Some Principles of Information

As a result of the work I have done designing the EON programming language, exploring human understanding, my time as a computer programmer, and just plain curiosity; I have had a number of thoughts about information itself percolating in my head lately. Initially I was just speculating about how data and other information can be classified, but after some experimentation I realized that some information can be categorized based on its mutual exclusivity and whether it can be considered categorizable or relational. So I decided to take a moment to write some of these thoughts down to make some sense of them, but before I knew it things snowballed and I got more than I asked for.

Meta-information is information that describes other information. There are 4 main types of meta-information:

Categorizable, Not Mutually Exclusive
The information may be described by multiple categories of other information
ex: "the round gold coin"

Categorizable, Mutually Exclusive
The information may be described by a mutually exclusive category of other information
ex: "the coin is heads up"

Relational, Not Mutually Exclusive
The information may be described by multiple relationships
ex: "the top left coin"

Relational, Mutually Exclusive
The information may be described by a mutually exclusive relationship
ex: "the first coin"

Information always has been, and always will be, an interpretation of the properties of the media on which it is transcribed. No matter the media or form, information is always a transcription of meaning or understanding. Because information is the consequence of the properties of a given medium, it cannot have meaning until interpreted by an observer.

Consequently we can say that
I = f(M, O)
where
I is information,
M is the Media on which the information is transcribed,
O is the Observer

While portions of information may frequently be described as quantitative, real world experience demonstrates it is not always thus. Take for example a to do list, or the phrase "black hat". In the first case the sum of the information is not quantitative but rather a collection of other information. In the second case the sum of the information is an assertion of additional information upon other information.

Based on our experiences we might conclude that in aggregate, a collection of information must have a nonnegative quantity of elements. Now, this line of thought suggested to me that information can be logically described using mathematical set theory, so I did some quick research on set theory and discovered that rather than there being a prohibition on the existence of sets with a negative number of elements, such sets are described as having negative membership. The main real life example of negative information that occurs to me (and which operates without consideration for the information's content) is the use of the word "not". This allows us to form pairs of information such as "black hat" & "not(black hat)" that are clearly negations of each other.

The role of the word "not" as an indicator of negative membership can also be extended to negate itself in some languages through the construct known as a double negative. There is of course a mathematical equivalent to this that applies to set theory. It occurs when multiplying (or dividing) two negative values together and the resulting product (or quotient) is positive. So how far can we take this extension of mathematical set theory to information theory? Well in mathematics, when you say x = 3 you are asserting that x is defined as 3. Likewise when you solve an equation to find the value of a variable you start by asserting that the variable has an undefined value that can be determined from the equation you are solving. It is effectively an assertion that some undefined information exists which possesses certain other defined information.

So what type of information could be described by an assertion of the existence of undefined information? Well the answer to that question is just that, a question. If we ask the question "what is a hat?", we are neither asserting the existence of a collection of defined information nor asserting information upon other information, but rather we are asserting the existence of a collection of undefined information which defines information about the information specified as a "hat".

But is the assertion of the existence of information, defined or otherwise, information itself?

Not necessarily.

The fact that an observer may observe the assertion of the existence of information means that relative to said observer, the said assertion is information. However, the observer is not necessarily the asserter and it must be noted that the asserter is asserting the existence of information by the act of transcribing the assertion itself upon a medium of communication. Since the assertion itself is an act of transcription and not the properties of the medium on which the transcription occurs, we must conclude that the assertion is not information itself but the meaning or understanding that is sought to be communicated by the creation of information. Consequently, communication is the assertion of the existence of information by creating information.

Because information is a transcription of understanding, it is limited to communicating information that the observer understands. Consequently, any communication requires a shared communication method between the transcriber and the observer. This communication method must be a common understanding and/or method of interpreting information. While communicators that share a communication method may build upon that method, those that do not must arrive at one together. Because receiving information is only accomplished through observation, the establishment of a communication method must evolve from mutual observations. The only place that observations may be sought by both communicators with no shared communication method is in their shared environment. As a result all communication methods evolve from the environment shared by the communicators.

And so we have arrived at some Fundamental Principles of Information:

1. Information is an interpretation of the properties of the media on which it is transcribed.
2. Communication is the assertion of the existence of information by creating information.
3. All communication methods evolve from the environment shared by the communicators.