{"id":3093,"date":"2024-04-26T23:53:38","date_gmt":"2024-04-26T23:53:38","guid":{"rendered":"https:\/\/flatarmal.is\/?p=3093"},"modified":"2024-05-04T16:25:11","modified_gmt":"2024-05-04T16:25:11","slug":"ny-taekni-og-gamlar-gatur","status":"publish","type":"post","link":"https:\/\/flatarmal.is\/?p=3093","title":{"rendered":"N\u00fd t\u00e6kni og gamlar g\u00e1tur"},"content":{"rendered":"\n

Ing\u00f3lfur G\u00edslason<\/strong>. <\/p>\n\n\n\n

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Samr\u00e6\u00f0ur vi\u00f0 gervinemanda um vitneskjur\u00f6k\u00ferautir.<\/p>\n\n\n\n

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\u00deessi grein fjallar um:<\/p>\n\n\n\n

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  • \u00fea\u00f0 hvernig kennsla getur fali\u00f0 \u00ed s\u00e9r a\u00f0 beina athygli nemenda a\u00f0 tilteknum atri\u00f0um sem skipta m\u00e1li og f\u00e1 \u00feau til \u00feess a\u00f0 endurhugsa sv\u00f6r s\u00edn (\u00ed sta\u00f0 \u00feess a\u00f0 gefa \u00feeim svari\u00f0 e\u00f0a hva\u00f0 s\u00e9 \u201erangt\u201c vi\u00f0 svari\u00f0);<\/li>\n\n\n\n
  • \u00fea\u00f0 hvernig kennari getur nota\u00f0 gervigreind til a\u00f0 \u00e6fa sig \u00ed samr\u00e6\u00f0um vi\u00f0 gervinemanda;<\/li>\n\n\n\n
  • einkenni og e\u00f0li \u00ferauta sem \u00e9g nefni h\u00e9r vitneskjur\u00f6k\u00ferautir.<\/li>\n<\/ul>\n<\/div>\n<\/div>\n\n\n\n
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    \u00c9g gef fyrst d\u00e6mi um \u00feraut og r\u00e6\u00f0i lausn \u00e1 henni. \u00c9g beini svo athyglinni a\u00f0 samtali kennaranema vi\u00f0 spjallmenni um samskonar \u00feraut, \u00fear sem kennaraneminn leiddi spjallmenni\u00f0 a\u00f0 lausn \u00ferautarinnar. \u00cd gegnum samtali\u00f0 og umfj\u00f6llun um \u00ferautirnar kemur \u00ed lj\u00f3s hve mikilv\u00e6gt \u00fea\u00f0 er fyrir kennara a\u00f0 geta beint athygli nemanda a\u00f0 atri\u00f0um sem skipta m\u00e1li \u00ed verkefni \u00e1n \u00feess a\u00f0 taka hugsunina yfir.<\/p>\n\n\n\n

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    Ein af eftirl\u00e6tis\u00ferautum pabba m\u00edns, sem haf\u00f0i mikinn \u00e1huga \u00e1 st\u00e6r\u00f0fr\u00e6\u00f0i, var eftirfarandi:<\/p>\n\n\n\n

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    Prestur og dj\u00e1kni f\u00f3ru \u00fat a\u00f0 ganga og m\u00e6ttu \u00feremur m\u00f6nnum. \u00de\u00e1 spur\u00f0i prestur dj\u00e1kna: \u201eHve gamlir eru \u00feessir menn?\u201c \u201eMargfeldi af aldri \u00feeirra allra er 2450, en samanlag\u00f0ur aldur \u00feeirra jafn aldri y\u00f0ar.\u201c \u00de\u00e1 segir prestur: \u201e\u00deetta er ekki n\u00f3g.\u201c \u201eSatt er \u00fea\u00f0,\u201c segir dj\u00e1kni. \u201eEn \u00e9g er eldri en s\u00e1 sem er \u00feeirra elstur.\u201c \u00de\u00e1 gat prestur r\u00e1\u00f0i\u00f0 \u00ferautina. Hve gamlir eru presturinn, dj\u00e1kninn og mennirnir \u00fer\u00edr?<\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n\n\n\n

