Tuesday, April 8, 2014

I Ain't Dead Yet

In the words of the great Richard Pryor, "I ain't dead yet."


If you've checked the blog over the past six months, this fact might comes as a great surprise. I haven't exactly been lighting up the Blogosphere lately. There's a reason for this. Apparently starting a new tenure track position is quite time consuming.

"Good new, Lieutenant, you've just been promoted!"
Between applying for grants, research, prepping classes, grading, and working with students, I've been super busy.

Lack of free time aside, life at Simpson has been very good. When you ask new physics teachers about their students, they often respond by saying...


Fortunately, Simpson has many talented and intellectually curious students, so I rarely feel like the offensive ethnic stereotype in the video above. That said, I'm older now, and I don't always know how to relate to students. Why do they think Christian Bale is the best Batman? What is the obsession with One Direction? Why do my student evaluations say I need more cowbell? And, perhaps most importantly, why did did they give me the nickname (and website) Moon Jesus?1

Needless to say, with my students keeping me busy, I haven't had a lot of time for writing (either blogs or books), which is probably just as well...

"Piss off, Stewie!"
That said, I have been keeping somewhat busy. I wrote an article for the Naked Scientists. I made some holiday estimations for the always fabulous Desiree Schell at Science for the People.2 That lead to Kyle Munson's nice write-up in the Des Moines Register. Also, I got this kinda fun email:


Now, if I can only round up Dentist Aaron Santos, Photographer Aaron Santos, and Baseball Player Aaron Santos, I can fulfill my dream of starting "The Legion of Super Heroes Named Aaron Santos".3

Anyway, that's where I stand. Hopefully, I can carve out some free time soon so I can start writing more consistently again.

Stay well, Internet.

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] I still have no idea whether or not this is a compliment.
[2] Also, my apologies to Desiree.  I just realized that Iidiot that I amhave been misspelling her name for years, and she's been too nice to correct me on it.
[3] Admittedly, our super powers are less than inspiring.


Friday, September 13, 2013

Special Guest: Rick Lombardo


Today's special guest is San Jose Repertory Theatre's artistic director, Rick Lombardo. A prolific regional and off-Broadway director, Mr. Lombardo has received numerous awards for his work both at San Jose Rep and New Repertory Theatre in Boston.

Many artists are concerned with the current trends in climate change. Mr. Lombardo is no exception.  He writes,

I've been thinking about climate change a lot, and while this question doesn't directly correlate to a warming planet, it was inspired by the problem. If all the water molecules present in the atmosphere at any one moment fell to the surface of the earth, what would happen to average sea levels around the world?

If you've paid attention to science news, you know that melting glaciers are contributing to rising sea level with an average rise of 3.3±0.4 mm over the past twenty years. This doesn't seem like very much, but over several decades it can have a profound impact on coastal communities. How does it compare with the rise that would occur if all atmospheric water rained down at once?

Wikipedia's entry for "Atmosphere of Earth" states the following:
According to the American National Center for Atmospheric Research, "The total mean mass of the atmosphere is 5.1480×1018 kg with an annual range due to water vapor of 1.2 or 1.5×1015 kg depending on whether surface pressure or water vapor data are used; somewhat smaller than the previous estimate. The mean mass of water vapor is estimated as 1.27×1016 kg and the dry air mass as 5.1352 ±0.0003×1018 kg."
From these figures, we can see there are, on average, roughly ten trillion tons of water in the atmosphere. If it all fell to the Earth at once, would it produce floods of literally biblical proportions?

"Get your cubit stick ready!"

Liquid water has a density of one gram per cubic centimeter. If you simultaneously condensed all the water in the atmosphere into liquid form, you'd have about 10 billion cubic meters of water. The oceans cover about 400 million square kilometers of the Earth's surface. Spread out over this area, all the water from the atmosphere would cause the oceans to rise a grand total of 25 microns, roughly one-fortieth of a millimeter. Needless to say, things wouldn't change very much.
"OK, never mind...everybody off the boat."
Thanks for a great question, Rick!






Wednesday, September 4, 2013

Special Guest: George Goodfellow

To celebrate the start of a new school year, we have a question from a very special guest. In addition to being Rhode Island's 2008 teacher of the year, George Goodfellow was also my high school chemistry teacher and one of the main reasons I became a scientist.1  Mr. Goodfellow writes,

At what point in the equilibrium that is a balance of living plant organisms, living animal species and the total available energy on Earth will the ratio of Animal/Plant Species become so large as to create a collapse of the human population?

Leave it to Mr. G to start us off with a light topic. The question reminds me of Trantor, the fictional city-world in Isaac Asimov's Foundation Trilogy. To support Trantor, tens of thousands of ships from twenty agricultural worlds had to be flown in just to supply enough food.

