3.6.2 ngokucacileyo

I-Amplified ukucela ukusebenzisa imodeli yokulandelela ukuhlanganisa idatha yolwazi oluvela kubantu abambalwa abanomthombo omkhulu wemithombo kubantu abaninzi.

Indlela eyahlukileyo yokudibanisa uphando kunye nemithombo ekulu yolwazi yinkqubo endiyibiza ngayo ngokukhulisa . Xa kukhuliswa ukubuza, umphandi usebenzisa umzekelo wokuqulunqa ukudibanisa idatha encinci yesaziso kunye nomthombo omkhulu wedatha ukwenzela ukuvelisa ukuqikelela kwinqanaba okanye ubuninzi bezinto ezingenakwenzeka kunye nomthombo wedatha ngokwabo. Umzekelo obalulekileyo wokubuza umbuzo uvela kumsebenzi kaJoshua Blumenstock, owayefuna ukuqokelela idatha enokukunceda ukukhokela uphuhliso kumazwe ahluphekileyo. Kwixesha elidlulileyo, abaphandi abaqokelela olu hlobo lwedatha ngokubanzi babefanele bathathe enye yeendlela ezimbini: uphando lweesampuli okanye iimpepha. Uphando lweempendulo, apho abaphandi abaphandululana nombolo encinci yabantu, banokuguquguquka, ngexesha elifanelekileyo, kwaye bancinci. Nangona kunjalo, ezi zophando, ngenxa yokuba zisekelwe kwisampuli, zihlala zikhawulelwe kwisisombululo sabo. Ngophononongo lwesampula, kudla nzima ukwenza uqikelelo malunga neendawo ezithile zeendawo okanye kwiindawo ezithile zabantu. I-Censuses, ngakolunye uhlangothi, uzama ukuphanda udliwano-ndlebe nomntu wonke, kwaye ngoko unokusetyenziswa ukuvelisa ukuqikelela kwiindawo ezincinci zendawo okanye amaqela abantu. Kodwa iicensis zibiza kakhulu, zincinci ekugxileni (ziquka kuphela inani elincinci lemibuzo), kwaye alikho ngexesha elifanelekileyo (lenzeke kwishedyuli esicwangcisiweyo, njengayo yonke iminyaka eyi-10) (Kish 1979) . Esikhundleni sokuba unamathele kwiisampulu zophando okanye ucingo, cinga ukuba ngabaphandi banokudibanisa iimpawu ezintle zombini. Cinga ukuba abaphandi banokubuza yonke imibuzo kumntu ngamnye imihla. Kucacile ukuba, le nto inobunzima, ukuqhubeka kwenzululwazi yintlobo yesayensi yenzululwazi. Kodwa kubonakala ngathi sinokuqala ukukhawulelanisa oku ngokuhlanganisana nemibuzo yesaveli ukusuka kwinani elincinci labantu abanomlinganiselo wedijithali kubantu abaninzi.

Uphando lwe-Blumenstock lwaqala xa edibanisa nomboneleli omkhulu wefowuni eRwanda, kwaye iinkampani zanikezela iirekhodi zokuthengiselana ezingabonakaliyo ezivela kumakhasimende angama-1.5 eziphakathi kuka-2005 no-2009. Ezi rekhodi ziqulethe ulwazi malunga nomnxeba ngamnye kunye nomyalezo wesicatshulwa, njengexesha lokuqala, ixesha , kunye neendawo ezikufutshane zomnxebi kunye nomkeli. Ngaphambi kokuba ndixoxe ngemibandela yamanani, kubalulekile ukubonisa ukuba le nyathelo lokuqala lingaba linye labanzima kubaphandi abaninzi. Njengoko ndichazwe kwisahluko 2, ininzi imithombo yedatha ayifumaneki kubaphandi. Idatha ye-meta-data, ngokukodwa, ayinakufikeleleka kuba kungenakwenzeka ukuba ingabonakali kwaye ngokuqinisekileyo iqulethe ulwazi abachaphazelekayo (Mayer, Mutchler, and Mitchell 2016; Landau 2016) . Kwimeko enje, abaphandi baqaphele ukukhusela idatha kunye nomsebenzi wabo wawujongene noluntu lwesithathu (okt, i-IRB yabo). Ndiza kubuya kule micimbi yokuziphatha ngokubanzi kwisahluko 6.

