I of course accept your criticisms Ophiolite .
Perhaps ,though you have answered my question in the main when you say "the majority of physicists doubt their reality, "
Whatever about my own lack of rigour I am glad that this seems (if you are right) to be the prevailing view.
I would find it unsettling otherwise.
PS your "Do you know the equations well enough to say this is what happens?" was a rhetorical question perhaps , since I said towards the end of my post " do I simply have my lack of proper scientific/mathematic education to blame for my blinkered vision? " -which concedes that point , I think.(although that might have come across as false modesty instead of being ,perhaps an overestimation of my capabilities)
The Mobius strip , yes I have heard of it. I don't follow what you mean by "what number comes after 12 ?".
I am also unclear as to what would constitute "two separated parts of a mathematical object." but perhaps I understand your overall meaning.