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ONCE OVER QUICKLY What's it good for? The good of information is its use in reducing our uncertainty about some issue that comes before us. Generally speaking, uncertainty comes in several flavors, and so the information that serves to reduce uncertainty can be applied in several different ways. The situations of uncertainty that human agents commonly find themselves facing have been investigated under many headings, literally for ages, and the classifications that subtle thinkers arrived at long before the dawn of modern information theory still have their uses in setting the stage of an introduction. Picking an example of a subtle thinker almost at random, the philosopher-scientist Immanuel Kant divided the principal questions of human existence into three parts:
The third question is a bit too subtle for the present frame of discussion, but the first and second are easily recognizable as staking out the two main axes of information theory, namely, the dual dimensions of '' Information '' and '' Control ''. Roughly the same space of concerns is elsewhere spanned by the dual axes of '' Competence '' and '' Performance '', '' Specification '' and '' Optimization '', or just plain '' Knowledge '' and '' Skill ''. A question of ''what's true'' is a ''descriptive question'', and there exist what are called '' Descriptive Science s'' devoted to answering descriptive questions about any domain of phenomena that one might care to name. A question of ''what's to do'', in other words, what must be done by way of achieving a given aim, is a ''normative question'', and there exist what are called '' Normative Science s'' devoted to answering normative questions about any domain of problems that one might care to address. Since information plays its role on a stage set by uncertainty, a big part of saying what information is will necessarily involve saying what uncertainty is. There is little chance that the vagueness of a word like 'uncertainty', given the nuances of its ordinary, poetic, and technical uses, can be corralled by a single pen, but there do exist established models and formal theories that address definable aspects of uncertainty, and these have enough uses to make them worth looking into. What is information that a sign may bear it? Three more questions arise at this juncture: # How is a sign empowered to contain information? # What is the practical context of communication? # Why do we care about these bits of information? A very rough answer to these questions might begin as follows: Human beings are initially concerned solely with their own lives, but then a world obtrudes on their subjective existence, and so they find themselves forced to take an interest in the objective realities of its nature. In pragmatic terms our initial aim, concern, interest, object, or ' Pragma ' is expressed by the verbal infinitive 'to live', but the infinitive is soon reified into the derivative substantial forms of 'nature', 'reality', 'the world', and so on. Against this backdrop we find ourselves cast as the protagonists on a 'scene of uncertainty'. The situation may be pictured as a juncture from which a manifold of options fan out before us. It may be an issue of ''truth'', ''duty'', or ''hope'', the last codifying a special type of uncertainty as to ''what regulative principle has any chance of success'', but the chief uncertainty is that we are called on to make a choice and find that we all too often have almost no clue as to which of the options is most fit to pick. Just to make up a discrete example, let us suppose that the cardinality of this choice is a finite ''n'', and just to make it fully concrete let us say that ''n'' = 5. Figure 1 affords a rough picture of the situation. o -o | ||
| ` ` ` ` ` ` ` ` ` ` ` `O` ` ` ` ` ` ` ` `n | 5` |
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| ` ` ` ` ` ` ` K 1 | 3 ` ` ` `k_2 = 2` ` ` ` ` ` |
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| ` ` ` ` ` ` ` ` ` ` ` `O` ` ` ` ` ` ` ` `n | 5` |
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| ` ` ` ` ` ` ` ` ` ` ` `O` ` ` ` ` ` ` ` `n | 4` |
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| ` ` ` ` ` `o` ` `o` ` ` ` ` `o` ` `o` `n 2 | 2` |
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| ` ` ` ` ` ` ` ` ` ` ` `O` ` ` ` ` ` ` `n 1 | 4` |
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| ` ` ` ` ` ` ` K 1 | 3 ` ` ` `k_2 = 2` ` ` ` ` ` |
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| ` ` ` ` ` ` ` ` ` ` ` `O` ` ` ` ` ` ` ` `n | 5` |
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