Calculating your life span

Size Matters: In the The Hidden Mathematics of Life Robert Krulwich argues that all creatures wax, we wane and then we die. It's the dance of life.

Every living thing is a pulse. We quicken, then we fade. There is a deep beauty in this, but deeper down, inside every plant, every leaf, inside every living thing (us included) sits a secret.

Below the pulse is a life/death cycle, a pattern that shows up in the teeniest of plants, (phytoplankton, algae, moss), also in the bigger plants, (shrubs, bushes, little trees) — and even in the biggest, the needle bearing giant sequoias. Everything alive will eventually die, we know that, but now we can read the pattern and see death coming. 

We have recently learned its logic, which "You can put into mathematics," says physicist Geoffrey West. But it shows up with "extraordinary regularity," not just in plants, but in all animals, from slugs to giraffes. Death, it seems, is intimately related to size.

Life is short for small creatures, longer in big ones. So algae die sooner than oak trees; elephants live longer than mayflies, but you know that. Here's the surprise: There is a mathematical formula which says if you tell me how big something is, I can tell you — with some variation, but not a lot — how long it will live. This doesn't apply to individuals, only to groups, to species. The formula is a simple quarter-power exercise: You take the mass of a plant or an animal, and its metabolic rate is equal to its mass taken to the three-fourths power. I'll explain how this works down below, but the point is, this rule seems to govern all life.

A 2007 paper checked 700 different kinds of plants, and almost every time they applied the formula, it correctly predicted lifespan. "This is universal. It cuts across the design of organisms," West says. "It applies to me, all mammals, and the trees sitting out there, even though we're completely different designs."

It's hard to believe that creatures as different as jellyfish and cheetahs, daisies and bats, are governed by the same mathematical logic, but size seems to predict lifespan. The formula seems to be nature's way to preserve larger creatures who need time to grow and prosper, and it not only operates in all living things, but even in the cells of living things. It tells animals for example, that there's a universal limit to life, that though they come in different sizes, they have roughly a billion and a half heart beats; elephant hearts beat slowly, hummingbird hearts beat fast, but when your count is up, you are over. 

Plants pulse as well, moving nourishment through their veins. They obey the same commands of scale, and when the formula says "you're done," amazingly, the buttercup and the redwood tree obey. Why a specific mathematical formula should govern all of us, I don't completely understand, but when the math says, "it's time," off we go ...

Of course these rules do not tell any particular bee or dog or person when they are going to die. Every individual is subject to accident, caprice, luck. No, this is a general rule. It governs species. Modern humans have managed, because of medicines and hygiene, to become an exception, but 50,000 years ago, we were probably part of the pattern. 

But to summarize, nature goes easy on larger creatures so they don't wear out too quickly. An elephant has trillions more cells than a shrew, and all those cells have to connect and communicate to keep the animal going. In any big creature, animal or plant, there are so many more pathways, moving parts, so much more work to do, the big guys could wear out very quickly. So Geoffrey West and his colleagues found that nature gives larger creatures a gift: more efficient cells. Literally.

The cells in an elephant do more work in a minute than the cells of a mouse. That's why an elephant cell can beat at a slower rate than the rattatat-tat of a mouse cell. Both wear out after a billion and a half beats, but the elephant does it more slowly. As for the peculiar quarter power scaling differences, that rule emerges from the data when you plot the different lifespans of animals or plants on a graph. According to West, lifespan is connected to size. Elephants, for example, live longer than birds or field mice because the larger animals' hearts beat slower and use energy more efficiently.

Apparently size does matter.

Giant turtles, elephants and blue whales move through their lives with a slow grandeur that seems very different from littler creatures. Watch a hummingbird dart through a garden, or hold the smallest mammal, a little mouse-like shrew in your hand and you can feel it trembling with a feverish energy.

Though big and little creatures look very different, below the surface there is a surprising unity. Biologists have compared the heartbeats of mammals and discovered that on average (this won't apply to any individual, just to groups) elephants and shrews and most of the critters in between have a limit of about a billion and a half heartbeats in a lifetime and then they die.

The reason an elephant lives longer than a shrew is not because its heart beats longer. It's because its heart beats slower. So it takes a few more years for the elephant to complete his or her up to one and a half billion beats.

Now comes the subtler question: Why do big things use up energy more slowly?

Three scientists at the Santa Fe Institute, an interdisciplinary institute in northern New Mexico, took up this question a few years ago and discovered that if you compare elephants to lions to housecats to mice to shrews, you discover that heartbeats vary in a precise mathematical way. The mathematical principal is called Quarter Power Scaling and it is described beautifully in "Of Mice and Elephants: A Matter of Scale," by New York Times writer George Johnson. But here is the heart of it: Nature goes easy on larger creatures so they don't wear out too quickly.

After all, an elephant has trillions more cells than a shrew and they all have to connect and communicate and distribute energy and keep the animal going. In a little animal, the job is easier. In a big animal, there are so many more blood vessels, moving parts, longer pathways, there is so much more work to do, the big animal could break down much more quickly.

Call it Nature's Gift to Big Creatures. So Geoffrey West, Jim Brown and Brian Enquist discovered that nature gives larger animals a gift: more efficient cells. Literally. The cells in an elephant slow down and do more work than the cells of a mouse. An elephant cell, lumpity-dumpities at a slower rate than the rattatat-tat of a mouse cell. They both wear out by a billion and a half beats, (yes, cells have metabolic or energy-using beats, too) but the elephant does it more slowly, all the way down to the cellular level.

Human beings used to fit into this pattern, but now that we have learned to drink safe water, wash and bathe and create medicines, we last longer than our size would predict.

And if you want, you can check out Professor West's latest observation: that big cities are like big animals. They are — deep down — more efficient than smaller towns and villages.