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.