## 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?

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.

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.

## Monday, June 17, 2013

### 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.

## Sunday, June 16, 2013

### 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

## Saturday, June 8, 2013

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.

## Thursday, June 6, 2013

### 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!

## Wednesday, May 22, 2013

### Special Guest: Jim Ottaviani

Today's special guest is author Jim Ottaviani. Jim has written several excellent comic books on science history including Dignifying Science: Stories About Women Scientists, Feynman, and Primates: The Fearless Science of Jane Goodall, Dian Fossey, and BirutÃ© Galdikas. Jim writes:

I live close to Detroit so I always have to hear about horsepower this, horsepower that. I prefer dinosaurs, though, so my question is this: How many Dryptosauruspower is under the hood of a beautiful, split-windowed, 1963 Corvette Sting Ray Coupe?

The whole point of "units" is to provide a convenient means of comparing quantities. Despite most scientists' insistence that the United States convert to metric units, there's nothing fundamentally special about meters and kilograms. You're perfectly welcome to continue measuring distance with a dead king's foot provided you don't mind remembering more complicated unit conversions. Still, perhaps it's better to have units we can all relate to. With that in mind, Mr. Ottaviani's question is a particularly useful one because the term horsepower is, at least for those of us in urban areas, a bit of an anachronism.1 According to Wikipedia,
The development of the steam engine provided a reason to compare the output of horses with that of the engines that could replace them. In 1702, Thomas Savery wrote in The Miner's Friend: "So that an engine which will raise as much water as two horses, working together at one time in such a work, can do, and for which there must be constantly kept ten or twelve horses for doing the same. Then I say, such an engine may be made large enough to do the work required in employing eight, ten, fifteen, or twenty horses to be constantly maintained and kept for doing such a work…"
In context, horsepower is a perfectly legitimate unit. If today an infomercial claims you'll lose weight three times faster with Bowflex than with a Shake Weight, than you could define

1 bowflex = 3 shake weights,

and in 100 years "shake weight" will be a legitimate unit of measure, not an utterly ridiculous punchline.

 The Shake Weight: laughing stock of the exercise community

Much like with the shake weight, we could easily standardize dryptosauruspower as a unit provided we can find the correct conversion factor between it and horsepower. A dryptosaurus is thought to have weighed about 1.5 metric tons or roughly 3.3 times the mass of a horse. This would put it closer to the weight of a giraffe or hippopotamus. Giraffes eat about 75 pounds (34 kilograms) of food per day, while a hippo eats about 88 pounds (40 kilograms) of food per day. Since a dryptosaurus is about the same size, it likely eats about the same amount of food.2 Let's assume the typical dryptosaurus takes in about 80 pounds of food each day.

 It's bigger than you, so it eats a lot more.

A 1000 pound horse takes in about 30 pounds of food per day, roughly 2.7 times less than the dryptosaurus. Food is a source of energy. Power is the amount of energy used in a given amount of time. Since power is proportional to energy which is proportional to the amount of food, it should be true that the dryptosaurus is roughly 2.7 times more powerful than a horse.3 We could use the following equation to convert from horsepower to dryptosauruspower:

1 dryptosauruspower  = 2.7 horsepower

 A 1963 Corvette Sting Ray Coupe with 100-dryptosauruspower

Depending on what kind of engine is installed in your Corvette, you could have a variety of different horsepowers. According to Wikipedia, typical values range from 250- to 340-horsepower. Using our conversion equation above, the horsepower of a 1963 Sting Ray Corvette ranges from 93- to 130-dryptosauruspower.

Thanks for a great question, Jim! You can find out more about Jim Ottaviani and his books at G. T. Labs or on Twitter.

