## Fish Story: Math Weighs In, Muskie Comes Up Short

July 6, 2006

Michelle Sipics

In 1949 a two-time record holder for muskie fishing caught another monster of a muskie: Put on the books as 63 and a half inches and 69 pounds, 11 ounces, the fish set another world record. It's doubtful that the angler, Louis Spray, could have predicted that his 1949 catch (nicknamed Charlie) would be at the center of a heated debate 57 years later.

What's most intriguing about the controversy over 57-years-dead Charlie and a fisherman who died in 1984 is that the director of the Institute for Mathematics and its Applications is right in the thick of it.

Late last year, IMA director Douglas Arnold was contacted by Scott Allen of the National Fresh Water Fishing Hall of Fame, which oversees many world records, including those held by Spray. Allen sent Arnold a photograph, black and white and a bit grainy, of Louis Spray holding his 1949 prizewinner.

He had a bit of an odd request.

Allen asked Arnold to estimate the length of the fish, given two pieces of information: the photograph, and the fact that Spray was six feet tall. Anglers often use the known length of a fish to determine whether a claimed weight is reasonable, based on loose ratios of length to weight. A human comparison: If a medium-build man claimed to weigh 200 pounds but was only 5'5", the weight claim has a good chance of being inaccurate. It seems that Spray was suspected of that famous fisherman's habit: exaggerating the size of his catch.

Arnold, himself an avid fisherman, decided to tackle the problem. His conclusion probably wasn't as definitive as Hall of Fame officials would have liked. Mathematics, he said, couldn't absolutely answer Allen's question based only on the photograph and Spray's known height. But it could provide an upper bound on the muskie's length: "The only conclusion that we can draw with certainty," he wrote in a memo to Allen, "is that the fish is shorter than 63 inches, perhaps considerably so." Basic projective geometry showed that Charlie hadn't eaten his Wheaties---not 63 and a half inches worth of them, anyway. And if the muskie's length fell short of Spray's claim, its weight would almost certainly be well below the record as well.

This wasn't a surprise to the World Record Muskie Alliance, which had already submitted a 93-page "Spray Summary Report" to the Hall of Fame in October of 2005. The group's conclusions? Among other things, Spray's behavior pre-Charlie "points to the Spray all tackle 1949 World Record being completely bogus." The report indicates, for example, that photographs of Spray's 1940 and 1949 record fish are mislabeled on Spray's personal stationery, on postcards he had printed, and in his autobiography, with the 1940 catch being listed as the 1949 muskie, and vice-versa. The report also cites numerous other photo "mix-ups," and in regard to one such error involving his 1940 catch, states that

We at the WRMA feel it a greater likelihood that a muskie angler be unable to properly identify pictures of his own children before being unable to distinguish an alleged photograph of his second world record fish from one supposedly representing a much smaller specimen.

In other words, in the opinion of the WRMA, Spray's record claims are almost certainly false. In addition to their investigation of Spray's character, the group commissioned a private company to perform a photogrammetric analysis---the determination of measurements and camera positions from photos---of multiple images, including Spray with his 1940 and 1949 catches. According to their results, Charlie was even shorter than Arnold's upper-bound estimate: They placed the muskie's length in a range of approximately 52 to 55 inches.
The Hall of Fame disagrees (in fact, the two groups even disagree about the spelling of "muskie," with the Hall of Fame preferring "musky"). The Hall's decision---regardless of Arnold's "muskie memo," WRMA's objections, and continued debates---is that Spray's record will stand.

The decision has riled not just anglers, but many mathematicians as well. Scott Allen, it turns out, also contacted Joseph Gallian of the University of Minnesota Duluth and Dorian Goldfeld of Columbia. Curiously, Arnold and Goldfeld were given completely different photos, and Gallian eventually received both. While the three mathematicians drew different numerical conclusions from the evidence they were given and the assumptions they were asked to use, all three were angered by the Hall's decision---as were many others.

"A bunch of people sort of took up the call," Arnold says. "There have been calls and newspaper articles and things like that, but the Hall has basically said, ‘We've done our analysis and we don't foresee looking into it any further.'" According to Arnold, the Hall has actually changed its rules: A \$1500 filing fee is now required for any challenges to its records.

Is mathematics being ignored in a situation where it could provide a valuable service?

"I think it's slightly worse than that," the IMA director says. "I think it's being manipulated . . . that there's an attempt, by giving out limited evidence and going to different people, to come up with a point of view that supports a decision that perhaps they had already come to in any case."

Arnold cites the Hall's giving different photos to the three mathematicians, instead of providing all three with all available evidence, and asking the mathematicians to accept what he considers dubious assumptions. The mathematicians, moreover, have received no response to their suggestion that an independent commission of experts be formed to examine the matter. The WRMA has put its weight behind that recommendation, stating that it would abide by such a commission's conclusions.

It's unlikely that the question of Charlie's size will ever be answered with absolute certainty. The building that housed the mounted fish was destroyed in a fire in 1959, and Spray committed suicide in 1984; at any rate, it is doubtful that his testimony would shed any additional light on the matter. Still, Arnold believes that an independent commission given all the evidence could actually settle the controversy, using both geometry and photogrammetry.

"I think if you were to look at all the evidence, you might well be able to get something fairly definitive. Of course it's not guaranteed," he says. "But I think that good math and good science could pretty much put the issue to rest, if people were willing to pay attention to it."

For the record: IMA director Doug Arnold demonstrates that the same 48" plank, held by the same 5'10" man, can appear substantially larger or smaller, depending on the angle and position of the camera.

***

Spray described his fishing career in an autobiography titled Looking Back At That Phase Of My Muskie Days. The interested reader can purchase the book, albeit at a high price: One of the 2000 copies reportedly printed sold for more than \$1000 on eBay in 2004.

Those unwilling to make a financial investment in the debate can consult the following resources:

Doug Arnold's documentation of the debate: http://www.ima.umn.edu/~arnold/muskie/;
The National Fresh Water Fishing Hall of Fame's Web site: http://www.freshwater-fishing.org/; and
The World Record Muskie Alliance Web site: http://www.worldrecordmuskiealliance.com/.

Michelle Sipics, a student in the graduate program in science writing at MIT, is spending the summer as an intern at SIAM News.

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