This Bear vs. Shark submission comes to us from Erin, a friend of The Couchwarmers. Due to both length and thoroughness of research, we feel that it requires its own post. We strongly encourage you to read on before coming to a final verdict:
First, let's examine the facts. The rules of the hypothetical stated that the bear in question is "the biggest, deadliest bear" and the same goes for the shark - biggest and deadliest. None of that basking shark nonsense. A quick Google Search gives me the following numbers:
Shark: The Great White can get as long as 26.2 feet and weigh as much as 5000 pounds.
Bear: The Polar Bear averages around ten feet, so let's give it an extra two and say 12. Weighs in at 2,500 pounds (heaviest recorded).
To put it in perspective, 26.2 feet is slightly taller than a two-story building. 12 feet is less than half of that. My car -- a 2000 Volvo S70 -- weighs 3210 pounds. More than the bear, less than the shark.
In terms of weaponry, the bear has four slashing appendages and a lot of teeth, plus the ability to walk on its hind legs. The shark simply has a mouthful of teeth. The bear can move forwards, backwards, side to side, and can stand on its hind legs. The shark can move forward and side to side, as well as vertically, as far as the upper limit of the 'neutral territory' they are in. There is a longstanding myth that punching a shark in the nose will drive it away; however, the Mythbusters busted that wide open (although punching a shark in the gills does seem to have some effect.)
Bears have a top speed of around 35mph; Sharks clock in at 25mph. I can't do physics, but the greater mass of the shark suggests that even at 25mph, it can do some some damage -- again, to go back to the car comparison, I'd rather not be run over at 25mph.
If it came to hand-to-hand, as it were, combat, the bear would obviously have the upper hand. The skin of the shark is tough, however, and would probably sustain a fair bit of damage before being fatally injured, but it would be difficult for the shark to get past the claws to attack. It might be able to get one or two blows in, but its slower speed and lack of multiple weapons makes it an unfortunately ineffective fights in close quarters.
In spite of all this, the shark would still appear to have the advantage. Although a shark cannot reverse or stop suddenly, it has the vertical element. A shark can attack from above, using its massive mouthful of teeth to break the spine of the bear before the bear can even get one dig in. The sheer force of a 5,000lb shark dropping down at 25mph would probably be enough to kill the bear by crushing its skill or breaking its neck; the teeth don't even have to come into it. Assuming the neutral environment extended far enough up to allow for this manouver, the shark will win every time.
It's not an exciting fight, but it is a fast one, so you've still got time to hit the pub before last orders.