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] There are those who might ask why we would want to convert to dryptosaurus power since the dryptosaurus, having lived over 60 million years ago, is an even greater anachronism than the horse. A fair point, Dear Reader, to which I have two responses. (1) Dinosaurs are awesome, and (2) horses suck.
[2] I am, of course, making a big assumption here by assuming food intake is related to body size. The difference between dryptosaurus and a giraffe could be substantial given that one is a carnivorous reptile and the other is a vegetarian mammal. Even within one species, you can have a pretty wide range of values for caloric intake. For example, I'm pretty sure I eat about twice as many calories each day as my wife does. That said, the caloric need for similarly-sized animals should be roughly the same to within an order of magnitude. We can see this by comparing the giraffe and hippo, two very different but similarly-massed creatures that take in roughly the same amount of food each day.
[3] Here, we're talking about the average power output as opposed to the peak power output, which is theoretically what we're quantifying when we talk about horsepower. These could be somewhat different, but I suspect they're still relatively close.

## Friday, May 17, 2013

### Star Trek Review and Estimation

There's not too much I'll be able to add to what other people have already said more eloquently, but I'm going to put in my two cents in anyway. I just saw Star Trek: Into Darkness, and I have to admit I was disappointed. It wasn't Catwoman bad or even Phantom Menace bad, but it was quite possibly "Phantom Menace minus the scenes with Jar Jar" bad.

Don't get me wrong, Benedict Cumberbatch was pretty good as Khan1, but I found the editing to be downright dreadful. In one scene, Spock just barely pulls himself onto the edge of a flying car and in the next shot Khan kicks him back 15 feet from the middle of the car. Now, I could easily overlook one or two poorly edited shots, but I can't ignore the scene with Chekov holding up the much larger Kirk and Scottie, who are dangling over the side of a bridge. Mind you, Kirk couldn't hold Scottie by himself, but somehow the 130 pound Chekov has no problem lifting them both. I can only assume some amazing and dramatic miracle feat of strength occurred while the cameras were off, because a second later they're all happy and running through the Enterprise without any explanation. Whatever Chekov did must have been amazing to see, but apparently J.J. Abrams just wants us to fill in the details by ourselves (more on that in a moment).

While we're on the subject, when did J. J. Abrams decide to become Michael Bay?2 Seriously, I'd much rather see how that bridge thing got solved than watch another giant explosion that I'm just gonna tune out. And, no, Mr. Abrams, you can't just lazily copy highly emotional moments from the old movies and expect to elicit the same emotional response in your audience. Kirk's "death" didn't make me sad or even nostalgic. It made me think, "Hmm...they've got a cash cow of a franchise here and there's no way they're killing off Kirk, so I guess the dead tribble's coming back to life." That said, having Spock tear up did make me feel some genuine emotion, so I guess there's that.

Still, the main source of my disappointment has little to do with these small quibbles3 and more about the general direction this franchise has taken. The best part about old Star Trek is that it was actual science fiction, not cheesy action-adventure set in space. With that in mind, you can't just freeze a volcano and call it cold fusion without Gene Roddenbury and Isaac Asimov rolling over in their graves so fast we could use them as a renewable energy source.4  I'm used to Star Trek having a bigger message, and if there was one here I totally missed it.

Since this is Diary of Numbers, I can't justify ending this rant without at least some bit of calculation. With that in mind, my friend John had the best explanation I've heard for how Chekov could suddenly gain superhuman strength. According to John, "Russian Special Forces kettlebell workouts gives you strength of two men..."  Where would this put Chekov in the pantheon of great Russian weightlifters?

There's nothing the Muscleless Wonder and I take seriously if not for science and weightlifting, and this estimate combines both. If Chekov is as small as I think he is, he'd be in just about the lightest weight class of lifters. To get both Kirk and Scottie back on the bridge, I imagine him doing a motion similar to a snatch. I'd put Chris Pine and Simon Pegg at about 175 pounds each, meaning their combined weight would be 160 kilograms. With a 138-kilogram snatch, Halil Mutlu of Turkey holds the world record in the 56-kg division. Chekov would easily smash this record. Unless he's the next Pocket Hercules, there's no way he's pulling Kirk and Scottie back on the bridge.

Seriously, get it together, J.J. Abrams. I'm willing to give you a pass on this one under the assumption that you're distracted putting together a kick ass Star Wars movie. No second chances after that.5 Help me, J.J. Abrams.  You're my only hope.

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] My buddy Matt was not so glowing in his endorsement of Cumberbatch: "I don't feel like I can call him 'Khan' because he isn't. He's British. And white. Khan Noonian Singh was of Indian descent. Hence the reason he took the title of Khan."
[2] QOTD from a friend on Facebook: "I'm pretty sure J.J. Abrams is the non-union Mexican equivalent of Christopher Nolan..."
[3] Let's call them "tribble quibbles"!
[4] Yes, I'm stealing that joke from somewhere, but I can't remember where, so I can't cite it.
[5] Though if I'm completely honest, I'm still probably going to spill out full price for whatever creatively emaciated junk they're going to throw at us. I can't help it....I need my cheesy movie fix.

### Father's Day Contest

Father's Day is in a month, and I know the perfect present for the sport-loving dad:

In fact, I'm holding a Father's Day contest. It's a little different than my usual contest. Normally, I give you guys a question to answer. This time, I want you to give me a question.  What's a good estimation question that every father would get a kick out of?

To enter, tweet your question to @aarontsantos by June 14, 2013. I promise not to spam your inbox or sell your email to evil corporate overlords. On the 14th, I'll select what I think is the most interesting question and answer it on the blog for Father's Day. The winner will receive a free signed copy of Ballparking to give to your dad (or anyone else you like).

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

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.

## Thursday, May 16, 2013

### Scientific Paper of the Week: Alpher, Bethe, Gamow

Oh, the things physicists do for a lark. Today's paper, titled "The Origin of Chemical Elements", describes how the Big Bang explains the relative abundance of hydrogen and helium in the universe.

 The universe expanding after the Big Bang.

While tremendously interesting in its own right, the content of the paper is not the reason for its selection. In my General Physics class, we just covered alpha, beta, and gamma decay. The authors of this week's paper are Ralph Alpher, Hans Bethe, and George Gamow.

"Well, that's a fun coincidence!" you say.

Well, not quite...

 Left to right: Ralph Alpher, George Gamow, and Hans Bethe, who's totally riding their coattails.

It turns out Bethe played no actual role in writing the paper. Gamow added him because he liked play on words with "alpha-beta-gamma". And they say physicists don't know how to have fun!

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.

## Friday, May 10, 2013

### Special Guest: Derek Lackaff

Today's special guest is Elon University School of Communications Professor (and also my coolest1 brother-in-law) Derek Lackaff. Derek is working on a project called Better Alamance, which uses social media to help local residents share ideas on how to improve their community:

Derek wants to know...

How long would it take the citizens of Alamance County to put everything they know on the Better Alamance: Wiki, and how big would the wiki be when they were finished?

Great question, Derek! According to Wikipedia, Alamance County in North Carolina is home to roughly 150,000 residents. According to at least one source, a human brain has on the order of 2.5 petabytes of memory, which means 150,000 brains would have roughly 370 exabytes of memory. This data includes everything from which Alamance park needs the most improvements to what the final score was in the last Duke vs. Tar Heels game.

If a wiki page is anything like a text document, it would require anywhere from 10 to 100 kilobytes of memory.2 At this many bytes per page, we'd have about four quadrillion wiki pages of material stored in the mental matter of Alamance citizens. If we printed every page of the wiki, it would be long enough to reach to the Sun and back!

If you like the idea of using social media to help improve your community, let your voice be heard. Go here and vote for Better Alamance in the MacArthur Foundation-sponsered contest, Looking@Democracy.

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] <cough> Caleb sucks <cough>3
[2] It could be substantially larger if contains large pictures.
[3] Just kidding.4
[4] No, I'm not.5
[5] No, just kidding again. I wuv u Cublub.

### Scientific Paper of the Week: Glowing Pickle

Have you ever tried to pass electric current through a pickle? "No...that sounds incredible stupid!" you say. But someone thought otherwise and discovered this:

 Homer Simpson: "Mmm...forbidden glowing pickle."

I first heard about this trick in Penn and Teller's How to Play with Your Food.  Penn and Teller heard of the trick through the Journal of Chemical Education.

