The X-Change Files explores the intersections of science and entertainment, regularly taking a look at the ways in which science is portrayed in film and television. Given that science is often the basis for provocative and compelling storylines, we’ll also highlight the latest scientific discoveries. Perhaps most importantly, we’ll examine the ways in which public opinion is shaped and behavior is changed by what people see on their television sets and in the movie theaters.
And it comes with an impressive list of contributors.
So I will welcome them, followed by picking some nits in the analysis of Pixar’s new movie, UP which they point out in the post Going UP! . They link to a WIRED story about the movie, which estimates the weight of the house needing to be lifted by helium-filled balloons as being 100,000 lbs.
One more simple calculation — 100,000 pounds divided by 0.067 pounds per cubic foot — and you’ve got that it would take 1,492,537 cubic feet of helium to lift the house.
Ignoring that we’re working in English units, which scientists don’t really do very much, the big thing that pops out to the budding, fully-bloomed, or dying scientist is the misuse of significant digits. Do we really believe the estimate of the house’s weight is exact? No, it’s probably good to 2 digits, at best — the house could easily weigh several thousand pounds more or less than the estimated value. So the answer is that it takes 1,500,000 cubic feet of Helium to fill the balloons. You can’t specify it any better than that. The same mistake propagates through the calculation of the number of balloons.
Now, let’s assume you’ve got a bunch of spherical balloons three feet in diameter. They’ve got a volume in 14.1 cubic feet, so you’d need 105,854 of them filled with helium to lift the house.
Same deal. Not only is the volume not precise, but the balloon diameter is an estimate as well. There is no way to make an exact count to the last balloon you would need. So while Pixar got the science right in estimating the number of balloons needed, and it’s great to be enthusiastic about that, it’s also important not to drop the ball when discussing how well they did.
(The most consistently egregious abuse of significant digits in the media (though not necessarily entertainment media) is when there is a conversion from one unit system to another. An approximation of “30 meters high” is converted using 3.28 feet per meter, so that this rough estimation is then given as 98.4 feet high, instead of 100 feet high, as it should be given.)
And, getting on to some more physics, I see that zapperz has taken a pass at analyzing the physics in this movie as well. The Physics in Disney/Pixar’s “Up” takes another look at the buoyancy issue, and points to what might be a little problem among the rest of the decent physics treatment of the buoyancy. Rhett also looks at this issue, as well as some other analysis.