On the album, Howard is joined by tenor saxophonist Frank Wright, pianist Bobby Few, and drummer Art Taylor.

Space Dimension is one of four albums recorded in Paris by the group, the others, credited to Wright, being Uhuru na Umoja (America, 1970), One for John (BYG, 1970), and Church Number Nine (Odeon, 1971).

[1][2][3] In a review of the 2019 reissue for The New York City Jazz Record, Pierre Crépon stated that the album "stands as the best document of one of the free jazz bands that mattered in a pivotal period and its return to circulation has been long overdue.

"[6] Author John Corbett noted that "where Wright is as voluble and gruff as can be, Howard is the perfect complement, a compact, focused sound."

He singled out "Church Number Nine" for praise, writing: "the whole machine takes its rightful shape, Wright screaming bloody murder, Howard joining for the ridiculously perfect little r&b/gospel riff, a maniacal laugh and corkscrew multiphonic ending the track on an unhinged note.