Size Matters: The Hidden Mathematics of Life : Krulwich Wonders... Can animal lifespan be calculated with a mathematical formula? Professor Geoffrey West and his colleagues at the Santa Fe Institute have found out not only why larger mammals live longer, but also how long they have to live.
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Size Matters: The Hidden Mathematics of Life

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Size Matters: The Hidden Mathematics of Life

Size Matters: The Hidden Mathematics of Life

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When you got to go, you got to go. But why do some animals have nice long lifespan while others sputter up more quickly?

NPR's Robert Krulwich has been mulling all these and has found a scientist who believes he's discovered why there is such a difference between how long different animals live.

ROBERT KRULWICH: Let's begin with mice - you know, ordinary field mice living in a barn. I asked Professor Geoffrey West, how long do mice live, just an approximate number?

Professor GEOFFREY WEST (President, Santa Fe Institute): That number would be just two or three years.

KRULWICH: Okay, so that's two or three years for a mouse. Now I want to conjure up an elephant. Elephants normally live for 60 years, so I need my elephant, please.

(Soundbite of an elephant)

KRULWICH: Yes, he's 50 years old, right?

(Soundbite of laughter)

Prof. WEST: That's one way of saying it, yes. Yeah. Yeah.

KRULWICH: Okay, and now a lion.

(Soundbite of a growling lion)

KRULWICH: Also a mammal, by the way. A lion…

(Soundbite of a growling lion)

KRULWICH: …may last about 15 years.

Prof. WEST: Yes.

KRULWICH: And a squirrel, they last about five years. So here is my question: Why these very lifespans? Why do different animals live for different lengths?

Prof. WEST: So let me just tell you, all my work in biology stem from asking that kind of question, where do those numbers come from?

KRULWICH: So you start with the same ingredients, that living things come from cells…

Prof. WEST: Right.

KRULWICH: …and that the cells seemed to have different timetables, depending on what species they are.

Prof. WEST: That's right. So why is it that if those cells are put together to form a rat that the timescales are different than if it's put together to be a human being or an elephant?

KRULWICH: Yeah. Why? Why do elephants live longer than rats?

Well, Geoffrey West thinks he has found the answer. With his colleagues at the celebrated Santa Fe Institute in New Mexico, it's a science think tank that he runs, right?

Prof. WEST: I'm the president of the Santa Fe Institute, indeed.

KRULWICH: Okay. Professor West says that he and his team have discovered why different creatures die at different times. And even more amazing, he can predict when each species should die on average.

Prof. WEST: Yes.

KRULWICH: Well, wait a second, wait a second. Has anyone else found a mathematical logic like this that runs to all living things? That's kind of…

Prof. WEST: Well, this is it.

KRULWICH: And here is how it works: All living things take in energy…

(Soundbite of chewing)

KRULWICH: We eat food, and food has energy in the form of calories. So the energy in the food that has to get passed around to all the cells in our body. And to do this, in humans, we get help from our hearts.

(Soundbite of heartbeat)

KRULWICH: Hearts are our pumps. And those pumps push blood, and fuel, and oxygen around our bodies.

Prof. WEST: But here's the fantastic observation.

KRULWICH: If you look at all creatures with heart starting with the big ones.

Prof. WEST: If I take the heartbeat of a whale…

KRULWICH: Which is very slow.

(Soundbite of a whale's heartbeat)

KRULWICH: And then you wait, and wait, and there you go.

(Soundbite of a whale's heartbeat)

Prof. WEST: It beats once every maybe…

(Soundbite of a whale's heartbeat)

KRULWICH: Maybe every three seconds or so, yeah…

(Soundbite of a whale's heartbeat)

KRULWICH: And the next one…

(Soundbite of a whale's heartbeat)

Prof. WEST: Whereas if I listen to a shrew, which is the smallest mammal.

(Soundbite of a shrew's heartbeat)

KRULWICH: A shrew's heart beats so much faster. Instead of 10 to 20 beats per minute…

Prof. WEST: It's over a thousand.

KRULWICH: Sometimes way over a thousand. Now, it is no big surprise that little creatures have fast beating hearts. We know that. But when Geoffrey West's team looked closely at individual species…

Prof. WEST: One of the things that comes out of the theory, this is astonishing fact that even though the shrew only lives a year or two and an elephant lives 80 years, they all use the same number of heartbeats.

KRULWICH: Estimating from sample heartbeats, scientists calculated the oldest elephants on record last for about a-billion-and-a-half heartbeat. That's their limit. Surprisingly, the oldest shrews on record, they also last about a-billion-and-a-half heartbeats - that's their limit - and the oldest lion, a-billion-and-a-half heartbeats, and the oldest rat, a-billion-and-a-half heartbeats. And the more they look, the more they found the same number. Meaning, that a rat and an elephant, while they have very different lifespans, they have, again roughly…

(Soundbite of a heartbeat)

KRULWICH: …the same number of beats. It's just that the elephant's beats are slower.

