Tuesday, July 27, 2010
A new Dentyne commercial claims we spend 20,000 minutes kissing. What kind of estimator would I be if I didn't check their math? How many minutes does the average person spend kissing?
Couples often kiss each other several times per day1. If we assume the average day consists of 30 seconds of kissing and the average persons spends 60 years in a relationship, then we can estimate the number of minutes spent kissing in a lifetime:
time kissing = (time kissing per day) · (days per year) · (years in relationships)
= (30 s per day) · (365 days per year) · (60 years in relationships)
= 11,000 minutes.
That’s an average of 11,000 minutes spent kissing in a lifetime. The commercial’s claim is well within what one might reasonably expect. Good job, Dentyne and “stub”.
 It’s can be a lot more if they make whoopee.
Tuesday, July 20, 2010
This week's question comes from special guest, Dr. Saul Griffith. In addition to being a 2007 MacArthur Fellow, Saul has received numerous awards for his inventions including the National Inventors Hall of Fame, Collegiate Inventor's award, and the Lemelson-MIT Student prize. When not inventing, he co-authors children's comic books called HowToons about building your own science and engineering gadgets. He is also a columnist and contributor to Make and Craft magazines. Saul writes,
"How many shot glasses of oil per day per person for the average American's personal contribution to the gulf oil spill?"
According to Wikipedia, the Deepwater Horizon oil spill released up to 16,000 m3 of oil per day. There are roughly 300 million Americans. One shot glass contains about 60 mL of volume. From this we can easily compute the contribution per American,
# of shot glasses = (vol. of oil per day) / [ (# of Americans) · (vol. per shot glass)]
= (16,000 m3 per day) / [ (300 million people) · (60 mL)]
= 1.0 glass per day per person.
The oil spill was basically the equivalent of having every American dump a shot glass of oil into the gulf every day. Thanks for the question, Saul!
Monday, July 19, 2010
We have a winner for our “Hamster-Powered Mansions” estimation contest. The question: How many buff hamsters would it take to completely power a mansion?
Mansions come in a wide range of sizes, and each will have different energy requirements. According to Factcheck.org, Al Gore’s mansion used 191,000 kilowatt-hours in 2006. Dividing by one year, we can compute his average power consumption to be 22,000 W.
From this MAKE magazine video1, we can see that a hamster is at least powerful enough to light up an LED, but this is only a lower bound since he might be able to power even more LEDs if we connected them in the circuit. According to Otherpower.com, their hamster Skippy had no trouble lighting up 6 LEDs, and they estimate he should be able to power 200. Being fairly conservative, I’ll assume our hamsters can power 50 LEDs. According to Wikipedia, the voltage drop across one LED is anywhere from 1.5-4.5 V and the current should be between 1 and 20 mA. Assuming the LED acts like an Ohmic resistor,2 we can estimate the electrical power created by a wheel-spinning hamster,
power = (# of resistors) · (current) · (voltage drop)
= (50) · (10 mA) · (3.0 V)
= 1.5 W per hamster.
From this and the power consumption of Al Gore’s mansion given above, we can estimate the number of hamster’s you’d need to power a mansion,
# of hamsters = (power per mansion) / (power per hamster)
= (22,000 W) / (1.5 W per hamster)
= 15,000 hamsters.
You’d need about 15,000 hamsters to power a mansion. Congratulations to our winner Bryan Merrill. Bryan will be receiving a free copy of How Many Licks? Keep reading for our next contest.
 Speaking of MAKE magazine, check out Maker Faire in Detroit July 31 and August 1. I’ve assumed LEDs require 3.0 V and 10 mA.
Tuesday, July 6, 2010
Anyone who reads Diary of Numbers regularly knows I’m far from a grammar nazi. Despite my best efforts, my grammar is typically atrocious. There is, however, one thing I’m very particular on. Even though both of the following are equally correct, I much prefer the latter:
(1) “Dorothy was afraid of lions, tigers and bears.”
(2) “Dorothy was afraid of lions, tigers, and bears.”
Recently, something struck me: since both usages are perfectly correct, I’ve been wasting printer ink all my life. How many cartridges of ink do you waste in your lifetime by always including the extra comma?
