wave absorbing layer. All of the other layers temperature responses would of course be computed using the diffusion equation too.
The computation of the diffusion equation is intimately connected with the Fourier Transform…they are essentially the same thing in this application. That is, the Fourier Transform is the analytic solution to the heat transfer problem, however, how this is computed numerically is via the diffusion equation.
The parts where the Fourier Transform is applicable via the diffusion equation, that is within each layer, is relatively simple to implement; however, as anyone who has done this before knows, the topological behaviour of the solution depends entirely upon the mathematical nature of the boundary conditions at each subsequent surface of each layer.
One can implement mathematical boundary conditions which would correspond with the concept of back-radiation and a radiative greenhouse effect, and one can implement boundary conditions where back-radiation has no further temperature-generating effect.
Either solution when computed in “real-time” appear aesthetically to be possibly perfectly valid, but clearly give very different topological results for their final equilibrium conditions with constant input (at 1000 W/m2 in this case):
How does one tell which result is the correct one, and thus which mathematical boundary conditions are the correct ones? The Ontological Mathematical purist would say that it is possible to use mathematics alone to solve which boundary conditions are the correct ones, and thus finally say whether or not there is a fundamental “greenhouse effect” that operates upon radiation.
And it is possible to do so. Not withstanding that, as discussed in the aforementioned paper, there are empirical results which give the answer already; the problem here however, I have found, is that the experimental conditions of such empirical results can be questioned to such an extent that either side of the debate will willingly write-off their opponent’s assessment of the results. This has been done to me, and I have done it to others, legitimately. And I see people presently doing that on other posts on this blog, to no end and never arriving at a final agreed empirical analysis. That is why I find it best to finally couch the problem in terms of basic ontological mathematics, to see which side conforms to 1 + 1 = 2, and which side does not. And as I said, it is possible to do this.
I won’t describe the final analysis here because in theory I am writing a paper about it. But I will say that it seems as though this scenario presents a test of ontological mathematics itself, in that it seems as though mind is presenting itself in the behaviour of the mathematical boundary conditions of the correct solution. An experiment that demonstrates mind operating at the fundamental basis of reality – and the interaction of photons with matter and the subsequent thermal response of matter is indeed such a scenario, involving even the mind-matter Fourier transform itself – is in my mind a minor “holy grail” of ontological mathematical research. It’s kind of a big deal. That being said, I got the impression that they hated that I was writing about all that in this fashion. I didn’t mean it, and have no ulterior motives: I am simply pursuing what I am finding within the context of what I have come to learn and know.
So I’ll try finishing the paper. Well, really I just need to make sure it’s all correct, that the model is running as it should and that the mathematics and logic is all correct; I’ve been running the models over and over again for a year now, trying to see if I find myself coming to a different conclusion, trying to see if there are any other ways to write the code and the boundary conditions, etc. I am getting near ready to finish my work on greenhouse stuff and finally be done with it, and if things stand as it seems they are as I have discussed here, it will be for me a satisfying finish, even if no one else gives a hoot.