 Fun Fact: Teller is actually normal height. He only looks short when standing next to the 6'6" Penn.

To brine a pickle, you put it in salt water. Salt contains sodium. When you pass electric current through the pickle, you excite the electrons inside the sodium. The atomic energy levels of sodium contain a unique doublet known as the sodium D line.

 "Atomic line spectra sure are purdy."

And thus we have our Scientific Paper of the Week:

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.

## Thursday, May 9, 2013

### I Love My Students (Part 2)

Once again, I love my students.  We're covering Bohr's model of the atom this week.

 "The Bohr model: Sure, it's wrong and will give our students  conceptual difficulties later on, but let's teach it anyway!"  said every physics and chemistry teacher ever.

After class, one of my students sent me this:

There seems to be a strange periodicity associated with searches for the Bohr atom. I suspect most classes teach it at the same time every year, generally October or February.  Why am I teaching it in May?  I guess I'm just different.

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, May 8, 2013

### Fire in a Bottle

Here's a fun physics demonstration where you get to burn stuff.  Just place some cotton in a syringe and press down quickly.

Voila!  Instant ignition. How hot does it get inside a fire syringe?

Let's assume you push down with 10 pounds (~44 newtons) of force over a distance of 10 centimeters.  While pushing you do work on the gas inside.  Work is equal to force times distance:

work = (44 newtons) × (10 cm) = 4.4 J.

A syringe with 0.25 cm2 cross-sectional area and a 20 cm length will contain roughly 5 milligrams of air. The heat capacity for the air in the container is about 1.0 J/g·K. From these numbers we can find the temperature of the air will rise by 9000 kelvin, giving a final temperature of 15,000 degrees Fahrenheit! For reference, the cigarette lighter burns at about 3000 degrees Fahrenheit, so the syringe is clearly hot enough to set the cotton on fire!

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.

## Friday, May 3, 2013

### Dirty-sounding Physics Term of the Week 4

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.

### I Love My Students....

We're covering relativity this week.  My students sent me this...

My day has officially been made.

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, May 1, 2013

### Scientific Paper of the Week

Mmm...I love me some fundamentals of quantum physics. Especially when they might lead to an experimentally falsifiable theory of quantum measurement and wave function collapse.

 These guys know what I'm talking about...

This week's Scientific Paper of the Week reviews how we might be able to do just that. Man, I really hope we come up with a more illuminating and experimentally falsifiable description of quantum measurement within my lifetime. Until then, Copenhagen interpretation me, baby!

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, April 24, 2013

### Dirty-sounding Physics Term of the Week 3

I'm not sure I'll be able to top this one.  Keep it classy, Mathematicians. Keep it classy.

## Tuesday, April 23, 2013

### Scientific Paper of the Week

I saw this paper referenced on the front page of Reddit a few days ago. Can you guess why it's special? (Hint: It has to do with one of the authors.)

Give up?

I'll let Family Guy's Tom Tucker write down the answer for you...

OK, perhaps you need some more explanation. If so, there's a nice Wikipedia article that sums it up pretty nicely here.

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.

## Monday, April 22, 2013

### Are You a Fan of Delicious Flavors?

SHAWN: Well, Buddy, I really hope you like this. It took me 19 hours to bake. I put it in last   night before bed.
GUS: It takes 19 hours to bake a pineapple upside-down cake?
SHAWN: It does when it's being heated by a 60 W bulb.
GUS: [Looking at the cake.]  It's not upside down, Shawn.
−A scene from USA's very funny Psych

"Psychic" detective Shawn Spencer may be a wiz at solving crimes, but does he or does he not know how to bake a pineapple upside-down cake? I've heard it both ways. How much heat (i.e. thermal energy) would a pineapple upside-down cake cooked with an Easy Bake Oven absorb over 19 hours?

An Easy Bake Oven might hold 100 grams of cake. According to Paula Deen, a pineapple upside-down cake should be placed in an oven preheated to 350°F (~180°C). This is an increase of about 160°C from room temperature. In order to increase the cake's temperature like this, you need to add some energy.

