My New Job at Gustavus Adolphus

I'd been at my new Gustavus office only a couple hours when someone stopped by and tacked my nameplate up.  I could get used to this.  Good schools really know how to treat their faculty with respect.

Give It a Rest, Fermi

I can't get away. I went to a "Night of Unbelieveable Fun" hosted by the Saint Paul Saints. Who do I find in the bathroom?  Enrico Fermi watching me pee:

A Question from Ninja Brian

Today's question comes from physicist Brian Wecht. Brian is co-founder of Story Collider, a podcast that shares people's personal stories about how science has affected their lives. Brian is also a member of Ninja Sex Party.¹

Here's a picture of Brian in ninja form:

Brian's a very good ninja.

Brian asks,

What is the weight of all the facial hair grown by the world population of men on a given day? If you concentrated all that hair into one curly, villainous moustache, how long would that moustache be?

If I go a week without shaving, I'll have about half a centimeter of facial hair, which means my hair grows about 0.1 centimeters per day. Follicles are separated by about 1.0 millimeter, and they span an area of roughly 100 square inches.  Assuming each hair has a thickness of 0.1 millimeters and the same density of water at 1.0 grams per cubic centimeter, I would grow about 60 milligrams of facial hair each day.

For simplicity, I'll consider myself to be a typical man. This is not necessarilly a safe assumption however, since, follically speaking, I'm much more Wolverine than Bieber. Still, it should be a safe assumption for an order of magnitude estimate. If that's the case and we assume 20 percent of the world population (~1.4 billion people) are facial-hair growing men, then the total weight of facial hair grown on a given day would be about 90 tons.

This brings us to the second part of Brian's question: How long of a villainous mustache can we make?

Ninja Brian will save us from this dastardly villain.

Mustaches take up much less area than beards. If you glue all the beard hair grown in one day to the ends of the mustache hair grown in one day, it would be as if the mustache grew about four times faster than normal, which amounts to roughly 0.4 millimeters of growth each day. Spread out over the 1.4 billion facial-hair-growing men, that would give a villainous mustache that's about 350 miles long. Snidely Whiplash would be proud.

Thanks for a great question, Brian!

Aaron Santos is a physicist and author of the books How Many Licks? Or How to Estimate Damn Near Anything and Ballparking: Practical Math for Impractical Sports Questions. Follow him on Twitter at @aarontsantos.


[1] Somehow how I'm super happy that the blog has gone from a Nobel Laureate to a member of Ninja Sex Party.

A Question from Nobel Laureate Bill Phillips

When I was an undergrad, I had this delusional desire to become an actor. As a male thespian with no experience and mediocre talent, I quickly discovered there's one sure way to get decent theatrical roles: audition for male parts at all girl schools. And so, I auditioned for student productions at Wellesley College where I met a variety of wonderful people. One of said people is my buddy Christine. Christine was (and is) super cool, and not only because she used to get me free food at the Wellesley cafeteria. Christine was also cool because she was taking physics.¹ I distinctly remember one conversation I had with Christine about her physics class:

Christine: I'm taking physics at Wellesley.

Me: You should really see if you can take it at MIT instead.

Christine: [trying to be nice] Um...my dad thinks they do a better job teaching physics at Wellesley.

Me: [offended] What the hell does your dad know about physics?

Christine: Well, he did get his doctorate from MIT, and he just won the Nobel Prize in physics.

Me at this point in the conversation.

This week's question comes from Christine's dad (aka Nobel Laureate Bill Phillips.) He asks, "How many grains of sand are there on the world's beaches?"

Judging from a map, the Eastern Seaboard of the United States appears to be about 2000 miles long. By comparing with other coastlines, we can estimate the total length of coastlines in the world to be about 50 times this.² I'll assume one-third of the world's coastlines are sandy beaches.

Assuming the Cape Cod beaches I grew up near are fairly typical, they might extend about 200 feet up from the water. The depth of sand varies quite a bit from place to place. I've been on beaches where you'll hit rock before finishing the moat around your sandcastle, but many beaches have sand that extends much deeper. I'll assume the sand extends 10 feet deep on average since the actual number is likely to lie between 1 foot and 100 feet. From this, we can calculate the total volume of sand on the beach to be about 10¹⁰ cubic meters.

One type of sand.

Like beach depths, sand grains too vary over a size range that's greater than one order of magnitude. I'll assume 0.3 mm for the width of a sand grain since even the largest sand grains are each only a few millimeters in size. This gives a total volume of 0.03 cubic millimeters. From this and the total beach volume above, we can estimate that there are 10²⁰ grains of sand on all the beaches in the world.

Thanks for the great question, Dr. Phillips!

