Show simple item record

dc.contributor.advisorÉrdi, Péter
dc.contributor.authorSilverman, Aaron
dc.description31 leavesen
dc.description.abstractSome time around 1881, Simon Newcomb (1) was flipping through logarithmic tables and was struck at how much more quickly the first tables wear out than the subsequent ones. After some investigation, he found that the reason lay in the frequency of digits in the natural numbers. To quote “the fist significant figure is oftener 1 than any other digit, and the frequency diminishes up to nine. 1” By noticing that the frequency of lookups in anti-logarithm tables was completely uniform, Newcomb was able to infer the following law: that the first significant digits in a random tabulation of data obey a logarithmic distribution, with 1 being the most common, at 30.1% and frequency decreasing for digits up to 9 with frequency 4.5%. He gave a table of frequencies, but no algebraic formulation of the law and practically no theoretical justification. The paper was duly forgotten, and no more significant developments came to light for 57 more years, until in 1938 a researcher named Frank Benford (2) at the General Electric Company laboratories in Schenectady, New York collected 20 different collected data sets such as the area of rivers, constants, or addresses of the first 342 names mentioned in American Men of Science. Averaging all these numbers out, he observed the same curve as Newcomb.en
dc.relation.ispartofKalamazoo College Physics Senior Individualized Projects Collection
dc.relation.ispartofseriesSenior Individualized Projects. Physics.en
dc.rightsU.S. copyright laws protect this material. Commercial use or distribution of this material is not permitted without prior written permission of the copyright holder.
dc.titleBenford's Lawen

Files in this item


This item appears in the following Collection(s)

  • Physics Senior Individualized Projects [318]
    This collection includes Senior Individualized Projects (SIP's) completed in the Physics Department. Abstracts are generally available to the public, but PDF files are available only to current Kalamazoo College students, faculty, and staff.

Show simple item record