Despite the similarities, I think that there is some difference between Ord’s notion of hyperbolation and what I’m describing here. In most of his examples, the extra dimension is given. In the examples I’m thinking of, what the extra dimension ought to be is not known beforehand.
There is a situation in which hyperbolation is rigorously defined: analytic continuation. This takes smooth functions defined on the real axis and extends them into the complex plane. The first two examples Ord gives in his paper are examples of analytic continuation, so his intuition that these are the simplest hyperbolations is correct.
More generally, solving a PDE from boundary conditions could be considered to be a kind of hyperbolation, although the result can be quite different depending on which PDE you’re solving. This feels like substantially less of a new ability than e.g. inventing language.
A few more thoughts on Ord’s paper:
Despite the similarities, I think that there is some difference between Ord’s notion of hyperbolation and what I’m describing here. In most of his examples, the extra dimension is given. In the examples I’m thinking of, what the extra dimension ought to be is not known beforehand.
There is a situation in which hyperbolation is rigorously defined: analytic continuation. This takes smooth functions defined on the real axis and extends them into the complex plane. The first two examples Ord gives in his paper are examples of analytic continuation, so his intuition that these are the simplest hyperbolations is correct.
More generally, solving a PDE from boundary conditions could be considered to be a kind of hyperbolation, although the result can be quite different depending on which PDE you’re solving. This feels like substantially less of a new ability than e.g. inventing language.