Abstract
Living with uncertainty is one of the few established facts of modern life (or any life for that matter). Although death and taxes do not fall far behind, the only thing we know for certain is that we know nothing for certain. The earliest philosophers were quick to recognize the nature of uncertainty, but it is only in recent times that attempts have been made to provide a rigorous description of uncertainty, at least for those less uncertain aspects of uncertainty that are amenable to mathematical description. Heisenberg’s1 uncertainty principle represents one such attempt. A related form of uncertainty is that of time-frequency uncertainty in spectrum analysis (Gabor, 1946). The entire field of statistics is concerned with the practical problem of reducing uncertainty in measurement and analysis and the relatively new field of information theory follows from the simple but far-reaching proposition that uncertainty can be quantified, bit by bit, so to speak.
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Notes
Also a man of uncertain principles, he was Germany’s leading scientist during the Hitler period.
“The speech of man is like embroidered tapestries, since like them this too has to be extended in order to display its patterns, but when it is rolled up it conceals and distorts them.” (Plutarch: Lives: Themistocles, sec. 29).
“Speech is a mirror of the soul: as a man speaks, so is he.” (Publilius Syrus: Maxim 1073).
“With the sense of sight, the idea communicates the emotion, whereas with sound, the emotion communicates the idea, which is more direct and therefore more powerful.” (Alfred North Whitehead: Dialogues, p. 231).
“Speech is civilization itself. The word, even the most contradictory word, preserves contact—it is silence which isolates.” (Thomas Mann: The Magic Mountain: Chapter 6).
Socrates was put to death for his iconoclastic views. We hope the reader will not be as harsh.
In order to calculate the information transmitted per phoneme it is necessary to consider all of the possible alternatives, including all of the phonemes of the language as well as silence.
Interaural phase is also an important consideration in binaural speech perception.
“The game’s going on rather better now,” she [Alice] said, by way of keeping up the conversation a little. “’Tis so‚” said the Duchess: “and the moral of that is—‘Oh‚’ tis love‚’ tis love‚ that the world go round!’” “Somebody said,” Alice whispered, “that it’s done by everybody minding their own business!” “Ah well! It means much the same thing,” said the Duchess, digging her sharp little chin into Alice’s shoulder as she added, “and the moral of that is—‘Take care of the sense, and the sounds will take care of themselves.’” (Lewis Carroll: Alice’s Adventures in Wonderland, 1865, Chapter 9).
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Levitt, H. (1984). The Phoneme. In: Raphael, L.J., Raphael, C.B., Valdovinos, M.R. (eds) Language and Cognition. Cognition and Language: A Series in Psycholinguistics. Springer, Boston, MA. https://doi.org/10.1007/978-1-4899-0381-5_15
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