Fun with Jelly Beans

January 14, 2009

One of my favorite visual analogies for the distribution of "stuff" (as my cosmologist spouse likes to call it) in the universe is a big old jar of jelly beans:

Note that most of them are black, with just a few colored jelly beans dotted about. Those scattered bits of colorful beans represent every single bit of visible matter in the universe: every star, every planet, every galaxy, every planet, every person. It adds up to about 4%. Another 26% is dark matter: we can't see it, but we know it's there because we can see the gravitational effects from all that invisible (to us) mass. The rest of the "stuff" -- a whopping 70% -- consists of dark energy, and scientists still know very little about what this mysterious energy might actually be. But again, they figure it's got to be there, because we can observe its effects in the accelerating expansion of the universe.

I like the image above because it drives home the point of just how insignificant we beings of ordinary matter are in the grand cosmic scheme of things. (As Sean likes to say, we are merely the olive in the martini.) Which in turn makes it all the more amazing that we can accomplish such feats as "weighing" the stuff in the cosmos in the first place -- or, more mundanely, a simple mathematical trick like guessing the number of jelly beans in a one-liter jar.

An episode of the popular TV series Monk showed the "defective detective," Adrian Monk, at a local carnival. In between dodging his usual phobias, he enters a contest to guess the number of jelly beans in a jar -- and naturally, he wins. Such a task is a snap for someone with OCD. That said, he figures it out in part because he observed a bunch of empty jelly bean bags near the jar, and made an educated guess.

Even without that, he could probably have come pretty close, using one possible calculation I found detailed on the back of brochure being distributed at the AAS meeting by the Chandra X-Ray Observatory:

1. First, it's useful to know that your average jelly bean is roughly 1 centimeter long and 1.5 centimeters wide (diameter). You also need to know the volume of the jar (1000 cubic centimeters).

2. Second, they are irregularly shaped, so they're not going to rightly packed in the jar; assume that about 80% of the volume will be filled.

3. Per the brochure, "The number of jelly beans is the occupied volume of the container (80% of one liter) divided by the volume of a single jelly bean." To figure out the volume of a single jelly bean, figure on the volume of a cylinder measuring 2 cm long and 1.5 cm in diameter. (Can't remember how to do this? That old geometry textbook will tell you. Go ahead, get it, we'll wait...) That's about 3.5 cubic centimeters.

So, the approximate number of jelly beans in a one-liter jar is (.80 x 1000 cubic centimeters. divided by 3.5 cubic centimeters... or around 229 beans. And if we're using the above jar as the sample case, and it accurately represents the distribution of stuff in the universe, we can then figure out how many of those jelly beans are going to be black (dark): 96% of them.

See? Was that so hard? There are supposedly other possible calculations, but most of us just need one winning strategy. Now we have one, courtesy of NASA. I just need to bide my time until I happen upon a "guess the jelly beans" contest....

Photo: Fermilab.

Comments

[rhett]

I bet it was pain in the rear to find that many black jelly beans. I guess you could just go around and find the left over beans after easter-time (many people don't like the black ones).