é ▁in ▁representing ▁space ▁and ▁time ▁together ▁in ▁complex ▁form ▁( x , y , z , ict ) ▁emphas izing ▁the ▁formal ▁similarity ▁with ▁E uclidean ▁space . ▁He ▁noted ▁that ▁space - time ▁is ▁in ▁a ▁certain ▁sense ▁a ▁four - dimensional ▁non - E uclidean ▁manifold . ▁Sommer feld ▁( 1 9 1 0 ) ▁used ▁M ink owski ' s ▁complex ▁representation ▁to ▁combine ▁non - col linear ▁veloc ities ▁by ▁spher ical ▁geometry ▁and ▁so ▁derive ▁Ein stein ' s ▁addition ▁formula . ▁Sub sequ ent ▁writers , ▁princip ally ▁Vari ć ak , ▁disp ensed ▁with ▁the ▁imag inary ▁time ▁coordinate , ▁and ▁wrote ▁in ▁explicitly ▁non - E uclidean ▁( i . e . ▁Lob ache v sk ian ) ▁form ▁reform ulating ▁relativ ity ▁using ▁the ▁concept ▁of ▁rapid ity ▁previously ▁introduced ▁by ▁Alfred ▁Rob b ▁( 1 9 1 1 ); ▁Ed win ▁B id well ▁Wilson ▁and ▁Gilbert ▁N . ▁Lewis ▁( 1 9 1 2 ) ▁introduced ▁a ▁vector ▁notation ▁for ▁spac etime ; ▁É mile ▁Bor el ▁( 1 9 1 3 ) ▁showed ▁how ▁parallel ▁transport ▁in ▁non - E uclidean ▁space ▁provides ▁the ▁kin ematic ▁basis ▁of ▁Thomas ▁pre cess ion ▁twelve ▁years ▁before ▁its ▁experimental ▁discovery ▁by ▁Thomas ; ▁Felix ▁Klein ▁( 1 9 1 0 ) ▁and ▁Lud wik ▁Sil ber stein ▁( 1 9 1 4 ) ▁employed ▁such ▁methods ▁as ▁well . ▁One ▁historian ▁arg ues ▁that ▁the ▁non - E uclidean ▁style ▁had ▁little