I-Blumenstock inomdla wokulinganisa ubutyebi kunye nenhlalakahle. Kodwa ezi mpawu azikho ngqo kwiirekhodi zeefowuni. Ngamanye amazwi, amarekhodi okufowunela awaneliswanga kulolu cwaningo-into eqhelekileyo yemithombo yolwazi emikhulu exoxwa ngayo ngokucacileyo kwisahluko 2. Nangona kunjalo, kubonakala ngathi iirekhodi zeefowuni zinokuba nolwazi olungazithe ngqo ngolwazi ngokuphathelele ubutyebi kunye impilo. Ngenxa yoko, i-Blumenstock yabuza ukuba kunokwenzeka yini ukuqeqesha imodeli yokufunda umatshini ukuqikelela ukuba umntu uza kuphendula njani uphando ngokusekelwe kwiirekhodi zabo zeefowuni. Ukuba oko kwakunokwenzeka, i-Blumenstock ingasebenzisa lo mzekelo ukuchaza kwangaphambili iimpendulo zenzululwazi zabo bonke abathengi abayizigidi eziyi-1.5.

Ukuze ukwakhiqe kwaye uqeqeshe umzekelo onjalo, i-Blumenstock kunye nabancedisi bokuphanda baseKigali yeSizwe kunye neThekhnoloji ebizwa ngokuba yi-sampuli engahleliyo malunga nabathengi abayiwaka. Abaphandi bachaza iinjongo zeprojekthi kubathathi-nxaxheba, bacela imvume yabo yokudibanisa iimpendulo zenzululwazi kwiirekhodi zeefowuni, baze babuze uluhlu lwemibuzo ukulinganisa ubutyebi babo kunye nenhlalakahle, njengokuba "Unayo umsakazo? "kunye" Ingaba unayo ibhasikidi? "(jonga umfanekiso 3.14 uluhlu oluthile). Bonke abathathi-nxaxheba kwi-survey bahlawulelwa ngemali.

Ngokulandelayo, i-Blumenstock isebenzisa inyathelo elinezibini eziqhelekileyo ekufundeni komatshini: ubunjineli bobunjiweyo obulandelwa ukufunda. Okokuqala, kwinqanaba lobunjineli , kuwo wonke umntu ogqitywa udliwano-ndlebe, i-Blumenstock yaguqula iirekhodi zeefowuni kwiimpawu zeempawu malunga nomntu ngamnye; Iingcali zenzululwazi zingabiza le mpawu "iimpawu" kunye neentlalo zenzululwazi ziza kuthiwa "ziguquko." Ngokomzekelo, ngamnye umntu, i-Blumenstock ibalwe inani leentsuku kunye nomsebenzi, inani labantu abahlukileyo umntu odibene naye, isixa semali esichithwa kwixesha lomoya, njalo njalo. Ngokuchanekileyo, ubuninzi bobunjineli bobuninzi badinga ulwazi lokulungisa uphando. Umzekelo, ukuba kubalulekile ukuhlukanisa phakathi kweefowuni zasemakhaya kunye namazwe ngamazwe (sinokulindela abantu ababiza umhlaba ngamazwe ukuba babe ngabacebileyo), oku kufuneka kwenziwe kwinqanaba lobunjineli. Umphandi onokungaqondi kakuhle iRwanda akanakho ukubandakanya le nkalo, kwaye ke ukusebenza kwangaphambili komzekelo kuya kubandezeleka.

Ngokulandelayo, kwisinyathelo sokufunda esiphezulu, i-Blumenstock yakha umzekelo ukuchaza kwangaphambili impendulo yempheno kumntu ngamnye ngokusekelwe kwimpawu zabo. Kule meko, i-Blumenstock isetyenziselwa ukuguqulwa kwezinto, kodwa isenokusebenzisa iindidi ezahlukeneyo zokufunda.

Ngoko yasebenza njani? Ngaba i-Blumenstock yakwazi ukuxela izimpendulo zemibuzo yolu vavanyo efana neyo "Ngaba unayo inomathotholo?" Kwaye "Ngaba unayo ibhayisiki?" Usebenzisa iimpawu ezivela kwiirekhodi zeefowuni? Ukuze ahlolisise ukusebenza komzekelo wakhe wokuqhelanisa, i-Blumenstock isebenzise ukuqinisekiswa kwesivumelwano , isicatshulwa esetyenziswa ngokubanzi kwisayensi yolwazi kodwa kunqabile kwintlalo yesayensi. Injongo yokuqinisekiswa komgaqo-mvume kukubonelela ngokufanelekileyo uvavanyo lokusebenza ngokulandelelanisa ngokuqeqesha kunye nokuvavanya kwii-subset ezahlukeneyo zolwazi. Ngokukodwa, i-Blumenstock yahlula idatha yakhe kwi-10 chunks yabantu abayi-100 nganye. Emva koko, wasebenzisa iisithoba ezithathayo ukuqeqesha imodeli yakhe, kwaye ukusebenza kwangaphambili komzekelo oqeqeshiwe kwavavanywa kwi-chunk esele. Uphindaphindile le nkqubo ngokuphindwe ngamaxesha angama-10-kunye neenkcukacha nganye zedata ukufumana enye into njenge-data-validation-and the results.

