## The infinite useful possibilities that exist on the back of an envelope

It has occurred to me that I probably lack a proper appreciation for junk mail. It isn’t the junk that needs appreciated. It’s the envelope. The ubiquity of paper envelopes is a seemingly infinite theater for developing ideas. One doesn’t need a cellphone, notebook — or the money to buy either — to sketch out a plan, make a calculation or write down an idea. A free envelope is sure to arrive in your snail mail within the next day or so.

Suppose one wanted to know how many water molecules there are in a water balloon. That’s not necessary information, of course, but the knowledge would add a great deal to the experience of hitting someone with a water balloon. It would be so satisfying to say something like, “You have just been hit with x number of water molecules!”

A satisfying approximation of the number of water molecules in a water balloon could be made on the back of an envelope. If we assume that an atom has a volume of 10-30 mm and then measure the circumference of the water balloon, we can calculate the volume of the water balloon. Then we divide the volume of the water balloon by the volume of an atom to calculate the number of atoms in the balloon. Then, since water consists of the equivalent of 10 atoms, two hydrogens, and an oxygen, and oxygen is eight times larger than hydrogen, we would divide by 10 to get the number of water molecules.

There are more accurate ways of doing this, of course, but they wouldn’t fit on the back of an envelope. One of the advantages of using envelopes is that they free you from such drudgery as literature reviews, research proposals, administrative restrictions and accuracy. No one would ever know if the number of water molecules in your water balloon was off by a factor of two or three, or even 10 followed by 20 zeroes.

There is another advantage. That is, if your envelope calculations are reasonable, you can proceed with confidence to make further calculations and investigations. Complete investigations are a lot more work and I’d rather not do a lot of work unless the expectations of success are high. I’d rather never do a lot of work under even the best conditions. Luckily, I seldom make further inquiries after my estimations because the chances of any of my calculations turning out to be anywhere near accurate is low. Envelopes are cheap, and work is, well, work.

Approximations don’t have to be very precise. If you are estimating whether to drink some water, it probably doesn’t matter whether there are 10 with 10 zeroes behind it of bacteria, or 12 with 10 zeroes behind it of bacteria in the water. Personally, I’m not drinking it.

Of course, you can also use envelopes for sketching an idea for building a micromanometer, a solar steam engine or an ingenious insect-rearing chamber. Actually, these days, I mostly make notes about things I need to remember to do. If that is all one needs, envelopes work just fine.

If you are looking for something to do, grab an empty envelope and estimate how many envelopes you think you receive in a year. From this, estimate the square centimeters of paper you receive for free each year. Compare the price of an equivalent amount of notepaper and determine which is cheaper. Ha. Try that on your smartphone.

My wife probably wouldn’t like me to stuff my shirt pockets with envelopes. I used to carry around three-by-five cards in my shirt pocket. She said it made me look like a nerd. Now I carry a field notebook in my shirt pocket. She says that makes me look like a nerd. Do you think if I switched to used, junk mail envelopes, I’ll get the same reaction?

Gary McCallister, .(JavaScript must be enabled to view this email address), is a professor emeritus of biological sciences at Colorado Mesa University.

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