According to Brian Hayes "There is a distinction between representation of information and information itself but both of these have always a physical form. Somehow, this increase of physical representations for information does not strengthen the conviction that information is subordinate to its physical representation. When we can write the same message in so many forms–everything from lines in the sand to holograms–the message itself begins to seem just as substantial as the physical medium, and perhaps more enduring".
The fact that the process of copying the bits of information is easier than capturing them, leads us to an argument from Rolf: "we can represent information in many physical forms: as packets of electric charge, as base pairs in a DNA molecule, as beads on an abacus. When we build machinery to process this information, we can also choose among many different computing technologies such as valves, transistors or even neurons".
We use numbers as representations of quantities, they are not pure information whatever that means. They make a reference to some quantity in a mind of an observer and that relation constitutes the information - the match between a physical instance of a symbol and the observers ability to connect that symbol to a certain quantity.
Some mathematical philosophy schools (Realists, Platonists and intuitionists) believed that mathematical concepts and propositions have meanings, and when we formalize the language of mathematics, these meanings are meant to be reflected in a more precise and more concise form. But according to the formalist school understanding mathematical object has no meaning; implying that all we have are marks and rules governing how these marks can be combined.
Haynes points at the fact that "There is a tendency to think of mathematics as a tool which somehow existed before and outside of our physical world. Mathematics, in turn, allowed the formulation of physical laws which then run the world. Nevertheless we emphasize that information handling has to be done in the real physical world, and the laws of physics exist as instructions for information handling in that real world. It, therefore, makes no sense to invoke operations, in the laws of physics, which are not executable, at least in principle, in our real physical world".
Here are two interesting riddles for you to think about:
- How do you distinguish the concrete from the abstract when the word “concrete” is in fact an abstract concept? Or how do you distinguish the physical from the nonphysical with the nature of the word “physical” is in fact nonphysical?
- How can we ask--not to mention answer--the question “What is information?” when the question itself is, in fact, pure information? - Bertrand Russell