I came across the above photo on Reddit the other day (original link here). As one Redditor so aptly put it, “The stupid, it burns!!!” Interestingly, there are multiple layers of stupid here. Like a giant stupid onion. Leaving aside the fact that water dumped into a sink would eventually wash back into the ocean, how many buckets of water would each Earthling need to dump to cancel out the rising sea levels?
According to the Wikipedia entry for "Current sea level rise", predicted values for the ocean rise due to global warming range anywhere from 90 to 880 mm. I'll take 90 mm and just calculate the lower bound. The total area of the oceans is roughly 3.4×1014 m2, meaning that the total volume is about 3.0×1013 m3. One bucket might hold 50 L and there are 6.7×109 people in the world. Form this, we can compute the total number of buckets needed,
# of buckets = (total volume) / [ (volume per bucket per person) × (number of people)]
= (3.0×1013 m3) / [ (50 L per bucket per person) × (6.7×109 people)]
= 90,000 buckets.
Even neglecting the fact that the water will just wash back into the ocean, this method would still require every person on the planet to dump 90,000 buckets of sea water down their sink. As Shakespeare might once have said, "The stupid, it doth burn."
Sarah Palin said there were “hundreds and hundreds of thousands of people.” Glenn Beck put the estimate at 500,000 people. Congresswoman Michelle Bachmann stated that she wouldn’t let anyone tell her there were less than 1 million people. AirPhotosLive.com estimated only 87,000 people based on aerial pictures it took. How many people were at the Glenn Beck rally?
As you can see from the photos on AirPhotosLive.com, most of the people assembled along the Lincoln Memorial Reflecting Pool. According to Wikipedia, the pool is approximately 618 m long by 51 m wide. Judging from the photos, attendees seem to cover an area between 3 and 4 reflecting pools wide, or roughly between 150 m and 200 m. Multiplying by the reflecting pool length, this means the total area taken up by the attendees is between 92,700 m2 and 125,000 m2. To be sure we’re not forgetting anyone, we’ll count the attendees that spilled over near the Washington monument and those that got a front row seat. This looks like no more than 20% of the total number of people, so we’ll say they cover a total area of at least 90,000 m2 and at most 150,000 m2.
Looking at the aerial photo, there’s a whole lot of green grass you can see between people. This makes sense since most people don’t like to be squished and you need some extra room so that people can move around. Each person needs at least 1.0 m2 of space to feel comfortable. Judging from the sparse parts of the crowd, there’s appears to be no more than 10 m2 of space between people on average. The average density certainly lies between these two extremes. From these densities, we can use the equation
number of people = (density of people) × (area)
to compute an upper bound,
number of people = (1.0 person per m2) × (150,000 m2)
= 150,000 people
and lower bound,
number of people = (0.1 people per m2) × (90,000 m2)
9,000 people.
As you can see, the “87,000 people” estimate from AirPhotosLive lies right in the middle of the two extremes. It is certainly a reasonable estimate, and it brings up an important point. One way to test the accuracy of your estimate is using upper and lower bounds. By using the largest and smallest realistic numbers in your estimation, you can put a cap on what the actual number must be. We know there’s certainly more than our lower bound of 9,000 people and certainly less that our upper bound of 150,000 people.
By using upper and lower bounds, we also see that our politicians and pundits are either lying or possess a certain degree of innumeracy. Of these two options, I sincerely hope it’s lying. I’ve grown accustomed to politicians bending the truth, but I’m absolutely terrified by the thought that people who have gained this much influence can’t do middle school math. This does beg one to ask, “Why even bother lying about numbers like this?” For one, false claims like this are easy to debunk even with mediocre math skills. In addition, 87,000 people at a rally is nothing to sneeze at, so why exaggerate?
Finally, I should note that I had some hesitation when writing this post. This is not intended to be a political blog, and I’m not here to spout my personal beliefs. The fact is that no matter what side of the political spectrum they’re on, rally organizers tend to exaggerate numbers to make it seem like they’re more popular than they really are, and it’s our duty as rationally thinking citizens to call them on it.
