Not just that, but whether or not any particular symbol manipulating system (such as a base ten numbering system) is somehow intrinsic to physics and can be interpretable in only one way which is a physical way. I don't think that's possible. A chain of zeros for example 00000000000000000000 could equally be represented as:Q_Goest was exploring whether there was any paradox in arrangement-0 not containing less mass-energy than other arrangements such as arrangement-29 that represents information "black cat from left running".
0oO 0000 00000 000000 00
Is this a chain of numbers? Or letters? Or is this a toy that a child made to string around a Christmas tree? If these are baby blocks, how are we to know that they are set down in order, or how we are interpreting that string is the correct one?
As many others have noted, not just here at PF but in the philosophical literature regarding symbol systems, these hieroglyphics have an interpretation as being some kind of information only when we base that interpretation on a given symbol manipulation system*. In the literature, I've seen this referred to as "mapping" the symbols such that a given physical state is "mapped" (ie: interpreted) as a given symbol - that symbol having to exist in the symbol manipulation system that we are using to interpret the symbol.
Clearly, mapping symbols to a physical state is arbitrary. Depending on what symbol manipulation system you have, the information content can vary in an infinite number of different ways. That information content then, can't have any physical attributes, only attributes that we as humans ascribe to the symbols. Therefore, if the only attributes that can be ascribed to a given string of symbols is subjective, then there is nothing physical about the information, and it doesn't contain additional entropy above and beyond the entropy that can be determined from the physical attributes of that system.
*Note: Examples of symbol manipulation systems:
- Egyptian hieroglyphics
- Various numbering systems
- Cryptographic systems
- Lanterns in a bell tower (1 if by land, 2 if by sea)
- A log across a trail or stack of rocks
- The number of atoms in a physical substrate
- The temperature gradient throughout a physical substrate
- The stress or density distribution or any physically measurable feature of a physical substrate
- The alignment of stars, planets or any astrological interpretation of the heavens
- the list is infinite... so any given physical feature has an infinite number of different possible interpretations based on mapping physical features to a given symbol system.