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.

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.

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] 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!!!!!!

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.

Father's Day Contest Winner

We have a winner! If you followed the blog for any length of time, you know I love quirky questions. This one is pretty quirky.  Carl writes, "How many beers did it cost me to give my kid flugelhorn lessons?"


Ah, the flugelhorn: bagpipe of brass instruments. I suspect Carl paid in more than just beer:

It's OK, Carl. Little Timmy has to get better sometime.

If flugelhorns are anything like pianos, then a single lesson likely costs somewhere between $10 and $50. Some kids take lessons for years, while others take one lesson and never go back. I'll assume that the average flugelhornist takes lessons once a week for a year at a cost of $20 per lesson. That gives a total cost of about $1000 for flugelhorn lessons. I'll assume Carl is a Dos Equis man.

At $7.99 for a six-pack, it would cost 750 beers to pay for Carl's kid's flugelhorn lessons.

Thanks for great question, Carl! You'll be receiving a free signed copy of Ballparking in the mail shortly.

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.

Happy Father's Day!!!

Happy Father's Day!  I'm travelling today, but will post the winner of the Father's Day contest soon.

-AS

Bad Ass Astronauts

Given my disappointment with the new Star Trek movie, it's nice to know there are still some legitimate (and non-fictional) bad ass space travelers out there. Canadian astronaut Chris Hadfield recently made headlines for an awesome video where he sings David Bowie's Space Oddity.

In a karaoke battle of the Chrises, Hadfield would totally destroy Pine.¹

While that video is awesome in its own way, I personally prefer how Hadfield explains cool science to the masses:

All this talk about astronauts and cool science reminds me of a question my physics buddy Kendall asked me to do:  How much extra time do astronauts gain by being in orbit?

According to Einstein's theory of relativity, time slows down as you move faster. Since the International Space Station (ISS) travels about 4.8 miles per second, Hadfield and the other astronauts on board should age somewhat slower than the rest of us.

Using the time dilation formula, we find that a person traveling at the speed of the ISS ages at a rate 0.000000033% slower than the rest of us. As our paper of the week demonstrates, even though this effect is tiny, it's still measurable if you've got a precise atomic clock.  After one year on the ISS,² an astronaut would age 10 milliseconds less than a person at rest on the Earth because of special relativity.

As amazing as our above result is, it's not quite correct. The problem above illustrates the principle of special relativity, which Einstein discovered was the correct way to describe fast moving objects in the absence of heavy masses. Eleven years later, Einstein published his general theory of relativity, which explains how time dilates in a gravitational field. According to general relativity, time slows down as you move closer to heavy masses (i.e. people on Earth would age more quickly than people far away from its gravitational pull). At a height of 230 miles above Earth's surface, astronauts age 0.000000098% slower than objects without any heavy masses in the vicinity. After one year on the ISS, astronauts would age 31 milliseconds less than a person far away from any masses, but 1.8 milliseconds more than a person on the surface of the Earth.

[1] However, in a battle of the Kirks, I'm pretty sure this means Pine could take Shatner.
[2] Valeri Polyakov holds the record for the longest time on the space station with a time of 437.7 days.


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.

Father's Day Contest Update

Per popular request, I'm gonna say it's OK if you want to mail me your Father's Day questions rather than tweet them. Send them to "aaron at aaronsantos period com".

Scientific Paper of the Week: Slowing Down Time

Today's paper of the week was published in 1972. To my knowledge, it's the first direct measurement of time dilation as predicted by Einstein's special theory of relativity. The authors used atomic clocks to measure time slowing down in fast moving commercial jets. Good stuff!

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.