*Oversized deadly fish chomp their way up the Amazon, destroying everything and everyone in their path.*

Good-hearted ichthyologist Tiffany - Tiffany "I Think We're Alone Now" Tiffany, no last name required, yo - has been genetically modifying Venezuelan piranhas to make them a bigger and therefore more bountiful food source for the people. Unfortunately, she hasn't just made their bodies bigger...she's made their teeth bigger, too.

These piranhas have METAL TEETH. DEATH METAL TEETH. F YES THEY DO. Turn off that Hall & Oates and crank some Carcass, because that's what's about to go down onscreen.

First 10 minutes shred count includes:

- locals

- tourists

- girls in skimpy neon bikinis

- the US Ambassador

- a boat

And these biters double in size every 36 hours! Extrapolate this algorithm: If there's nothing to stop them from growing, how long will it take until the earth's surface is destroyed with nothing left to sustain them but each other's flesh? How big will the last fish standing be, and would its mass create a pull too strong to sustain the physical balance of the universe? COULD THERE BE A SEQUEL EXPLORING THESE ISSUES PLEASE.

Anyway, back to the lab, where Tiffany feels awful. So does Greg Brady, who plays Government Dude In DC Trying To Get Things Done By Yelling Into A Cell Phone. (Greg Brady's character is named Bob Grady, maybe to make it easier for Greg to remember his own name? Everyone has days like that.) Someone throws a dead piranha on the Venezuelan Colonel's desk to prove a point ("this is bad!") and he is most displeased. How will he get the smell out of his paperwork???

And then there is fish-kicking: Paul Logan on his back at the water's edge, bicycling away the piranhas like an aerobics champ, right before a fellow scientist declaims something like "They won't get away with it this time!" and then gets chomped by an enormous piranha. As for Tiffany, well, she hates it! Really! Hates hates hates! And wants to kill them all!

What happens next is a bit of a mystery because my viewing companions and I ate seconds on pasta before snuggling down into the couches with the dogs and consequently, somewhere post fish-kicking we were all zzzzzzzzz. So please tune in shortly for reportage on a conclusion sure to involve MAYHEM and PULVERIZED FISH BITS.

Special thanks to Julie and Quincy for hosting.

Well, the average piranha is about 8 inches long. If we assume, for ease of calculation, that each piranha is somewhat less than 4 inches wide, then an 8-inch square would accommodate 2 piranhas. The only remaining piece of data needed is how many piranhas you start with. I'm going to pull a number out of thin air -- let's say 200. So 200 piranhas cover 100 8-inch squares. That means that their initial total area was 6400 sq in (100 * 8^2).

ReplyDeleteNow I'm not sure what "double in size" means here, but, again, for ease of calculation I'm going to assume that this refers to length, and that the piranhas grow proportionally, so that in 36 hours a piranha would go from 8 inches to 16 inches in length, and two piranhas would now cover a square 16 inches on a side.

But of course that means that your piranhas are now covering an area FOUR times larger than they were 36 hours before, because area multiplies twice as fast as length.

The surface of the earth is approximately 7.9 * 10^17 square inches.

Define T as time in hours that it would take to cover the planet with piranhas. Define X as T/36 -- X is, in other words, the number of 36-hour periods it would take to reach T. Then:

(6400 sq in)*(4^X) = 7.9 * 10^17 sq in

or

X = log base-4 of (7.9 * 10^17)/6400

According to a logarithm calculator I found on the internet, that's about 14.09, so

T = X * 36

= 507.24 hours, or about 21 days.

Keep it coming, please! Assume each piranha has a starting mass of 6.5 lbs. Uh, then what? I'm only good at fake applied math.

ReplyDeleteWell, while area increases as a square of length (assuming proportional growth), weight increases as a cube of length, because weight can be approximated as a measure of volume. So since length is growing by a factor of 2 every 36 hours, weight is increasing by a factor of eight. Hence:

ReplyDelete6.5 lbs * 8^14.09 or 3.447 * 10^13 lbs

per fish. Since we started with 200 fish, that's a total of 6.894 * 10^15 lbs of fish altogether.

Of course, I've done a lot of hand-waving here -- I assumed 200 fish to start with, fish aren't perfectly rectangular, etc. But I feel like this is a good first approximation.

Oh, and I forgot to answer the last question -- how big would the last fish standing be? But I feel unqualified to answer that question; it leaves the realm of applied mathematics and involves animal behavior, efficiency of digestion, and some other factors. We'd need to consult a biologist -- maybe Tiffany? But I suspect that'd be one whoppin' big fish.

ReplyDeleteI applaud your calculations. Thank you, sir.

ReplyDeleteThere still remains the question of how the last fish standing might affect the balance of the universe - perhaps a study for another time.