"Cosmic Girl" is a disco song, a dance music song based on rhythmic "looped beats" "to give it an off-center, otherworldly" sound. The syncopated rhythm contains 10 pulses which occur inside a 32-beat pattern, with pulses on beats 4, 7, 10, 13, 16, 19, 22, 25, 27 and 30. Coincidentally, the first four beats of this pattern are the same as the George Gershwin song "I Got Rhythm". Jamiroquai's psychedelic lyric evokes a spacey environment, using terms such as "zero gravity", "hyperspace", "galaxy" and "quasar". A disco-era aura is achieved by incorporating early electronic synthesizers along with disco-style string parts also produced by synthesizers.
While the single, and especially its chart performance, received mixed reviews from critics, it has become one of the better-known tracks of the band, and a concert staple. Live versions usually last for 7–8 minutes, nearly double the duration of the album version. In 2006, it was reissued as part of the "Classic Club Mixes" series, which also included "Space Cowboy", "Deeper Underground", "Love Foolosophy" and "Alright". The B-side to the single was an instrumental, "Slipin' 'N' Slidin'", a rather obscure song originating from another old Jamiroquai tune called "Mr Boogie", which was a live-only song. "Slipin 'N' Slidin'", just like "Mr Boogie", also had a vocal version.
The follow-up to Virtual Insanity gave Jamiroquai their first consecutive run of Top 10s, featured some of petrol-head Jay's very lovely – and very fast – cars in the video and peaked at Number 6. Along the way, it managed to sell 250,580 copies and helped Travelling Without Moving become the band's best-selling album, with sales of 1.2 million. It's his second most streamed too – 2.75 million plays.
The video, directed by Adrian Moat, shows three famous supercars driving and racing each other through several highways and mountain roads across a desert landscape from clear daylight to dawn. The cars on the video are a black Ferrari F355 GTS, a purple Lamborghini Diablo SE30 and a red Ferrari F40. Jay Kay appears to be driving the purple Lamborghini with Stuart Zender on the co-pilot seat, but the driver of the black Ferrari is not shown in detail. It has four different edits: Versions 1–3, and the so-called 'Jay's cut' version. In a Top Gear interview, Jay Kay explained that before filming one car had been totalled during transportation, and the windscreen of the second was smashed after one of the precision drivers knocked the camera off the cliff: