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Feature

Doug Arnold holding up a 48-inch board in front of him in two different photos--one taken from the front and one from the side.

The photos above both show Doug Arnold (who is 5'10" tall) holding a 48-inch board to simulate a fish. In the photo on the left, the board appears to be about 60 inches long, while in the photo on the right it appears to be closer to its actual size.

A new angle on an old fishing record

'Muskie memo' from math institute could help settle dispute

By Rick Moore

January 6, 2006

Leave it to projective geometry to bring new life to a 56-year-old fishing tale.

To those for whom the term "projective geometry" just brought a quickened pulse, do not stop reading. This is about applied mathematics--the kind that illuminates everyday problems, and the kind routinely brought to light by the University's world-renowned Institute for Mathematics and Its Applications (IMA). The IMA's director, Doug Arnold, has been called in to help settle a long-running dispute over whether a muskie caught in Wisconsin is really a world record.

First, there's the tale of the fish--an intriguing saga that includes a bootlegger by the name of Spray, another character named Chin Whiskered Charlie, an evidence-destroying fire, a 93-page protest document, and a "muskie memo" (with a very revealing Figure 1, we might add).

It began in 1949, when Louis Spray (a known Prohibition-era bootlegger) caught a very large muskellunge (muskie, for short) on October 20 in the Chippewa Flowage in northern Wisconsin. The fish was determined to be 69 pounds, 11 ounces, with a length of 63 1/2 inches, good enough to be considered the world freshwater record, and it was acknowledged as such by the National Fresh Water Fishing Hall of Fame (NFWFHF). There are sworn affidavits by people who witnessed his catch, as well as a number of photographs of Spray holding up his trophy, later dubbed "Chin Whiskered Charlie."

Arnold has become a go-to guy on all things math- and numbers-related, such as the question, "What are my odds of winning the Powerball jackpot when it reaches that hard-to-belittle $300 million mark?" (The answer: About seven times less than your odds of getting killed driving to pick up a ticket at the convenience store a mile away.) Sometimes, Arnold's truths hurt.

The story only gets more interesting from there. Spray was a fairly prolific fisherman, and "Charlie" was the last of three world-class muskies that he caught. While facsimiles of Charlie exist--the photographs and a life-sized replica in a display case at the NFWFHF--the original fish was destroyed in a fire in 1959. For many years that hardly mattered, as Spray's record was eclipsed by a few ounces on a fish caught by New Yorker Art Lawton on the St. Lawrence River in 1957. However, in 1992, John Dettloff, the president of the NFWFHF board of trustees, did a photo analysis of Lawton's fish and determined that its size had been exaggerated. At that point, the record went back to Spray.

End of story, right? Not even close. About a dozen years hence, and two decades after Spray committed suicide in 1984, a group called the World Record Muskie Alliance began seriously scrutinizing Spray's record, focusing in part on photographs of him holding the fish. By counting the pixels in the photos of Spray and comparing the total to the pixels in the fish, the group concluded that Charlie was well short of its recorded length, perhaps by as much as 10 inches, and could not have weighed anywhere near 69 pounds, 11 ounces. It conveyed its findings in a 93-page report to the NFWFHF on October 20, 2005--56 years to the date after Spray netted Charlie.

That's where the University of Minnesota and the IMA come in. As the Hall of Fame began contemplating the report and its assertions, Scott Allen, a member of the NFWFHF's executive board of trustees, turned to Arnold for his mathematical analysis and opinion. Arnold has become a go-to guy on all things math- and numbers-related, such as the question, "What are my odds of winning the Powerball jackpot when it reaches that hard-to-belittle $300 million mark?" (The answer: About seven times less than your odds of getting killed driving to pick up a ticket at the convenience store a mile away.) Sometimes, Arnold's truths hurt.

Here's where the projective geometry comes in. Arnold responded to Allen's request with his so-called "muskie memo," in which he diagrammed what math can tell us about Spray's record fish. The only givens in this case are that Spray was 6 feet tall, and he was holding Charlie in front of him. If a person is holding a fish in front of him, you can make the fish appear bigger and bigger by taking your pictures closer and closer to it. "In fact, by bringing the camera close enough to the fish, you could make it appear as large as you want relative to the fisherman behind it, if you had a sufficiently wide-angle lens," Arnold said in the memo. Image(56118)

The relative size of the photographed images of the angler and the fish depend on the placement of the camera, as shown in this reproduction of Figure 1 from Doug Arnold's "muskie memo." The image from the camera closest to the fish results in a much larger portrayal of the fish than the image taken with a camera farther away. Therefore, Arnold wrote that "it is not possible to estimate the size of the fish from the photo." He did note, though, that no matter how far away the camera is from the fish and fisherman, the image could appear no smaller than the distance between the parallel dotted lines in Figure 1. Using simple proportion, Arnold estimated 63 inches as the maximum length of the fish--one-half inch shorter than the stated record. Said the memo: "Thus, the only conclusion that we can draw with certainty is that the fish is shorter than 63 inches, perhaps considerably so."

That leaves the folks at the NFWFHF with more evidence to ponder as they consider the fate of Spray's catch. Emmett Brown, director of the NFWFHF, has said that he expects the group to make a decision early in 2006.

Arnold is hesitant to give his prediction of the outcome, but suggested that at a certain point, the debate becomes "not a matter of scientific fact, but of a preponderance of evidence," and the evidence seems to tip the scales in favor of the World Record Muskie Alliance and its protest. Stay tuned.

Whatever the outcome and however effectively it settles the controversy, a few things do seem clear. Anglers can be prone to exaggeration. If you are going to exaggerate by an inch or two or six, make sure your claims will stand the scrutiny of future technologies (and smart mathematicians). And projective geometry can be used to help solve some of the weightier problems of the world.