This post is a Dr. Jeff’s Weekly Challenge and a Driving with Jordi.

Photo caption: the Hawaiian Islands, with the Big Island of Hawai’i at lower right. The Big Island was formed from five volcanoes including Mauna Kea. True color from the NASA Terra satellite, May 27, 2003.

The solution to this Challenge will be posted Monday, October 26, 2009.

It’s a new school year, and I couldn’t wait to get back into the routine of my morning drive with Jordi. I missed our daily conversations about Earth, space and everything else in his known universe while we navigate the fabled Washington, DC, Beltway to his school. Sure, we spent lots of great family time together over the summer at the pool club, and in New York. But there was something magical about taking 30 minutes of dull driving each morning and turning it into a free-for-all ‘Jordi where do you want to take the conversation today?’

To help you picture it, I’m always driving with my cup of coffee, glancing in the rear view mirror—waiting. He’s usually staring forward, transfixed. You’d almost think that my now 7-year-old is just zoning—except that he’s got that slight squint which tells me wheels are turning furiously inside. Then BOOM! He launches our great morning adventure with a simple, elegant, deep thought.

So last week, like always, just out of the blue—

“Daddy, how many Empire State Buildings tall is the tallest mountain?”

Today he wanted daddy to help him conceptualize the height of a really tall mountain. He wanted to use a familiar ruler.

Whenever we take a family a drive to New York (my Mom and sister are an hour north of the City) we always take time to go into Manhattan. We bike the Park or along the Hudson, eat in Little Italy making sure to get a box of the best pastries in the City at La Bella Ferrara—and then drive up 34th Street where we stop the car and let Jordi look straight up to the top of the Empire State Building. He LOVES that building. To him, it just touches the sky. I know exactly how he feels. For me it was always the World Trade Center.

So for Jordi, if one wanted to measure the size of the tallest mountain, using the Empire State Building as a ruler was surely the way to go. Cool kid. (Proud daddy.)

Not too long ago, I actually wrote a Post that used the height of the Empire State Building, so I remembered it was about 1,500 feet tall. I also know something about the height of mountains. My planetary atmospheres research took me to the telescopes on the summit of Mauna Kea so many times that I could be a tour guide for the Big Island of Hawai’i. On the summit I liked walking over to the U.S. Geological Survey marker identifying the highest point on Earth in the Pacific. But the short walk at 13,803 feet (4,207 meters) above sea level always left me out of breath. On one trip to the marker I had a friend take a picture of me next to it, with the clouds in the background a mile below us. I love to show that photo when I talk to kids and families and tell them that’s Jeff on top of the World (it is!)

But before going ‘UP’ with Jordi (something I suspect that’s much like what Carl Fredricksen felt flying off with Russell the wilderness explorer), I decided to go ‘down’ (because good stories have to build to a crescendo.) So we first talked about the Grand Canyon in Arizona, a hole in the ground that left me awestruck when I visited many years ago. At its deepest, the Grand Canyon is 6,000 ft (1,830 m) measured vertically from the rim of the Canyon to the Colorado River below. “Jordi, imagine you’re walking toward the rim and see this really large spike sticking up 100 feet above you. That’s about the height of a 10-story building. As you get closer to the rim and start to look down, you see the spike extends another 100 feet below you, and it’s attached to the top of a BIG building sitting in the Canyon. It’s the antenna mast …. of the Empire State Building.” He thought that was just so cool! Then shock set in when I told him this was just the top of a stack of FOUR Empire State Buildings with the base of the first sitting in the Colorado River! BIG canyon.

Then we went ‘up’, going back to his mountain question. Everybody thinks the tallest mountain on Earth is Mt. Everest and so did Jordi. So I went with the flow. “Jordi, Mt. Everest is about 29,000 feet above sea level. The Empire State Building is about 1,500 feet tall so, you’d need (daddy calculating in his head while driving) nearly …. TWENTY of them, one on top of the other, to get to the top of Everest.”  Then … Jordi says, “20?!!  20?!!!  … (5 second delay)…. 20?!!!!!” He was jaw—dropping stunned. In his mind that Building was huge! But How Big is Big? is all relative.

Now that I’ve got the internet and a calculator right here, I can do it more precisely. The summit of Everest is 29,029 feet (8,848 m) above sea level, and the Empire State Building is 1,472 feet (449 m) to the top of the antenna mast. So Everest is 19.7 Empire State Buildings Tall.

Ok, just getting you primed for your challenge. You didn’t think I’d give everything away did you?

Here now the challenge—

1. How many Empire State Buildings tall is the tallest mountain on Earth (Jordi’s original question)?

Hint: when is a mountain not just a mountain.

And by the way, my 210 mile high (340 km) mountain pictured in THIS Post, a photo presumably taken from the space shuttle, WASN’T REAL (the power of Photoshop). The fact that it was located “south of the Land of Make-Believe” was supposed to be the clue.

