Ascending and Descending was influenced by, and is an artistic implementation of, the Penrose stairs, an impossible object; Lionel Penrose had first published his concept in the February 1958 issue of the British Journal of Psychology.
The Lark Ascending | Orpheus Descending | Nude Descending a Staircase, No. 2 | The Seven Sins: The Tyrant Ascending | Orpheus Descending (film) | ''Nude Descending a Staircase, No. 2 | Nude Descending a Staircase | "John Brown ascending the scaffold preparatory to being hanged", from the December 17, 1859 edition of ''Frank Leslie's Illustrated Newspaper | Ascending branch of medial circumflex femoral artery | Ascending branch of lateral circumflex femoral artery |
The group has four generators, which can be identified with the ascending and descending semitones and the ascending and descending perfect fifths.
It is also identified as the rock upon which Jacob dreamt about angels ascending and descending on a ladder and consequently consecrating and offering a sacrifice upon.
Wolfgang Krull (Über verallgemeinerte endliche Abelsche Gruppen, M. Z. 23 (1925) 161–196), returned to G.A. Miller's original problem of direct products of abelian groups by extending to abelian operator groups with ascending and descending chain conditions.
The new locomotives were the JNR Class EF63 banking engines used for help in both ascending and descending the 66.7‰ (1 in 15) gradient line.