/Users/andrea/_magisterarbeit/korpus/clean/testkorpus/30/file10.html NN ----------------------------------------- : Search NP . SENT Lycos NP Angelfire NP Texas NP Hold VVP Em NP Share NP This NP Page NP Report NP Abuse NN Edit VV your PP$ Site NN Browse VV Sites NP Previous JJ Top NP 100 CD Next JJ To TO Contents NNS Amy NP C NP . SENT EdmondsonA NP Fuller NP Explanation NN Chapter NP 1 CD , , Return NN to TO Modelabilitypages NP 6 CD through IN 9 CD Operational JJ Mathematics NNS We PP can MD imagine VV the DT young JJ Bucky NP , , an DT enthusiastic JJ misfit NN sensing VVG that IN he PP is VBZ alone RB in IN his PP$ skepticism NN about IN the DT fundamental JJ premises NNS of IN geometry NN . SENT Does VVZ no DT one NN see VV what WP I PP see VVP . SENT Does VVZ no DT one NN else RB sense VVP the DT terrible JJ problems NNS that WDT lie VVP ahead RB if IN we PP follow VVP these DT absurd JJ premises NNS to TO their PP$ logical JJ ends NNS . SENT While IN his PP$ grade NN school NN classmates NNS were VBD apparently RB content JJ to TO go VV right RB along RB with IN the DT teacher's JJ strange JJ games NNS without IN complaint NN , , Bucky NP was VBD astonished VVN by IN the DT implausible JJ new JJ concepts NNS . SENT Bucky NP would MD tell VV us PP that IN he PP tried VVD , , constantly RB , , to TO accept VV the DT rules NNS be VB a DT good JJ student NN , , make VV his PP$ family NN proud JJ , , submit VV to TO and CC even RB excel VVP at IN the DT illogical JJ activities NNS but CC somehow RB his PP$ efforts NNS at IN model NN behavior NN were VBD always RB thwarted VVN . SENT He PP just RB couldn't NN help NN pointing VVG out RP that IN the DT teacher's JJ straight JJ line NN was VBD not RB at IN all DT straight JJ , , but CC rather RB slightly RB curved VVN and CC definitely RB fragmented JJ . SENT Perplexed VVN by IN her PP$ lack NN of IN accuracy NN , , Bucky NP saw VVD a DT trail NN of IN powdery JJ chalk NN dust NN left VVN on IN the DT blackboard NN , , a DT trace VV of IN the DT motion NN of IN her PP$ hand NN , , and CC it PP seemed VVD quite RB unlike IN her PP$ words NNS . SENT Bucky NP was VBD virtually RB blind JJ until IN he PP got VVD his PP$ first JJ eyeglasses NNS at IN the DT age NN of IN five CD , , so RB he PP had VHD truly RB experienced VVN life NN without IN this DT primary JJ sense NN . SENT Now RB he PP was VBD insatiably RB curious JJ about IN the DT visual JJ patterns NNS around IN him PP . SENT An DT infinite JJ straight JJ line NN . SENT He PP would MD turn VV toward IN the DT window NN , , thoughtfully RB pondering VVG where WRB that DT infinite JJ line NN stopped VVD . SENT Out IN the DT window NN and CC over IN the DT hill NN and CC on IN and CC on IN it PP goes VVZ . SENT it PP didn't VVD seem VV right RB somehow RB . SENT Bucky NP , , childishly RB earnest JJ even RB in IN his PP$ eighties NNS , , would MD tell VV this DT story NN , , explaining VVG that IN he PP didn't VVD mean VV to TO be VB fresh JJ , , he PP just RB couldn't NN help NN wondering VVG if IN that DT teacher NN really RB knew VVD what WP she PP was VBD talking VVG about RB . SENT Much RB later RBR , , fascinated VVN by IN Eddington's NP 5 CD definition NN of IN science NN as IN the DT systematic JJ attempt NN to TO set VV in IN order NN the DT facts NNS of IN experience NN , , Fuller NP had VHD a DT plan NN . SENT It PP must MD be VB possible JJ to TO develop VV a DT mathematical