The world record muskie controversy

Douglas N. Arnold, Ph.D., Professor of Mathematics
   and Director, Institute for Mathematics and its Applications

Background. According to the National Fresh Water Fishing Hall of Fame, the all tackle world record muskellunge (Esox masquinongy) was caught by Louis Spray on October 20, 1949. Recently the size of Spray's fish has been disputed and the record brought into question. More information can be found at the National Fresh Water Fishing Hall of Fame website and at the website of the World Record Muskie Alliance.

On November 28, 2005, Scott Allen of the Executive Board of Trustees of the National Fresh Water Fishing Hall of Fame contacted me. He sent several copies of a single photograph of Spray with the record-winning muskie and asked if it were possible mathematically to estimate the fishes height from the photo, given that Spray was 6' tall. He wrote: "We need someone of highly credible mathematics background (preferably a Dr. of Mathematics) to do the calculation of the length of the fish in the photo. We expect the entire process to take less than an hour. Unfortunately, we cannot offer any compensation accept a big thank-you in our monthly publication (called The Splash) distributed nationally to all of our members, and the media."

Here is my memo responding to the query. (The memo includes several diagrams and photos, shown in low resolution below. Click any image to see a higher resolution version.)

It is important to note that I was provided with only a single photo (and this photo did not contain any of the parallel lines that were critical to the analyses made by others using other photos).

Update. On January 16, 2006, the Hall of Fame announced that it was upholding the record. Three mathematicians were quoted in the Hall's report, Professor Joseph Gallian of University of Minnesota at Duluth, Professor Dorian Goldfeld of Columbia University, and me. We are all three concerned that the Hall did not fully understand the results of our analyses and also are all concerned by the manner in which the Hall chose to communicate with us. On February 1, 2006 we wrote this letter to Emmett Brown, the Executive Director of the National Fresh Water Fishing Hall of Fame, about this. We have not yet had a response from Mr. Brown or anyone else at the Hall. In the interest of furthering understanding of what mathematics has to contribute to the determination of the validity of this record, we are sharing our conclusions with all interested parties. Some key points from the letter are:

  • There is no disagreement among Professors Gallian, Goldfeld and myself in this matter.
  • None of us is willing to say, based on the limited information made available to us and the limited investigations we have made thus far, whether or not we believe the record is valid.
  • The credibility of the results of our analyses depends not only on the mathematics, but also on the assumptions that we were asked to make, or chose to make and explicitly state.
  • We believe that a much more definitive result can be obtained from the photos which are available.
  • It is our recommendation that an independent group, including experts on mathematics and photogrammetry, be impaneled, supplied with the all known photos of the fish in original format, and allowed to pursue the evidence as they feel most justified.

Two other university professors were quoted in the Hall's decision: Bonnie Higgins of the Department of Technological Studies, Bemidji State University, and William F. Brown of the Department of Art at University of Evansville. After the letter was made public Professor Higgins wrote me, saying "I support your letter of February 1, 2006 to Emmett Brown, and, in particular, the recommendation than an independent group of experts be impaneled, provided with the full information available and allowed to pursue the evidence as they feel most justified," and Professor Brown wrote me that "[i]n reading all the related materials I would agree to your thoughts of requesting another review from outside sources."

Last modified February 21, 2006 by Douglas N. Arnold,