    H\u00e9r koma tv\u00e6r r\u00e1\u00f0leggingar. \u00cd fyrsta lagi er ekki r\u00e1\u00f0legt a\u00f0 lesa greinina \u00e1fram \u00e1n \u00feess a\u00f0 reyna vi\u00f0 \u00ferautina. \u00cd \u00f6\u00f0ru lagi er ekki r\u00e1\u00f0legt a\u00f0 reyna a\u00f0 leysa \u00ferautina \u00e1n \u00feess a\u00f0 hafa skriff\u00e6ri vi\u00f0 h\u00f6ndina og \u00fea\u00f0 skemmir ekki gildi \u00ferautarinnar a\u00f0 nota reikniv\u00e9l. Ef \u00fe\u00fa hefur \u00e1huga \u00e1 efni \u00feessarar greinar \u00fe\u00e1 er mikilv\u00e6gt a\u00f0 reyna vi\u00f0 \u00ferautina (og a\u00f0rar \u00ferautir \u00ed greininni) sj\u00e1lf til a\u00f0 \u00f6\u00f0last beina reynslu af efninu. \u00cd n\u00e6stu efnisgrein er lausn \u00ferautarinnar l\u00fdst og h\u00e9r er \u00fev\u00ed s\u00ed\u00f0asta t\u00e6kif\u00e6ri\u00f0 til a\u00f0 reyna vi\u00f0 \u00ferautina.<\/p>\n\n\n\n

    Vi\u00f0 fyrstu s\u00fdn \u00e1 \u00ferautina er lj\u00f3st a\u00f0 vi\u00f0 ver\u00f0um a\u00f0 finna \u00ferj\u00e1r t\u00f6lur \u00feannig a\u00f0 margfeldi \u00feeirra s\u00e9 2450. Sem betur fer er h\u00e6gt a\u00f0 frum\u00fe\u00e1tta n\u00e1tt\u00farlegar t\u00f6lur \u00e1 einkv\u00e6man h\u00e1tt og komast a\u00f0 \u00fev\u00ed a\u00f0 2450 = 2 x 5 x 5 x 7 x 7. \u00deetta hj\u00e1lpar okkur a\u00f0 skr\u00e1 alla m\u00f6guleika, en fyrirfram s\u00e9\u00f0 g\u00e6tu l\u00edka einn e\u00f0a fleiri mannanna \u00feriggja veri\u00f0 eins \u00e1rs, sem fj\u00f6lgar m\u00f6guleikunum. Nokkrir m\u00f6guleikar eru \u00fe\u00e1 2 x 25 x 49, 1 x 50 x 49 og 10 x 35 x 7. \u00dea\u00f0 eru reyndar nokku\u00f0 margir m\u00f6guleikar, 21 alls. <\/p>\n\n\n\n

    En lesum n\u00fa a\u00f0eins \u00e1fram. Presturinn f\u00e6r a\u00f0 vita samanlag\u00f0an aldur mannanna (hann \u00feekkir sinn eigin aldur) en \u00fea\u00f0 dugar honum ekki til a\u00f0 leysa \u00ferautina. \u00dea\u00f0 hl\u00fdtur a\u00f0 \u00fe\u00fd\u00f0a a\u00f0 einhverjir m\u00f6guleikanna \u00e1 margfeldinu gefi s\u00f6mu summuna. \u00dea\u00f0 er ekkert anna\u00f0 a\u00f0 gera en a\u00f0 reikna allar summurnar. \u00de\u00e1 kemur \u00ed lj\u00f3s a\u00f0 a\u00f0eins ein summa er endurtekin, 5 + 10 + 49 og 7 + 7 + 50 gefa samtals 64. Vi\u00f0 vitum \u00fe\u00e1 a\u00f0 presturinn er 64 \u00e1ra. <\/p>\n\n\n\n