Ukuchaneka kweziprofeto kwakuphezulu kwezinye izici (umfanekiso 3.14); umzekelo, i-Blumenstock inokuqikelela nge-97.6% ukuchaneka ukuba umntu unomathotholo. Oku kunokuzwakala kukuthabatha, kodwa kubalulekile ukuqhathanisa indlela ecacileyo yokubikezela ngokubhekiselele kwindlela elula. Kule meko, enye indlela elula kukuqikelela ukuba wonke umntu uya kunika impendulo eqhelekileyo. Ngokomzekelo, i-97.3% yabaphenduli babike ukuba benomathotholo, ukuba iBlumenstock ibikezele ukuba wonke umntu uya kubika ukuba unomathotholo uza kuba nokuchaneka kwe-97.3%, into emangalisa ukufana nenkqubo yakhe eyinkimbinkimbi (97.6% ngokuchanekileyo) . Ngamanye amagama, yonke idatha ebalulekileyo kunye nokufakela imodeli kwandise ukuchaneka kokucetyiswa ukusuka kwi-97.3% ukuya kwi-97.6%. Nangona kunjalo, ngeminye imibuzo, efana ne "Ngaba unayo ibhasikidi?", Izibikezelo ziphucukile ukusuka kuma-54.4% ukuya kuma-67.6%. Ngokuqhelekileyo, isibalo 3.15 sibonisa ukuba ezinye iimpawu ze-Blumenstock azizange ziphuculwe ngaphaya kokukwenza nje ukucacisa okulula, kodwa ukuba ezinye izici zazikho ukuphucula. Ujonge nje kwezi ziphumo, nangona kunjalo, usenokungacingi ukuba le ndlela ithembise ngokuthe ngqo.

Umzekeliso 3.14: Ukuchaneka kwangaphambili kwendlela yokulinganisa imodeli eqeqeshiwe ngeirekhodi zeefowuni. Ukutshintshwa kwi-Blumenstock (2014), itafile 2.

Umzekeliso 3.14: Ukuchaneka kwangaphambili kwendlela yokulinganisa imodeli eqeqeshiwe ngeirekhodi zeefowuni. Ukutshintshwa kwi- Blumenstock (2014) , itafile 2.

Umzekeliso 3.15: Ukuthelekiswa kokuchaneka kwangaphambili kwendlela yokulinganisa imodeli eqeqeshiwe ngeirekhodi zeefowuni ukuya kwisicatshulwa esilula. Iingongoma zincinci ukugwema ukungena. Ukutshintshwa kwi-Blumenstock (2014), itafile 2.

Umzekeliso 3.15: Ukuthelekiswa kokuchaneka kwangaphambili kwendlela yokulinganisa imodeli eqeqeshiwe ngeirekhodi zeefowuni ukuya kwisicatshulwa esilula. Iingongoma zincinci ukugwema ukungena. Ukutshintshwa kwi- Blumenstock (2014) , itafile 2.

Nangona kunjalo, unyaka omnye kamva, i-Blumenstock kunye nabalingane ababini-uGabriel Cadamuro noRobert On-banyathelise iphepha kwiSayensi ngeempembelelo ezingcono (Blumenstock, Cadamuro, and On 2015) . Kwakukho izizathu ezibalulekileyo zobugcisa bokuphucula oku: (1) basebenzise iindlela ezithe gqolo (oko kukuthi, indlela entsha yokwenza ubunjineli kunye nemodeli eyinkimbinkimbi yokuqikelela iimpendulo ezivela kwiimpawu) kunye (2) kunokuba uzame ukuphendula iimpendulo kumntu ngamnye imibuzo yombuzo (umzekelo, "Unayo inomathotholo?"), bazame ukuphawula inkcazelo yorhwebo. Ezi phuculo zeteknoloji zithetha ukuba bangenza umsebenzi ofanelekileyo wokusebenzisa iirekhodi zeefowuni ukuxela ubutyebi kubantu kwisampuli zabo.

