Sunday, November 2, 2014

Ask Santos: Goofy Edition

Now we go from the seriousness of Ebola to something a little more goofy. Today's question comes from Kaylee.  She writes,

Since I was little and watched A Goofy Movie quite often, I always wondered what the answer would be to Goofy's question he asks Max while sleeping, trapped in their car due to the presence of Bigfoot: How many cups of sugar does it take to get to the moon? 

I'm not sure if it's even possible to calculate, or what exactly the question is specifically asking (whether it is meaning to use the sugar as fuel, or to build a bridge from sugar), but I'm just curious. Call it a question that's plagued me since childhood.

Why is it that Goofy can talk, but Pluto can't? Seriously, what mutation lead to this genetic monstrosity?
I'd hate to see the Punnett square on that one!  (Image from Wikipedia.)

As you point out, the answer to your question depends on context. Unfortunately, I've never seen A Goofy Movie (I'll have to check it out when I get a chance), so I'll need to use your interpretations:

(1) Building a bridge of sugar. There are obvious practical problems with this (e.g. structural integrity of the sugar, aligning the bridge with the constantly moving moon, not being able to breathe in space, the base of the bridge dissolving when its humid out, etc.) However, from a pure volume perspective, we might imagine building a ladder bridge that was two feet wide, half a foot thick, and long enough to reach to the moon. The moon is 240,000 miles away. If we use the equation 

volume = base*width*height, 

we can get a rough estimate of the volume of sugar ladder and use the density of sugar (1.6 grams per cubic centimeter) to find the total mass of sugar needed. By my estimate, you'd need about 60 million tons (~57 billion kilograms) of sugar to build a bridge to the moon.

(2) Using sugar as a fuel. Food is just like gasoline: both act as fuel. "Calories" are a unit of energy. Just like we talk about the miles per gallon you get out of a good car, you could talk about miles per gram of sugar you get out of a fit person. However, rather than power people, we're using the sugar energy to power a rocket. To escape Earth's gravitational pull, you need an "escape speed" of roughly 12 km/s.1 Rockets typically have a mass of around 5 million pounds, which means they'd require about 40 billion food calories to reach the moon. Carbohydrates have about 4 calories per gram, meaning you'd need about 5000 tons of sugar to reach the moon.2

Just to compare, it would take 5000 tons of sugar to power a rocket to the moon, and 60,000,000 tons to build a ladder to the moon. That's about 10,000 times more sugar required for the ladder.

Thanks for a great question, Kaylee!

Do you have a question you'd like to ask Santos? Try Tweeting him at @aarontsantos for a chance to have your question appear on Diary of Numbers.

[1] This ignores important effects like air resistance.
[2] This weighs more than the rocket itself, meaning you'd need even more energy to reach the moon. For comparison, you can get a rough idea how much rocket fuel is needed here:

Saturday, November 1, 2014

Another Reddit AMA

My last Reddit AMA was fun. I'm going to try to do another "Ask Me to Calculate Anything" next Tuesday, November 4. Tell your friends...or your enemies, I'm not picky.

Ask Santos: Ebola Edition

Today's question comes from my buddy Karen at the University of Michigan:

What are the odds of an individual being killed in an auto accident in Michigan (~680 deaths in 2014 so far) vs. ANY individual in MI contracting Ebola?

Not sure if ebola or modern art. Possibly both. (Image from Wikipedia)

At present, there are no reported cases of Ebola in Michigan. The only way to contract the disease is through direct contact with the bodily fluids of someone who already has the disease. For this reason, the only way of infecting someone in Michigan is by bringing an infected person to Michigan. Roughly 2.8 million people fly internationally into Detroit Metropolitan Airport each year.1 That's out of a total of 800 million passengers flying to or from the United States.2 According to the news, no more than 10 people have gotten on a plane with Ebola in their system. From these numbers, we can compute

probability of a random person on a plane having Ebola = 0.00000125%
probability of that plane flying to Detroit = 0.35%

This means the probability of someone with Ebola making it to Michigan is 0.0000000044%. Even if we assume the probability of contracting the disease when exposed is 100%, that's still a minuscule probability. You're about 2 million times more likely to die in a car crash in Ann Arbor than you are to catch Ebola. Thanks for a great question, Karen!

Do you have a question you'd like to ask Santos? Try Tweeting him at @aarontsantos for a chance to have your question appear on Diary of Numbers.


***Update***  After reading this post, a friend of mine commented on the inaccuracy of using data from relatively new phenomena to make predictions. In his words, "using prior cases over a few months for an event without precedent is bad modeling." I agree wholeheartedly. The exact numbers should be taken with a grain of salt. Statistics like the "likelihood of someone getting on a plane with Ebola" are clearly complex, time-dependent phenomena and need more than just an order of magnitude estimate to make useful predictions. In a more professional setting, I would model it as such. However, that's not really the point of this blog. My main goal is to get people interested in working out the numbers on their own, and using very complex models would quickly alienate readers who might already be math-phobic. If the blog inspires these people to learn more about math, and they eventually realize I'm pulling some numbers out of my ass, my mission will complete. However, even for the math-phobic, my description could have been more precise.  In my friend's words, 

It is better to say: 
"Contracting Ebola is non-quantifiably improbable and if you're living anywhere in the developed world, you, as an individual, have bigger problems.  
On the other hand, West Africans could use your government's directed attention. Perhaps you should be focusing your attention and advocacy on Ebola in West Africa because it is both morally good and in your enlightened self-interest. "

I couldn't have put better myself.

Sunday, May 11, 2014

Ask Santos: Scrooge McDuck Diving

This one is for my buddy Carolyn and her wife Heather.  They ask,

How much money would you have to have to be able to pull off swimming around in it Scrooge McDuck-style?

An Olympic-size swimming pool is 50 meters long, 25 meters wide, and one to three meters deep, giving a total volume of roughly 2500 cubic meters. Swimming in gold coins is a lot more expensive than swimming in pennies. To make this more cost effective, I'm first going to assume he's swimming in pennies rather than gold. A penny has a volume of 0.349 cubic centimeters, meaning you'd need roughly 7.2 million dollars to fill an Olympic-sized swimming pool with pennies.1 Even a smaller non-Olympic pool would require over one million dollars.

If money is no option, you could instead fill the pool with gold coins. Given that one cubic centimeter of gold costs about 80 dollars, a gold-filled swimming pool would require roughly 2.0 trillion dollars, or about 12% of the national debt. This is certainly a hefty amount of coin, but I would contend the sheer dollar amount is not the main obstacle to swimming around in a swimming pool Scrooge McDuck-style. Once again, Family Guy does a pretty good job illustrating the practical difficulties of the matter,

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] You need slightly less money if you take into account the packing fraction of pennies.

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... 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.