Dear Hector Zenil,
You say above that "certain phenomena can be modeled assuming that matter and space exist as a continuum, meaning that matter is continuously distributed over an entire region of space. [but] matter is composed of molecules and atoms, separated by empty space."
Then you say to Lawrence: "I have difficulties seeing how the world could be digital and analog at the same time, but it might be."
I argue in my essay that the primordial gravity field is distributed over all space. But the continuous field is not initially composed of molecules and atoms. Maxwell taught fields have energy, and Einstein that energy has mass. Because gravity interacts with mass, it interacts with itself, in Yang-Mills fashion, producing fundamental particles that lead to molecules and atoms.
These particles are discrete and stable enough to last forever [protons] in a 'low temp' environment, while the 'hi temp' of colliders restores the local mass to the 'field state' as in the 'perfect fluid' seen at RHIC and LHC when heavy ions are collided. Upon re-cooling the field again 'condenses' to stable particles, although not necessarily the same mix as pre-collision.
This is one way that the world could be analog and digital at the same time, and my essay describes experiments to prove this.
You also respond to James Putnam by saying that it: "may be as simple as to believe that the universe is just computing itself", then say, "if someone or something ran the universe code,...".
My essay assumes that only one thing exists [the primordial field] and so evolution of the universe must proceed by self-interaction, which reasonably leads to our current reality. But a continuous field, interacting with itself, is essentially an analog computer.
If the field itself is a 'real' analog computer, neither 'program code' nor 'digital computer' concepts are required. David Tong states that "no one knows how to formulate a discrete version of the laws of physics," and also that "no one knows how to write down a discrete version of the Standard Model" and so we cannot simulate the known laws of physics on a computer. And as I noted in Brian Whitworth's 'VR' essay, if the "computer" is analog, there need be no "program code" since analog computers may simply be designed via the connections. In that sense analog models are compatible with Tom Ray's remark that E=mc^2 'powers' this universe.
Tommaso Bolognesi seems to agree when he states that "Perhaps ... there is no actual, physical, Digital Computer that runs it, in the same way as we do not require power for an Analog Computer to run, say, the Navier-Stokes or Einstein equations, under an analog-based understanding of the universe."
The field equations are analog and the field itself is the actual physical 'analog computer' that 'executes' the 'code' for our universe. I can see how those concerned with simulating reality on a digital computer might be concerned with 'algorithmic processes', but I don't believe that the idea of replacing a real analog computer [field] capable of explaining today's reality with an imagined 'digital computer' that exists in some other dimension, if not some other world, is a step forward.
Nevertheless, you have written a very interesting essay.
Edwin Eugene Klingman