Wolfgang Dick on October 4, 2024 supplied the answer to the question, Do you know the citation for a 1965 article by Ole Sand that mentions knowledge doubling? (Many thanks.)
A scholar recounts their search for the source of the knowledge doubling idea in a 2021 video:
https://www.youtube.com/watch?v=kH-9tnCAsEc
The Ole Sand article is found in:
Comprehensive Musicianship
Volume 2 of CMP (Series)
Volume 2 of CMP, Contemporary Music Project for Creativity in Music Education
Publisher Contemporary Music Project, Music Educators National Conference, 1965
At page 79 in the book with the article:
“Never before have the dynamic forces of change spun with such incredible speed. In the nearly two thousand years since the birth of Christ, there has been first a very slow and then a rapidly accelerating growth in the accumulation of knowledge. If this accumulation is plotted on a time line, beginning with the birth of Christ, the first doubling of knowledge occurs in 1750,the second in 1900, the third in 1950, and the fourth only ten years later, in 1960!”
What is the original source for these claims?