Chapter 10

Some Quantitative Evaluations of Semantics

by Dr. Werner Gitt on April 30, 2009

We can now begin to evaluate semantic information quantitatively, after having considered the essentials at the semantics level in the preceding chapters. Let us take the semantic value S to represent a quantitative evaluation of the quality of the information. Then six quantities can be used, namely semantic quality q, relevance r, timeliness a, accessibility z, existence e, and comprehensibility v. It is obvious from these concepts that we are considering the information from the point of view of the recipient and his subjective appraisal. These quantities are normalized on a scale from 0 to 1, and they are all positive, except for q which can also take on negative values, as should be clear from the previous chapter. These six variables are now discussed briefly.

1. Semantic quality q (a subjective concept, mainly concerns the recipient): This is used as a measure of the importance of the meaning of some information. Different qualities can be considered according to the goal and the kind of information. Some significant aspects of creative information in particular are depicted in Figure 22 (page 109). For a computer program, for example, the following criteria are relevant and crucial on the semantic level and in part at the pragmatic level:

—Efficacy of the applied algorithm (e.g., simple method of solution, speed of convergence, and absence of instability).
—Minimal computing time (this can be a decisive cost factor when time has to be paid for).
—Portability, meaning that the program can also run on other computer systems.
—Reliability, meaning that the program has been tested comprehensively and is fully debugged so that the desired results will be obtained with a high degree of certainty.
—The programming language used.

The weight of each aspect depends on both objective and subjective evaluations. For inane or nonsensical information, q is taken as zero, while for the best possible information q = 1.

2. Relevance r (subjective concept, mainly concerns the recipient): This aspect reflects individual interests in particular and it includes its relevance for achieving some purpose (e.g., an economical, a technical, or a strategic goal, collector’s value, or life purpose). If r = 1 for person A, the same information can be totally irrelevant for B (r = 0). The weather forecasts for Australia are normally of no importance for somebody in Europe (r = 0), but their relevance can increase dramatically when that person is planning to go there. For a farmer, the agricultural news has a relevance completely different from the latest research results in physics. It is obvious that relevance depends entirely on the recipient. A gale and storm tide warning over the radio is highly relevant for inhabitants of a coastal island, while continental residents who live inland are not concerned. The main problem of relevance is to estimate it correctly. If relevance has been appraised erroneously, it might have catastrophic effects. There are innumerable cases in human history where wrong decisions were made on the grounds of a faulty appraisal of the relevance of information. The cost was astronomical in terms of lives and property.

3. Timeliness t (subjective concept, mainly concerns the recipient): It is in many cases necessary that relevant information should be available at the required moment. Newsworthiness is time-dependent, so that t = 0 for yesterday’s news, and t = 1 for highly relevant information received at the right moment. When a person is standing in the rain and somebody tells him that it is raining, the newsworthiness of this information is zero (t = 0), although it is topical and relevant.

4. Accessibility a (subjective concept, mainly concerns the recipient): The most important information is worthless if it cannot be accessed; then a = 0 (no access). On the other hand, a = 1 when the recipient has full access to the information transmitted by the sender. With the increasing flood of information the “know-where” is becoming steadily more important, and aids like catch-word registers, lexicons, card systems, and databanks are available. Associative storage would be a great help, but only the brain can provide this ideal access principle. In many countries there are computer centers with online facilities which provide direct access to information (Internet). These databanks contain information on such diverse topics as technology, physics, materials, books, and the social sciences, etc.

Even if information is accessible, a rating may still be zero when:

—the information cannot be seen by the recipient (e.g., I am dying of thirst in the desert close to a spring, but I do not know that it is there.)
—the information is coded in a language that the recipient does not understand (e.g., an English tourist in China who cannot read Chinese)
—the information is coached in technical terms which can only be understood by adepts (e.g., legal texts that laymen cannot follow, or a mathematical book which is “Greek” to the uninitiated)
—the sender deliberately excludes some potential recipients (e.g., secret encrypted information, data protection in EDP systems, and sealing a letter)

5. Existence e (objective concept, mainly concerns the sender): Whereas accessibility involves the possibility that an individual can lay his hand on information which is in principle available, existence concerns the basic question of whether the information exists at all. Accessibility involves the recipient only, but existence depends solely on the sender. The value of e lies between 0 and 1, and it indicates how much of the available or desired information about the present case can be obtained (e.g., what fraction has already been researched). The existence e is zero for questions which are completely open, and if something is fully known, e = 1. The previously open question of whether there is life on the moon (e = 0) has now been answered completely (e = 1). For information to cure cancer of the liver, e = 0; in the case of stomach cancer it lies somewhere between 0 and 1, depending on the stage of development. It is quite difficult to make an estimate of the value of e, since the totality of relevant information is in general not known at a given moment. The great physicist Isaac Newton (1642–1727) estimated his contribution to scientific research as a very small e value in spite of his many valuable findings. He said [M3], “I do not know what the world thinks of me; but to myself I appear as a little boy playing on the beach and who finds joy in discovering a smoother pebble or a prettier seashell than the ordinary, while the great ocean of truth lay undiscovered before me.”

6. Comprehensibility c (subjective concept, concerns both the sender and the recipient): This factor describes the intelligibility of information; when the information cannot be understood at all, c = 0, and c = 1 when it is completely understood. Both sides may be at fault if all of the transmitted information does not reach the recipient. The sender might not have expressed himself clearly enough so that the recipient grasps the intended semantics only partially in spite of being highly intelligent, or the recipient may not be intelligent enough to understand everything correctly. The mental alertness of the recipient is also important for another reason: Verbally formulated information (the explicit part) often contains implicit information which has to be read “between the lines.” The recipient only receives this latter part by contemplation and having the required background knowledge.

Note: Many of the above-mentioned factors cannot be distinguished sharply and might overlap. The question of interlinking between the six parameters is not discussed further at this stage; it might be investigated in the future.

In the Beginning Was Information

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