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RABIN TAKARDUN EINSTEIN SUNA SAMUN KASHI 1.5% NA AMBATONSA

Yaya rashin daidaito yake a aikin kimiyya? Klaus M. Frahm da Dima L. Shepelyansky, masana kimiyyar lissafi a Laboratoire de Physique Théorique a Toulouse (CNRS), sun aro akwatin kayan aikin masana tattalin arziki don gano hakan.

Arziki, amma a cikin ambato

Masana tattalin arziki suna bayyana rashin daidaito da Lorenz curve: a jera gidaje daga mafi talauci zuwa mafi arziki kuma a zana wane kaso na jimillar arziki kowane rukuni na jama’a ke riƙe da shi. Gini coefficient yana taƙaita layin: 0 yana nufin cikakken daidaito, 1 yana nufin gida ɗaya ya mallaki komai. Takardar ta ambaci duniya gaba ɗaya a 2021: Gini na 0.843, inda rabin matalauta ke mallakar kashi 2% na arziki kuma kashi 10% na sama ke mallakar kashi 75%.

Marubutan sun musanya arziki da ambato. Ga masanin kimiyya, kowace takarda gida ce kuma ambatonta shi ne arzikinta. Ga jami’a, kowane mai bincike da ke da alaƙa da ita gida ne kuma jimillar ambatonsa shi ne arzikinsa. Bayanan sun fito ne daga Google Scholar, an tattara su tsakanin 11 da 17 ga Satumba 2026.

Ayyuka ashirin da biyar

Sun zaɓi masana kimiyya 25: waɗanda suka ci kyautar Nobel 15, daga Albert Einstein da R. Feynman zuwa M. Devoret, wanda ya ci kyautar kimiyyar lissafi a 2025, tare da shugabannin kimiyyar hanyoyin sadarwa (network science), ka’idar chaos, kwamfutar quantum da koyon na’ura (machine learning). Don kwatanci, sun kuma haɗa da wani abokin aikinsu daga ɗakin bincikensu da kuma kansu.

  • Einstein: takardu 498 da aka ambata, ambato 200,742, Gini 0.883. Rabin takardunsa da aka fi ƙarancin ambato suna tara kashi 1.5% kawai na ambatonsa; kashi 10% na sama suna tara kashi 84%. Takardarsa da aka fi ambato ita ce ta biyu-biyun Einstein-Podolsky-Rosen, da ambato 28,657, adadin da marubutan suka ce haɓakar bayanan quantum (quantum information) ta ƙara masa.
  • Feynman: takardu 126, Gini 0.850.
  • Ayyukan da suka fi rashin daidaito na Reka Albert, K. Novoselov da Y. LeCun ne (Gini daga 0.91 zuwa 0.93). Ga LeCun, takardu uku da aka fi ambato kaɗai suna ɗaukar kusan rabin dukkan ambatonsa.
  • A tsakanin waɗanda suka ci kyautar Nobel 15, matsakaicin Gini shi ne 0.81: rabin ƙasa na takardunsu yana tara kashi 2.7% na ambato, kashi 10% na sama yana tara kashi 71% kuma kashi 1% na sama yana tara kashi 31%. Wannan, marubutan sun lura, yana kama da rashin daidaiton arzikin duniya sosai.

Marubutan biyu da abokin aikinsu, masu ambato daga dubu kaɗan zuwa dubu goma sha biyar, suna da ƙananan Gini, kusan 0.6. Gaba ɗaya, duk da haka, takardar ba ta sami wata alaƙa kai tsaye tsakanin yawan ambaton da mutum ke da shi da yawan rashin daidaitonsa ba.

Jami’o’i a matsayin ƙananan ƙasashe

Ga jami’o’i takwas, marubutan sun ɗauki kowane mai bincike da ya rubuta cibiyar a Google Scholar mai aƙalla ambato 500, don barin ɗalibai da masu bincike bayan digirin digirgir (postdocs) waɗanda ke zuwa da ambaton da suka samu a wani wuri.

Princeton ita ce mafi rashin daidaito, da Gini na 0.802: rabin masu bincikenta 2,454 suna samar da kashi 2.6% kawai na ambatonta, kuma kashi 10% na sama suna samar da kashi 69%. Sunan da aka fi ambato a cikinta shi ne Daniel Kahneman, wanda aka san shi da prospect theory, da ambato 666,949; Einstein yana na tara. Cambridge da ETH Zurich suna biye a 0.775, yayin da makarantun Paris biyu da ke cikin samfurin, ENS da ESPCI, da Technion na Isra’ila suke kusan 0.68. A matsakaici, kashi ɗaya cikin goma na masu binciken jami’a suna samar da kusan kashi 61% na ambatonta.

Taruwa, daga kimiyyar lissafi zuwa al’umma

Marubutan sun daidaita dukkan waɗannan layuka da wani samfuri da suka gabatar a baya don arziki, bisa ga Rayleigh-Jeans distribution daga kimiyyar lissafin raƙuman ruwa da zafi. A ƙaramin jimillar kuzari, yawancin yiwuwa yana “taruwa” (condenses) cikin mafi ƙasƙancin yanayi: babban rinjaye na matalauta da ƙaramin ƙoli na masu iko kaɗan (oligarchic). Samfurinsu ya dace ba da Lorenz curves kaɗai ba har ma da dogayen wutsiyoyin takardun da aka fi ambato, a kan matakai da yawa na girma, abin da suke ganin goyon baya ne mai ƙarfi.

Sun yarda cewa hujjojinsu na dalilin da ya sa takardu ko masu bincike za su yi hulɗa ta wannan hanya har yanzu na kintace ne (heuristic), kuma Google Scholar yana dogara ga alaƙar cibiya da masu bincike suka bayyana da kansu. Wani rumbun bayanan ambato mafi tsauri, in ji su, zai iya ƙara fayyace hoton, kuma suna fatan tunanin taruwa iri ɗaya zai sami amfani a wasu sassa na kimiyyar lissafin al’umma (social physics).