Divine geometers notwithstanding, I think you've discovered the crux of your mistake and the reason for part of my criticism. You are doing metaphysics with science.
It may appear so, cornelis. But I thought I was doing science with an "assist" from metaphysics! I know that one is "beyond" the other in substance and by definition.
It seems to me that one of the things integrative science is trying to do is to find a way to do science that does not depend on the unsupported, untested assumption that one can successfully infer the structure and functions of an organic whole just by investigating its parts. Especially when that whole is a "higher-order infinity" than any of its parts and all of them put together.
The whole is more than just the simple sum of its parts. To think otherwise is a grave mistake, IMHO FWIW. I think it is precisely that assumption that is arresting further scientific progress, and causing an undue focus on matter to the exclusion of spiritual things -- you know, such "little things" as consciousness, freedom, experience, feelings, thought, ideas, etc., etc.
So you try to figure out what the higher-order structure may "look like." Then the parts might become explicable.