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To keep within the guidelines of only asking questions that have a definite answer, I will stipulate that I am asking about cases where the question has been considered in an academically respectable context.

The argument I have in mind goes something like this: Shannon's definition of information might be summarized as there being information wherever things are arranged one way, when they might be otherwise (this is a simplification, of course, leaving out how one measures it.) This simplified view appears to be agnostic as to whether the things in the arrangement are physical or not.

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  • The information, the arrangement of objects, still needs physical objects. It has to be represented physically somehow, even if that somehow is the connections of neurons in a brain using ganglia, or bits on a HDD through the polarity of tiny spot magnets. Etc.
    – Dan Bron
    Jan 22 '20 at 14:48
  • @DanBron For all practical purposes, if there are no certifiably non-physical things, or if there is no sense in which they can be in an optional arrangement, then this is what it amounts to, and if nonphysicality is an incoherent concept, then the question is moot, but the definition of information itself seems to be very broad, and does not seem to either require or depend on metaphysical physicalism.
    – A Raybould
    Jan 22 '20 at 15:19
  • It is not agnostic, it is orthogonal to the question of physicality the same way any mathematical definition is so orthogonal. We can define "energy" for any Hamiltonian system of ODE, it only relates to physical energy when the system actually describes something physical. Moreover, Shannon's "syntactic" notion of information is basically hollow, it is not the concept of information that it even makes sense to ask the physicality question about.
    – Conifold
    Jan 22 '20 at 20:51
  • @conifold To help me follow your point, if someone had knowledge of a particular hamiltonian, would that only be physical knowledge if it was a description of something physical (and maybe also only if the person knew that it was?) Or perhaps would it be inappropriate to call it physical knowledge in any context?
    – A Raybould
    Jan 22 '20 at 23:36
  • Knowledge of a Hamiltonian as such is always knowledge of an abstraction, which is "non-physical" if you want. It provides knowledge of something physical only if the Hamiltonian represents something physical.
    – Conifold
    Jan 23 '20 at 0:01
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Information is a non-physical concept, but it is very common to implement this information via organization of physical objects. For example, the 1's and 0's of a computer program are a non-physical concept, but the magnetic spins used to represent this information are very physical indeed. Information stored in the brain is implemented via neural connections and chemical balances.

For a physicalist, who believes everything supervenes on physics, this is a mere convenience. It lets us easily see how information can be converted from one representation to another without losing the information. I can argue very clearly why a particular process preserves the information stored on a hard-drive as I run sensors over the magnetic material and store the information in memory as a particular configuration of electrostatic charges.

For someone approaching the world in any other way, we find the non-physical nature of information to be more important. Consider one who believes that there is a mental substance which is not physical that makes up a mind. It is almost always considered possible for that mind to contain information, despite the mind being a non-physical entity. And likewise, we typically like to declare that it is possible to have information about a mind. Putting them together, it is reasonable to argue that there is non-physical information about a non-physical mind.

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Shannon information (entropy, actually) is an abstract concept that applies first and foremost to strings over an alphabet of symbols. In that sense, it is nonphysical (I would prefer to call it abstract, in the sense of abstracting from the real world onto simpler models of the world).

Curiously, it turns out that defining entropy still makes sense more generally in statistical mechanics and it looks pretty much the same as Shannon entropy. Read more on Wikipedia. This has implications about the physicality of information (even abstract information). Since any abstract information needs to be represented physically, it turns out, for example, that erasing (abstract) information from a physical medium takes a minimum amount of energy to perform. (Landauer's principle)

This is important, because it means you can do things like argue about algorithms (in particular cryptographical ones where entropy matters) in terms of minimum energy expenditure instead of runtime (or abstract complexity), and arrive at things like:

https://security.stackexchange.com/a/6149/35094

As a starting point, we will consider that each elementary operation implies a minimal expense of energy; Landauer's principle sets that limit at 0.0178 eV, which is 2.85×10^-21 J. On the other hand, the total mass of the Solar system, if converted in its entirety to energy, would yield about 1.8×10^47 J (actually that's what you would get from the mass of the Sun, according to this page, but the Sun takes the Lion's share of the total mass of the Solar system). This implies a hard limit of about 6.32×10^68 elementary computations, which is about 2^225.2. (I think this computation was already presented by Schneier in "Applied Cryptography".)

The whole answer is worth a read and the comments, too.

I think that makes information pretty physical, even if the original definition by Shannon is abstract.

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