Ukuqikelela ubungcambu babantu kwisampuli, nangona kunjalo, kwakungeyona nto injongo yokuphanda. Khumbula ukuba injongo ekugqibeleni yayikudibanisa ezinye zezinto eziphambili zeesampulu zophando kunye neenqwelo-mvume zokuvelisa ukuqikelela ngokuchanekileyo, ukuphakanyiswa okuphezulu kweentlupheko kumazwe asakhulayo. Ukuvavanya ukukwazi kwabo ukufezekisa le njongo, i-Blumenstock kunye noogxa basebenzise imodeli yabo kunye nedatha yabo ukuqikelela ubuncwane bonke abantu abayi-1.5 yezigidi kwiirekhodi zeefowuni. Kwaye basebenzisa i-geospatial ingcaciso efakwe kwiirekhodi zeefowuni (khumbula ukuba idatha ibandakanye indawo yesitishi esiseduze nganye kwifowuni) ukuqikelela indawo ehlala kuyo umntu ngamnye (umfanekiso 3.17). Ukubeka ezi ngqi kelelo ezimbini, i-Blumenstock kunye noogxa bavelise uqikelelo lobungakanani bendawo yokuthengiswa kobutyebi kwi-spranal granularity. Ngokomzekelo, banokuqikelela ubuncwane bomyinge kwiiyunithi ezingama-2,148 zaseRwanda (incinci yezona zincinci zokulawula kweli lizwe).

Ezi ziqikelelo zilingana njani ngokubhekiselele kumgangatho wobuhlwempu kule mimandla? Ngaphambi kokuba ndiphendule lo mbuzo, ndifuna ukugxininisa into yokuba kukho izizathu ezininzi zokungaqiniseki. Ngokomzekelo, ukukwazi ukwenza izibikezelo kwinqanaba ngalinye lalinomsindo (umfanekiso 3.17). Kwaye, mhlawumbi okubaluleke ngakumbi, abantu abanefowuni banokuthi bahluke ngokuthe ngqo kubantu abangenayo ifowuni. Ngako oko, i-Blumenstock kunye noogxa bangabandezeleka kwiintlobo zeempembelelo zokukhawuleza eziye zaphazamisa uphando lwe-1936 Literary Digest endichazile ngaphambili.

Ukuze ufumane umgangatho wemilinganiselo yazo, i-Blumenstock kunye noogxa kufuneka baqhathanise nenye into. Ngethamsanqa, malunga nexesha elifanayo kunye nokufunda kwabo, elinye iqela labaphandi liqhuba uphando oluntu lwentlalo e-Rwanda. Olunye uphando-oluyinxalenye yenkqubo yophando lweMveli kunye neNdawo ehloniphekileyo-yayinebhajethi enkulu kwaye isetyenziswe ngendlela ephakamileyo, iindlela zendabuko. Ngoko ke, uqikelelo oluvela kwi-Survey and Demographic Survey lucinga ukuba lucatshangelwe ngokulinganisela kwegolide. Xa uqikelelo lwababini luqhathaniswa, befana ngokufanayo (umfanekiso 3.17). Ngamanye amagama, ngokudibanisa idatha encinci yesaziso kunye neefowuni zeefowuni, i-Blumenstock kunye noogxa babenakho ukuvelisa uqikelelo olufana nalabo abavela kwiindlela eziqhelekileyo zegolide.

