A Sense of Scale

My best math teachers and professors used to encourage the class to get a better feel for numbers by playing estimating games of all sorts: “How many jellybeans do you think are in this jar?” “How many bricks do you think are in the far wall?” “”How many houses are there on the next block?” This sort of estimating game has found its way into the interview process at Microsoft, where they ask questions like “How many gas stations are in the U.S.?” (Yes, the point of the question is to see how you go about solving problems and not to test your trivia skills, but having good estimation abilities is part of problem solving.)

Here are a few interesting sites and pages that I’ve come across recently that should help hone your estimation abilities by giving you a sense of scale.

First on the list is The Megapenny Project, which aims to help you visualize large numbers by showing you what different orders of magnitudes of pennies look like. It covers scales from oen penny to one quintillion (that’s one followed by 18 zeroes) pennies. Pictured below is what one hundred million pennies would look like:

I would be a bad Tucows employee if I didn’t make special mention of the bonus session of The Megapenny Project that uses cows: MegaMoo, which shows how large 1, 5, 72 and one million cows are. Pictured below is a cube made of one million cows, posed beside the Empire State Building and the Sears Tower for comparison. Note that if we decided to gather a collection of made up of one cow for every domain Tucows has under management, we’d need at least 5 of those cubes.

Taking things to a more cosmic scale, our next site on the list is The Size of Our World, which compares the size of Earth to the other planets in the solar system and our sun to other stars in the galaxy. If you thought it was a long trip to IKEA, wait until you see how tiny the sun is compared to some of the better-known red giant stars (better-known because their names have been used in Star Trek.

I can’t mention sites that cover varying scales without making mention of the classic educational film Powers of Ten, which was created for IBM by the office of those masters of gorgeous plywood designs, Charles and Ray Eames. The film expores a vast range of scale, from the human to the galactic, then back to the human and into the subatomic. Luckily, someone’s posted the whole film (it’s just under nine minutes long) on YouTube.

I’ll close this list with my favourite “couch gag” from The Simpsons. Since many of their writers are nerds, they’ve seen Powers of Ten and created what is probably the best homage to the film: a Homer-based recursive parody.