It’s my sister Laurie’s birthday today, and much as it pains me to say it, it’s never easy being the four-years-younger brother of a super genius. When you’re graduating middle school, she’s graduating high school. When you’re graduating high school, she’s graduating college. When you’re getting a BS from MIT, she’s getting a PhD from Harvard. When you publish your first book, she’s giving a TED talk and getting tenure at Yale. Even today as she grows ever older and more decrepit, turning an age I can remember our mom and dad being, I can still feel that familiar tingle of our (usually) healthy sibling rivalry. If there's one thing I take solace in, it's that I've never had to worry about getting monkey poo in my hair. What’s the probability that at some point in her career as a primate researcher, Dr. Santos has gotten monkey poo in her hair?
Cayo Santiago is one of the places my sister does research on primates. Located southeast of Punta Santiago, Puerto Rico, the 600 m by 400 m (240,000 m2) island is home to about 950 Rhesus monkeys. As can be seen from the photo on the right, Cayo is a fairly lush island featuring lots of trees monkeys can climb.1 I’ll assume a typical monkey spends about 50% of its time climbing, meaning that at any moment there are about 475 monkeys in the trees.
Each year, Laurie generally spends about 2-4 weeks on Cayo, and she has done so for about 10 years. If she works 8 hours per day, she’ll have spent up to 93 days on the island. Assuming a Rhesus monkey’s digestive schedule is similar to that of a human, each monkey probably “uses the bathroom” at least once per day. From this and the information above, we can estimate the total number of high altitude monkey poos taken while Laurie has been on the island
(# of poos per day per monkey) · (# of monkeys) · (# of days)
= (1.0 poo per day per monkey) · (475 monkeys) · (93 days)
= 44,175 poos.
From a bird’s—er—monkey’s-eye view, her hair will appear to have about 1.0 ft2 of area. Our monkey bombardier will have to hit this spot if Laurie is to spend the rest of her night shampooing. From this we can calculate the probability of a random poo landing in her hair,
P = (area of hair) / (total area)
= (1.0 ft2) / (240,000 m2)
= 3.9×10-7.
The probability of a poo not landing in her hair is, of course, 1 – P. The probability that none of the 44,175 monkey poos have landed in her hair is (1 – P) 44,175 ~ 0.98. This means there’s a 2% chance that a monkey has poo-ed on my sister’s hair at least once.
Happy Birthday, Laurie! You’re as good a science role model and an even better sister than I could reasonably have hoped for.
[1] For simplicity, I’ll assume that 100% of the island is covered in trees.
Look at your math. Now back at mine. Now back at your math. Now back to mine. Sadly, yours isn’t mine. But if you enter the Diary of Numbers Estimation Contest then your math could seem like it’s mine. Look down. Back up. You’ve won a book featuring the math your math could look like. Anything is possible when you enter the Diary of Numbers Estimation Contest. I’m on a blog.
The Question:Isaiah Mustafa (aka the sexy Old Spice man) reached meme status because of his work in a very funny Old Spice commercial. Recently, he created a series of humorous personalized Youtube videos featuring his character from the original commercial. If he worked nonstop for the rest of his life, how many personalized Youtube videos could Mr. Mustafa make?
Rules: You can win a free copy of How Many Licks? To enter, estimate an answer to the question below and send it to “aaron at aaronsantos period com.” If your answer is closest to my estimate1, I'll mail you a free, signed copy of How Many Licks? To be eligible, you must submit your entry on or before September 15, 2010. Don't worry; I won't spam you or share your email with any third parties.
[1] I know, I know. How do I know my answer is correct? I don’t. I make no pretenses that my answer is correct or even close. Your answer may very well be a better estimate than mine. In fact, your estimate may even be exactly right and you still may not win the contest if somebody else's answer is closer to mine. Sorry about that. This is the best way I could come up with to pick a winner and I'm not changing it now. Like any good game, there's an element of luck required even if you do have great skill. With that disclaimer out of the way, good luck and happy calculatings!
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”.
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!
