Kara Sears
Benford's law, also known as the First Digit Law, is named after American physicist Frank Benford, who published a paper in 1938 called The Law of Anomalous Numbers. However, Benford was not the first person to discover this law—in 1881, Canadian astronomer Simon Newcomb first observed this phenomenon and published a short paper on it.
| Characteristics | Values |
|---|---|
| Name | Frank Benford |
| Profession | Research physicist at General Electric |
| Year of discovery | 1938 |
| Title of paper | "The Law of Anomalous Numbers" |
| Number of data sets in the paper | 20 |
| Number of numbers in the data sets | 20,000 |
| Sources of data sets | 20 disparate sources |
| First to posit the leading digits theory | Simon Newcomb |
| Year of Simon Newcomb's discovery | 1881 |
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What You'll Learn
Simon Newcomb first observed the law in 1881
Simon Newcomb, a Canadian or American astronomer, first observed Benford's Law in 1881. He noticed that books of logarithm tables were much more worn and dog-eared at pages corresponding to numbers starting with 1 or 2. This inspired him to write a short, mathematically oriented paper on the topic, which, at the time, few picked up on.
Decades later, in 1938, Frank Benford, a physicist at General Electric, independently rediscovered the phenomenon. Benford collected more than 20,000 numbers from 20 disparate sources and showed that these data sets all satisfied the law. Benford's paper has since gained much more attention, particularly in the last 20 years.
Benford's Law, also known as the First Digit Law, is an observation about the leading digits of the numbers found in real-world data sets. It predicts a specific frequency of leading digits using base-10 logarithms that decrease as the digits increase from 1 to 9. For example, in natural data sets, numbers with 1 as their leading digit should occur around 30% of the time, 2 around 17% of the time, and so on, up to 9, which should appear as a leading digit only 4-5% of the time.
Benford's Law is named after Frank Benford, in keeping with Stigler's Law of Eponymy, which states that no scientific discovery is named after its original discoverer.
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Frank Benford, a physicist, rediscovered it in 1938
Frank Benford, an American physicist working at General Electric, rediscovered the eponymous Benford's Law in 1938. In a paper titled "The Law of Anomalous Numbers", Benford collected more than 20,000 numbers from 20 disparate sources and demonstrated that these data sets all satisfied the law.
Benford's work built upon the findings of Canadian or American astronomer Simon Newcomb, who first posited the theory in 1881. Newcomb noticed that pages in books of logarithm tables were much more worn and dog-eared at numbers starting with 1 or 2. This led him to write a short, mathematically oriented paper, which few picked up on.
Benford's paper, on the other hand, gained widespread recognition, especially in the last 20 years. He observed that many diverse datasets closely adhered to a distribution of first digits, with numbers starting with 1 occurring around 30% of the time, 2 around 17-18% of the time, and so on, until 9, which appeared as the first digit only about 4-5% of the time.
Benford's Law, also known as the First Digit Law, is a mathematical theory that describes the frequencies of first digits of numbers observed in datasets. It predicts the probability of a digit appearing as the first digit in a dataset, with the probability decreasing as the digits increase from 1 to 9.
Benford's rediscovery of the law popularized the concept and brought it to the forefront, leading to its association with his name.
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It was named Benford's Law, despite Newcomb's earlier discovery
Benford's Law, also known as the First Digit Law, is a mathematical theory that describes the frequencies of first digits of numbers observed in datasets. The law predicts that in many datasets, the digit '"1"' is the most frequent first digit, with '"2"' being the second most frequent, and so on, with '9' being the least frequent first digit.
The phenomenon described by Benford's Law was first discovered by Canadian or American astronomer Simon Newcomb in 1881. Newcomb noticed that books of logarithm tables were more worn and dog-eared at pages corresponding to numbers starting with '1' or '2'. This observation led him to publish a short, mathematically oriented paper on the topic, which received little attention at the time.