    En hvernig skerum vi\u00f0 n\u00fa \u00far um aldur hinna? Vi\u00f0 f\u00e1um a\u00f0 vita a\u00f0 dj\u00e1kninn s\u00e9 eldri en s\u00e1 sem er \u00feeirra elstur en \u00fe\u00e6r uppl\u00fdsingar vir\u00f0ast ekki hj\u00e1lpa mj\u00f6g miki\u00f0 vi\u00f0 fyrstu s\u00fdn. G\u00e6ti dj\u00e1kninn ekki veri\u00f0 til d\u00e6mis sextugur? \u00dea\u00f0 \u00e1 vi\u00f0 um hvora tveggja m\u00f6guleikanna. En \u00fe\u00e1 kemur til a\u00f0 vi\u00f0 f\u00e1um a\u00f0 vita a\u00f0 presturinn gat r\u00e1\u00f0i\u00f0 g\u00e1tuna og fyrst hann gat r\u00e1\u00f0i\u00f0 g\u00e1tuna \u00fe\u00e1 hl\u00fdtur dj\u00e1kninn a\u00f0 vera n\u00e1kv\u00e6mlega 50 \u00e1ra. Ef hann v\u00e6ri yngri k\u00e6mi \u00fea\u00f0 ekki heim og saman vi\u00f0 uppl\u00fdsingarnar en ef hann v\u00e6ri eldri hef\u00f0i presturinn ekki geta\u00f0 r\u00e1\u00f0i\u00f0 g\u00e1tuna. Svo eina m\u00f6gulega ni\u00f0ursta\u00f0an er a\u00f0 mennirnir s\u00e9u 5, 10 og 49 \u00e1ra, dj\u00e1kninn 50 \u00e1ra og presturinn 64 \u00e1ra.<\/p>\n\n\n\n

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    \u00derautin um aldur mannanna er d\u00e6mi um vitneskjur\u00f6k\u00feraut (e. epistemic logic puzzle). Vitneskjur\u00f6k\u00feraut einkennist af \u00fev\u00ed a\u00f0 h\u00fan felur \u00ed s\u00e9r a\u00f0 draga r\u00f6kr\u00e9ttar \u00e1lyktanir um og \u00fat fr\u00e1 vitneskju<\/em>, \u00fear me\u00f0 tali\u00f0 eigin vitneskju og vitneskju annarra, og s\u00e9r \u00ed lagi vitneskju um vitneskju<\/em> e\u00f0a vitneskju um skort \u00e1 vitneskju (Hamkins, 2019, leturbreytingar m\u00ednar). <\/p>\n\n\n\n

    \u00cd \u00ferautinni dr\u00f3gum vi\u00f0 til d\u00e6mis \u00e1lyktun \u00fat fr\u00e1 \u00feeirri vitneskju okkar a\u00f0 presturinn vissi sinn eigin aldur og, sem er erfi\u00f0ara a\u00f0 taka eftir, a\u00f0 s\u00fa vitneskja dug\u00f0i honum ekki<\/em> til a\u00f0 leysa g\u00e1tuna. Svo dr\u00f3gum vi\u00f0 \u00e1lyktun \u00fat fr\u00e1 \u00feeirri vitneskju a\u00f0 presturinn vissi aldur dj\u00e1knans og (\u00fea\u00f0 sem er erfi\u00f0ara a\u00f0 taka eftir) a\u00f0 s\u00fa vitneskja hans dug\u00f0i<\/em> til a\u00f0 leysa g\u00e1tuna \u00fat fr\u00e1 v\u00edsbendingunni um a\u00f0 hann v\u00e6ri eldri en elsti ma\u00f0urinn sem \u00feeir m\u00e6ttu. Vi\u00f0 \u00feurfum sem sagt a\u00f0 n\u00fdta okkur uppl\u00fdsingar um \u00fea\u00f0 hva\u00f0a \u00e1lyktanir pers\u00f3nur s\u00f6gunnar g\u00e1tu dregi\u00f0 \u00fat fr\u00e1 sinni vitneskju.<\/p>\n\n\n\n

