Hi Sara,
Good story, nice idea. My comments are partly covered in your essay, yet I wish to extend it for further clarification.
> .. that information, or abstractions have causal consequences. It is however difficult to explain this beyond mere anecdote.
No, it is not so difficult to see why information has causal consequence, only that we have to understand reality of information differently. From the first principles of constancy of causal relation in the nature of change, if an interaction among physical systems results in an observable state S of a physical system P, then S of P must remain congruent with, or correlate with the information of the causal context effecting the change. Otherwise, measurements do not have an interpretation relating to the cause. Causal context includes precursor state descriptions of interacting systems. For example, mass of a physical system Q denotes its causal power in an interaction, which constitutes Q's function or the basis of its relation with other systems. If a system P interacts with Q and gains a state S due to this causal function of Q, then S of P is said to correlate with this information; `mass' is mere label for the causal function of Q, which constitutes primitive of semantics, upon which more structured and abstract semantics can be constructed.
For the same reasons of natural causal dependence, S of P also must correlate with what the observed precursor states of interacting systems correlate with. This is a second order correlation which inductively takes into account all causal descriptions responsible for S of P. It is the second order correlation that allows construction of structured and abstract semantics as shown in Fundamentals of Natural Representation Would you like if I state that reality of all information arises only from causal correlation of states of matter? Therefore, all information has causal consequence. Of course, most of them could be limited to the neural system of the brain without external action.
> What separates information from other physical attributes such as charge or mass? Take for example the charge of an electron. It is often considered to be a physical attribute because every electron in the universe has a charge and because the charge cannot be separated from the electron.
The concept of an electron as an isolated entity is not driven from any ontological first principles, but rather it depends on what consequences are observable due to the associated causal qualities (charge, mass, spin). So, the electron is defined as an entity that has rest mass of 0.511 MeV, charge of 1 negative electronic charge, and spin of one half. That is, the very identity of an electron (or any physical system) is defined in terms of constancy of certain observable causal powers. As it is so, the charge cannot even be conceptualized to be separated from its identity. In fact, causal states (observable qualities) are fundamental (primary), identity of an entity emergent (secondary / dependent). This distinction is crucial in associating the causal reality of information with the observable states rather than with the entity as is mistakenly done in physics.
I agree with your assertion, "If mathematics were not copiable there would be no way to build mathematical models of any physical phenomenon". If we consider two extents of physical system, one that is limited to an individual system like brain, and another that involves many. Indeed, the neuronal system of a brain does exchange the semantic values of information that has consequence in the physical world due to the causal dependence of neurons on each other. But, for the lack of such causal dependence or constraints, inter-personal transmission must be coded. Mathematical coding is far more precise as you mentioned, yet it has it limits Kako, E.; Wagner, L. The semantics of syntactic structures.
In my essay, I take a dig on, "The unreasonable effectiveness of mathematics in describing physical reality", which might entertain you for a moment or longer depending on your tolerance.
> These mathematical descriptions have a different property than the systems they are intended to describe. They can readily be copied between different physical media. .. I can take Coulomb's law and formulate it in my mind, write it on a piece of paper.
Coulomb's law in the mind has a semantic content, structure, and function, it does not require an interpretation. But what we copy from one medium to the next is not the information, but the bits that encode the information under certain scheme. I strongly felt that you were talking about the causal reality of semantics of information, not the artificial mechanism of coding. This treatment of information that entails storing, copying, transmitting in bits, has come at a cost; the cost is the formation of a mental image that information may come into play only when encoded, interpreted, and stored in bits etc., in some manner. This mental frame has kept the generations of researchers away from dealing with the semantics of information, and how causally they come into existence without a need for an interpreter. We know a device (brain) exists that processes semantics of information, but we never attempted to shed the Shannon's idea of quantity of information, or statistical properties of information to get to the semantics of information. So much so that even when such a mechanism is presented from first principles, Fundamentals of Natural Representation , it remains ignored.
Since your awareness has a causal basis, it can cause consequences. Though, states of registers (bits) may also cause consequences in physical universe, but without human constructor they would not be relevant to the mathematical idea because of the artificial coding involved.
Rajiv