When you say "information" what do you mean exactly? I can see information as a set of constraints that arises in the system due to how it evolves, and that those constraints enable structure to emerge, and that with the law of conservation of energy no energy can be created or destroyed, it means that all those structures can only do what they can do, any deviation from the constraints will require new energy or removing energy from the system to alter the course.
I like your needles - hyperdimensional record analogy. I would say mathematics encodes for and predicts a certain set of constraints, but we can never be sure we have observed or found the most fundamental constraint, and so to us, an incomplete mathematical 'law' will look like it needs energy added or removed to fit with the real world, but in reality it's just a constraint somewhere that we haven't seen that will readjust the series. All of this is kind of written on a whim, I'm not sure I thought it through enough :
I like your needles - hyperdimensional record analogy. I would say mathematics encodes for and predicts a certain set of constraints, but we can never be sure we have observed or found the most fundamental constraint, and so to us, an incomplete mathematical 'law' will look like it needs energy added or removed to fit with the real world, but in reality it's just a constraint somewhere that we haven't seen that will readjust the series. All of this is kind of written on a whim, I'm not sure I thought it through enough :