The Seven ! Bridges ! of ! Königsberg is ! a ! notable ! problem ! in ! mathematics ! and ! its ! ! negative ! resolution ! by ! Leonard ! Euler ! in ! 1735 ! laid ! the ! foundations ! of ! graph ! theory ! and ! pre fi gured ! the ! ! modern ! idea ! of topology. ! Konigsberg ! ! had ! a ! peculiar ! topography. ! It ! was ! set ! on ! both ! sides ! of ! a ! river, ! and ! included ! two ! large ! islands ! which ! were ! connected ! to ! each ! other ! and ! the ! mainland ! by ! seven ! bridges. ! The ! problem ! ! set ! by ! Euler ! was ! to !fi nd ! a ! walk ! through ! the ! city ! that ! would ! cross ! each ! bridge ! once ! and ! only ! once. ! The ! islands ! could ! not ! be ! reached ! by ! any ! route ! other ! than ! the ! bridges, ! and ! every ! bridge ! ! had ! to ! be ! crossed ! completely ! every ! time; ! one ! could ! not ! walk ! halfway ! onto ! the ! bridge ! and ! then ! turn ! around ! and ! later ! cross ! the ! other ! half ! from ! the ! other ! side. ! The ! walk ! need ! not ! start ! and ! end ! at ! the ! same ! spot. ! ! The ! good ! citizens ! of ! Koenigsberg ! ! tackled ! the ! problem ! ! with ! customary ! Prussian ! thoroughness ! and ! ! took ! their ! Sunday ! constitutional ! walks ! across ! the ! bridges, ! but ! despite ! all ! their ! efforts ! they ! could ! not !fi nd ! a ! solution. ! ! They ! proved ! that ! the ! problem ! had no solution ! in ! strictly ! territorial ! terms ! . ! There ! could ! be ! no ! non-retracing ! the ! bridges. ! Euler’s ! problem ! was ! ! to ! develop ! a ! model,a ! ! theoretical ! map ! to ! ! establish ! this ! ! fact ! with ! mathematical ! rigor. ! For ! this ! purpose ! ! the ! only ! important ! feature ! of ! a ! route ! was ! the ! sequence ! of ! bridges ! crossed. ! This ! allowed ! him ! to ! reformulate ! the ! problem ! in ! abstract ! terms, ! eliminating ! all ! features ! except ! the ! list ! of ! land ! masses ! and ! the ! bridges ! connecting ! them. ! Each ! land ! mass ! was ! replaced ! with ! an ! abstract ! node, ! and ! each ! bridge ! with ! an ! abstract ! connection ! or ! edge. ! !
! Under ! the ! Third ! Reich, ! the ! work ! of ! Euler ! , ! who ! happened ! to ! be ! a ! Jew, ! was ! banned. ! Topology, ! it ! seemed ! was ! a ! Jewish ! science. ! The ! actual ! topography ! of ! the ! city ! was ! destroyed ! during ! ! WW2 ! ! by ! a ! combination ! of ! RAF ! bombing ! and ! the ! fi nal ! assault ! by ! the ! Red ! Army. ! Many ! of ! the ! bridges ! ! were ! damaged, ! several ! destroyed. ! The ! Soviet ! regime ! rebuilt ! the ! bridges, ! but ! ! the ! intricate ! ! mediaeval ! street ! layout ! was ! replaced ! by ! an ! ! ! urban ! planning ! grid. ! The ! city ! centre ! was ! ! dominated ! by ! a ! monumental ! House ! of ! the ! Soviets ! from ! which ! boulevards ! radiated ! out. ! ! This ! new ! Stalinist ! topography ! ! actually ! reproduced ! the ! very ! Prussian ! state ! culture ! ! ! it ! was ! designed ! to ! erase ! , ! while ! the ! fact ! that ! topology ! was ! founded ! on ! the ! mapping ! of ! an ! unsolvable ! problem ! was ! denounced ! as ! an ! example ! of ! petit ! bourgeois ! defeatism ! , ! in ! contradiction ! with ! Marx’s ! assertion ! that ! human ! beings ! only ! ! create ! problems ! ! ! they ! are ! capable ! ! of ! solving. ! !
Christaller’s ! polycentric ! or ! decentred ! model ! of ! urban ! growth ! ! - ! challenging ! central ! place ! theory. ! l !
Mapping ! Communication ! Flows ! 1 !
Diagram ! of ! an ! actor-network !
Flight ! Paths ! across ! the ! UK ! in ! daylight !
Derek ! Harris !
Cy ! ! Twombly ! !
Chris ! Kenny ! ! Fetish ! Map ! of ! London !
Jackson ! Pollock !
Julie ! ! Mehretu ! ! Fractal ! Map !
Every ! map ! tells ! a ! story... !
Swallows ! and ! Amazons !
Pilgrims ! Progress !
! ! ! ! ! ! ! ! ! ! ! Schuiten ! and ! Peeters ! ! ! ! ! ! ! ! ! ! ! The ! Invisible ! Frontier ! !
The ! embodied ! landscape !
Franco ! Moretti ! : ! The ! village ! neighbourhood ! ! !
The ! impact ! of ! enclosure ! !
Moretti ! graphs ! the ! novel !
Treasure ! island: ! the ! map ! as ! protagonist !
The !fi ctional ! East ! 20 ! !
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