Aaron Santos is a physicist and author of the books How Many Licks? Or How to Estimate Damn Near Anything and Ballparking: Practical Math for Impractical Sports Questions. Follow him on Twitter at @aarontsantos.

[1] Taking physics automatically makes you cool.
[2] It will certainly be between 5 and 50 times the Eastern Seaboard.

ABC Radio National Interview

Check out my interview with Robyn Williams on ABC Radio National.

Maxim

So, I'm in the latest issue of Maxim, and I noticed a funny thing happens when you tell people this...

Thank you to my cousin Matt for the picture of the article.

Curiosity

Just a quick note on NASA's Curiosity Rover that landed on Mars earlier this week.  Someone on Reddit described it as being like sinking "an interplanetary hole-in-one."  A typical golf hole might be about 500 yards with a cup that's about 4 inches wide, meaning that the angle of the golfer's shot can't be off by more than 0.006 degrees.  The Curiosity Rover landed on a planet with a diameter of 6800 kilometers located 1.669 astronomical units away, meaning that the angle of NASA's "shot" can't be off by more than 0.0015 degrees.  It's a great comparison, but even as unlikely an event as a hole-in-one underestimates the precision that NASA engineers obtained.

End of Summer Rollercoaster Contest

I normally like to come up with my own questions for contests. However, every once in awhile I get a question that's so good, I have to use it. My former student Ben sent me this question the other day, and it falls into this category.

You know the rules.  I post a Fermi question below. To enter, estimate an answer and send it to “aaron at aaronsantos period com.” If your answer is closest to mine, I'll mail you a free signed copy of Ballparking: Practical Math for Impractical Sports Questions.¹ Second prize receives a signed copy of my other book, How Many Licks? Or How to Estimate Damn Near Anything. Submit your entry on or before August 31, 2012. Don't worry…I won't spam you or share your email with any third parties.

Here's what Ben asked:

I was at Cedar Point (the amusement park in Ohio) with Che and David the other day and we had an idea for another estimation problem that I think is pretty cool so I thought I would send it to you.  There's a ride at Cedar Point called Top Thrill Dragster - it looks like this :

Basically you get launched, climb the tower, and then tumble back down.  For a better idea of the ride, here is a passenger's point of view: 

Occasionally, though, this happens: 

It's called a "rollback".  As you might imagine, this means that once in a blue moon, this actually happens: 

Question is, how many times?  I actually do know the real life answer to this, although it could change any day.

Alright, fellow estimators!  How many times does the roller coaster get stuck on top each year?

[1] 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!

We Have a Winner!

We have a winner for the "Look Out!" contest.  Here's my estimate:

In order for the camera to break, the puck must be slapped against the boards at the exact spot where the camera is.  Pucks are dumped against the boards more than twice and fewer than 200 times per game, so a reasonable estimate is about 20 hits per game.  The puck itself needs to land in a space the size of a camera lens.  The size of the lens depends on whether we're talking about a regular camera or a video camera. 

This digital camera is a fair bit smaller...

...than this professional video camera.

For the sake of the problem, I'll assume we're talking about regular digital camera since that is what I was looking at during the game.  From the picture above, the lens appears to have a diameter of roughly 3 inches giving an area of around 10 square inches.  The circumference of a hockey rink is about 500 feet with a height of about 12 feet giving area of 6000 cubic feet.  Assuming the pucks are distributed uniformly over the boards (not necessarily a safe assumption), you'll have about a you'll have about a 1 in 100,000 chance that the puck hits the camera.  Since the cameraman was only there about 20 percent of the time, that decreases the probability that any given hit will break a camera to 1 in 500,000.  Since there are 20 pucks hit hard against the boards per game and a 1 in 500,000 chance that any given puck will hit a camera, there must be a probability of 1 in 25,000 that any given game will feature a broken camera.

At present, each team plays 82 games per year.  If we consider that many of the early years in NHL history had teams playing fewer than 50 games, we can estimate that on average about 60 games are played each year.  Half of these might have a camera man.  That gives 30 games with a camera per team per year.  On average, there've been about 15 teams each year throughout the 90 years of NHL history.  From this we can conclude that 40,000 games had a camera that could have been broken.  

Since there have been about 40,000 games with a camera and a 1 in 25,000 chance that a game with a camera will end a s a game with a broken camera, we can conclude that roughly 1.9 cameras have been broken.  Since this is an order of magnitude estimate, any it's possible that anything up to 19 camera have been broken.

Congratulations to the winner and runner up who will receive a free copy of Ballparking: Practical Math for Impractical Sports Questions and How Many Licks?, Or How to Estimate Damn Near Anything, respectively.