On (Newcomb-)Benford's law: a tale of two papers and of their disproportionate citations. How citation counts can become biased
This study uses citation analysis to demonstrate that the formalization of "Benford's law" by Raimi in 1976, which overlooked Simon Newcomb's earlier 1881 discovery, created a disproportionate citation bias that significantly marginalized Newcomb's contribution in favor of Frank Benford's.
Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer
The Story of Two Scientists and a "Dirty" Book
Imagine a library filled with massive books of logarithmic tables (used for complex math before calculators existed). In 1881, a scientist named Simon Newcomb noticed something odd: the first few pages of these books were much dirtier and more worn out than the last few pages.
He realized this meant people were looking up numbers starting with the digit 1 way more often than numbers starting with 9. He published a short note about this in 1881.
Six decades later, in 1938, a physicist named Frank Benford noticed the exact same thing. He didn't know about Newcomb's note. Benford did a massive study, checking everything from river lengths to atomic weights, and confirmed the pattern. He published a long, detailed paper.
The Problem:
Because Benford's paper was longer, more detailed, and published in a more popular journal, the scientific world started calling this pattern "Benford's Law." Newcomb's name was almost completely forgotten.
The "Citation" Scoreboard
In the academic world, how famous a paper is, is measured by citations. This is like a scorecard: when a new researcher writes a paper, they list the old papers they used as references. Every time they list a paper, that paper gets a "point."
The authors of this new study (Mir and Ausloos) decided to act like detectives. They looked at the "scoreboard" for the last 80+ years to see why Benford has so many more points than Newcomb.
The Investigation: Why is Newcomb Losing?
The researchers found that Newcomb's low score isn't just bad luck; it's a chain reaction of three specific events:
1. The "Bad Seat" at the Dinner Table
Newcomb's original 1881 note was published in a journal sandwiched between two other articles that were very boring and not very useful. Because the neighbors were "dull," no one looked at Newcomb's paper. It was like sitting at a dinner party between two people who never speak; you get ignored even if you have something interesting to say.
2. The "Name-Tag" Mistake
In 1976, a researcher named Raimi wrote a big review paper to summarize everything known about this pattern. He found Newcomb's old note and gave him credit in the text. However, Raimi decided to officially call the phenomenon "Benford's Law."
The researchers argue this was a fatal mistake. By putting Benford's name in the title and the official name, Raimi accidentally told future scientists: "This is Benford's thing. You don't need to look up Newcomb." It's like if a movie director made a sequel and called it "The Batman Returns," even though the original story was written by someone else. Everyone assumes it's all about Batman.
3. The "Follow the Leader" Effect
After Raimi named it "Benford's Law," the most famous scientists in the field (the "leaders") started writing their own papers.
- They knew about Newcomb (because Raimi told them).
- They knew about Benford.
- But, because the law had a catchy name ("Benford's Law"), they only cited Benford. They forgot to give Newcomb a "point."
The study found that even when these famous authors knew Newcomb existed, they often ignored him. It's like a group of friends going to a concert. They know the opening act (Newcomb) was great, but because the headline act is Benford, they only talk about the headline act and forget to mention the opener.
The Numbers Don't Lie
The researchers crunched the numbers from a massive database of scientific papers:
- Benford's paper has been cited 1,325 times.
- Newcomb's paper has been cited only 925 times.
- Even worse: When people cite Newcomb, they almost always cite Benford too. But when they cite Benford, they rarely cite Newcomb.
It's as if Newcomb is only allowed to speak if Benford is holding the microphone.
The Conclusion: A "Matthew Effect"
The paper concludes that this is a classic example of the "Matthew Effect" (a fancy way of saying: "The rich get richer").
- Benford got a lucky break (a good journal placement and a detailed paper).
- Newcomb got a bad break (a short note between boring articles).
- Once Benford got the name "Benford's Law," the momentum kept growing, while Newcomb was left in the shadows.
The authors argue that the scientific community has been unfair. They didn't just forget Newcomb by accident; the way the field was organized (the name, the famous papers following Raimi) actively pushed Newcomb's contribution aside.
In short: Newcomb discovered the pattern first, but Benford got the fame. The study shows that how a discovery is named and who cites whom can change history, leaving the true pioneer with a much smaller legacy than they deserve.
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