 Not enough butter for Ms. Deen's tastes

According to Shawn, the Easy Bake light bulb operates at 60 Watts.  Only a fraction of this power goes into actually heating the cake, while the rest heats the air, metal, plastic, and other materials that make up the Easy Bake Oven. Assuming only 10 percent of the power goes into actual productive heating of the cake, over 19 hours the cake would absorb 400,000 Jules of energy.1
 Easy Bake Oven...the real slow cooker

Since 400,000 Jules of energy isn't a particularly enlightening figure, let's see if we can put it another way. How much would the cake's temperature rise with this much energy? For a given amount of energy, the change in an object's temperature can be determined by its heat capacity.2 I suspect no one's ever measured the heat capacity of a pineapple upside-down cake. That said, pineapple upside-down cake is, like most food, made largely of water. As such, its heat capacity should be similar to water's. That would put it around 4.2 J/g·°C.3 With this heat capacity, a 100 gram cake heated with 400,000 Jules of energy would have its temperature increase to about 1300°F. Note that this assumes all the thermal energy absorbed by the cake stays in the cake. In actuality, as the cake gets hotter it will start losing some of its thermal energy to the cooler air outside the Easy Bake.

This was a fun calculation. The only way it could have been better, is if someone did an actual experiment involving an Easy Bake Oven and a pineapple upside-down cake. Wait a minute...what's this? Someone doing an actual experiment involving an Easy Bake Oven and a pineapple upside-down cake and kicking ass with science? Come on, Son....you know that's right!

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] Yes, I am aware that "Jules" is actually spelled "Joules", but somehow, I suspect Shawn Spencer would prefer it this way.  On a related note, Shules really needs to get back together pronto.  Seriously, we've all had a crappy week.  It'd be awesome to get some good news for a change.
[2] An object's heat capacity measures an object's "capacity" for storing heat.
[3] According to at least one reference, bread has a heat capacity between 1.65 and 2.73 J/g·°C.  Another reference lists pineapples as having a heat capacity between 1.72 to 3.68 J/g·°C, so we're at least in the ballpark.

## Friday, March 22, 2013

### Dirty-sounding Physics Term of the Week 2

Dirty-sounding Physics Term of the Week: Particle in a Box.

 (A) A classical particle in a box. (B-D) The three lowest energy wave functions for the quantum mechanical particle in a box. (E-F) A superposition of different energy eigenstates.
"That doesn't sound dirty," you say. It didn't, but then this happened. Now, good luck trying to make it through lecture without someone giggling and saying, "One. Cut a hole in a box."

(**Edit** Thank you to Sean Robinson for the correcting me on the caption. I wrote this quick and was not paying attention to the fact that the last two states are not energy eigenstates.)

## Thursday, March 14, 2013

### Weird Calculation of the Week

 Warning!!! Do not accept eye drops from this man.
Today's special guest is strength coach, blogger, and former weightlifter with Lyme disease Norm "The Muscleless Wonder" Meltzer. Norm trains a variety athletes, from high school amateurs to professional hockey players. His hilarious Weird Lift of the Week videos offer a fun way to incorporate variety into your training routine and embody his slogan, "Serious fitness with an edge of irreverence."

Norm wants to know,
How long would an Olympic bar have to be in order to lift it overhead without the plates ever leaving the ground?
Anyone who's ever watched an Olympic weightlifting meet with the super heavies knows the bar bends substantially. The amount it bends depends on a variety of factors (e.g. the mass of the plates, elasticity of the bar, position of the hands, etc.) If we want a large bend, we need a lot of weight. Consider a 260 kg jerk like the one shown below.

 Anatoly Pisarenko jerks 260 kg, courtesy of 70sbig.com

We can clearly see some curvature to the bar. This curve could take many forms, but for simplicity I'm going to fit it to a parabola.

 Pisarenko's 260 kg jerk with a parabolic fit superimposed on top in red.

