Dear Ian Durham,
I found some errors in this essay:
You write: ''Any interaction necessarily requires an exchange of information''.
It is an erroneous statement; I can show you an example of interaction without any exchange of information. The Black Hole's event horizon is a boundary in spacetime through which matter and light can only pass inward towards the mass of the black hole. Nothing, not even light, can escape from inside the event horizon. Therefore, if a body cross the event horizon, the exchange of information between the Black Hole and falling body is not possible because information can flow in one direction only. Thus, this statement is wrong.
You write: ''This idea simply formalizes the somewhat intuitive notion that causality is somehow related to continuity. If spacetime is discontinuous, how do we know that this information couldn't jump around' from point to point? Continuity guarantees that the information follows a nice, orderly 'path' between A and B. This should make it easy to see the conceptual attraction of a continuous reality''.
1) In quantum mechanics particles don't follow a nice, orderly 'path' between A and B, and the position of a free particle is uncertain - so we can consider space as discontinuous. In spite of fact that particles don't follow a nice, orderly 'path' between A and B and all macroscopic bodies are made of quantum particles, we do not observe any violation of causality in our everyday life or macroscopic experiments. Thus, your statement is wrong: even if the space and behavior of the particles is discontinuous, the causality holds in our everyday life.
You write: ''Now, any attempt to measure velocity (or just about any other physical quantity, for that matter) requires an interaction between the observer and the system under observation (sorry folks, there's just no way around that)''.
It is an erroneous statement; we can know the velocity of a particle (or even a macroscopic body) without measurement/interaction. Imagine the radioactive decay of an atomic nucleus when two its clusters/parts fly in opposite directions. If we measure the energy (mass and velocity) of one cluster/part, we'll know the mass and velocity of another cluster without measurement (interaction) with this object.
Another example - we can know the velocity of distant star without interacting with one by observing its motion concerning other stars. in fact, we do not interact with this star but we know its velocity.
You write: ''Though the universe itself has cleverly prevented us from determining whether or not it is continuous, I'd like to believe that it is''
It is an erroneous statement; we can determine whether or not the Universe is continuous by observing the expansion of the Universe: If the distance between galaxy clusters is increasing today, everything must have been closer together in the past. It means that in the first microseconds of expansion the Universe was very small and therefore finite in volume. Since the Universe has a finite age, the Universe will have the finite volume always, in spite of expansion. Since the Universe has a finite volume, it must have the edges (holes), because all objects with finite volumes have borders. And the space with holes is discontinuous because a hole is the absence of spacetime. Thus, since the Universe is expanding, therefore it must be finite and discontinuous. Do you see any flaws in this reasoning? Hence, the Universe is discontinuous but not continuous.
Sincerely,
Constantin