This is excellent work Torsten!
I have a quibble, that in human brain learning studies it was found that the naive view holding that similarities of structure between table result in similar memory encoding is untrue, but it was found that memory images were grouped by function instead. So there are several places a coffee cup appears represented in the brain, depending on whether it is empty or full, clean or dirty, and so on. It's usage determines how it is stored. So we might find table and couch represented in the same brain areas.
But this is in keeping with your observation of the importance of top-down influences, because to a living being in the real world objects are meant to be used or to have uses - which affects how we conceive of it. The old Chinese proverb is that the value of an urn is the space it contains. But this is an object fashioned by humans because it can fulfill a particular purpose. It is interesting though, that this purpose orientation is a driver of neurological specialization.
It was worth taking the time needed to digest the Maths, so I could get a better perspective of your intended meaning. But more digestion is required; you have given me a lot of food for thought, between your essay and comments, so I'll likely have some questions or a few comments of my own. An excellent read overall, and I hope you do well in the contest.
All the Best,
Jonathan
