One of my problems with Barthel is that his theory necessarily postulates a fourth dimension or sorts, which is the dimension in which the other three curve. I consider this an unacceptable presumption even worse than gravity and Newton's laws.
No, Barthel's theory does not postulate "a fourth dimension or sorts, which is the dimension in which the other three curve." It correctly states that space is three-dimensional, yet a closed totality, which necessarily follows from its cyclical nature, which is logically necessary. You are the one who presupposes Euclidean infinity geometry to be correct, which is logically contradictory. How about first reading what Barthel actually wrote before misrepresenting his theory?
You completely missed my point. Regardless of what geometry you use, the laws of mathematics still apply. And it is obvious to me that if something is curved, it is curved in a space. Disagreeing with this obvious and logical idea is simple theoretical spherical gibberish.
No, I did not completely miss the point, and I'm afraid the gibberish is yours. Which laws of mathematics are you talking about? Euclidean geometry laws founded on the wrong parallel axiom perhaps? It has been sufficiently demonstrated in this thread why the Euclidean parallel axiom (there are two straight lines in a plane, which never intersect, the so-called parallels) is wrong and must be replaced with the Riemannian one (any two straight lines in a plane always have two intersection points 180° apart). The only thing that might be argued about is the question how big this space constant of 180° is. A lot of arguments point to the size of that constant being roughly 20000 km, i.e. half of the Earth's circumference. Again, this is exactly the point, that space is closed without being curved. Curvature can only apply to objects or light within space. If space itself were curved you could lay a tangent to it, which would then be outside that "space". The only problem with the necessity of space being closed without being curved is, as was repeatedly said, the inability of the human mind to visualize, imagine the totality at once. But it can be thought, and what's more, it is inevitable, logically compelling.
Lactantius
This doesn't make any sense. Only a ridiculous "theoretical" approach can produce such a nonsensical result. Two parallel lines don't intersect, and that's obvious. This makes about as much sense as "gravity." The problem with all of these "theories" is the idea inherent in them that something which explains some results can be true, even though it doesn't make any logical sense.
Before jabbering on that things you don't (want to) understand allegedly don't make any logical sense, please go to page 6 of this thread where the proof (the persisting intersection point of a rotating straight with another straight line) is presented that there are no two straight lines in a plane which infinitely keep equal distance, there are no so-called parallels, which should better be named co-verticals at a certain point. You either have not studied what has been presented in this thread or, of course, you are a troll also. Or, third possibility, you simply don't get it, but then I can't help you.
Lactantius
Here's another possibility; you're wrong. Woah, never thought of that?
I saw your proof. It makes no sense and is based on theoretical conjecture of the sort that is in complete defiance of the zeitetic process. Since I am a form adherent to said process, I find your position inherently flawed and your attitude elitist and mind-blowingly ignorant and inflexible. You refuse to even consider the possibility that you're wrong, which makes you susceptible to such outrageously unscientific "theories."
If Barthel's theory is wrong then the whole idea of a flat Earth is wrong and incredibly silly, and you perfectly well know that. There is a reason no one has ever found an edge of the world or an infinite frozen wasteland beyond the imaginary antarctic ice wall. Applying Occam's Razor the simplest reason is: they don't exist. Are you yourself a Flat Earth believer? If so, which version do you adhere to, the disk or the infinite plane? Do you seriously, honestly believe any of those two?
In Barthel's time there were several mathematicians who admitted that his theory was geometrically possible and consistent, you (and practically the whole world) not knowing about that or Barthel's works in general doesn't change that. The zetetic method is fine and well, but it is not everything, and most of all it also depends on a priori assumptions, in this case, which geometrical axiom to choose. BTW, if you could read Barthel's works you would see that also as a philosopher he far surpassed Rowbotham et al.
Anyway, to people like you there is only one advice: Be careful not to fall off the edge of the world resp. not to get lost in the vast ice desert beyond the wall ...
Lactantius
Once again, a non-adherent uses personal insults to convey an argument. I think your position is silly, and I wish you realized that it is. Occam's razor has nothing to do with this, although it would definitely enliminate your theory, which actually postulates that the world is some sort of multi-dimensional theoretical geometry. Flat earth makes sense to anyone who looks out his window. It is a perfectly coherent theory, unlike your theoretical nonsense. I believe in a flat earth disk, which is the only historical version of flat earth adherence your theory makes no sense and involves some mathematical backflips in order to render itself obscure enough to avoid being exposed as a nonsensical and fake theory, much like gravity.
As for your claims about Barthel's philosophy, it is not even on the same level of thinking as Parallax's. Rowbotham was a genius for understanding that reality is reality, and nothing more. That is the most important realization in scientific history. Barthel not only fails to see this, but creates an even more convoluted model than round earth, which falls flat and has never been thought of as more than quackery, by anyone.
My advice to yyou: don't make an argument personal. You sound like a discontetnted child, shouting and refusing to acknowledge anyone but himself. Your post reveals an immature mind not ready for zetetic enlightenment. Read Rowbotham's work a little, and open your mind a lot, then maybe you'll be able to lay out a normal argument, not one laced with childish inability to think.