Re: "The framework, which is being developed by physicist Benjamin Schumacher... and mathematician Michael Westmoreland... put information at the center--along with a hypothetical, microscopic observer known as Maxwell's demon. ...Schumacher and Westmoreland ...were interested in how information theory could help illuminate quantum mechanics... I started wondering if information is more fundamental than probabilities":
In the real world, fundamental-level information cannot exist as binary digits (true/false, 1/0, yes/no or on/off), because a string of these symbols can have no inherent context or meaning, and no inherent relationship to any other such string of binary digits.
In the real universe, fundamental-level information seems to exist as categories: mass, position and velocity (speed and direction) seem to be natural categories, where every category has context and meaning because it is built out of relationships between other, seemingly pre-existing, categories. Categories seem to exist as part of a network of relationships, relationships that we represent with mathematical symbols.
Information also seems to exist as (what we would represent as) numbers. Seemingly categories must have pre-dated numbers in the universe because: 1) categories/relationships can seemingly exist without numbers being applied to them; 2) the number one can be constructed by dividing a category by itself, and (rational) numbers can be constructed using the number one; and 3) standalone numbers have no inherent context unless they are applied to a category.
Information can also be built out of (what we would represent as) algorithms. So, Maxwell's demon 1) does an algorithmic analysis of the particle's velocity, and 2) acts on the results of that analysis. If the number representing the particle speed is greater than a cut-off number, and if the particle's direction is towards the chamber door, then the demon opens the door to let the particle through. To put it another way: If condition 1 is true, and condition 2 is true, then action is true. The true/false binary digit information only exists in the context of the existing category/relationship information, the existing number information, and the algorithmic question asked about that information.
So, the information that the hypothetical Maxwell's demon acquires is highly sophisticated: it is not fundamental-level information.