Dear Simon,
I do find your essay particularly volcanic -- full of stimulating ideas combined in original ways. I also think it would benefit, having more space and time, from a more patient and detailed description of the different types of memory-related features and associated self-reference skills (the exact intended nature of this association is not completely clear to me) that originate at the different layers you mention, in particular at the lowest ones, which I like to imagine of pure computational nature.
Early in your text you claim that (1) it is easy to describe everything, and (2) much harder to describe one thing. This remark immediately rang a bell in my mind: according to Juergen Schmidhuber, if the universe is computable then it is easier to compute all universes than just one. Here is the reference, in case you find it useful for future versions of your essay:
https://arxiv.org/abs/quant-ph/9904050
Now a possibly pedantic point. Is it not the case that even the first derivative requires memory, or, more precisely, the ability to look both at f(t) and a bit ahead, at f(t dt), for then taking the limit dt->0? Is this not exactly the same 'skill' required for carrying out the second derivative, and the third (jerk)? Why then do you bring on stage the memory feature only with the third derivative? (This is a separate issue than wondering whether in Nature most or all phenomena are adequately described by just first and second derivative.)
The importance of temporal memory in human perception, even on the shortest (physiological) temporal scales, is quite clear (e.g. in listening to music), and it nicely combines with a similar form of spatial memory, for visual perception: we cannot make sense of a scene in the envoronment if we cannot absorb finite time and space segments of it. (Wasn't there another story by Borges about a man who suffered from some form of memoryless perception?)
Thank you and congratulations for the originality of your ideas.
Tommaso