Information — Part1 — Is Information extensive?

does information increase as the number of physical objects that contain or reflect that information increases?

For clarity,

• An extensive property is a property of matter that changes as the amount of matter changes. Like other physical properties, an extensive property may be observed and measured without any chemical change (reaction) occurring.

An example of an extensive property of matter is mass. The mass of a sample increases in proportion to the number of particles in the sample. Double the sample size (volume), and the mass doubles.

• m(V) proportional to N
• m(V) = density * Volume
• density = mass / volume

Doubling the number of particles, doubles the volume which doubles the mass. In this case, the new mass, m(2V), is exactly 2 times the original mass, 2*m(V)

• m(2V)=density*2Volume = 2*m(V)

Information Content in an object

Take physical system A. It has information content Alpha.

Duplicate physical system A, creating system A’. System A’ has exactly the same information content as system A.

Initially, one is in possession of system A only. One is in possession of information content Alpha, reflecting the full state of information of system A.

Later, when one has duplicated system A, one is in possession of systems A and A’; does one now have possession of 2 times the information?

Does one now have 2 times Alpha?

Or is the second Alpha, a perfect copy of the first, entirely redundant?

Generic Property of Information — Information is non-extensive

It would appear that information, simply put, is not extensible.

Doubling the physical states that contain the same information does not double the amount of information. It doubles the links between the information and the objects to which the information pertains, but but it does not double the core information content.

Putting aside for a moment whether or not this is physically possible, if the second system is identical in every regard to the first system, and if the second system evolves identically to the first (let us assume), then the information content of system A — Alpha— is 100% adequate to represent the information in system A’. In fact, Alpha is informationally identical to alpha’.

If 1 hard drive of size 1 TB can hold the total information content Alpha, how many hard drives would one need to hold the information content for system A’ eg Alpha’? How many additional bytes?

Zero additional drives are required to hold the information of Alpha’.

However, some bytes are needed to remember that Alpha is identical to Alpha’ and that the information content of systems A and A’ are on the main, 1Tb drive.

Information content is loosely connected to physical states. Information in fact de-couples from physical states and can be attached, as desired, to other physical states. Information can apply to an arbitrary number of physical entities.

Information Processing — Enabled by its non-extensivity

Non-extensivity appears to be a generic property of information. Information is not extensible. For instance, when one sees a cat, we can label that entity ‘cat’. When one sees another cat, one can label the second object ‘cat’ as well. It’s the same information — but the information pertains to two separate physical objects. If this were not true, systems would run out of memory in their attempts to describe the physical world, since they would need terms 1–1 with physical objects. But such is not the case. It’s in fact possible to abstract across many physical objects a salient piece of information, and hence there is a natural economy of reference that is afforded by information. It is this economy upon which all information processing is based.

This economy is the first step in the processing of information.

Information is different from other measures. This economy is one of the key ways in which it is different. The possibility of logical operations like abstraction and inference is based on this economy. It is precisely information’s lack of extensibility that causes information processing to be possible in the first place e.g. logical inference, abstraction are examples of information processing operations. And these operations are possible because of the unique properties of information.

Information Processing Example

Here follow some trivial examples of information processing. These acts of processing are in fact enabled by the fact that information is non-extensible.

Example of information processing.

• Object 1 — labelled as ‘cat1’
• Object 2 — labelled as ‘cat2’
• Processing step
• Step type — Abstraction
• Inputs — ‘cat1’ and ‘cat2’
• Result — object 1 and object 2 are both referred to as ‘cat’

Master Vase — Information vs Information and its referents

In the above example, as a result of information processing, both cats are referred to by a single piece of information — the label ‘cat’. A single memory location is required to store this information; two additional locations are required, one for each of the 2 pointers.

At the level of pure information — without referents — or just referring to a master referent set — information is entirely non-extensible. At the level of information but including referents, the information is nearly non-extensible. It is extensible only insofar as additional reference pointers are required to separate the different objects being referred to. But in some sense, all objects can be pointed to by a single master referent.

For example, If one wishes to create a vase, a blueprint for that vase can be created. Each vase that is created will have been created from that blueprint. That blueprint can be stored in a data disk. Each time I create a new vase, I don’t need to duplicate the blueprint. I only have a single blueprint — and that blueprint refers correctly and uniquely to all created vases.

If I want to keep track of all created vases, I will need reference pointers to each created vase. However, if I want to create more cases, I only need the master blueprint — and the one hard drive on which that master blueprint is stored. I can then stamp out more copies from the master piece of information.

Once 1 or more vases have been created, information processing can be performed on the set of vases. All vases are instances of the master blueprint located on the data disk holding this information.

Information Processing

• Type — Abstraction
• Inputs — vase1, vase2, …, vaseN
• Result — Vase1…VaseN are instances of Vase0
• Vase0 is the master blueprint

Information Commingling and de-coupling

The master blueprint is information. In and of itself it is non-extensive. Its lack of extensivity means that information processing can be performed on it. Commingling non-extensive information with extensive entities e.g. physical objects, will make the combination extensive. However, it’s always possible to separate out information from its referents and arrive at the non-extensive elements.

Information is hence non-extensible and subject to a different set of processing laws than extensive entities.