Icy lens ignites kindling

Question: Out in the frozen wilderness, you lose your backpack in a fall. You still have a knife but your matches are gone. It's getting really cold and you need a fire. There's wood around but no sparking material. What to do?

Answer: If you read Jules Verne's "The Desert of Ice," you know of Captain Hatteras and a few loyal men abandoned near the Arctic, facing the above circumstances, says Jearl Walker in "The Flying Circus of Physics." Their ingenious doctor fashioned a convex lens out of a clear section of ice (no air bubbles), using a hatchet to shape it and smoothing it with his knife and warmth from his fingers. Then he focused the bright sunlight onto the kindling and within seconds it ignited. Such an idea may have originated with British scientist William Scoresby, Arctic pioneer, whose ice lens ignited wood, tobacco in a sailor's pipe, etc.

Or why not use an eyeglass lens, if available, as was done with Piggy's glasses in William Golding's "Lord of the Flies." This can work, says Walker, but NOT if the wearer is nearsighted, as was Piggy; these lenses won't focus the rays. "The story is flawed. You'd need the glasses of someone farsighted for this to work."

Question: On, no, elevator cable snaps and you're freefalling 20 stories! Anything you can do to up your survival chances, such as leaping skyward at the last instant?

Answer: In principle you can soften your fall this way, in practice you'd need superhuman leaping ability, says University of Oregon physicist Raymond E. Frey. Assuming 16 feet per floor, you're in for a 320-foot drop, accelerating to close to 100 mph — the speed you need to overcome.

A person with a 30-inch vertical jump attains about 9 mph. This does not help much ... it could reduce your speed to the equivalent of merely(!) a 17-story drop — assuming you time your jump perfectly.

Here, however, is a winning strategy. When the cable snaps, you have 4.5 seconds to climb the wall and go through the car roof escape door. Remember, you're in free fall, "weightless" like an orbiting astronaut, so it is not hard to climb but maneuvering is tricky. "Now, standing on the car roof, fire up your 4,000-pound-thrust backpack rocket. Cover your eyes."

Question: Can't be just coincidental, can it, that we have 10 fingers for counting and enumerating and a base-10 number system to go along with them?