[2] Editors at AllMusic rated this album 4 out of 5 stars, with critic Paul Simpson writing "Imagine This Is a High Dimensional Space of All Possibilities is perhaps the furthest-out release in a discography full of inventive, inspired music, and it's some of Holden's most exciting and impressive work".

[5] At The Line of Best Fit, Janne Oinonen rated this album 9 out of 10, stating that it "packs a bewildering and borderline disorientating (in a very good way) array of musical ideas, with results that combine dense layering and wealth of detail with plenty of alluring spaces between the notes for the listener to get lost in".

[6] Dominic Haley in Loud and Quiet scored Imagine This Is a High Dimensional Space of All Possibilities a 7 out of 10, noting that "an atmosphere of hauntology looms over" the recording and is made up of "a hypnotic world of pulsing bass and blissful noise".

[7] Ben Hogwood of musicOMH rated this album 4.5 out of 5 stars, comparing this work to artists as varied as Can and The Orb, summing up his review that "Holden has created a life-affirming hour in the musical heavens, just as the title promises".

[8] The Observer's Kitty Empire gave this album a five-star review for "integrating all that has gone before" in Holden's career, with a result that "is magnificent: "dance" music that bursts out of the grid with retro textures, prelapsarian oscillations, birdsong and bells".