It is widely assumed that active RNA polymerases track along their templates to produce a transcript. We test this using chromosome conformation capture and human genes switched on rapidly and synchronously by tumour necrosis factor alpha (TNFalpha); one is 221 kbp SAMD4A, which a polymerase takes more than 1 h to transcribe. Ten minutes after stimulation, the SAMD4A promoter comes together with other TNFalpha-responsive promoters. Subsequently, these contacts are lost as new downstream ones appear; contacts are invariably between sequences being transcribed. Super-resolution microscopy confirms that nascent transcripts (detected by RNA fluorescence in situ hybridization) co-localize at relevant times. Results are consistent with an alternative view of transcription: polymerases fixed in factories reel in their respective templates, so different parts of the templates transiently lie together.