I-skeptic inokubona ezi ziphumo njengento edumalayo. Emva koko, enye indlela yokubukela kukuthi ngokusebenzisa idatha enkulu kunye nokufunda komatshini, i-Blumenstock kunye noogxa nabo bakwazi ukuvelisa ukuqikelelwa okunokwenziwa ngokunyaniseka kwiindlela ezikhoyo. Kodwa andicinga ukuba yindlela efanelekileyo yokucinga malunga nale sifundo ngezizathu ezibini. Okokuqala, uqikelelo oluvela kwiBlumenstock kunye noogxa lwabafundi lwaluba malunga namaxesha angama-10 ngokukhawuleza kwaye amaxesha angama-50 angabizi (xa ixabiso lilinganiswa ngokweendleko eziguquguqukayo). Njengoko ndaphikisana kwangaphambili kwesi sahluko, abaphandi bazinqabile iindleko kwiingozi zabo. Kule meko, umzekelo, ukuncipha okuphawulekayo kwiindleko kuthetha ukuba kunokuba kuqhutywe yonke imbalwa embalwa-njengokuba umgangatho woPhando lweMveli kunye nezeMpilo-olu hlobo lwenzululwazi lunokuqhutywa nyanga zonke, oluza kubonelela ngeenzuzo ezininzi kubaphandi kunye nomgaqo-nkqubo abenzi. Isizathu sesibini sokuba ungathathi ngcamango yembali kukuba le ngcaciso inikezela iresiphi eyisiseko enokukwenziwa kwiimeko ezininzi zophando. Le recipe inezithako ezimbini kuphela kunye namanyathelo amabini. Izithako zi (1) umthombo omkhulu wedatha obalaseleyo kodwa umxhesho (oko kukuthi, unabantu abaninzi kodwa ingengcaciso efunekayo malunga nomntu ngamnye) kunye (2) novavanyo oluluncinane kodwa lukhulu (okt, luphela abantu abambalwa, kodwa unayo ulwazi oluyidingayo ngalabo bantu). Ezi zithako zidibaniswa ngamanyathelo amabini. Okokuqala, kuba abantu kwimithombo yomibini yedatha, bakhe umzekelo wokufunda umatshini osebenzisa umthombo omkhulu wedatha ukuxela kwangaphambili iimpendulo zophando. Emva koko, sebenzisa lo mzekelo ukuba uphendule iimpendulo zemphenkethi ngamnye kumthombo omkhulu wedatha. Ngaloo ndlela, ukuba kukho umbuzo othi ufuna ukucela abantu abaninzi, khangela umthombo omkhulu wedatha kulabo bantu abangasetyenziselwa ukuqikelela impendulo yabo, nokuba ngaba unganandaba nomthombo omkhulu wedatha . Oko kukuthi, i-Blumenstock kunye noogxa abazange bakhathalele ngokukodwa malunga neirekhodi zeefowuni; Baye banakekela kuphela iirekhodi zeefowuni kuba babengasetyenziselwa ukuqikelela iimpendulo zeempendulo ezazinyamekelayo. Lo mbandela-kuphela wenzalo engqalileyo kwimithombo enkulu yedatha-yenza ukuba kuphakanyiswe ukubuza ezahlukeneyo kwi-intanethi ecelayo, endichazile ngaphambili.

Umzekeliso 3.16: Isikimu sesifundo seBlumenstock, iCadamuro, ne-On (2015). Iirekhodi zeefowuni kwinkampani yefowuni yaguqulwa yaba matrix ngomqolo omnye kumntu ngamnye kunye nekholomu enye yesici ngasinye (i-variable). Okulandelayo, abaphandi bakhela imodeli yokufunda egadiweyo ukuxela kwangaphambili iimpendulo zenzululwazi ukusuka kumatrix ngomntu. Emva koko, imodeli yokufunda egadiweyo yayisetyenziselwa ukuphazamisa impendulo yemphenyitha kubo bonke abathengi abayizigidi ezili-1.5. Kwakhona, abaphandi baqikelela ukuba indawo yokuhlala yokuhlala kuyo yonke i-1.5 million amakhasimende asekelwe kwiindawo zabo zeefowuni. Xa ezi zimbini ziqikelela-ubutyebi obuqikelelwayo kunye nendawo yokuhlala yokuhlala-ezidibeneyo, iziphumo zazifana nokuqikelelwa kwiSaveyi yeMveli kunye nezeMpilo, uphando oluqhelekileyo lwegolide (umfanekiso 3.17).

Umzekeliso 3.16: Blumenstock, Cadamuro, and On (2015) . Iifowuni zeefowuni ezivela kwifowuni yefowuni zaguqulwa zaba matrix ngomqolo omnye kumntu ngamnye kunye nekholomu enye kwento nganye (okokuthi iguqule). Okulandelayo, abaphandi bakhela imodeli yokufunda egadiweyo ukuxela kwangaphambili iimpendulo zenzululwazi ukusuka kumatrix ngomntu. Emva koko, imodeli yokufunda egadiweyo yayisetyenziselwa ukuphazamisa impendulo yemphenyitha kubo bonke abathengi abayizigidi ezili-1.5. Kwakhona, abaphandi baqikelela ukuba indawo yokuhlala yokuhlala kuyo yonke i-1.5 million amakhasimende asekelwe kwiindawo zabo zeefowuni. Xa ezi zimbini ziqikelela-ubutyebi obuqikelelwayo kunye nendawo yokuhlala yokuhlala-ezidibeneyo, iziphumo zazifana nokuqikelelwa kwiSaveyi yeMveli kunye nezeMpilo, uphando oluqhelekileyo lwegolide (umfanekiso 3.17).