This is a tricky problem because the amount of printer ink a person uses varies considerably depending on his/her career, hobbies, etc. If you’re a novelist, you’ll probably be printing a lot more commas than a rodeo clown. Moreover, the problem’s a little wishy-washy because of how I originally phrased it1. A better way to phrase the question would have been, “How many cartridges of ink would you waste in your lifetime if everyone included the extra comma?”
Some days I print 100 pages, other days I print none. On average, I probably print about one full page per day2. Lists appear about once every 10 pages3. This means I’d be printing one superfluous comma every 10 days. At this rate, I’d produce 2900 needless commas over an 80-year lifespan.
According to HP’s website, the average HP LaserJet Q2612A Black Print Cartridge yields 2000 pages worth of ink. A single comma requires about one-fourth the ink of a letter and according to one of my MS-Word documents, there are about 2000 letters per page. This means one page worth of ink is equivalent to about 8000 commas. From this and the info above, we can estimate the number of printer cartridges one will waste in a lifetime,
# ink cartridges = (# ink cartridges per page) · (# pages per comma) · (# of commas)
= (1 ink cartridge per 2000 pages) · (1 page per 8000 commas) · (2900 commas)
= 0.00018 ink cartridges.
Over the course of your lifetime, you will waste 1/5,000th of an ink cartridge by including the extra comma. Even if everyone in America included the extra comma, we’d waste only about 680 printer cartridges each year.
After posting this problem, a good friend, who had previously worked for Yale University Press as a copy editor, told me that Yale never included the extra comma to save ink!
 Sorry about that.
 This is more than printing one page every ten days and less than printing 10 pages per day, which seems like reasonably good bounds for and order of magnitude estimate.
 Again, this estimate is reasonably good if you consider upper and lower bounds. A list certainly does not appear on every page but you’ll probably see more than one on a hundred pages of text.
Friday, July 2, 2010
I like mime. There. I said it. Just to be clear, I’m not talking about the guys who stand on street corners painted gold pretending to be statues just to get money. Those guys are creepy1. I’m talking about real mime. The kind that requires actual talent. I’m talking about the Marcel Marceau kind of mime.
About ten years ago, an acting teacher suggested I see Marceau perform in town that night. Knowing the type of reputation mimes had, I hesitated, not wanting to associate with their type. Ultimately, I decided to go since Marceau was 77 at the point2, and I was unlikely to get another chance to see him perform if I changed my mind3. I wish I could say I had an instant conversion to becoming a mime-lover during the show, but my reaction was more of a “meh.” It was a cute show, definitely entertaining and at certain points even laugh-out-loud funny. It was even good enough for me to admit that not all mimes were bad. But this was supposed to be the best mime in the world, and with that kind of reputation, I expected something better than a bunch of funny and occasionally thought-provoking skits.
I went back to work on Monday. I’d told a postdoc about the show beforehand and she’d chided me about it, but she asked me how it went:
Her: How was the show?
Me: It was all right. Pretty funny actually. There was one bit with a mask maker where he gets a smiley mask stuck on his face. There was also one with a kid in a park where he kicks a ball through a window. In the background, there are these two old ladies watching and gossiping. I think my favorite one was this dating service that keeps sending him women who are either too tall or too fa—
Her: Wait. I thought you said it was just him.
Me: [Confused] It was.
That’s when I realized the magic of Marcel Marceau. None of those other people were there. There were no set, no props, no text nor sound of any kind. Not even a lighting change. Just a silent 77-year-old man alone on a stage.
In honor of the great Marcel Marceau, see if you can calculate how many fewer words he said during his lifetime because of his career choice.
People usually say about 3 words per second when talking. The only times mimes don’t speak is during performance. Marceau might have averaged 5 shows per week during his 60 years of performing. Each show is about 1.0 hour long. If we assume only 5% of his time was spent talking, we can estimate the number of extra words he could have spoken in his lifetime,
words = (yrs performed) · (wks per yr) · (shows pr wk) ·(hrs per show)
· (fraction of time talking) · (words per s)
= (60 yrs) · (52 wks per yr) · (5 shows pr wk) ·(1.0 hr per show) · (0.05) · (3 words per s)
= 8.4×106 words.
Marceau would have said about 8.4 million extra words had he not been a mime.
 I’m convinced they’re the reason real mimes are listed below jugglers and magicians on the street performer totem pole.
 As another member of our class put it, “He’s still alive?!”
 Plus, he was in a Mel Brooks movie. How bad could he be?