Emhlabeni wezinombolo, uhlala uhlangabezana namaphethini amangalisayo angamangalisa futhi akhanyisele. Enye ilukuluku elinjalo uMthetho kaBenford, owaziwa nangokuthi uMthetho Wedijithi Yokuqala. Lesi senzakalo sezibalo sichaza ukusatshalaliswa kwemvamisa kwamadijithi okuqala kumasethi amaningi edatha yangempela futhi sinikeza imininingwane ethakazelisayo mayelana nemvelo yezinombolo njengoba zenzeka endaweni yethu.
Umthetho ka-Benford, oqanjwe ngesazi sesayensi yemvelo uFrank Benford owaphinde wawuthola ngo-1938, uwumbono othakazelisayo: kumasethi amaningi edatha yemvelo, ezomnotho neyesayensi, idijithi yokuqala yezinombolo ayisakazwa ngokulinganayo. Kunalokho, idijithi \(1\) ivela njengedijithi yokuqala kaningi kunezinye izinombolo. Ngokucacile, amathuba okuthi inombolo iqale ngedijithi enikeziwe \(d\) anikezwe ifomula
$$P(d) = \log_{10}(1 + \frac{1}{d})$$
lapho \(d\) enye yamadijithi \(1\) kuya ku \(9\) . Le fomula ithi, isibonelo, idijithi \(1\) ivela njengedijithi yokuqala mayelana \(30,1 \%\) yesikhathi, kuyilapho idijithi \(9\) ivela kuphela mayelana \(4,6 \%\) isikhathi siyenzeka.
Umthetho ungachazwa ngokushintshashintsha kwesikali kwama-logarithms. Uma ubheka izinombolo ezivela kuma-oda ahlukene wobukhulu futhi uzihlele ngesilinganiso se-logarithmic, amadijithi ambalwa okuqala azosatshalaliswa njengoba kubikezelwe umthetho ka-Benford. Lokhu kungenxa yokuthi isikhala se-logarithmic phakathi kwamandla amabili alandelanayo okuthi \(10\) (isb. phakathi kuka-10 no \(100\) noma phakathi kuka \(100\) kanye \(1000\) ) siba sikhulu uma izinombolo ziyi-Nombolo. Lokhu kusho ukuthi amadijithi amancane okuqala athatha "isikhala" esiningi ngakho-ke maningi amathuba okuthi avele.
Umthetho kaBenford unezinhlelo zokusebenza ezindaweni ezihlukahlukene, kusukela ku-forensics kuya kwisayensi yedatha:
- Ukutholwa kokukhwabanisa: Abacwaningi mabhuku basebenzisa umthetho ukuze bathole okungahambi kahle kudatha yezezimali. Uma ukusatshalaliswa kwamadijithi okuqala kumakhasi ebhalansi enkampani kuchezuka kakhulu kuMthetho ka-Benford, lokhu kungase kubonise ukukhohlisa noma ukukhwabanisa.
- Ukuhlaziywa kwedatha yesayensi: Abacwaningi basebenzisa umthetho ukuhlola ukwethembeka kwamasethi edatha. Ukuchezuka ekusabalaliseni okulindelekile kungase kubonise amaphutha ekuqoqweni kwedatha.
Naphezu kokusebenza kwawo okubanzi, umthetho kaBenford awuvumelekile emhlabeni wonke. Isebenza ngokuyinhloko kumasethi edatha aqukethe izinombolo zosayizi abahlukene futhi asatshalaliswa ngokwemvelo. Uchungechunge lwezinombolo olungaphakathi kwebanga elincane noma olukhawulelwe ngokuzenzisa (njengamakhodi e-zip noma izinombolo zokuphepha komphakathi) ngokuvamile aluwulandeli lo mthetho.
Umthetho kaBenford uhlala ungesinye sezibonelo ezithakazelisa kakhulu zokuthi izimiso zezibalo zingavela kanjani emhlabeni wangempela ngezindlela ezingalindelekile nezibonisa ukuqonda. Ukusetshenziswa kwayo ekusebenzeni kubonisa ukuthi izibalo akuyona nje isayensi engabonakali, kodwa ithuluzi eliwusizo lokuhlaziya iqiniso. Kungakhathaliseki ukuthi okokuthola ukukhwabanisa noma ukuqinisekisa idatha yesayensi, uMthetho we-Benford unikeza umbono ohlukile ngezinombolo ezilolonga umhlaba wethu.