Prof. WEST: The elephant's beats are slow.

KRULWICH: So the elephant lasts longer but the limit, the magic number is…

Prof. WEST: A billion and a half, roughly, roughly.

KRULWICH: A-billion-and-a-half beats, and then you're over.

Prof. WEST: Then you're over. It's almost like, you know, the analog of three score and ten or something (unintelligible) the biblical…

KRULWICH: Who knew there was this deep symmetry inside all animals?

Prof. WEST: I certainly didn't but I came across it, I was so intrigued. I don't know what words to use, sort of, primitively exciting about it. It somehow was - it must be what makes people religious when they, you know, I don't know what it is. I don't know what to say exactly. I'm not a religious person but, God Almighty, you know, that's what - if these laws are true, what they're telling you is there is an extraordinary unity to all of life.

KRULWICH: And yet we die at different times, says Professor West, because we come in different sizes. Lifespan, it turns out, is very connected to size. The bigger a species in general, the longer it lives.

Prof. WEST: That's correct.

KRULWICH: Okay. Set this up. I'm going to bring a small cat into the room weighing maybe five pounds - a lovely little cat.

(Soundbite of cat's meow)

KRULWICH: I couldn't make it lovelier than that. Make a little…

(Soundbite of cat's meow)

KRULWICH: Yeah. Better. Good. And then into the same room I'm going to bring an ordinary-sized cow.

(Soundbite of bellowing cow)

Prof. WEST: Yes.

KRULWICH: Now, everybody knows that a cow is bigger than a cat, but here is something you don't know. If you take a cell from a cow and then you take a cell from a cat.

(Soundbite of cat)

KRULWICH: So now you've got two cells. They're more or less identical.

Prof. WEST: They look the same. They act the same. They do the same; they have the same functionality.

KRULWICH: But when you look closely there's a big difference. It turns out that a cow cell is much more efficient. A cow cell will do its business. It will make proteins. Take things in. Push things out. Take things in. Push things out. Take things in. Push things out.

It does this so efficiently it can do a lot of work in relatively few beats. While the cat cell to make the same number of proteins, it has to go…

(Soundbite of fast beating of cat cell)

Prof. WEST: You would find that the cell in a cat has to work much harder.

KRULWICH: So while the cat's cell has to pump and pump and pump, the cow's cell can take it easy - real easy.

(Soundbite of slow beating of cow cell)

Prof. WEST: So what that says is that a cow is more efficient than a cat.

KRULWICH: Apparently, and this is true across all animals and even plants, the bigger the creature the more efficient its cells. It's nature's gift. You're big, you have more cells, you got to cut down on the wear and tear, and we do that by giving you cells that work a little less, a little slower. So that's the formula. The bigger you are, the slower you go. So bigger creatures wear out more slowly.

Prof. WEST: The pace of life is much slower.

KRULWICH: In the bigger animals?

Prof. WEST: In the bigger animal, in a very - in a calculable, predictive way.

KRULWICH: Big things last longer most of the time, but not all the time. There's one rather crucial exception.

Prof. WEST: And that is human beings. Because if you look at all the data, everything I've talked about, about lifespan, we are actually - we today - are in violation.

KRULWICH: After all, we human beings are much smaller than elephants. So according to the theory, we should live shorter lives than elephants. But now, more and more of us are living elephant-long lives. We didn't used to, but now we live 60, 70 years. There is a reason for this change, says Dr. West. We humans have invented medicines.

Prof. WEST: And probably most importantly, we use hygiene.

KRULWICH: Because we wash and drink clean water and, therefore, don't get as many parasites or diseases, we don't wear out as quickly as we used to. And with medicines, we now know how to repair ourselves better. So our size no longer determines our average lifespan. We've broken free. But while we are an exception…

Prof. WEST: On the average, it pretty much fits.

KRULWICH: And it's a powerful formula. The size of a creature predicts a lot, says Professor West.

Prof. WEST: I can tell you how many children, how many offspring it's expected to have with just phase(ph) and period. I can tell you its heart rate. I can even tell you what its growth curve looks like…

KRULWICH: All the way up to, and including, the big one - when, on average, it's likely to die.

Prof. WEST: Yes. Exactly.

KRULWICH: I'm Robert Krulwich, NPR News in New York.

SIMON: Robert's podcast has all kinds of nifty things, if not exactly the key to life, like how Mt. Everest may not be the highest point on Earth. You can find it at

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