Can Math Settle a Fight over Fish Size?

The National Fresh Water Fishing Hall of Fame wants to resolve a dispute over the size of a fish hailed since 1949 as a world-record holder. Three photos and geometry techniques may establish the actual length of the Muskie. Stanford professor Keith Devlin, Weekend Edition math expert, tells Scott Simon how math might resolve the quarrel.

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SCOTT SIMON, host:

This is WEEKEND EDITION from NPR News. I'm Scott Simon. There's a great mathematical controversy coming out of northern waters, and it involves, what else, a fish. The Muskie fish, to be exact, also known as the muskellunge. It's a rare fish found in freshwater lakes, and it's part of the pike family.

The National Freshwater Fishing Hall of Fame has on record that Louis Spray, a good name for a fisherman, caught the largest Muskie ever at a whopping 69 pounds, 63.5 inches. He caught it in 1949. But the world-record Muskie alliance is skeptical. There are three pictures that capture Mr. Spray holding up the fish, maybe evidence that the fish is smaller than he claimed.

Here to help us sort out this dispute is our friend, our math guy, Keith Devlin at Stanford University. Keith, thanks very much for being with us.

Mr. KEITH DEVLIN (Stanford University): Hi, Scott, nice to be here.

SIMON: Firstly, how do mathematicians get drawn into this controversy?

Mr. DEVLIN: This is a first...

SIMON: There are a few other things going on in this world, Keith, yeah.

(Soundbite of laughter)

Mr. DEVLIN: This is the first time I've come across a case like this. In fact, the president of the Hall of Fame contacted three mathematicians asking if they would help resolve this dispute as to what the world-record catch was, sent each of them one of the three photos and said the person involved, Louis Spray, shown in the photographs, was six feet tall. Given the photograph and the information that the person was 6 foot tall, could the mathematicians calculate the exact length of the fish from looking at the photograph?

SIMON: Uh-huh. Well, tell us what kind of science they use.

Mr. DEVLIN: You're really in the area of mathematics known as projective geometry. This is a branch of mathematics that was developed in the Renaissance at the same time as artists were developing perspective drawings.

And in fact, projective geometry is the mathematics of perspective, and so anyone who's a painter who paints perspective pictures is at least implicitly a projective geometer.

The task here is looking at these photographs using what we know about projective geometry to be able to figure out exactly what the size of the fish is. And it boils down to trying to determine where the camera was when the picture was taken and what the angle of the camera was to the ground. Those are the two key parameters that you have to determine in order to be able to calculate the height of the fish on the photograph using the methods of projective geometry.

SIMON: And how could you know that?

Mr. DEVLIN: It actually is rather tricky. You have to look for pairs of lines in the photograph, which in the real world would be parallel, but because of perspective would not be parallel in the picture, and you measure the angle between them in the picture. Then you can actually figure out, using actually just middle-school, high-school trigonometry - it's very basic mathematics at that point - you can figure out where the camera must've been and what the angle would be.

SIMON: We might describe the picture for folks at home.

Mr. DEVLIN: I've only seen one of the three photographs, and that shows Louis Spray standing in what looks like a field, holding up the fish in front of him. And in the picture I saw, there were no lines that you could look at to measure the angle between them, and so - apparently there are other photographs where there are one or two such clues, and the mathematicians that have looked at this have said, you know, if we put all of the three pictures together and we put our heads together, we might just be able to figure this one out.

SIMON: But no results so far, right?

Mr. DEVLIN: This is where the story actually gets a little bit fishy, if you'll pardon the expression, because when...

SIMON: Keith?

Mr. DEVLIN: Yup?

SIMON: How many days have you been preparing that little pun?

(Soundbite of laughter)

Mr. DEVLIN: Oh, at least two days, Scott.

SIMON: All right. Go ahead, please.

Mr. DEVLIN: The Hall of Fame sent the three mathematicians three different photographs. Now, it could be that they didn't realize that the mathematicians really needed all photographs in order to do their job properly...

SIMON: But it does occur to me, I mean we're having a certain amount of fun with it, but it does strike me that you would be able to use this in forensic scenes, for example.

Mr. DEVLIN: Well, indeed. These techniques are used all the time in criminal detection in order to find out the paths of automobiles before crashes, to look at the various paths of aircraft that are in trouble, to look where snipers would've been when they were firing guns, and so forth.

So this is mathematics that's extremely important and used all the time to reconstruct actual events from photographs and various other kinds of records.

SIMON: Keith, always nice talking to you.

Mr. DEVLIN: Fun as always, Scott, thanks for having me on.

SIMON: See you at the old fishing hole this weekend.

(Soundbite of laughter)

Mr. DEVLIN: Maybe, and then again maybe not.

SIMON: Perhaps maybe not in both our cases. Keith Devlin, who's executive director of the Center for the Study of Language and Information at Stanford University, joining us from the campus.

Your most recent book is called...

Mr. DEVLIN: The Math Instinct: Why You're a Mathematical Genius Along with Lobsters, Birds, Cats and Dogs.

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