The Earth is Overall, Flat

In regards to the three depictions at the beginning of my opponents opening argument: If I'd realised the purpose was to illustrate what my opponent meant by "overall flat" (I thought they were like premises for an argument) I may have treated his argument differently. Then again, his argument from the fourth dimension takes a different line to his argument from smoothness so which way pro is trying to go with this is a little confusing. Due to a lot of ambiguity actually, this entire debate has been inadequately defined and clarified from the outset. There are two senses the word "flat" has been used, both of which can be defined as "level, even": The sense my opponent intended to use it which is simply a surface that is continuously smooth and mostly without uneven bumps (so, synonymous with "smooth"). And the sense I assumed to use the term which was of a geometrical understanding; a surface with a curving gradient is curved, not flat and a surface that is "level, even" (so the gradient is 0) is flat. For the moment I'll call these two senses "Gflat" and "Sflat" _____ I hold that it was more reasonable for me to assume from the outset of the debate, the term "flat" as it was defined was intended as "Gflat" not "Sflat" as my opponent actually, initiall intended, for three reasons: Reason 1 is the title of the debate "The Earth is overall, flat": this title causes one to think of the ancient belief that the earth was flat. That is to say, that the earth did not have a curving gradient to form a shape like a globe but that it was flat. So, I was deceived (intentional or not) by this title into debating a topic which was not what it was more obviously reasonable for me to think it was. Reason 2 is the ambiguous usage of the term "flat": as defined in the first round, it didn't clarify the sense my opponent actually intended to use it and so it did not correct my geometric understanding of how I thought the term was intended. As my understanding of the use of the term (as implied by the title) was not clarified by anything my opponent said in the first round, I thought it reasonable to assume we were on the same page. Reason 3a is my opponents arguments: It was not clear to me that the three depictions at the beginning of round two were intended to clarify what my opponent meant by the term "flat" (the first depiction of the represented 3D object mind you didn't at all clearly indicate that the surface was meant to have bumps). It seemed to me rather that they were sort of a kind of set of premises that were meant to lead the reader to the sneaky subliminal conclusion that a surface with a very small gradient can be considered "flat overall" and so this was what I attempted to refute. Granted, if these depictions were meant as premises to an argument designed to lead to that subliminal conclusion using "Gflat", it'd have been a ridiculous argument, especially considering what I thought was premise three with the person's face. So, I should have begun to suspect the misunderstanding at that point and given my opponent the benefit of the doubt that he wouldn't make such a ridiculous argument. I apologise for not being more sympathetic and I also apologise for not making sure that I and my opponent were on the same page in regards to the term "flat". However, I do suspect that my opponent was deliberately ambiguous in the debate title and in round one so as to promote such a confusion and catch whoever accepted the debate out. Quote, "No, you do not see where I am going with this." If my opponent was so confident that I wasn't aware of where the debate was going this suggests they were deliberately ambiguous to catch me out. Granted, perhaps this was in reference to a confidence that I couldn't have suspected the argument from the 4th dimension... which brings me to the second part of my third reason. Reason 3b is that it was and still is unapparent to me which argument my opponent was/is making: As I understood and still understand my opponent's argument from the 4th dimension, his usage of the term "flat" here is "Gflat" and not "Sflat" like in the section concerning the three objects. Either he's trying to argue in both senses or he in one of them, or maybe one of the arguments is the fallback. Either way, I can't see a reasonable way to carry the same understanding of the term for both arguments. I have to assume he is using one or the other in each case but it's ambiguous because he always just says "flat". I have to assume when he is arguing with a different understanding of the term. This of course added to my confusion in the second round because as my opponent did not make clear that he intended to use the term flat in two different senses I naturally assumed he meant it in one of the senses which was of course "Gflat". So, since it was more reasonable for me to understand his argument from the 4th dimension with "Gflat" this led me to further refute anywhere he equated flatness with smoothness. Henceforth, I demand that my opponent from here on specify whether or when he is arguing that the earth is "overall smooth" and whether or when he is arguing that the earth is "overall Gflat" (now simply "flat"). And that for the purposes of removing further ambiguity, he no longer uses the term "flat" in the smooth sense and instead simply says "smooth" (the article linked in my opponents round three post not once uses the term "flat" which further leads to my suspicion of his deliberate and unfair ambiguity). _____ Now, for my round three ;] As I currently understand my opponent, he's made two different arguments; one from smoothness and one from the 4th dimension (I have a sneaking doubt that I have incorrectly understood the latter dimension but for the purposes of this round's argument I am going to go with my impression). - In regards to my opponents argument from smoothness, that is to say, the earth is overall smooth (smoother than a billiard ball) I concede: depending on the POV the earth can be considered overall smooth and geometrically speaking, it is technically smoother than a billiard ball. - In regards to my opponent's argument from the 4th dimension, I carry my refutation (disregarding confusions over "Gflat" and "Sflat") from the second round, which my opponent has neither defended against or commented on (although he did agree on something else relevant to this): I said, "Pro doesn't claim the universe PROBABLY IS four dimensional and the article he linked cites no evidence for such a claim either. It is all a conjectural possibility." Pro said in agreement to this and I quote, "Yes, it is entirely possible the world is fourth dimensional, which makes it possible that the earth is "flat"." My refutation to the argument from the fourth dimension is as surmised below (I believe pro agrees with the second premise): 1. It is pointless in this debate for pro to prove that the earth can appear to be flat from the perspective of a dimension that has not been shown to PROBABLY be an objective feature of reality. 2. Pro has not proven that our three dimensional universe is within a four dimensional universe (it has only been shown to be a possibility). So it has not been shown to probably be an objective feature of reality. 3. Therefore it is pointless for pro to make an argument from the 4th dimension (whilst it is interesting). Disclaimer: If my opponent's intent was only to show that it is a possibility then I do not penalise him for making the interesting contribution and I apologise if I have misunderstood him to be using it as an argument. __________________________________________________________________________________________________________________________________ Onto you, pro.