JJ system NN consistent JJ with IN experience NN . SENT He PP concluded VVD that DT humanity NN had VHD been VBN on IN the DT wrong JJ track NN all RB these DT years NNS . SENT Experimental JJ Evidence NN It PP seemed VVD to TO Fuller NP that IN mathematicians NNS arbitrarily RB invent VVP impossible JJ concepts NNS , , decide VV rules NNS for IN their PP$ interaction NN , , and CC then RB memorize VV the DT whole JJ game NN . SENT But CC what WP did VVD he PP propose VVP as IN an DT alternative NN . SENT Starting VVG from IN scratch NN . SENT Mathematical JJ principles NNS must MD be VB derived VVN from IN experience NN . SENT Start NN with IN real JJ things NNS , , observe VVP , , record NN , , and CC then RB deduce VV . SENT Working VVG with IN demonstrable JJ as RB opposed VVN to TO impossible JJ concepts NNS , , the DT resulting VVG generalizations NNS would MD reflect VV and CC apply VV to TO the DT world NN in IN which WDT we PP live VVP . SENT It PP seemed VVD highly RB likely JJ that IN such PDT an DT experimental JJ approach NN would MD lead VV to TO a DT comprehensive JJ and CC entirely RB rational JJ set NN of IN principles NNS that WDT represented VVD actual JJ phenomena NNS . SENT Furthermore RB , , Bucky NP suspected VVD that IN such PDT an DT inventory NN would MD relate VV to TO metaphysical JJ as RB well RB as IN physical JJ structure NN . SENT Fuller NP decided VVD that IN to TO begin VV this DT process NN of IN rethinking VVG mathematics NNS he PP had VHD to TO ask VV some DT very RB basic JJ questions NNS . SENT What WP does VVZ exist VV . SENT What WP are VBP the DT characteristics NNS of IN existence NN . SENT He PP proposed VVD that IN science's NNS understanding VVG of IN reality NN should MD be VB incorporated VVN into IN new JJ models NNS to TO replace VV the DT no RB longer RBR appropriate JJ cubes NNS and CC other JJ solids NNS that WDT had VHD kept VVN mathematicians NNS deliberately RB divorced VVN from IN reality NN since IN the DT days NNS of IN ancient JJ Greece NP . SENT To TO begin VV with IN , , there EX are VBP no DT solids NNS . SENT matter NN consists VVZ exclusively RB of IN energy NN . SENT Things NNS are VBP actually RB events NNS transient JJ arrangements NNS of IN frenetically RB vibrating VVG atomic JJ motion NN . SENT It's NP almost RB unthinkable JJ , , but CC perhaps RB if IN we PP get VVP our PP$ vocabulary NN and CC models NNS to TO be VB more RBR consistent JJ with IN an DT energy NN event NN reality NN , , humanity NN can MD be VB retuned VVN to TO become VV comfortable JJ with IN the DT invisible JJ discoveries NNS of IN science NN . SENT In IN short JJ , , simplifies VVZ Fuller NP , , we PP have VHP the DT option NN to TO tell VV children NNS the DT truth NN about IN nature NN in IN the DT first JJ place NN . SENT What WP if IN we PP do VVP go VV along RP with IN the DT rule NN that IN mathematics NN cannot NN define VV and CC depend VV upon IN a DT concept NN that IN cannot NN be VB demonstrated VVN . SENT where WRB does VVZ that RB leave VV us PP . SENT Fuller NP saw VVD inconsistencies NNS even RB in IN the DT notion NN of IN an DT imaginary JJ straight JJ line NN , , for IN imagination NN relies VVZ on IN experience NN image NN ination NN he PP would MD say VV to TO construct VV its PP$ images NNS . SENT Therefore RB an DT operational JJ mathematics NN must MD rely VV on IN concepts NNS that WDT correspond VV to TO reality NN . SENT Bucky NP pulls VVZ us PP back RB into IN the DT turn NN of IN the DT century NN schoolhouse NN of IN his PP$ childhood NN . SENT The DT teacher NN stood VVD at IN the DT blackboard NN , , made VVD a DT little RB dot VVP , , and CC said VVD , , This DT is VBZ a DT point NN . SENT it PP doesn't VVD exist VV . SENT So RB she PP wiped VVD that DT out RP . SENT Then RB she PP drew VVD a DT whole JJ string NN of IN them PP and CC called VVD it PP a DT line NN . SENT Having VHG no DT thickness NN , , it PP couldn't NN exist VVP either RB . SENT Next IN she PP made VVD a DT raft NN out RP of IN these DT lines NNS and CC came VVD up RP with IN a DT plane NN . SENT I'm NP sorry RB to TO say VV it PP didn't NN exist VVP either RB , , sighs VVZ Bucky NP . SENT She PP then RB stacked VVN them PP together RB and CC got VVD a DT cube NN , , and CC suddenly RB that IN existed VVN . SENT Telling VVG the DT story NN , , Bucky NP scratches VVZ his PP$ head NN as RB if IN still RB puzzled VVN seventy CD years NNS later RBR . SENT I PP couldn't NN believe VVP it PP . SENT how WRB did VVD she PP get VV existence NN out RP of IN nonexistence NN to TO the DT fourth JJ power NN . SENT So RB I PP asked VVD , , How WRB old JJ is VBZ it PP . SENT She PP said VVD , , don't JJS be VB naughty JJ . SENT . SENT . SENT . SENT It PP was VBD an DT absolute JJ ghost NN cube NN . SENT 6 CD Instead RB of IN a DT dimensionless JJ point NN , , Fuller NP proposes VVZ the DT widely RB applicable JJ energy NN event NN . SENT Every DT identifiable JJ experience NN is VBZ an DT energy NN event NN , , he PP summarizes VVZ , , and CC many JJ are VBP small JJ enough RB to TO be VB considered VVN points NNS , , such JJ as IN a DT small JJ deposit NN of IN chalk NN dust NN . SENT An DT aggregate NN of IN events NNS too RB distant JJ to TO be VB differentiated VVN from IN one CD another DT can MD also RB be VB treated VVN as IN a DT point NN . SENT Consider VV for IN example NN a DT plastic JJ bag NN of IN oranges NNS carried VVN by IN a DT pedestrian NN and CC viewed VVN from IN the DT top NN of IN the DT Empire NP State NP Building NP , , or CC a DT star NN consisting VVG of IN immense JJ numbers NNS of IN speeding VVG particles NNS appearing VVG as IN a DT tiny JJ dot VVP of IN negligible JJ size NN despite IN having VHG an DT actual JJ diameter NN far RB greater JJR than IN that DT of IN the DT earth NN . SENT 7 CD The NP mathematician's NNS straight JJ line NN , , defined VVN as IN having VHG length NN but CC no DT width NN , , simply RB cannot NN be VB demonstrated VVN . SENT All DT physical JJ lines NNS upon IN closer JJR inspection NN are VBP actually RB wavelike JJ or CC fragmented JJ trajectories NNS . SENT even RB a DT line NN of IN sight NN is VBZ a DT wave NN phenomenon NN , , insists VVZ Fuller NP . SENT physics NN has VHZ found VVN no DT straight JJ lines NNS . SENT 2 CD But CC forces NNS exist VVP , , and CC they PP pull VVP or CC push VVP in IN a DT line NN , , which WDT can MD be VB modeled VVN by IN a DT vector NN . SENT We PP shall MD explore VV vectors NNS and CC their PP$ role NN in IN synergetics NNS in IN great JJ detail NN in IN later JJR chapters NNS . SENT Finally RB , , the DT continuous JJ plane NN with IN no DT thickness NN must MD be VB replaced VVN by IN a DT mesh NN of IN energy NN events NNS interrelated VVN by IN fine JJ networks NNS of IN tiny JJ vectors NNS . SENT To TO Fuller NP , , these DT