Numbers at work: a cultural perspective by Rudolf Josef Taschner

By Rudolf Josef Taschner

Drawing essentially from old examples, this publication explains the super function that numbers and, particularly, arithmetic play in all features of our civilization and tradition. The full of life variety and illustrative examples will interact the reader who desires to comprehend the various ways that arithmetic permits technological know-how, expertise, artwork, song, politics, and rational foundations of human suggestion. each one bankruptcy specializes in the impact of arithmetic in a selected box and on a particular old determine, resembling "Pythagoras: Numbers and Symbol"; "Bach: Numbers and Music"; "Descartes: Numbers and Space."

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For this purpose, we continue to stack fi hs one on top of the other or move downward in intervals of fourths and transpose the tones obtained in this manner until they fall within the compass of one octave. If you stop short—arbitrarily—at G♯/A♭ and arrange the tones in sequence according to pitch, the result is the intervals of Pythagorean tuning. In this scale, the tones A♭ and G♯ are extremely close to each other. 0136. 053497). 4% between G♯ and A♭), which is not necessarily noticeable even for a musician, has been called the Pythagorean comma.

In the theme of the last fugue of The Well-Tempered Clavier, Part I, if we follow the succession of intervals through, the final F♯ is by no means identical with the initial one. 95367. 24 C D♯ E B G B A♯ F♯ D F♯ 40 N U M BE R S AT WOR K The pianist has no option but to strike the same key again and again, yet the F♯ at the end of a melody that is haunted by unfulfilled longing forcefully presents itself to our ears as shrouded in darkness. Did Bach bring this about intentionally, or is it the work of his intuitive genius?

Where has that smile gone? Where’s that glance at the camera, so shy and yet so full of expectation? What has become of that half-articulated yearning for acceptance? We look into the eyes of a li le child as she stretches out her arms to us; we gaze at her face transfigured with the joy of recognition. What does the future have in store for her? How will she cope 41 Hugo von Hofmannsthal. 42 N U M BE R S AT WOR K with unrequited love or with obstacles that block her ambitions? What decisions will shape her life a er we ourselves are gone?

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