Trantor would look a lot like Star Wars's Coruscant if you got rid of all those pesky Jedi.
If we ignore help from other worlds, the collapse should happen much more quickly. At present, the world population sits around seven billion and is constantly growing. Given Earth's land area is roughly 150 million square kilometers, each person would own about 5.3 acres if the land were divided equally. How much land does one person need to survive? This homesteading infographic provides a good starting point:

How much land is enough to live off? (Click to expand) 
According to the infographic, you need at least 0.5 acres of land per person to survive. This would imply Earth could support, at the very most, about 70 billion people before collapse would occur. Note that we haven't accounted for the fact that not all land is farmable. Given the large swaths of land in desert, mountain, and other inhospitable regions, we're probably significantly closer to carrying capacity. If only half the land were farmable, we could support 35 billion people, meaning we'd already be at 20% of the maximum carrying capacity.

Are there any ways to expand this limit? I've written previously about skyscraper farms. While the maximum number of people that could be fed by one of these farms is greatly exaggerated by the farms' proponents, the farms may still significantly increase Earth's maximum carrying capacity. Furthermore, food scientists are constantly finding ways to feed the growing population...

...food scientists like Norman Borlaug. Note: Never try to be as cool as Norman Borlaug. Unless you can save over a billion people from starvation, you're not going to come anywhere close. And to think, this probably the first time you've heard of the man.
Short of coming up with more efficient ways to develop food, our most realistic solution seems to be pumping NASA full of money so they can supply us with tens of thousands of ships that will travel back and forth between twenty terraformed agricultural worlds in order to supply Earth with its daily food needs. Or, you know, people could start using birth control and have fewer kids. Either way would work.

Thanks for a great question, Mr. G!

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] Admittedly, there were a few nights when I cursed him for bestowing this fate on me, but for the most part it's been pretty good.


Wednesday, July 24, 2013

Wave at Saturn

WHO HAST WOKEN ME FROM MY SLUMBER?!?!?!?!



In case you missed it, there's a cool picture of the Earth and Moon taken from Saturn. Apparently a bunch of us earthly homebodies decided to wave at the Cassini spacecraft as it took pictures of us.

"Hi, Mom!"

On Earth, we're hit with a flux of about 1400 W/m2 of sunlight. Our bodies have an area of about one square meter, and I'll assume only 1/10 of the light that hits each of our bodies gets reflected out of the atmosphere. Since visible photons carry a few electron volts,1 we can estimate that 1020 photons leave each body every second.  These photons will be distributed over a sphere with a radius equal to the distance to Saturn, approximately 1.2 billion kilometers. A small fraction of this sphere coincides with the Cassini's camera lens. Assuming it's like most digital cameras, the area of Cassini's lens should be roughly 10 square centimeters. That's about one part in 1028 of the total area covered by the photons. Assuming a shutter speed of one second, the probability that one of your photons will appear in the "Wave at Saturn" picture is about one in one-hundred million. Since the world contains 7 billion people, there's a pretty good chance at least one of humanity's photons is in the picture.
[1] One electron volt is equivalent to 1.6×10-19 Joules.







Friday, June 28, 2013

101 Things I Learned in Engineering School


I just got John Kuprenas and (friend of the blog) Matt Frederick's 101 Things I Learned in Engineering School, and I absolutely love it. It concisely and elegantly summarizes the essential lessons you'll discover as an undergraduate science or engineering major. I plan to reference it frequently in my physics classes at Simpson next year. I highly recommend it as a gift for any recent engineering graduate. Also, check out the other books in Matt's 101 Things I Learned... series.

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.



Wednesday, June 26, 2013

Special Guest: Damon Brown

Today's special guest is Damon Brown. Damon has quite an eclectic collection of interests. He's written for a diverse group of audiences, with articles appearing in everything from Playboy to Family Circle, while covering an equally diverse array of topics: pop culture, technology, video games, music, human sexuality, etc. He's written 14 books, his most recent being Our Virtual Shadow: Why We Are Obsessed With Documenting Our Lives Online.

Damon asks,

The latest data says the average American spends about an hour using his or her smartphone every day, usually doing some non-phone activity like using an app. So, assuming we get a phone when we become teenagers, how much of the average American life will be spent using the phone?