Here, I'm using the width between the plates (which is approximately 1.3 meters) as a measuring stick. All distance measurements from the picture are based off this length. While the bar is not exactly perpendicular to the sightline of the camera, it should be close enough to get an order of magnitude estimate. Just by fiddling with numbers, I visually get a pretty good fit for the form,

h(x) = 2.13  ̶̶̶  0.1 x,

where h is the height of the bar at a distance x away from the center. The maximum height of the bar is roughly 7 feet. We want to know the length at which the plate will still be touching the ground. Since a 20 kg plate has a radius of about 23 centimeters, we want to know distance x at which the height of the bar is 23 centimeters off the ground. Solving our fitted equation, we find x = ±4.4 meters. Since this is only the distance from the center of the bar to the plate, the total length of the bar will be a little more than twice this, i.e. roughly 9 meters or about 30 feet. By itself, this bar would weigh about 170 pounds.

Thanks, for the great question, Norm. You can check out Weird Lift of the Week and other amusing fitness tidbits at Norm's blog and follow him on Twitter at @mwstrength.

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.

## Tuesday, March 12, 2013

### Scientific Paper of the Week

Here's the scientific paper of the week.  If you've ever had a reviewer complain that your paper wasn't impactful enough, you'll weep when you read the title.  Apparently science was a bit simpler 120 years ago.

## Tuesday, March 5, 2013

### Dirty-sounding Physics Term of the Week

Dirty-sounding physics term of the week: Wiener Process.

## Saturday, March 2, 2013

### Smoothie Thermodynamics

I've been drinking lots of smoothies lately, and I've developed a small annoyance. Right when I start blending, nothing happens. No matter how hard I push down, my immersion blender just whirls away with blades spinning but no chopping. "What's wrong, Blender? Have you been talking to the printer again?" Just when I'm ready to give up, it starts dicing up strawberries like Michael Myers does teenage babysitters.What gives? Must I needlessly waste energy for two minutes before any delicious goodness gets chopped up? Perhaps my blender needs to warm up first? While I like the visual of my blender doing calisthenics and some light stretching before going to work, I'm actually speaking quite literally. How much of the frozen fruit in the smoothie does my blender melt before it begins chopping?

In the 1840s, James Prescott Joule showed that mechanical energy and heat were different forms of the same thing. To do this, Joule tied a string from a falling weight to a paddle submerged in water. As the weight fell, it pulled the string which turned the paddle which stirred the water. During this process, the temperature of the water rose. By making careful measurements, Joule was able to show that the mechanical energy lost by the falling weight was gained by the water as heat.

 The illustration of Joule's experiment features a paddle submerged in a water tank on the left and a falling weight on the right.   A meter stick measures the distance the weight falls, which can be used to find the mechanical energy lost.
Much like Joule's experiment, my immersion blender has a rotating "paddle," i.e., the blade. In this case, the paddle is turned by electrical energy rather than mechanical energy. As the blade turns, it stirs the liquid in the smoothie and heats it. Let's assume the 2.0 cm long blade weighs 1.0 grams and takes 0.5 seconds to reach its top angular velocity of 10,000 rpms.2 Using dimensional analysis, we find this costs about 1.0 Watt of mechanical power. If I blend for two minutes, I'll gain 120 Joules of thermal energy.

My smoothie might have 250 grams of ice in the form of frozen strawberries and other fruits. The heat given off by the blender will melt some of this ice. The heat required to melt a solid is called the heat of fusion. The heat of fusion for ice is 334 Joules per gram. Since two minutes of blending only provides 120 Joules of heat, I will only melt about one-third of a gram of the ice in the container. That's about one one-thousandth of the total ice. It's much more likely the warmer air in the room is melting my smoothie. If I need the air to melt some of the smoothie before blending, I'd be better off just waiting two minutes rather than wasting energy by needlessly running the blender.

[1] I am, of course, referring, to Michael Myers the character who brutally murders his victims in the slasher classic Halloween, not Michael Myers the actor, who brutally murders comedy in The Love Guru.
[2] Within an order of magnitude, this rotational speed is typical of what you find in immersion blender advertisements.

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.