RS reformulates/reduces the term "algorithmic revolution" as: >1. A social revolution.. >2. A scientific revolution.. >3. An epistemological revolution.. >4. A mathematical revolution..
all true. however, wolfram-fredkin-zuse et al are not merely proposing a mere "epistemological revolution" as you state with (3). they're saying, the "next state" of the universe _really_is_ a computation, that we really are (and all reality is) built out of cells in a very large 3D or 4D cellular automaton. its not merely a metaphor. in this sense it probably cannot be seen on the same level as the clockwork mechanism for the universe, or the "universe-as-energy" from the thermodynamic/industrial/steam engine perspective. this is a physical hypothesis about the universe. so far it is not yet testable or falsifiable. but I would argue there is very good circumstantial evidence. RS says (3) is "potentially as wrong as the clockwork model of the universe". but, I would argue the clockwork model is not really "wrong", only that it was a steppingstone that is now obsolete or incomplete relative to new data. it was an outstanding metaphor for reality & is arguably still a very strong element of all modern scientific thought. with 4, RS says this refers to "algorithmic information theory" and "the jury is still out" on it. technically this is the name for the field that is involved with compressibility, i.e. chaitin-kolmogorov ideas (is this what RS meant?). which is mostly seen as a specialized subfield of computational complexity theory. this is a strange reduction from my point of view & is definitely not the mathematical revolution associated with "the algorithmic revolution" I referred to earlier.