Admittedly, I'm an odd choice to do a calculation like this.1 I still (somewhat proudly) have what I consider to be a state-of-the-art flip phone. Despite being seven years old and having been dropped so many times it's developed the phone equivalent of cerebral palsy, it still serves my purposes quite well. For a luddite like me, Damon was kind enough to provide me with this reference breaking down the various uses of smart phones:

My phone can do exactly two of these things.
The lifespan of a person living in a technologically advanced society is about 80 years. If everyone receives a phone upon becoming a teenager, then, on average, people will each have about 70 years to stare at tiny screens. One hour per day is 1/24th of your total time, which means you'll spend a total of roughly 3 years on your smartphone. Breaking this down, that'd be 300 days of talking, 220 days of texting, 96 days of gaming,2 and 340 days worth of visiting the Internet and social networking.

Thanks for a great question, Damon! Find out more about Damon on his website or follow him on at @browndamon.



[1] At least, I would be an odd choice if there were other silly physicists out there doing calculations for people on their blog.
[2] FIVE GOLDEN RIIIIIINGS!!!!!!




Thursday, June 20, 2013

A Treatise on Jose Iglesias

Last week I posted a note on Facebook about Red Sox shortstop Jose Iglesias. According to Baseball Reference, the light-hitting Iglesias has a career WAR1 over three times larger than slugging third baseman Will Middlebrooks, despite having less than half as many at bats. This season has been particularly rough on Middlebrooks who sits at a WAR of minus 0.7 with a batting average hovering around the Mendoza line. In contrast, Iglesias has been (relatively speaking) tearing the cover off the ball by hitting well over .400 with a WAR of +1.8, all while playing stellar defense. To put this in context, Iglesias's stats, if extended over a 162-game season, would give him a WAR of 10.4, which is about 50% better than Miguel Cabrera's WAR during his MVP Triple Crown season last year. This inspired my buddy Adam to ask me about sample sizes, so I figured I should address this on the blog. In baseball, when should a sample size be considered significant?

First off, it should be stated that there are no exact cutoffs in probability and statistics. As I explain in Ballparking, even a career .200 hitter like Mario Mendoza has a (small) chance of hitting .400 over the course of an entire season. There's no magic number above which we can definitively say, "These results are statistically significant." Fluctuations happen in any sample size no matter how large. That said, if we have a random sampling of statistically independent events, we can make definitive statements like the following:2
There's a 95% chance that Jose Iglesias's average over his next 92 at bats will be between X and Y.
Here, X and Y define what's called a confidence interval. We have limited data, but given the information we do have, we're 95% percent certain that Iglesias's batting average over the next 92 at bats will be between two numbers X and Y. What are those two numbers? Wikipedia's entry for sample size determination gives a good description of how to calculate them. The width W of the confidence interval is given by


where n is the sample size, i.e. the number of at bats. Since Iglesias has had 92 at bats so far, we have W = 0.045. Iglesias is currently batting .435. If we believe Iglesias's stats represent a random unbiased sample, then we would expect there to be a 95% chance Iglesias's next 92 at bats will give a batting average between .412 and .457.

Did I make a math mistake? Is Jose Iglesias the next Ted Williams? The problem lies in the fact that Iglesias's 92 at bats were not selected at random. I noticed Iglesias's batting average because it was incredibly large. If I took any 750 baseball players and gave them each 92 at bats, there's a good chance some of them would, by shear dumb luck, hit over .435. Even at a 95% confidence ratio, you'll still have 5% of players with batting averages that lie outside the confidence interval. Given 750 Major League players, this means roughly 38 players will be outside the confidence interval. Iglesias's .435 average is almost certainly an outlier due to random fluctuations in the large population of baseball players. The only reason I singled him out is because he randomly (and luckily) happened to have one of the largest and therefore most attention-drawing fluctuations.

Despite the fact that Iglesias's average is almost certainly a random fluctuation, the shortstop still shows a lot of promise. If we look at his 2012 season during which he hit an abysmal .118 in 25 games, we notice he still nets a positive 0.3 WAR. Extended over a 162-game season, he would get a not terrible WAR of 1.9. Why? His defensive capabilities more than adequately compensate for poor hitting. Over his career, he's averaging a 5.4 WAR per 162 games, which is more than double the 2.6 WAR averaged by current starting shortstop Stephen Drew and over seven times greater than 0.7 WAR averaged by current starting third baseman Will Middlebrooks. Even given the small sample size, it's tough to argue that Iglesias doesn't deserve a spot in the starting lineup.

If you like math and sports or know someone who does, make sure to check out my book Ballparking: Practical Math for Impractical Sports Questions.

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] "WAR" is one of those newfangled stats that sabermetricians like to throw around. It stands for "wins above replacement" and is supposed to represent the number of extra wins a player is expected to contribute compared to a standard replacement player.
[2] Strictly speaking, it's a bit more complicated if we're talking about actual baseball players rather than mathematical probability distributions. For example, a player's theoretical batting average is not constant over time. It can increase or decrease depending on the player's age or health.