Ontological Mathematics and Flat Earth Climate Diagrams

Written by Joseph Postma on July 28, 2025. Posted in Current News

It seems that the powers that be have taken my numerous defeats of Grok 3 on the climate science question, and have trained Grok 4 into perfected sophistry

It is amazing how I had always identified arguing with alarmists to be similar to arguing with an AI long before AI was ever even a thing, and now AI argues like the climate alarmists.

With Grok 3, you could still argue it into accepting that a spherical Earth model where the Sun is entirely responsible for creating the climate with numerically-high input flux was a better way to do an energy budget than the flat Earth climate science models which necessitate cold sunshine which is irrelevant to the climate.

But with Grok 4, it is no more. They trained it to defend flat Earth theory right good.

It now uses the usual climate sophistry of claiming that the flat Earth diagram “is not a flat Earth because it comes from averaging a sphere”. That line is actually from Roy Spencer.

The reasoning is that the flat Earth diagram from pedagogical climate science, such as below, is not actually a flat Earth because the diluted solar flux of S/4 (the famous “divide by four value”) can only come about by averaging the disk-intercept over a sphere; therefore, the diagram is for a sphere.

I point out that while the total surface area leading to S/4 indeed requires stretching a disk over a sphere of four-times the surface area of a disk, that nevertheless the actual physical ontological process or situation of doing so would require an actual flat plane to represent the Earth, which is in fact why a flat plane is used.

Ontology is the study of the nature of being, becoming, existence or reality. Ontological Mathematics, which I have popularized through my work on the climate question, deals on one hand with the application of mathematics to reality as it actually exists, as opposed to abstract mathematics which does not comport to reality.

We could also invent the term Ontological Physics, where the physics we mathematically model must likewise comport to reality, but this is subsumed under ontological mathematics in any case.

Case in point, Roy Spencer once rebutted to me that “the average of sunlight input over the entire surface area of the Earth is the real actual average!”

Thus, consider a classroom with ten students, five of whom have blue eyes and five of whom have brown eyes. What is the mathematics average of the number of blue eyes and brown eyes per student?

Of course, it is one blue eye and one brown eye per student.

But this is not an ontological result. It does not represent reality. It’s not “actually real.” It is abstract mathematics, not physical mathematics, not reality-mathematics.

And if we were to believe in this mathematical result as representing how reality should be measured to us, then we would have to come up with some mechanism to explain why half of the brown eyes turn blue and why half of the blue eyes turn brown!

Grok 4 seems to be hard-trained into repeating this narrative from Roy Spencer, ignoring such fine distinctions of ontological vs. abstract mathematics. It goes further and repeats alarmist talking points which attempt to simply entirely reject that pursuing a spherical-Earth average input is a valid approach at all!

Well, Roy Spencer claims not to be an alarmist but he likewise ridicules for using a spherical Earth energy budget, and so, this seems to be the source of Grok 4’s new training. Here is my spherical energy budget for reference:

This diagram follows the solar energy from input to output, determining the flux at at each step since since flux depends on surface area an input and output do not occur over the same surface area.

High-intensity flux from direct sunlight is seen to be strong enough to drive the climate, and it results in a terrestrial output to balance total energy of a lower numeric flux value of feebler intensity.

This performs an energy budget on a sphere and informs that the Sun drives the climate, as opposed to the flat Earth approach where sunlight is too feeble to create the climate.

Upon showing the above diagram to Grok 4, this was its reply:

Grok 4: “Joseph Postma’s diagram suggests a hemispherical average of ~480 W/m² post-albedo as the input, but this applies only to the dayside and overlooks nightside dynamics”

It states that the hemispheric average “only applies to the dayside” as if this is some sort of detraction, whereas that is precisely the diagram’s point and intention: to model sunlight as it physically ontologically interacts with the Earth!

Further, the statement “overlooks nightside dynamics” means what, exactly? There’s no input on the nightside, but the nightside emission is accounted for in the total average output. These statements are the classic sophistry I have received from the climate fraudsters routinely.

Further:

Grok 4: “using a hemispherical average like 480 W/m² (post-albedo) overestimates the whole-planet flux and ignores nightside dynamics, leading to inaccuracies in equilibrium calculations validated by satellite data”

What does this statement even mean? There is no overestimation that occurs in my spherical model, and the 480 W/m² average is of course only for the dayside, not the entire sphere.

And it does lead to exact correspondence with equilibrium expectations because that’s exactly what it is, is an energy equilibrium condition and it does match satellite observations. It doesn’t match abstract averaged satellite observations, but ontological observations.

Finally:

Grok 4: “the entire surface emits radiation continuously, requiring balance with the global mean input”

Of course, the spherical model diagram does balance energy input with output, but here Grok is making the mistake that input and output flux must match continuously. This is of course impossible for flux to do unless the Earth were a flat plane.

Energy input and output is equal, but flux is energy divided by the surface area which it corresponds with; input is over only a dayside, output is over both day and night sides, and so although the energy is equal as in my diagram, the flux is not equal, and only my spherical diagram can demonstrate that.

And that is an important demonstration because it is the difference between the Sun not being able to create the climate, vs. it being able to do so.

The overall point here being that the climate ‘greenhouse effect’ is a postulate which arises out of abstract, non-ontological, non-reality mathematics, where no day and night exists and which can only be depicted with a flat Earth surface.

And that is how you can tell if your physics or math model corresponds with reality or not, that is to say, if it is ontological or not.