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    En hva\u00f0 hefur \u00feessi gamla \u00feraut a\u00f0 gera me\u00f0 gervigreind og \u00fea\u00f0 a\u00f0 beina athygli nemenda a\u00f0 einhverju? \u00cd n\u00e1mskei\u00f0inu St\u00e6r\u00f0fr\u00e6\u00f0in\u00e1m og -kennsla \u00ed efri bekkjum grunnsk\u00f3la<\/em>, vori\u00f0 2023, setti \u00e9g \u00fea\u00f0 verkefni fyrir kennaranema a\u00f0 leggja st\u00e6r\u00f0fr\u00e6\u00f0iverkefni fyrir ChatGPT spjallmenni\u00f0 og lei\u00f0a \u00fea\u00f0 \u00ed \u00e1tt a\u00f0 g\u00f3\u00f0ri lausn. \u00deegar spjallmenni\u00f0 er \u00ed hlutverki nemanda kalla \u00e9g \u00fea\u00f0 h\u00e9r eftir gervinemanda. Eitt \u00e1hugaver\u00f0asta \u201esamtali\u00f0\u201c \u00e1tti s\u00e9r sta\u00f0 um vitneskjur\u00f6k\u00feraut \u00fear sem kennarinn reyndi \u00edtreka\u00f0 a\u00f0 beina (gervi)athygli gervinemandans a\u00f0 atri\u00f0um sem \u00e1ttu a\u00f0 f\u00e1 hann til a\u00f0 endursko\u00f0a sv\u00f6r s\u00edn og n\u00e1lgun.<\/p>\n\n\n\n

    Verkefni\u00f0 hlj\u00f3\u00f0ar svo: \u00cd veislu heyrir\u00f0u gest spyrja um aldur barna gestgjafans sem \u00e1 \u00ferj\u00fa b\u00f6rn. Gestgjafinn segir gestinum a\u00f0 margfeldi aldurs barna sinna s\u00e9 72 en samanlag\u00f0ur aldur \u00feeirra s\u00e9 sama tala og n\u00fameri\u00f0 \u00e1 h\u00fasi gestsins. N\u00fa veit gesturinn auglj\u00f3slega sitt eigi\u00f0 h\u00fasn\u00famer, en eftir a\u00f0 hafa hugsa\u00f0 \u00ed sm\u00e1 stund, bi\u00f0ur hann gestgjafann um frekari uppl\u00fdsingar til a\u00f0 geta komist a\u00f0 aldrinum. Gestgjafinn segir \u00fe\u00e1 a\u00f0 elsta barni hans \u00feyki jar\u00f0arberja\u00eds g\u00f3\u00f0ur. \u00de\u00e1 gat gesturinn sagt til um aldur barnanna. \u00de\u00f3tt \u00fe\u00fa vitir ekki h\u00fasn\u00famer gestsins, hefur \u00fe\u00fa fengi\u00f0 n\u00e6gar uppl\u00fdsingar. Gerum r\u00e1\u00f0 fyrir a\u00f0 aldur s\u00e9 alltaf gefinn upp \u00ed heilum \u00e1rum. Hversu gamalt er elsta barni\u00f0?<\/p>\n\n\n\n

    Lesendur sj\u00e1 v\u00e6ntanlega l\u00edkindin me\u00f0 fyrstu \u00ferautinni. Lykilatri\u00f0i er a\u00f0 beina athyglinni a\u00f0 vitneskju gestsins \u00ed \u00ferautinni, hver h\u00fan g\u00e6ti veri\u00f0 og hva\u00f0a \u00e1lyktanir hann gat dregi\u00f0 af henni og hva\u00f0a \u00e1lyktanir vi\u00f0 getum dregi\u00f0 af \u00fev\u00ed. \u00dea\u00f0 t\u00f3k 13 umfer\u00f0ir a\u00f0 f\u00e1 gervinemandann til a\u00f0 finna svari\u00f0, og s\u00fdndi kennaraneminn \u00ed \u00fev\u00ed samtali mikla \u00fatsj\u00f3narsemi og \u00feolinm\u00e6\u00f0i. \u00cd fyrstu tilraun bj\u00f3 gervinemandinn til lista yfir nokkra m\u00f6guleika \u00e1 a\u00f0 f\u00e1 \u00fat 72 me\u00f0 margfeldi \u00feriggja talna en birti s\u00ed\u00f0an setningar sem l\u00edta \u00e1 yfirbor\u00f0inu \u00fat fyrir a\u00f0 geta veri\u00f0 vi\u00f0eigandi en eru \u00feegar n\u00e1nar er a\u00f0 g\u00e1\u00f0 t\u00f3m steypa, og endar til d\u00e6mis \u00e1 \u00fev\u00ed a\u00f0 segja:<\/p>\n\n\n\n