Despite Newcomb's earlier discovery, the law was named after American physicist Frank Benford, who independently rediscovered it in 1938. Benford's paper, titled "The Law of Anomalous Numbers," collected data from 20 diverse sources, providing further evidence for the law. Unlike Newcomb's paper, Benford's work gained significant traction, especially in the last 20 years.
The phenomenon of a scientific discovery being named after someone other than the original discoverer is so common that it has its own name: Stigler's Law of Eponymy. Proposed by American statistics professor Stephen Stigler in 1980, Stigler's Law states that no scientific discovery is named after its original discoverer. Interestingly, Stigler acknowledged that American sociologist Robert Merton had previously discovered "Stigler's Law," thus providing an ironic example of his own law in action.
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Newcomb and Benford noticed worn pages at the front of books of logarithms
In 1881, Canadian astronomer Simon Newcomb noticed that the pages at the front of books of logarithms were more worn than those at the back. Specifically, the pages corresponding to numbers starting with 1 or 2 were dog-eared and soiled, indicating that these numbers were being sought more frequently. This observation led Newcomb to publish a short, mathematically oriented paper on the phenomenon, which, unfortunately, went largely unnoticed.
Over half a century later, in 1938, American physicist Frank Benford, working at General Electric, independently rediscovered this phenomenon. Benford collected data from 20 diverse sources, finding that numbers with 1 as the first digit appeared around 30% of the time, 2 around 17-18% of the time, and so on, with 9 only appearing as the first digit about 4-5% of the time.
Benford's paper, titled "The Law of Anomalous Numbers," gained significant traction, especially in the last two decades. It described the frequencies of first digits in various datasets and provided mathematical explanations for the observed pattern. Benford's work built upon Newcomb's earlier insight, and together, they are credited with uncovering what became known as Benford's Law.
Benford's Law is a mathematical theory that describes the distribution of leading digits in datasets. It predicts that in many real-world datasets, the frequency of leading digits will follow a specific, non-uniform pattern, with smaller digits as the first digit being more common than larger ones. This law has found applications in various fields, including fraud detection, accounting, and economics.
The discovery of Benford's Law is an example of Stigler's Law of Eponymy, which states that no scientific discovery is named after its original discoverer. In this case, Newcomb's initial finding was overlooked, and the law was named after Benford, who popularised it with his comprehensive paper.
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Benford's paper included 20 data sets from diverse sources
In 1938, American physicist Frank Benford published a paper called "The Law of Anomalous Numbers", which detailed his research on the frequencies of first digits of numbers observed in datasets. Benford's paper included 20 data sets from diverse sources, with a total of 20,229 observations.
The data sets Benford used in his research included the surface areas of 335 rivers, the sizes of 3,259 US populations, 104 physical constants, 1,800 molecular weights, 5,000 entries from a mathematical handbook, 308 numbers contained in an issue of Reader's Digest, the street addresses of the first 342 persons listed in "American Men of Science", and 418 death rates.
Benford's law, also known as the First Digit Law, observes that in many real-life sets of numerical data, the leading digit is likely to be small. In sets that follow this law, the number 1 appears as the leading digit about 30% of the time, while 9 appears less than 5% of the time. This law applies to data drawn from specific distributions, such as the lengths of rivers, stock prices, population numbers, death rates, and financial information.
Benford's law has been used to detect fraud and manipulation in financial records, tax returns, and decision-making documents. Analysts compare the distribution of leading digits in these datasets to Benford's law, as unnatural distributions of leading digits can indicate fraudulent activity.
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Frequently asked questions
Benford's law was first discovered by Canadian or American astronomer Simon Newcomb in 1881.
Simon Newcomb noticed that books of logarithm tables were much more worn and dog-eared at pages corresponding to numbers starting with 1 or 2.
In keeping with Stigler's law of eponymy, which states that no scientific discovery is named after its original discoverer.
Frank Benford was a research physicist at General Electric who rediscovered Benford's law in 1938.
