Jen Lynn Barnes on Taylor Swift and Werewolves

We're continuing our string of ridiculously multi-talented scientist guests.  Today's question comes from acclaimed author and newly minted psychology PhD Dr. Jennifer Lynn Barnes.  (She still has that new PhD smell!)  Earlier this year, Jen successfully defended her PhD thesis "Fiction and Development: What Adults' and Children's Story Preferences Tell Us About the Cognitive Science of Fiction" at Yale University.  While in graduate school, she somehow found time to write several young adult novels. At present, she has 11 titles to her name, including her most recent book, Taken by Storm: A Raised by Wolves Novel, the finale of the Raised by Wolves trilogy.

Jen writes,

If Taylor Swift were a werewolf, how tall would she be in her wolf-form (assuming conservation of mass during shifting)?¹

While there's normally no guarantee of mass conservation in fictional worlds (see my earlier estimation on The Incredible Hulk), we're explicitly told that the lovely Ms. Swift gains no mass in her hirsute form.  As such, our first task is to figure how much she weighs at present.  Since I only claim my estimates are accurate to within an order of magnitude, I could justifiably state her weight as being any number between 10 and 1000 pounds.  Still, there's a reason Enrico Fermi was a physicist and not a carnival weight-guesser.  I suspect it might have had something to do with disliking the feeling one gets after being whacked upside the head by the heel end of a starlet's shoe after you tell her she looks like she's roughly 1000 pounds.  If only to avoid a nasty suit from Ms. Swift's lawyers, I'm going to try to be more accurate on this one.²

Google has apparently added a new feature that lists a celebrity's vital stats when you search for his/her name.   I was surprised to find Ms. Swift listed at 5'11".  While certainly slender, Taylor Swift is fairly tall.  As such, a reasonable guess would be about 120 pounds.

If we consider gray wolves, we find they're about 34 inches tall at the shoulder and weigh roughly 85 pounds.  In Ballparking, I discuss scaling in the context of animal sizes.  Assuming everything remains proportional, an animal's mass m will increase as its height h cubed,

m ~ h³.

Taylor Swift weighs about 1.4 times as much as a typical wolf.  If you scale a wolf up to this weight, its height will increase by a factor of about (1.4)^1/3≈ 1.12.   That's about 12 percent larger than a normal wolf.  As such, a lupine Swift would be about 38 inches tall.

Great question, Jen!  You can order Jen's new book on Amazon and follow her on Twitter at @jenlynnbarnes.

 
[1] What's with this correlation between lycanthropes and the name Taylor?  Taylor Lautner, Taylor Swift, Chicago Wolves assistant coach Karl Taylor....
[2] I know weight is a sensitive topic for some people.  Ms. Swift, if you're reading this and at all offended, I will personally do any calculation you like to make it up to you.

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.

Radio Interviews Tomorrow

I'm doing live radio interviews tomorrow.  Feel free to tune in if you're in the right location or find a streaming version online if there is one:

8:05-8:30 AM	BENNINGTON, VT	WBTN-AM/FM (NPR)	DAYBREAK
8:40-8:50 AM	BROWNWOOD, TX	KXYL-FM	MORNING SHOW
8:50-8:55 AM	NATIONAL	USA RADIO	DAYBREAK USA
9:30-9:40 AM	RICHMOND, VA	WRVA-AM	MORNING NEWS
9:40-9:45 AM	MINNEAPOLIS, MN	KBEM-FM	MORNING SHOW
9:45-10:00 AM	NEW YORK-Hudson Valley	WKNY-AM	MORNING SHOW
10:20-10:30 AM	BOSTON-south shore	WBET-AM	MORNING SHOW
10:50-11:00 AM	DULUTH, MI	WOJB-FM (NPR)	LOCAL MORNING EDITION
12:42-12:55 PM	BOSTON-Worcester, MA	WCRN-AM	MIDDAY REPORT

I'm also doing some taped interviews, so listen for these shows when they air:

PHILADELPHIA, PA KYW-AM NEWS FEATURE NATIONAL WESTWOOD ONE JIM BOHANNON SHOW NATIONAL CRN SPORTS SHOW KANSAS CITY, MO KCMO-AM MORNING SHOW ST. LOUIS, MO KMOX-AM TOTAL INFORMATION AM REGIONAL SOUTH VARIOUS KAT SIMONS MIDDAY WASHINGTON/RALEIGH  WFHS-AM, WCBQ-AM   MORNING SHOW SAN ANTONIO, TX TX PUBLIC RADIO SOME BOOKS CONSIDERED NATIONAL ACHIEVE RADIO A CLOSER LOOK PORTLAND, OR KEX-AM MORNING UPDATE NATIONAL WESTWOOD ONE FIRST LIGHT

Running Off With The Circus

Many people dream of dropping out of school and running off to join the circus.  Today's guest did just that (minus the dropping out of school part).  Tanya Burka is an MIT graduate and circus artist currently performing the aerial silk act in Cirque Du Soleil's Quidam.  Through her unique blend of science and athletic talent, Tanya has composed quite an impressive resume, one perhaps better-suited to an aspiring superhero or possibly a sexy James Bond villain.