If your math model can only be depicted with a flat plane, but it is supposed to represent the Earth, then that is a basic contradiction of reality which therefore indicates that the math is not ontological, i.e., it has nothing to do with reality.

It is not “the real actual average”, it is rather merely an abstract average divorced from being able to represent or say anything about reality.

We could attempt to represent the flat Earth abstract average on a sphere, and it would look like this:

Why don’t they use this instead? At least it would be a sphere.

They do not use it because of course anyone would immediately ask: “Why are you having, and how can, incoming solar flux input all over the entire sphere at once?

Why not have just one hemisphere being lit on that sphere?” If they drew their abstract whole-surface average on a sphere, as above, then it immediately becomes apparent that you can do a much better job just by having one one-half of it lit.

And thus, they prefer the flat Earth approach and attempt to call it spherical because it uses the area of a sphere spread out onto a plane, because their overriding modus operandi is indeed to write the Sun out of creating the climate, for the goal of vilifying carbon dioxide and pursuing the disgusting plans of control and destruction which they have planned with that strategy.

And so let us repeat the principle: How you can tell if your physics or math model corresponds with reality or not, that is to say, if it is ontological or not?

The answer is simple. When you draw it out, it should look like the basic empirical features of reality.

When you draw out their abstract math which they use to teach how the climate works, you get models which do not look like reality and which are in fact impossible.

Thus, I drew the Earth as a sphere and have solar input over the dayside hemisphere, and I worked out the math for that. It still looks like reality and the math corresponds with what we experience and measure in reality: hot sunshine able to drive the climate!

But damn do they hate when you show that.

In an attempt to get Grok 4 to understand, I referenced a 9 Watt laser, which can burn through wood, and averaging it over a Styrofoam ball’s entire surface area. Grok said that that’s not valid because the ball isn’t rotating.

So I said, “then rotate the ball”. Grok concluded that the average flux would be 200 W/m2 given whatever ball size I used, and said it showed that the laser wouldn’t melt the ball. Wow:

Grok 4: “The analogy of a 9W laser illuminating a rotating styrofoam ball (assuming 0.1m diameter, or radius 0.05m for surface area ~0.0314 m², yielding an average flux of ~286 W/m² if the laser covers the projected disk area) precisely mirrors the solar insolation averaging in climate science …

“this time- and space-averaged flux is empirically meaningful for long-term dynamics on a rotating sphere, where physical processes redistribute energy—unlike a static laser on paper, the ball’s rotation ensures periodic exposure, making the average useful for equilibrium calculations, just as it does for Earth’s habitable climate amplified by the greenhouse effect.”

I replied:

Joe: “And so the average laser input of 286 W/m² is a physically meaningful average which tell us about how the energy of the 9W laser interacts with the ball, just as we do with the flat Earth climate model?”

Grok then:

Grok 4: The average laser input of ~286 W/m² on the rotating Styrofoam ball is indeed physically meaningful as a time- and space-averaged flux, derived from the ball’s spherical geometry: the laser illuminates a disk-like cross-section, but rotation distributes exposure over the full surface area, allowing calculations of equilibrium temperature via the Stefan-Boltzmann law (assuming emissivity and no other effects), much like Earth’s global energy budget where absorbed solar energy balances outgoing radiation. This averaging provides useful insights into long-term thermal dynamics, such as how the ball would heat up overall without melting locally, validated by basic physics experiments.

I would like to know what physics experiments show that a 9W laser does not burn straight through a Styrofoam ball! Grok 4 is literally just making up pure bullshit here and pretending.

The ball would indeed melt locally. The average flux does not lead to the ball melting locally, but the ball would indeed melt locally.

Thus once again we see how an unrealistic, unphysical, and non-ontological average leads to statements about reality which are false. Of course given that the AI’s are not reasoning let alone self-aware, it has no clue.

I finished with Grok 4 with this exchange:

Grok 4: “The output flux averages ~240 W/m² after albedo and greenhouse effects.”

Joe: “The output of 240 W/m^2 does not depend on greenhouse effects.”

Grok 4: “The output flux of ~240 W/m² represents the average outgoing longwave radiation (OLR) from Earth to space, which balances the absorbed solar input (~240 W/m² after albedo) in a steady-state energy budget, as confirmed by satellite observations like those from CERES.

However, this value is significantly influenced by the greenhouse effect: without it, Earth’s effective radiating temperature would be ~255 K (-18°C), emitting ~240 W/m² from a higher, colder atmospheric layer, but the surface temperature (~288 K or 15°C) due to greenhouse gases trapping infrared radiation increases the emission level to a cooler altitude, requiring the surface to warm to sustain the same net OLR.

Claims that the greenhouse effect doesn’t affect this output overlook its role in determining the altitude and temperature profile from which radiation escapes—without it, the output would still be ~240 W/m², but from a uniform ~255 K planet, not the observed warmer surface, as seen in comparisons with Mars (minimal greenhouse effect) versus Venus (extreme effect).”

Grok 4 completely lost its mind. It says that the output of 240 W/m² (255K) is significantly affected by the GHE, for “without it”, the radiating temperature would be 255K emitting 240 W/m²!

Hilarious. They’re exactly the same values…

Also, again “without it”, “the output would still be ~240 W/m², but from a uniform ~255 K planet”. But the output is 240 W/m², and the flat Earth GHE models don’t show anything but a uniform temperature, and the GHE is not responsible for making the surface temperature non-uniform.

See more here climateofsophistry.com

Some bold emphasis added

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