Another point of view

The idea of complexity is significant in the evolution of human beings' thought processes.
But in some occasions this complexity is apparent, only due to our incomplete knowledge of reality.
Beautifully demonstrated in this video is...where do Moebius transformation come from?:
http://www.youtube.com/watch?v=JX3VmDgiFnY
I hope some day when I try to explain something complex I will be able to find another point of view to explain it in such a clear way.
A point to take into account is that sometimes if you change the sphere of thinking (kind of the "dimension") you can find an easy answer to something that has been bothering you. This tends to happen to me when I am putting a string of verbal arguments, and I reach an impasse or an absurd proposition. Depending on the realm of the thought process, I can put it in graphical/geometrical display and I am able to get out of the problem, a lot of times very easily. This is actually very helpful when you are inmersed in verbal circular thinking and you have not realized it...yes, it happens to me a lot, I need more practice!
The question that I therefore ask myself is...is this difference in resolution capacity due to the nature of reality/thought process (if it's not based in reality) or is this difference due to the intrinsic capacities of different modes of thinking?
Reading some arguments about string theory made me think that probably the nature of thought reality is similar to a model whose characteristics you are able to calculate with string theory tools while another one, that is theoretically equivalent to the first one, is impossible to calculate. That phenomenon always astounded me from a down to earth stand point. Let me put it in another way...
For two objects/dimensions/versions of reality/whatever you want to call them, that by definition are equivalent, you have one mathematical/physical tool that tells you that you can obtain the properties of one of this objects very easily, but for the other it's almost impossible! And sometimes only by changing the tool you can obtain the absolute opposite result. Just amazing (This has to do with Calabi-Yau shapes, but for those who are allergic to physics, you don't need to know them to understand the underlying concept).
This could be a nice approximation to my point about the different modes of thinking, but sadly I can only connect these two sets of thought pathways through analogic reasoning, not through any other mode of thinking...and analogies can happen without being actually real associations(yeah, correlation does NOT signify causation. Stupid reality messing up with my beautiful theoretical constructions).
It would make sense anyways that different types/modes of reasoning have different areas of dominion of reality, just like you can't really apply logical thinking to an artistic evaluation and viceversa...or can you? Could this be another example of me not knowing that "extra" dimension that would link several types of reasoning?
Sadly due to the intrinsic characteristic of this thought pathway I can't really obtain a result, because the argument is based on my inability to find this relationship! (argghh, I hate when I do this, because most probably it reflects a mistake in my train of thought, but again, that is why this blog is called Learning to think, not "I know how to think, and let me show you how easy it is!")
Well, is time to think another thought
Bye