Inches per mile per mile is not the same thing as inches per mile.

I will repeat: it's not the value itself (as long as it is not zero), but *the bending* that is ridiculous. And I'd appreciate it if you could explain what it means for a line to be bent "8 inches per mile per mile". Since when is the deviation measured in such a unit? And if what you calculated is not the deviation, than what value do you find for the deviation?

The deviation would be equal to _{0}∬^{x1} 8 inches per mile per mile * dx^{2}, where x_{1} is the horizontal distance travelled by the ray of light.

You still didn't explain (supposing you are able to) what does it mean for a line to be bent "8 inches per mile per mile". Can you explain it or not?

As for the formula, it is very ... useless, since you say nothing about the double integral, and what it means. How do you calculate a double integral using one dimension (from 0 to x1) ? Are you joking here or what? Could you at least show here how did you derive such a (ridiculous) formula?

And since you are supposed to know how to use it, could you tell me what is the value you obtain for a horizontal distance of, say, 3 miles? It would be nice to show you (and Tom Bishop) how ridiculous your hypothesis is with some numbers, as you don't seem to get it only qualitatively...

Nothing is able to follow such a path, as the word "follow" implies the presence of a temporal dimension.

I hope you're not being intentionally dense about this...

In order to visualize a trajectory, without needing the time dimension, you could do the following: Take a number of objects and make them follow the said trajectory, at short (as short as possible) intervals of time. Then, when enough of them are “on the way”, you take a picture and voila! You can see it. So don't give me that excuse. Just tell me what do I need to do to have something follow a horizontal straight line. Please.

What you would be seeing in that case is not a geodesic in three-dimensional space, but a three-dimensional view of a geodesic in four-dimensional spacetime. You cannot have something follow a path in three-dimensional space without a temporal dimension, and therefore you cannot make something follow a geodesic in space, only in spacetime.

Ok, so you're being dense.

In order to compare the surface of the Earth with a "straight" line (in three dimensions, where the "flatness" has a useful meaning for us), we need useful a definition of "straight" lines (in three dimensions). All your talk about "geodesics" as "straight lines in four dimensions" is therefore useless for this. I proposed a way to

*visualize* the three spatial dimensions of such a geodesic, such as not to need the time as a fourth dimension, but you decided to ignore it.

It's not the "following" that interests me (that needs "time"), but the visualizing of

**a straight line in three spatial dimensions**. So I reiterate my question: Does your "theory" contain a useful definition of "straight lines" in three dimensions? Relative to what did you evaluate the "bending"? (That should be obvious once you show me how you have derived the double integral formula.)

I already told you, the path light follows may be compared to a geodesic in four-dimensional spacetime. My calculation of 8 inches per mile per mile, however, represents an appropriation of the phenomenon to our own non-inertial frame of reference, such that it is relative to the surface of the Earth.

And my question for you is: compared to what "straight line" did you evaluate the "bending"? Again, don’t tell me it’s a line drown on the surface of the Earth, because that is a circular definition for Earth’s flatness. (Which renders the FET nonsensical and useless. Not helping!)

**Assuming the Earth is flat and light does bend in the way I have supposed, then the calculation of "8 inches per mile per mile" is relative to the surface of the Earth.** Simply add the Earth's acceleration of 9.8 m s^{-2} to this figure to get the acceleration of light relative to a geodesic in spacetime.

-- emphasis added --

But this is circular logic! You can't use the assumption of a flat Earth in order to calculate the bending of the light, which then would explain why we see what we see on our flat Earth! That would amount to "the Earth is flat because we started with the assumption that the Earth is flat", which is not what Zetetics is about. So that's how you're hurting FET, even if you don't get it. If you want to deduce from observations the true form of the Earth, you can't use the flatness as an axiom of your theory!

BTW, by constructing this ridiculous hypothesis about "bending light" , you're implicitly assuming that the observations agree with a "curved" shape of the Earth, which they don't! The restoring of the "sinked ship" image is not possible on the supposedly RE!

Without an independent definition of "straight", all your hypothesis does is make the flatness indistinguishable (by direct observation) from the "curvature" of the RET. That means throwing away one of the most powerful arguments revealed by Parallax, who showed that the zoom does restore the "sinked ship" effect, which means that we CAN

*observe* (with adequate optical instruments) the fact that the Earth is flat! That is why so many people try to discredit Parallax, because his argument is so powerful.

Here is the direct question: Do you claim that your "bendy light" is *compatible* with the direct observation made by Parallax about restoring the sunken ship image with a powerful zoom? This is not a detail on which you could "approximate" better, it is a fundamental observation. Your disregarding that is what hurts the FET.

No, it is not.

Ok, so at least you admit the incompatibility. It seems that Tom Bishop still doesn't see it...

If what Parallax observed can be reduced to a particular case (a limit) of your theory, then you have a chance of improving the FET. Can you show that this is the case? Try and you’ll see that you can’t.

There are no special cases. I'm not going to trust what Parallax might have seen over my own rational thought.

Unfortunately, your "rational thought" is circular and therefore useless. Plus, you ignore all the hard zetetic work done by Parallax, with a hypothesis based on circular definitions ... That's exactly what Parallax wanted to avoid, the mistakes of all the "scientists" who started with their conclusions in order to "prove" them correct. And that's what you are doing.

Is your true intention to discredit the FET? Well, all you're doing is revealing the fallacies you personally call "rational thought".

Steve, does this mean that you believe that because of bendy light, the sunken hull of a ship cannot be restored, no matter how powerful the magnification? If so, that directly contradicts one of the fundamental tenets of FET.

Perhaps over short distances, it can. Certainly nothing more than ten kilometres or so.

Well, it seems that we need to start using exact numbers, because Tom Bishop said that the effect of "bending light" is already noticeable from no more than one mile! So, please do the calculation for, say, 3 miles, to begin the precise evaluation of the ridiculousness of this hypothesis.