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1. Make a fist around two fingers (borrowed from someone else’s hand) and squeeze hard for half a minute or more. Then relax your fist, but don’t open it. Delicately slip the fingers out, and then gently try to open your fist. What does it feel like?
2. Stand in a doorway. Push your arms outward, pressing the backs of your hands into the doorframe, hard. Do this for at least half a minute. Then step out of the door, relaxing your arms and shoulders. What happens?
3. Lie on the floor on your back. With your legs straight (knees locked!) have a friend raise one leg and press gently so the leg muscle is stretched. It should be a little uncomfortable (and definitely a little weird) but not painful. Pause for at least half a minute. Close your eyes while your friend lowers your foot slowly back to the ground, holding by the toe. What does it feel like?

The first one in particular is good for moments when you are waiting around or standing in line with a friend. If you know more of these, post them in the comments!

I wrote a Beats-per-Minute calculator. Tap any key to a beat and it will display the tempo. It’s a step above other implementations around the web because it shows correct precision and it changes color once it has an accurate reading. Try it!

You can turn a piece of paper into a sort of puzzle piece in just a few quick folds. With 6 pieces, you can make a cube. With 12 pieces or 30 pieces, you can make pointy stars. (Mathematicians call them stellated icosahedra.) Making the pieces is simple, and assembling them into these shapes is easier than it looks.

Check out more possibilities and video instructions →

I considered two questions about the board game Risk.

1. What are the odds of winning a particular dice roll? (like 3 dice vs. 2 dice, 3 dice vs. 1 die, etc.)
2. What are the odds of conquering a territory? (for example, 20 men invading 17 men)

Anyone who has played risk has an intuitive sense of the answers to the first question. Odds of winning a 3 dice vs. 2 dice battle are about 50/50. The invading army gets the advantage of an extra die, but ties go to the defender. It turns out that these advantages roughly balance each other out. (Full results.)

Question #2 is harder because battles between a large number of soldiers are complicated. It all comes down to who has to roll with a reduced number of dice. For example, if a large army is cut down early with a string of bad luck, its odds of winning go down much faster.

Read more →

Moses Lei, a professional musician and fan of Dr. Horrible’s Sing-Along Blog, has posted some excellent (free) transcriptions.  He has full scores and more generally useful Piano/Vocal reductions.

Carbon dioxide (CO2) is heavier than most other molecules and elements in the air.  In the same way that Helium rises (think of party balloons), CO2 sinks.

With a very large bowl or container and lots and lots of vinegar and baking soda, you can make a little “puddle” of CO2.  When soap bubbles – which are filled with normal air – hover over this puddle, they float in place like beach balls sitting on top of a pool.  You can see this in the picture, but of course it’s much weirder-looking in person.  Bubbles serenely unmoving in midair.

A Giant Bowl. You need a bowl big enough that the CO2 can slosh around without completely seeping away.

Recipe for CO2. A back-of-the-napkin calculation shows that one big box of Baking Soda is good for about six big bottles of vinegar.  Their reaction produces CO2 gas and a big mess.

Bubbles! The classic recipe is 12 parts water to 1 part blue Dawn dish detergent.  A few tablespoons of glycerin (which can be bought at a pharmacy) help the bubbles last longer.  We tried some variations, like all-glycerin bubbles.  It also seemed like a good occasion for the Bubble Thing!

Click an image to flip through a larger view.

Finding the CO2 line. This Four Gas Tester, designed to check if air in a workplace is safe to breathe, showed that the air was normal above the bowl.  But when I dipped the sensor under where the bubbles were floating, red alarm lights indicated that the air was not breathable – too much CO2!