How Many Licks...?

How many licks does it take to eat a lollipop? How many ants would you need to carry a person? Aaron Santos' new book looks at the statistics of the everyday world, and how...
06 September 2009

Interview with 

Aaron Santos, University of Michigan


Chris -   Now, have you ever wondered how many babies are getting born everyday or how many solar panels it might take to power the UK?  Well, one man has not only answered these questions but he's also gone on to show us how we can work it out for ourselves.  He's written a book and it's called "How many Licks" and it's been published and it's come out this week in the US.  It comes out here in the UK very shortly and his name is Aaron Santos and he's a mathematician & physicist of the University of Michigan.  Hello, Aaron.

Aaron -   Hi.  How are you?

Chris -   Very well.  Thank you.  Good to have you with us on The Naked Scientists.  So first of all, before we come onto "How Many Licks" and perhaps why it's called that, tell us a bit about yourself and what do you do?

Aaron -   Well, I'm a postdoctoral researcher in the Chemical Engineering Department at the University of Michigan and my background is in physics which is basically where I learned to do all these sort of problems, these sort of calculation problems.

Chris -   What sort of physics are you doing?

Aaron -   I do mostly statistical physics.  So, a lot of the things with nano scale systems, a lot of different self-assembly systems and nano particles, and a little bit of biology, but much more just regular straightforward chemistry.

Chris -   And so, what led you to come out of the physics world and say, "Right.  Let's write a book in which we try and look at some of these complicated calculations about the world around us."

A girl with a lollipopAaron::  Well it was actually, it was in the middle of my graduate class when I was studying for them and there's a problem that was on the class that was basically, how do you - you have to calculate something that you have no idea how to calculate it first and it's a general problem first originally proposed by Enrico Fermi, and I think the problem he originally used was something like how many piano tuners are in Chicago and this was something that his students were expected to answer by just doing straightforward calculations.  So, it just seemed like it would be a good idea to just put a clutch of these problems into a book for math.

Chris -   And the name "How Many Licks," how did that come about?

Aaron -   Well, there was a commercial.  I'm not sure if in the U.K., you guys get Tootsie Roll pops, but it's basically a Tootsie Roll encompassed in a lolly pop and there was a pretty famous commercial back in the '80s about - there was this owl when the cape goes up and he asked the owl, how many licks does it take to get to the Tootsie Roll center of a tootsie pop and the owl basically just takes a bite out of it and says three.  So, this was kind of the real answer to that question because that's one of the things what we consider in the book.  How many licks would it really take if you were actually going to sit down there and do it?

Chris -   Well, one of the other things you've been considering is say, the question, you sometimes see TV adverts where they use scalability and lots of small increments of something, adding up something very big.  One of the examples you give in your book is how many ants would you need in order to carry humans.  So talk us through that one.

Aaron -   Yeah.  That's one of the simpler problems in the book.  So, it's commonly said that an ant can carry 50 times its own weight and if that's true, how many would you need to actually pick up a human being and just kind of use it to walk you around?  Well, ants come in a lot of different sizes.  If you look on, I think it's Wikipedia, I think there's a factor of 500 between the smallest ant and the largest ant weight.

Chris -   I wouldn't like to guess what the factor is for humans, probably depending on some countries is quite big.

Aaron -   Yeah.  One would imagine, those countries probably should remain nameless.

Chris -   I think our country is between the two of them, probably leading the way actually!  So go on.  How do we calculate this then?

Aaron -   So, if you look at the ants, the ones that are crawling around my apartment, they're about 20 milligrams in mass and if they can carry 50 times their own weight then that means that they can each carry a gram.  So, a normal human being is somewhere around 65 kilograms.  If I divide 65 kilograms by 1 gram, then you can calculate pretty simply that it's about 65,000 ants that you need to pick up one human being.

Chris -   Do you think it's reasonable?

Aaron -   I never get into whether things are reasonable or not in the book.  I mean, there's a lot of things to consider.  First of all, how are you going to fit that many ants underneath you?  You either need very large shoes or you need to be lying on your back and then there is some question, whether or not you could even fit that many ants.  So, I try to avoid any pretense of reality in any of these calculations.  It's not really what we're going for here.

Chris -   Now, I got sent an email the other day, Aaron, where someone - it said on there - it said that, "Don't scroll down until you've read the top line" and then it said, "Around the world, about 35 million people are having sex at this precise moment."  And it said "Now scroll down, now scroll down, it set apart from one old timer who's currently reading his emails."  So, how many people are currently engaging in sexual congress right now then and how would you calculate something like that?

Aaron -   I should say before I answer this one that I answered a similar question in a talk that I gave once.  And was heckled mercilessly by a woman in a crowd who was convinced that the percentage of time that I thought people were actually having sex was much too low.  So, you might get a few angry calls in from this but...

Chris -   We won't judge it by your own standards Aaron.  It's all right.

Aaron -   Okay.  So to do a problem like that, you'd want to say, "Alright, well how often does a normal person have sex and this clearly depends on what type of person you are."  If you're a priest, it's going to be much rarer than if you were in a committed relationship in your early 20s.  But the number I used to calculate this one, it was, I'd say once every three weeks seemed like a reasonable number.  You're certainly not going to be having sex once every day, at least not by my lifestyle.  And once a year seems much too long, so once a week seems like a good compromise.  And then you say well alright, how long does a typical sexual encounter last and then it depends on do you count foreplay, do you count what counts as a sexual encounter.  But I thought, 15 minutes seems like a reasonable amount of time for that.  So, that gives you...

Chris -   People here in the studio are nodding.  They think that's okay.

Aaron -   Okay good, good.  Although I have to say that the people that I have generally asked these questions to tend to be scientists, so I think my results might be a little skewed, but you guys fit that demographic.  So, maybe that's why you guys are nodding in agreement.  But that would be 15 minutes out of three weeks, so you could calculate that that's about 0.05% of the time and then if that percentage also applies to the number of people that are having sex, then it's just 0.05% of the population which would be about 3.3 million people.

Chris -   So also my estimate was far too high.  My email that I got then was ten-fold too high probably.

Aaron -   It could be or I could have messed up on one of the numbers that I gave you, but I would question the email more than the numbers because I at least know where those are coming from.

Chris -   But the point of all this is that it's basically showing people how you break down a big complicated problem which scientists frequently encounter into a series of small steps and make a few small assumptions in each step in order to arrive at a ball park sort of figure.

Aaron -   Exactly.  I mean, you want to start with the things that you know how to do first.  I mean, you don't want to just guess at the number of people having sex because you could be way off with that.  But if you start doing things that you are familiar with and then just multiplying them together then usually, you can come up with something that's pretty close.


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