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The Big Word Book says information is knowledge derived from study, experience, or instruction. Hurray! We just replaced a word we don't know with others we don't know!

The second meaning is that information is knowledge of a specific situation -- i.e., intelligence. I presume this is stuff you pick up in experience, using reading skills, or pattern recognition skills.

Third, information is a collection of facts or data: statistical information. Well! Now we've got an association with something called facts or data, which has to do with perception! These terms seem to be even less clear than information. Or are they?

Statistically, information is said to be a numerical measure of the uncertainty of an experimental outcome. That's a bit too specialized, or maybe even esoteric, but at least it gets into the spirit of trying to quantify something.

That's it. But where are we? Information and knowledge and facts and data all seem to be tied together, or at least they seem to come together in significant ways. We now have different words for it, but nothing has been said about what information is or how it can be represented, whether it has dimensionality, or can be imaginary or not, and other things like that.  (See Laws of Form for a fascinating work on the imaginary.)

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In Simulations for Skills Training I compared information with knowledge, facts, and data by distinguishing between two widely accepted meanings of knowledge. In one form, a person has knowledge if he or she has information. This is knowledge about something, as the dictionary says. I might know, for example, that John is playing golf. Perhaps I see him playing. The form is information as fact.

The other form is spoken knowledge about something. As information, the two modes are equal but are "expressed" in different "languages" -- i.e., the language of the senses and the language of words. Call them forms of know-what, as in "Ya know what?"

Then there is knowledge in the form of know-how. I.e., knowing how to do something, like playing golf, or riding a bike. You might know what you have to do to hit a tennis ball, say, but the hitting, itself, requires know-how -- not that you can say something about it, but that you can actually do it. That's the basis for my distinction between information acquisition skills and motor skills. In this sense of knowledge one uses information to perform one or another action.

Actions like speaking or signing, just like writing, obviously express information directly, i.e., in linguistic form, but they also require know-how -- i.e., you must be able to speak or sign. And they can be modeled through equations. It's the same for the process of acquiring information through observation. This too requires know-how. You have to learn to use the instruments of observation, like a microscope and your eyes. (It's with your brain, however, that you see.)

Information (or knowledge in the sense of knowing about something) is an expression in the form of an explicit sentence (proposition, statement) or in the form of an implicit sentence (as in an observation), and has truth value. A particular piece of information, often seen as a specific sentence, can be understood as a specification of a sentence form. The specification is obtained by plugging data (not in the sense of information but rather in the form of a variable, like 3-ft) into the form. ("3-ft" isn't information until you connect it with something, like the height of a child.) The result is what I call the basic unit of information. For example, the sentence:

The table is red.

is a specification and basic unit of the sentence form (equation):

The ________ is _________.

If any of the blanks are not filled in, there is as yet no information. A completed specification is needed to yield information.

The specification (proposition) is either true or false or meaningless. It is true if it coincides with the facts to be observed. This is a correspondence form of representation. If you look at the table and see it is red (observation, or measurement), the proposition is true. Otherwise it is false. The specification is otherwise meaningless if there can be no way to establish the facts -- no arena in which the statement can possibly be true or false. (Suppose you can imagine a space in which the statement can be true or false -- would that make the truth-value of the statement imaginary?)

Facts and information are interchangeable in the sense that if you have the facts you have the information. If you see that the table is red, you see that "The table is red." And if you have the information, implying truth, you have the facts. That is, information is represented both by the specification and by the empirical experience. To repeat, you can observe the fact that the table is red and you can express the fact that the table is red. Both require the same know-what. Contrariwise, you cannot observe that the table is red without simultaneously having the information that the table is red. The observed fact is unexpressed (but implicit) information. And the specification expresses observable fact explicitly.

Contrariwise, too, data (in the sense of a variable) is not observable. In this sense, data provides no information. For example, you can't observe two-feet or 90-degrees. You might see that a stick is two feet long or that the air temp. is 90 degrees -- facts or information -- but there is no such observable thing as two-feet or 90-degrees. Nor can you observe red. The sky might be red. The paper might be red. The table or chair might be red, but, again, there is no red that is fact -- not without something being red. Similarly, a stack of numbers in computer memory is referred to as data, but that has to be data in the information sense, if it is to be meaningful. I.e., there has to be a framework, a conceptual structure (pattern) that puts the numbers in context to provide information.

The point is that experience, in any form, comes in clumps. It is unified. Data impinges, mind imposes, and experience occurs. This is a creative process. Experience is patterned and informative. This is the gestalt-like character of it. You get all knowledge (information, facts, data) that way -- as patterns.