adjustments NNS were VBD crucial JJ , , for IN mathematicians NNS games NNS with IN continuous JJ planes NNS and CC sizeless JJ points NNS were VBD ultimately RB irrelevant JJ diversions NNS . SENT however RB enticing VVG the DT intellectual JJ pursuit NN might MD be VB , , they PP do VVP not RB lead VV to TO a DT better JJR understanding NN of IN how WRB nature NN works NNS . SENT The DT essential JJ nature NN of IN the DT above JJ revolution NN is VBZ semantic JJ and CC can MD easily RB seem VV trivial JJ . SENT The DT difficulty NN in IN evaluating VVG the DT impact NN of IN such JJ changes NNS lies VVZ in IN the DT subtlety NN of IN the DT effect NN of IN words NNS and CC the DT images NNS they PP produce VVP . SENT Only RB through IN experimenting VVG with IN Fuller's NP substitutions NNS for IN some DT period NN of IN time NN can MD we PP judge VV the DT merits NNS of IN mathematical JJ terminology NN that WDT reflects VVZ science's JJ new JJ understanding NN of IN reality NN . SENT Back RB to TO the DT starting VVG point NN . SENT Nothing NN can MD be VB accepted VVN as IN self NN evident JJ . SENT a DT new JJ mathematics NN must MD be VB derived VVN though IN operational JJ procedure NN . SENT Fuller NP decided VVD that IN through IN sufficient JJ observation NN of IN both DT naturally RB occurring VVG and CC experimentally RB derived VVN phenomena NNS without IN reference NN to TO a DT specific JJ framework NN , , nature's NNS own VVP coordinate VV system NN might MD emerge VV . SENT He PP sought VVD a DT body NN of IN generalizations NNS describing VVG the DT way NN patterns NNS are VBP organized JJ and CC able JJ to TO cohere VV over IN time NN . SENT We PP shall MD see VV how WRB these DT principles NNS can MD be VB discerned VVN both CC in IN deliberate JJ experiments NNS with IN various JJ materials NNS and CC by IN recording NN existing VVG natural JJ patterns NNS . SENT Bucky's NP grade NN school NN skepticism NN was VBD thus RB the DT beginning NN of IN a DT lifelong JJ search NN for IN nature's NNS coordinate VV system NN . SENT After IN rejecting VVG traditional JJ academia NN through IN his PP$ dramatic JJ departure NN from IN Harvard's NP freshman NN class NN in IN 1914 CD , , 8 CD he PP began VVD an DT independent JJ exploration NN of IN mathematics NNS which WDT he PP was VBD to TO pursue VV for IN the DT rest NN of IN his PP$ life NN . SENT A DT sort NN of IN philosophical JJ geometry NN gradually RB began VVD to TO take VV shape NN , , consisting VVG of IN a DT rich JJ body NN of IN facts NNS and CC principles NNS , , some DT new JJ and CC others NNS newly RB considered VVN . SENT Synergetic JJ geometry NN is VBZ tied VVN together RB as IN one CD cohesive JJ system NN by IN the DT unmistakable JJ presence NN of IN Bucky NP Fuller NP in IN conventional JJ and CC bizarre JJ observations NNS alike RB . SENT Including VVG expositions NNS called VVN Tetrahedron NN Discovers VVZ Itself PP and CC Universe NN , , Life NP , , Cosmic JJ Hierarchy NN , , Complex JJ of IN Jitterbugs NNS , , and CC the DT more RBR conventional JJ Closest JJS Packing NN of IN Spheres NNS , , Synergetics NP does VVZ not RB fall VV neatly RB into IN any DT preconceived VVN category NN . SENT This DT volume NN will MD attempt VV to TO clarify VV these DT multifaceted JJ or CC polyhedral JJ observations NNS , , which WDT together RB constitute VVP synergetic JJ geometry NN . SENT To TO Contents NNS