Sea serpent reports have definitely dropped off in recent decades, to less than one per year. But how often should they be sighted, if there is a real animal involved?
I caution at the outset there are no good numbers for many of those figures, and I chose numbers that seemed reasonable and made the math simpler. So this is a simplification of a complex situation using arbitrary numbers, but one has to start with something, and the problem of how often humans might be expected to spot a possible sea serpent niggled at me until I had to try something.
The world’s oceans cover139,000,000 square miles (statue miles). A variety of Web sources give figures of 12,000 to 90,000 vessels on the oceans at any moment. Let’s use a high number, 50,000, which covers (we are presuming) everything large enough to have a lookout (small pleasure craft, for example, would be excluded for the moment). A lookout can see 1.17 times the square root of his or her eye height above the ocean, in nautical miles (note the diversion in units here: you'll see it's not enough to matter), so from an arbitrarily chosen 49-foot spot on a mast or bridge that’s 8.19 miles. An object rising above the water essentially raises the horizon: you could, in perfect conditions, spot the head/neck of an animal rearing 9 feet out of the ocean 8.19 + 3.51 miles away, or 12.7 nm.
In practice, no one can identify much of anything at that range, especially if sea serpents are sometimes wont to stick only the head or a small section of body or neck (if it has a neck) above water. Let’s say you can definitively identify a sea serpent (assuming there is such a thing) and rule out debris or known marine life at one half a statute mile. There’s no way to calculate the average eye height of the lookouts of all the ships at sea (and not every ship will have a lookout at all), not to mention who’s carrying what binoculars, so this business quickly gets rather silly, but if we assume, say, a ship can watch a circle of ocean a mile in diameter (area 3.14 miles) for sea serpents, and there are 50,000 ships with lookouts, then you get a figure of 157,000 square miles being observed. If there are 139 million square miles of ocean, then 1/874th (0.1129 percent) of the surface would be under observation, and a population of 1,000 sea serpents showing themselves for, say, five percent of their time at the surface (it could be far lower), 20 might be visible somewhere, and if they are identifiable in an area of 3.14 square miles, you get an area of 62.8 square miles, or 1/221338 the area of the sea (or 0.0005 %) showing sea serpents at any time, and if you try to calculate the likelihood of these areas intersecting the other the math goes from extremely hypothetical to absurd (any readers care to take a crack at it?). Actually, it’s worse than this: half the time it’s dark, a considerable percentage of the time there is a sea state that makes identification harder, or it’s raining, or it’s foggy, and the fact that lookouts on the open sea spend most of their time looking forwards… well, you get the picture. Or no one gets any pictures.
Comments and brickbats welcome.