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In case you wouldn't know a vector if it bit you on the nose, it is a mathematical form using dimensional components to represent a point in space. The components are considered to be orthogonal (right-angled), which simply means the components are independent, which means that changes can be made in any one of them without affecting the others. One such vector is a creation I'm calling an information vector. It's a vector that I'm in the process of defining, so bear with me, if you would -- it could take years.

What I mean by an information vector is a set of independent components that relate to, and in some way define, specific information in an information space. You can also think of the components as properties that define an information class. For example, I might be able to construct a stock market information space this way -- if I could figure it out. Specific skills can also form classes.

(More and more I feel I'm talking about information stretching understanding, hence expanding your operating space -- like stretching your tennis space: (See my work on tennis Target-Shooting Games.)

Among the factors I'm considering for the space are:

1. Power -- the level of explicitness of the information. (G. Spencer Brown uses the word 'power' to describe level of condensation or degeneracy. Power is achieved "by condensing as much as is needed in as little as is needed, and so making that little as free from irrelevance (or from elaboration) as allowed by the necessity of writing it out and reading it in with ease and without error.")
2. Know-What -- the kind or class of information acquired, or its subject matter.
3. Know-How -- the ability to acquire information or to use information.
4. Competence Level -- the level of difficulty acquiring or using the information. Example: The skill rneeded to observe -- to measure -- the position of electrons is greater than that required to observe ordinary objects. (You must learn to use the measuring equipment.) So information gained about electrons has a higher level of difficulty of understanding than information gained about the latter, I think.
5. Objectivity -- the range of privacy/objectivity of the information -- for instance whether it expresses more hope than reality, or not.
6. Age -- the age of the information -- how old it is, or how long it has been known by somebody.
7. Range -- how widely the information is known, or how public it is -- like info about the stock market,.
8. Context -- the environment of the information, the arena where it gets its meaning, or where it is normally used.
9. Fuzziness -- the truth-value of the information, which could range from 1 to 0, if partial truths are acceptable. (Check here.) Apply this to skills, for example, considering that no two people execute any skill exactly the same way.
10. Utility -- how useful the information is, what it can do for you.
11. Fitness -- how the information relates to other information, in a given context.
12. Pattern -- to have information you must have pattern; there is no information in randomness.
13. Value -- like utility as a measure of its usefulness but more in the sense of how it increases your context understanding, or stretches your context space.
14. Form -- how the information is expressed, as in a proposition.
15. Perceptual Information.
16. Verbal Information.
17. Types of Information.

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The issue is whether information is meaningful in imaginary form, i.e., whether we can have both Real and Complex information. We already have Real and Complex information forms in math. And in our ordinary, everyday life, we view as imaginary all mirror reflections of real things. Can a proposition with 'imaginary' as its truth-value express information? Might the imaginary be a component of my information vector? (In quantum mechanics, the imaginary number has been used to define what E. Walker calls potential states.) In these terms information would be imaginary if it could be verified as true or false in some possible but as yet undetermined context.

The issue stems from the question, raised by Brown, whether logical proofs are missing an important ingredient by not considering at least quadratic forms of expression and imaginary truth-value. In other words, should propositions be allowed to have not only the truth-values: true, false, and meaningless, but also the truth-value imaginary? Does the imaginary contribute to meaning? Or is it more in the nature of a facilitator?

Brown's argument is based on the use of complex (imaginary) numbers to solve algebraic equations.  If in quadratic numerical equations, why not also in quadratic statement equations!

You might even raise the question regarding the use of many-valued logics in this context, or perhaps even fuzzy logic (which has been identified with many-valued logic and with statistics and which also sounds a bit like neural network theory).

I don't know the answers, here, or even the questions, for that matter, but I'm working on it.

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It might be stretching things a bit to connect imaginary statements with quantum mechanics, but I'm thinking in terms of:

• The difference between the real world and the perceived world -- i.e., between what's really out there and what we observe as being out there (really real states as opposed to virtually real states -- two kinds or levels of reality.).
• The role imaginary could play in reference to the difference. In quantum mechanics there is a real world of the underworld, which isn't actual until observed. And there is the real world (virtual world) of observation.

Unimaginable things happen in the underworld of electrons and protons, et al, and probability is the villain. Things are probably here and probably there and also likely over yonder. But along comes observation to eliminate the improbable probabilities and produce real values in their stead. Observation -- measurement --converts potentiality into actuality, yielding information. (Isn't this also like ordinary experience?)

Perhaps the imaginary statement has a similar role to play in the ordinary world. Unrealized but possible arenas of skill could be the imagined realm. Here again, observation would be the hero to resolve an imaginary condition to yield real information. We ensure existence by observing?

I have no idea how this might work, but quantum mechanics does use the imaginary number to define vectors and thus implicate vector states. And that sounds like what I'm trying to do.

Stay tuned.

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