
Actually an ad-lib introduced by Rutland Barrington when playing the rôle of Pooh-Bah, to the annoyance of Gilbert.
The Mikado (1885)
The Mikado (1885)
Actually an ad-lib introduced by Rutland Barrington when playing the rôle of Pooh-Bah, to the annoyance of Gilbert.
The Mikado (1885)
What Is A Jazz Composer? (1971)
24th November, 1814
Source: Johann Wenzel Tomaschek, "A Talk with Beethoven", The Musical Times and Singing Class Circular, Vol. 33, Beethoven Supplement (Dec. 15, 1892)
Source: Science and Hypothesis (1901), Ch. I. (1905) Tr. George Bruce Halstead
Context: This procedure is the demonstration by recurrence. We first establish a theorem for n = 1; then we show that if it is true of n - 1, it is true of n, and thence conclude that it is true for all the whole numbers... Here then we have the mathematical reasoning par excellence, and we must examine it more closely.
... The essential characteristic of reasoning by recurrence is that it contains, condensed, so to speak, in a single formula, an infinity of syllogisms.
... to arrive at the smallest theorem [we] can not dispense with the aid of reasoning by recurrence, for this is an instrument which enables us to pass from the finite to the infinite.
This instrument is always useful, for, allowing us to overleap at a bound as many stages as we wish, it spares us verifications, long, irksome and monotonous, which would quickly become impracticable. But it becomes indispensable as soon as we aim at the general theorem...
In this domain of arithmetic,.. the mathematical infinite already plays a preponderant rôle, and without it there would be no science, because there would be nothing general.<!--pp.10-12
“Words are like money; there is nothing so useless, unless when in actual use.”
Thought and Word, viii
The Note-Books of Samuel Butler (1912), Part VII - On the Making of Music, Pictures, and Books
...the children had to live, so while waiting for logic to sanctify their existence, they throve and multiplied.
Number: The Language of Science (1930)