Umzobo 3.17: Iziphumo ezivela eBlumenstock, iCadamuro, ne-On (2015). Kwinqanaba ngalinye, abaphandi bakwazi ukwenza umsebenzi ocacileyo ekuqikeleleni ubutyebi bomntu kwiirekhodi zabo zeefowuni. Uqikelelo lobutyebi bezinga lesithili kwii-30 zezithili zaseRwanda-ezisekelwe kwiingqikelelo zamanqanaba nendawo yokuhlala-zifana neziphumo ezivela kwi-Survey and Demographic Survey, uphando oluqhelekileyo lwegolide. Ichithwe kwi-Blumenstock, iCadamuro, ne-On (2015), amanani 1a no-3c.

Umzobo 3.17: Iziphumo ezivela Blumenstock, Cadamuro, and On (2015) . Kwinqanaba ngalinye, abaphandi bakwazi ukwenza umsebenzi ocacileyo ekuqikeleleni ubutyebi bomntu kwiirekhodi zabo zeefowuni. Uqikelelo lobutyebi bezinga lesithili kwii-30 zezithili zaseRwanda-ezisekelwe kwiingqikelelo zamanqanaba nendawo yokuhlala-zifana neziphumo ezivela kwi-Survey and Demographic Survey, uphando oluqhelekileyo lwegolide. Ichithwe kwi- Blumenstock, Cadamuro, and On (2015) , amanani 1a no-3c.

Ekugqibeleni, i-Blumenstock ephakanyisiweyo yokubuza idibene kunye nedatha yesaziso kunye nomthombo omkhulu wedatha ukuvelisa uqikelelo olufana nalabo abavela kwi-survey-standard standard. Lo mzekelo uphinde uchaze ezinye zee-trade-offs phakathi kokuphakanyiswa kokubuza kunye neendlela zokuhlola zendabuko. Ukuphuculwa kokucela ukuqikelela kwakukho ngexesha elifanelekileyo, elibi kakhulu, kunye ne-grranular. Kodwa, ngakolunye uhlangothi, akukabikho isiseko esiqinileyo solu hlobo lobunzima bokubuza. Lo mzekelo omnye awubonisi ukuba le ndlela iza kusebenza nini kwaye xa ingayi kuyenza, kwaye abaphandi abasebenzisa le ndlela bafanele bakhathazeke ngokukodwa malunga neengxaki ezibangelwa ngubani odibeneyo-kwaye ngubani ongabandakanywa-kumthombo wazo wedatha omkhulu. Ukongezelela, indlela yokubuza ephakanyisiweyo ayinayo iindlela ezilungileyo zokulinganisa ukungaqiniseki malunga noqikelelo lwayo. Inhlanhla, ukukhulisa ngokubanzi kunxibelelwano olunzulu kwimimandla emithathu emikhulu kwimilinganiselo-ukulinganisa kwamancinci (Rao and Molina 2015) , imputation (Rubin 2004) , kunye ne-post-stratification esekelwe kwimodeli (ehambisana ngqo noMnu P., indlela endichazwe ngaphambili kwisahluko) (Little 1993) . Ngenxa yezi zinto ezinzulu, ndikulindele ukuba ezininzi zeziseko zendlela yokukhulisa ngokukhawuleza ziya kuphuculwa.

Ekugqibeleni, ukuqhathanisa i-Blumenstock yokuqala kunye neyesibini kubonisa nesifundo esibalulekileyo malunga nophando lwezentlalo-zenzululwazi: isiqalo asiyikuphela. Oko kukuthi, amaxesha amaninzi, indlela yokuqala ayiyi kuba yinto engcono kakhulu, kodwa ukuba abaphandi baqhubeka besebenza, izinto zingaba ngcono. Okuqhelekileyo ngokubanzi, xa uvavanya iindlela ezintsha zophando loluntu kwixesha ledijithali, kubalulekile ukwenza uvavanyo olwenziwe ngokucacileyo: (1) Le nto isebenza kakuhle ngoku? kunye (2) Le nto iya kusebenza njani ngokuzayo njengoko iimeko zelizwe zitshintsha kwaye njengoko abaphandi baqwalasela ngakumbi ingxaki? Nangona abaphandi baqeqeshwa ukwenza uhlobo lokuqala lokuhlola, okwesibini kubaluleke kakhulu.