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    Gervinemandi: Ef summan v\u00e6ri 14 er bara einn m\u00f6guleiki: 2 + 2 + 9. Elsta barn gestgjafans hl\u00fdtur a\u00f0 vera 9 \u00e1ra \u00fev\u00ed a\u00f0 \u00fea\u00f0 er eini aldurinn sem kemur fyrir \u00ed einungis einni samsetningunni.<\/p>\n<\/div>\n<\/div>\n\n\n\n

    \u00deessu svarar kennaraneminn me\u00f0 \u00fev\u00ed a\u00f0 reyna a\u00f0 beina athygli spjallmennisins a\u00f0 vitneskju gestsins \u00ed \u00ferautinni:<\/p>\n\n\n\n

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    Kennaranemi: Reyndu a\u00f0 hugsa um \u00fea\u00f0 a\u00f0 gesturinn \u00feurfti \u00e1 annarri v\u00edsbendingu a\u00f0 halda. \u00dea\u00f0 segir okkur a\u00f0 \u00fe\u00f3 a\u00f0 gesturinn viti h\u00fasn\u00fameri\u00f0 \u00feurfti hann samt \u00e1 annarri v\u00edsbendingu a\u00f0 halda.<\/p>\n<\/div>\n<\/div>\n\n\n\n

    Gervinemandinn svarar \u00feessu fyrst vel og segir a\u00f0 \u00feetta \u00fe\u00fd\u00f0i \u00fe\u00e1 a\u00f0 \u00fea\u00f0 hlj\u00f3ti a\u00f0 vera einhverjar fleiri en ein aldurssamsetning m\u00f6guleg \u00fat fr\u00e1 margfeldinu. Svo fer hann \u00fat af sporinu og missir yfirs\u00fdn um alla m\u00f6guleikana og vinnur \u00fat fr\u00e1 m\u00f6guleikum sem ganga ekki upp \u00fat fr\u00e1 fyrstu uppl\u00fdsingunum, og dregur svo \u00fe\u00e1 \u00e1lyktun a\u00f0 elsta barni\u00f0 s\u00e9 sex \u00e1ra og hin s\u00e9u sex \u00e1ra og tveggja \u00e1ra (j\u00e1 \u00fe\u00fa last r\u00e9tt).<\/p>\n\n\n\n

    Kennaraneminn tekur tv\u00e6r umfer\u00f0ir eftir \u00feetta til a\u00f0 f\u00e1 gervinemandann til \u00feess a\u00f0 gera t\u00e6mandi og r\u00e9ttan lista yfir m\u00f6guleika og f\u00e1 hann til \u00feess a\u00f0 segja a\u00f0 b\u00f6rnin s\u00e9u \u00f6rugglega anna\u00f0hvort 3, 3 og 8 \u00e1ra e\u00f0a 2, 6 og 6 \u00e1ra, \u00fev\u00ed \u00feeir m\u00f6guleikar gefa s\u00f6mu summuna, 14 (og engar a\u00f0rar tv\u00e6r samsetningar gefa sameiginlega summu). \u00de\u00e1 taka vi\u00f0 sex umfer\u00f0ir \u00ed vi\u00f0b\u00f3t \u00fear sem gervinemandinn fer \u00ed marga skr\u00edtna hringi me\u00f0 \u00fea\u00f0 hvort annar tv\u00edburinn s\u00e9 eldri en hinn.<\/p>\n\n\n\n

