As far as I see, we mostly agree on content. 

I just can't make sense of reducing computation to emulability.
For me the intuitive sene of computation is much more rich than this.

But still, as I think about it, we can also create a model of computation
(in the sense of being intuitively computational and being implementable on
a computer) where there are computations that can't be emulated by universal
turing machine, using "level breaking" languages (which explicitly refer to
what is being computed on the base level). I'll write another post on this.

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