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Benford's Law and Free Will
by Jeremy McNabb
12/30/04
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Author’s note: This is not a work of apologetics but of theology in general. My reason for posting it in apologetics is that no “Religion” or “Theology” section exists. Thank you and enjoy.

In 1938, a physicist by the name of Dr. Frank Benford noticed that the pages of logarithms which corresponded with the digit one were noticeably more worn and smudged than those that did not.

Soon, Benford realized that he had discovered a mathematical law. It is most commonly known as Benford’s Law, but other names include the first digit law, the first digit phenomenon, and the leading digit phenomenon. This law states that the digit “one” makes up thirty percent of all digits in any large assembly of figures (1). If you have the time and determination to copy down all the license plates in any given mall parking lot, approximately thirty percent of the digits on the page will be one. As with any experiment, the larger one’s test area, the more accurate the results will be. Obviously, testing two license plates will not yield as accurate a result as the testing of two hundred.

At this point, you may be wondering what on earth this has to do with theology. Simply put, Benford’s Law illustrates a portion of natural order.

God’s sovereign will dictates what natural order is. If you count thirty entries in the phone book and find that ten of the numbers systematically correspond with the number one, that is Benford’s Law, but it is also God’s natural order.

This, however, is the rub: Benford’s Law has a fatal weakness. Whenever the numbers are manipulated or are intentionally chosen, Benford’s Law disappears from the equation. Whenever free will is exercised, Benford loses his grip.

This failure of Benford’s Law to ride out the storm of free will is so reliable that many income tax agencies check tax forms against Benford’s Law. If the numbers do not fall into line, it is almost certain that someone has doctored them (2).

Some of you may see where I am going. If our ability to choose (or manipulate) did not really exist and we could not exert our will upon the natural order of things, Benford’s Law would never fail. As California’s income tax agency shows, it does.

Dr. Frank Benford may not have been concerned with the theological implications of his discovery, but his work is as useful to us as it is to tax auditors. Free will, according to mathematics, exists after all.

1. Barlow, J.L. and Bareiss, E.H. “On Roundoff Error Distributions in Floating Point and Logarithmic Arithmetic.” Computing 34, 325-347, 1985

2. Livio, Mario “The Golden Ratio” pgs. 232-236 (Broadway 2003)


Jeremy McNabb (st_jeremiah@hotmail.com) is an amateur fiction and essay writer. He is currently at work on his first novel. This is one of several articles published on FaithWriters.com.

If you died today, are you absolutely certain that you would go to heaven? You can be! TRUST JESUS NOW

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Member Comments
Member Date
Penn Tomassetti 11 Jul 2008
Maybe you should think about what you are saying before making your conclusion that people have free will. Mr. Benford's Law proves free will about as much as me choosing what shirt to wear tomorrow. Do you know what saith the Scripture?
Lucian Thompson 02 Jan 2005
I never heard of ole Doc. Benford, but what you have written makes sense to me.
Gregory Eckrich 31 Dec 2004
Short, sweet, organized and a message for all to consider! BRAVO!!




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