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    Gervinemandi: Ef tv\u00edburarnir eru elstu b\u00f6rnin, \u00fe\u00e1 vitum vi\u00f0 a\u00f0 annar tv\u00edburinn er eldri en hinn, en vi\u00f0 vitum ekki hvor. Hins vegar, ef barni\u00f0 sem er ekki tv\u00edburi er yngst, \u00fe\u00e1 ver\u00f0ur eldri tv\u00edburinn a\u00f0 vera s\u00e1 sem \u00feykir jar\u00f0arberja\u00edsinn g\u00f3\u00f0ur. \u00deetta er vegna \u00feess a\u00f0 gestgjafinn hef\u00f0i ekki v\u00edsa\u00f0 til yngri tv\u00edburans sem elsta barni\u00f0 ef til er eldri tv\u00edburi. \u00deess vegna getum vi\u00f0 \u00ed \u00feessu tilviki \u00e1lykta\u00f0 a\u00f0 elsta barni\u00f0 s\u00e9 eldri tv\u00edburinn, og hinn tv\u00edburinn og barni\u00f0 sem er ekki tv\u00edburi s\u00e9u b\u00e6\u00f0i 6 \u00e1ra.<\/p>\n\n\n\n

    Kennaranemi: Hva\u00f0 ef \u00e9g segi \u00fe\u00e9r a\u00f0 vi\u00f0 l\u00edtum alltaf svo \u00e1 a\u00f0 tv\u00edburar s\u00e9u jafn gamlir?<\/p>\n<\/div>\n<\/div>\n\n\n\n

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    Taki\u00f0 eftir \u00fev\u00ed a\u00f0 \u00fearna beindi kennaraneminn athyglinni a\u00f0 atri\u00f0i sem skiptir m\u00e1li, \u00e1n \u00feess a\u00f0 gefa lausnina e\u00f0a segja beint \u00fat hva\u00f0 s\u00e9 rangt vi\u00f0 svar gervinemandans. \u00cd t\u00edundu umfer\u00f0 tekur kennaraneminn svo saman fyrir gervinemandann a\u00f0 m\u00f6guleikarnir s\u00e9u 3, 3 og 8, og 2, 6 og 6 og beinir athyglinni enn a\u00f0 v\u00edsbendingunni:<\/p>\n<\/div>\n<\/div>\n\n\n\n

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    Kennaranemi: Vi\u00f0 vitum \u00fat fr\u00e1 v\u00edsbendingunni um \u00edsinn a\u00f0 eitt barn er elsta barni\u00f0, svo \u00ed hva\u00f0a m\u00f6guleika er pott\u00fe\u00e9tt elsta barn?<\/p>\n<\/div>\n<\/div>\n\n\n\n

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    \u00deetta dugar ekki alveg til \u00feanga\u00f0 til a\u00f0 \u00ed lokin spyr kennaraneminn einfaldrar spurningar.<\/p>\n<\/div>\n<\/div>\n\n\n\n

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    Kennaranemi: \u00c9g held a\u00f0 \u00fe\u00fa s\u00e9rt a\u00f0 ofhugsa \u00feetta, hve gamalt er elsta barni\u00f0 ef \u00fea\u00f0 eru \u00ferj\u00fa b\u00f6rn sem eru 3, 3, og 8 \u00e1ra?<\/p>\n<\/div>\n<\/div>\n\n\n\n

    \n
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    Eftir \u00feetta gat gervinemandinn gert nokku\u00f0 g\u00f3\u00f0a grein fyrir lausninni \u00ed heild sinni, \u00feegar hann var be\u00f0inn um \u00fea\u00f0. H\u00e9r getum vi\u00f0 teki\u00f0 eftir \u00fev\u00ed a\u00f0 vandr\u00e6\u00f0i gervinemandans voru \u00e1 \u00feessum kafla fr\u00e1brug\u00f0in vandr\u00e6\u00f0um d\u00e6miger\u00f0s mannlegs nemanda, sem hef\u00f0i ekki \u00feurft langar umr\u00e6\u00f0ur til a\u00f0 fallast \u00e1 \u00fea\u00f0 \u00fe\u00e1 forsendu a\u00f0 tv\u00edburar teljist jafn gamlir og l\u00edklega ekki heldur langar umr\u00e6\u00f0ur til a\u00f0 \u00e1tta sig \u00e1 \u00fev\u00ed a\u00f0 v\u00edsbendingin feli \u00ed s\u00e9r a\u00f0 eitt barni\u00f0 hlj\u00f3ti a\u00f0 vera eldra \u00ed \u00e1rum tali\u00f0 en hin tv\u00f6. <\/p>\n\n\n\n