Tanya Burka is the lone point of intersection in this Venn diagram.

Tanya writes, 

It's not a circus-related question (or if it is, only tangentially in that an elephant is referenced), but I've always wanted to know how many ants it would take to lift an elephant, and whether or not it would be possible in practical terms in having enough surface area on the elephant at some angle (lying down, for example) for the ants to all support his weight.

It's often said that ants can lift 50 times their own weight.  Even if we assume this is true, there's still some ambiguity about exactly how much weight they can lift.  There are over 12,000 species of ants spanning a wide range of sizes.  For simplicity, I'll assume ants weigh 20 mg so that they can each hold 1.0 gram of weight.  In contrast, an elephant can weigh anywhere from 100 kg (~200 lbs) as a newborn to 10,000 kg (~20,000 lbs) as a large adult.  If we take 1000 kg as an average, we can estimate that it would require about one-million (10⁶) ants to lift an elephant.

To fit that many ants under an elephant, you'll need a wide area.  For this reason, it's better if we have the elephant lay on its side.  With a shoulder height of about 3 m, we can estimate that the side of an typical elephant would have an area of about 4.5 square meters.  This would mean each ant would need to fit in an area of about 4.5 square millimeters.

This result is a fair bit smaller than the ant we assumed originally, but it's closer than I would have guessed.  It's just as well.  Logistically, it would be a nightmare trying to lay the elephant down exactly evenly over all the one-million ants before they could get away.

Thanks for a great question, Tanya!

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.   

If I Fits, I Sits

Today's special guest is biologist/bioengineer Joanne Manaster.  In addition to lecturing at the University of Illinois-Urbana, Joanne does great science promotion through her blog Joanne Loves Science.  She writes, "How about you do a more thorough answer to my 'Cats in Sinks' video?"

The video, which illustrates the differences between theoretical and experimental work, asks, "How many cats can fit in a sink?"

If you've ever tried to fit all your personal belongings in a small U-Haul, you're familiar with the packing problem.  In its most basic form, the problem asks "How many X can you fit in a space Y?"  The packing of irregularly-shaped objects has been studied since antiquity, and there's a lot of physics involved.  Current research on packing has applications in cancer treatment, secure wireless networks, microelectronics, demolitions, and apparently putting cats in sinks.

Cats are certainly no strangers to packing themselves in tight places, and there are many ways to determine just how tightly they can pack themselves.  For example, cats are about as dense as water, so you could weigh the cat and use this density to find its volume.  A less scrupulous way of accomplishing the same goal would be to use a blender, but this inevitably leads to some cat juice slipping through the drain and throwing off the final number.

Since I don't have an experimental budget or a team of lawyers to defend me from animal cruelty charges, I'm going to tackle this problem theoretically.  Very theoretically.

You may have heard of Schrödinger's "Cat in a Box."  It's a quantum mechanical thought experiment, but here we'll be using a relativistic cat in box.  According to Einstein's theory of relativity, the length of a moving object contracts as it goes faster and faster.  For velocities in our everyday experience, the effect is too small to notice unless we make a very precise measurement.  The effect is, however, very noticeable for objects moving close to the speed of light.  According to Einstein, a moving object's length contracts by a factor of

f = (1 − v²/c²)^1/2,

where v is the speed of the object and c = 3×10⁸ m/s is the speed of light.  If 10% of people in the world have cats, there would be roughly one-billion (~10⁹) cats.  These cats could fit quite comfortably in a rocket ship that was one-billion meters long.  For this rocket ship to fit in the sink, it would need to contract by a factor of about three billion (f = 3.0×10^-10).  Solving for the velocity, we find that every cat in the world could fit in the sink if they were loaded on a rocket ship traveling with a speed

v =  99.999999999999999995% the speed of light.

Since this rocket ship is essentially traveling at the speed of light, the cats would, admittedly, not remain in the sink very long.  While you might think that cats moving at the speed of light would suffer just as much as the cat in a blender, I assure you they remain quite comfortable.  According to relativity, the cats (in their own frame) remain the same size as normal and go about as usual, blissfully unaware that they're traveling at the speed of light.  For them, it is the sink and the rest of the world that is contracted.  I'll leave it to the reader to see if he/she can resolve the seeming paradox of how one-billion cats can fit in a contracted sink.

Rarely do I get the opportunity to answer a question that involves relativity, hypothetical animal cruelty, and cats.  Thanks, Joanne.  The internet should be pleased.  To find out more about Joanne, visit her blog or follow her on twitter @sciencegoddess.

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.  

Lessons from Stick Figures: Metals

More Lessons from Stick Figures.  Voiced by Matthew Grace.