I read Amos Smalley's account in Reader's Digest many years ago. He was an old harpooner who claimed he that in 1902 he had killed a white 90-foot sperm whale (or Physeter macrocephalus, to be proper) and he was a guest at the 1956 premiere, introduced by John Huston as the man who harpooned the real Moby Dick. This account is a bit odd. For one thing, no other source records it. For another, Nature has (sadly) not furnished us with 90-foot sperm whales. Measurements for whales landed in the 20th century ranged up to about 67 feet long. There is anecdotal evidence they used to get bigger: the whale that sank the whaleship Essex was claimed to be 80 feet, although it obviously was not caught, and whalemen whose ship has "been stove by a whale" are hardly likely to underestimate their adversary. Richard Ellis, author of The Great Sperm Whale, the best book on this animal, is cautious about claims of whales of 70-90 feet, although he mentions teeth 11 inches long in a museum collection and wonders how big their former possessor was: 8 inch teeth would be normal for an adult male. Whatever the upper size limit, the animal is one of the most remarkable creatures in the oceans, now or ever: that 20-foot nose alone sets it apart! The skull of the largest males is almost exactly the size of the Ford Freestyle SUV in my garage, which is 17.5 feet.
We don't even know what the whale sees. Its eyes, separated by that nose, can't see an overlapping field like ours can: it scans two separate fields of view. We can't be sure what this looks like to the whale, though. Does the world's largest brain put these pictures together and create an approximation of what may lie between them, or does it examine each view individually? Does it synthesize a single multi-sensory image from its vision and its superb sonar equipment?
Speaking of sonar, if the sperm whale isn't exactly the answer to Dr. Evil's demand for "sharks with frickin' laser beams," it does possess a sonic cannon unlike any other weapon, natural or technological, in the world. (There is some evidence killer whales may have evolved this on a smaller scale.) It uses this apparatus to stun giant squid: these amazing pictures from 2009 show an adult sperm actually carrying a squid trophy in her mouth. We know even less about the squid, of course, although we at least now have video of the animal alive. Video or photography of an actual hunt and capture of the squid by the whale has eluded us, despite efforts that include attaching cameras to the whales.
Hank Searls wrote an interesting novel, Sounding, in an attempt to give us a look into the whale's brain. It's a good novel, though it always bothered me that whales somehow seem to know they are part of a group called Cetacea.
Sounding: a sperm whale shows its flukes as it dives. Sperm whales are known to dive well over a mile deep and may approach two miles. (NOAA)
We have only one species of sperm whale, or cachalot, and there have been only a few hints of unknown types. Robert Sibbald, the first great authority on whales, believed reports of a version with a high dorsal fin. He thought this was a separate species, Physeter tursio, though, even if accurately reported, the whale involved seems more likely to have been an oddball (a fluke? even I wouldn't make a pun that bad). Sperm whales Sibbald examined in person didn't have the dorsal fin. We do have at least one example from Nature (and the pages of National Geographic) of an all-white cachalot, so they do exist - even if not as big as Amos Smalley claimed.
Overall, the study of this animal doesn't give the cryptozoologists much to do, other than examine the interesting accounts of huge giant squid arms vomited up by these whales in their death throes. A sperm whale also produced the famous Naden Harbor carcass, thought by most biologists to be a decaying basking shark, but odd enough so there is some debate about it being an unknown species of animal.
The sperm whale, though, has no need of mystery bretheren to make it intriguing: it is, complete and by itself, one of the most remarkable animals ever to live. There is enough mystery to this species to keep cetologists busy for generations to come.