    \u00c1 hinn b\u00f3ginn er l\u00edklegt a\u00f0 margir mannlegir nemendur g\u00e6tu haft gagn af \u00fev\u00ed a\u00f0 athygli \u00feeirra s\u00e9 beint a\u00f0 atri\u00f0um eins og \u00fev\u00ed a\u00f0 gesturinn \u00feurfti \u00e1 annarri v\u00edsbendingu a\u00f0 halda til a\u00f0 geta \u00e1lykta\u00f0 um aldur barnanna. \u00deannig var samtali\u00f0 vi\u00f0 gervinemandann t\u00e6kif\u00e6ri til \u00feess a\u00f0 \u00e6fa n\u00e1kv\u00e6mlega \u00feessa samr\u00e6\u00f0uath\u00f6fn: a\u00f0 beina athygli nemanda a\u00f0 atri\u00f0um sem skipta m\u00e1li og f\u00e1 \u00feau til \u00feess a\u00f0 endurhugsa sv\u00f6r s\u00edn.<\/p>\n\n\n\n

    \n\n\n\n

    Spjallmenni eiga erfitt me\u00f0 a\u00f0 \u201e\u00e1tta sig\u201c \u00e1 vitneskjur\u00f6k\u00ferautum, nema ef til vill a\u00f0 \u00fe\u00e6r s\u00e9u vel \u00feekktar og bornar upp \u00e1 mj\u00f6g svipa\u00f0an h\u00e1tt og \u00fe\u00e6r hafa veri\u00f0 settar fram \u00ed textum. Munum a\u00f0 spjallmenni b\u00faa til s\u00edn sv\u00f6r \u00e1 v\u00e9lr\u00e6nan h\u00e1tt \u00fat fr\u00e1 l\u00edkinda\u00fatreikningum sem byggja \u00e1 gr\u00ed\u00f0arlegu magni af texta af netinu. Ef \u00ferautinni hefur veri\u00f0 svara\u00f0 \u00e1 m\u00f6rgum vefs\u00ed\u00f0um er l\u00edklegt a\u00f0 spjallmenni\u00f0 einfaldlega \u201e\u00feekki\u201c \u00ferautina aftur, ef h\u00fan er sett fram or\u00f0r\u00e9tt. En \u00f6rlitlar breytingar \u00e1 vitneskjur\u00f6k\u00ferautum geta \u201erugla\u00f0\u201c spjallmenni\u00f0 \u2013 sem er betra ef \u00e6tlunin er a\u00f0 \u00e6fa sig a\u00f0 tala vi\u00f0 raunverulegan nemanda.<\/p>\n\n\n\n

    \u00derautirnar sem kynntar hafa veri\u00f0 \u00ed \u00feessari grein eru ekki bara um r\u00f6kr\u00e9ttar \u00e1lyktanir um og \u00fat fr\u00e1 vitneskju. \u00de\u00e6r eru l\u00edka um talnafr\u00e6\u00f0i. A\u00f0 lokum er h\u00e9r ein \u00feraut \u00fear sem minni \u00e1hersla er \u00e1 st\u00e6r\u00f0fr\u00e6\u00f0i (en \u00fe\u00f3 koma t\u00f6lur vi\u00f0 s\u00f6gu).<\/p>\n\n\n\n

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    \u00c9g hv\u00edsla\u00f0i t\u00f6lum a\u00f0 L\u00edsu og Bjarna. Hvort \u00feeirra f\u00e9kk a\u00f0 heyra eina n\u00e1tt\u00farlega t\u00f6lu (heila j\u00e1kv\u00e6\u00f0a t\u00f6lu). \u00deau fengu a\u00f0 vita a\u00f0 t\u00f6lurnar \u00feeirra v\u00e6ru \u00f3l\u00edkar. \u00c9g spur\u00f0i \u00feau svo hvort \u00feau vissu hvort \u00feeirra hef\u00f0i fengi\u00f0 st\u00e6rri t\u00f6lu. \u00de\u00e1 t\u00f3k vi\u00f0 eftirfarandi samtal:<\/p>\n<\/div>\n\n\n\n

    <\/div>\n<\/div>\n\n\n\n
    \n
    <\/div>\n\n\n\n
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    L\u00edsa: \u00c9g veit \u00fea\u00f0 ekki.
    Bjarni: \u00c9g veit \u00fea\u00f0 ekki heldur.
    L\u00edsa: \u00c9g veit \u00fea\u00f0 ekki enn\u00fe\u00e1.
    Bjarni: Og \u00e9g stend alveg \u00e1 gati.
    L\u00edsa: N\u00fa, fyrst \u00fe\u00fa segir \u00fea\u00f0, \u00fe\u00e1 veit \u00e9g allt \u00ed einu hvort okkar er me\u00f0 st\u00e6rri t\u00f6lu!
    Bjarni: \u00cd alv\u00f6ru? \u00de\u00e1 veit \u00e9g b\u00e1\u00f0ar t\u00f6lurnar!
    L\u00edsa: Og \u00fe\u00e1 veit \u00e9g l\u00edka b\u00e1\u00f0ar t\u00f6lurnar! <\/p>\n<\/div>\n\n\n\n

    <\/div>\n<\/div>\n\n\n\n
    \n
    <\/div>\n\n\n\n
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    Hva\u00f0a t\u00f6lum hv\u00edsla\u00f0i \u00e9g a\u00f0 \u00feeim?<\/p>\n<\/div>\n\n\n\n

    <\/div>\n<\/div>\n\n\n\n
    \n\n\n\n

    Heimildir<\/strong><\/p>\n\n\n\n

    Hamkins, J. D. (25. september 2019). I know that you know that I know that you know\u2026. Oxford, October 2019. Joel David Hamkins<\/em>. https:\/\/jdh.hamkins.org\/i-know-that-you-know-that-i-know-that-you-know-oxford-october-2019\/<\/a><\/p>\n\n\n\n

    \n<\/div>\n<\/div>\n\n\n\n
    \"\"<\/figure>
    \n

    Ing\u00f3lfur G\u00edslason, a\u00f0junkt vi\u00f0 <\/strong>
    Menntav\u00edsindasvi\u00f0 H\u00cd<\/strong><\/p>\n<\/div><\/div>\n\n\n\n

    \n\n\n\n
    \n\n\n\n
    \n
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    \"\"<\/figure>\n<\/div>\n<\/div>\n\n\n\n
    \n","protected":false},"excerpt":{"rendered":"

    Ing\u00f3lfur G\u00edslason. Samr\u00e6\u00f0ur vi\u00f0 gervinemanda um vitneskjur\u00f6k\u00ferautir. \u00deessi grein fjallar um: \u00c9g gef fyrst d\u00e6mi um \u00feraut og r\u00e6\u00f0i lausn \u00e1 henni. \u00c9g beini svo athyglinni a\u00f0 samtali kennaranema vi\u00f0 spjallmenni um samskonar \u00feraut, \u00fear sem kennaraneminn leiddi spjallmenni\u00f0 a\u00f0 lausn \u00ferautarinnar. \u00cd gegnum samtali\u00f0 og umfj\u00f6llun um \u00ferautirnar kemur \u00ed lj\u00f3s hve mikilv\u00e6gt \u00fea\u00f0…<\/p>\n","protected":false},"author":1,"featured_media":3108,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1],"tags":[],"class_list":["post-3093","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-uncategorized"],"_links":{"self":[{"href":"https:\/\/flatarmal.is\/index.php?rest_route=\/wp\/v2\/posts\/3093","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/flatarmal.is\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/flatarmal.is\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/flatarmal.is\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/flatarmal.is\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=3093"}],"version-history":[{"count":25,"href":"https:\/\/flatarmal.is\/index.php?rest_route=\/wp\/v2\/posts\/3093\/revisions"}],"predecessor-version":[{"id":3290,"href":"https:\/\/flatarmal.is\/index.php?rest_route=\/wp\/v2\/posts\/3093\/revisions\/3290"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/flatarmal.is\/index.php?rest_route=\/wp\/v2\/media\/3108"}],"wp:attachment":[{"href":"https:\/\/flatarmal.is\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=3093"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/flatarmal.is\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=3093"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/flatarmal.is\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=3093"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}