2. You’re on a cruise ship in the Pacific, 1,700 miles south of Tokyo and 200 miles south west of Guam (get out your maps.) You’ve slipped the captain a big wad of bills to stop the ship so you can go swimming. The crew lowers the inflatable zodiac, you jump into the water, but realize you left your spiffy waterproof, gold-encrusted watch in the dingy. The captain’s only given you 30 minutes of frolic time. “Hey crew member guy, can you toss me my watch?” Oops … he did and you missed. You do a quick dive and …. almost catch up to it as it gently descends. But you needed to stop ’cause you felt you were going too deep. There goes your watch on its way to the bottom. But come on, how deep could it really go? You figure if you slip the captain another wad of bills he’ll send in a diver to fetch it. Does he? How far is the bottom?

Hint: I want the answer using a (now) familiar ruler.

3. How many Empire State Buildings do you need to stack on top of one another to go from sea level to ‘outer space’?

Hint: read my Post The Business Trip for a clue.

Use a familiar ruler:

There’s a good chance you’re not familiar with the Empire State Building, so you might choose to use a different ruler for the heights and depths we’re considering above. Here are some tall structures in other parts of the USA and around the world you might want to use instead—

Statue of Liberty, New York City, USA: 305 ft (93 m) above ground level
Washington Monument, Washington, DC, USA:  555 ft (169 m)
Space Needle, Seattle, USA:  605 ft (184 m)
Eiffel Tower, Paris, France:  1,063 ft (324 m)

Tokyo Tower, Tokyo, Japan: 1,092 feet, (333 m)
Kiev TV Tower, Kiev, Ukraine: 1,263 feet (385 m)

Empire State Building, New York City, USA: 1,472 feet (449 m)

Petronas Twin Towers, Kuala Lumpur, Malaysia:  1,482 feet (452 m)

Shanghai World Financial Center, Shanghai, China: 1,614 feet (492 m)

Taipei 101, Taipei, Taiwan: 1,671 feet (509 m)

Willis Tower (formerly Sears Tower), tallest building in US, Chicago, USA: 1,730 feet (527 m)

CN Tower, Toronto, Canada:  1,815 ft (553 m)

Guangzhou TV and Sightseeing Tower, Guangzhou, China:  2,001 ft (610 m)

KVLY-TV mast, Blanchard, USA:  2,063 feet (818 m)
World’s tallest building—Burj Dubai (Dubai Tower) , Dubai, UAR:  2,684 feet (818 m)

Photo credit: NASA

This post is a Driving with Jordi.

This is crossposted at Huffington Post HERE.

Note to reader: click on the links in the text for the real data. This is not a work of fiction.

From Dr. James Hansen, Director of the NASA Goddard Institute for Space Studies concerning this post—

Public understanding of climate change depends on an understanding of time scales. Goldstein [Dr. Jeff] does a brilliant job of making clear the rapidity of the human-made intervention in the climate system, and the correlation of global warming with the appearance of technology powered by fossil fuels.

“Daddy, how long is a billion years?”

As soon as we got in the car this morning, and buckled up, I said “so Jordi, I need some help. I need more material for the blog.” “Daddy, what do you mean by ‘material’?”  “That’s what writers call the stuff they use to create stories”, said daddy.

It was a beautiful, sunny morning, so he started talking about … the Sun. He had lots of questions—where did it come from, what’s burning on it to make it so bright, how old is it, what will happen to Earth when it stops burning? The last one was particularly cool. I asked him if he thought the question “what will happen to the Earth when the Sun dies?” is something lots of kids might ask. He said “yes!!” I asked him who he thought was the first person to actually figure it out. He didn’t know. I told him it was me.

When I was a grad student at Penn, one of the undergrads in the class I was teaching asked that question. I didn’t know the answer, so I told her I’d find out. I tried but I couldn’t. Nobody had done it before. So I decided to be the first. I didn’t know if I could, and I didn’t know what I’d find, but it was incredibly exciting—and that’s science. Here’s the result. (And it was far from the end of the story.)

Jordi said, “YOU DID?” I looked at his surprised face in the rearview mirror and said “yup, your daddy.” Then he said, “that’s sooo strange! That’s sooo cool! I asked a question that YOU figured out!!” He was very proud. I felt so connected to him. (We’ll see later if he told his friends.) And I promise that I’ll make this story into a blog post, because now YOU’RE waiting for the rest of the story.

By the time we arrived at the school 20 minutes later, I had a month’s worth of ‘material’ for Driving with Jordi (stay tuned). The conversation was incredible. At one point though, Jordi ran into a conceptual wall when I was talking about the Sun’s lifetime being 10 billion years, and that it’s now half way through its life. He said “Daddy, how long is a billion years?”—which is why I wrote this post.

It is actually such an important question, and I thought about it all the way home. It’s at the heart of a key recurring problem in science education in that the VAST majority of humans truly don’t understand lengths of time that are far longer than our lifetimes. No wonder that folks don’t understand global warming as due to human intervention, and think it reasonable to interpret the data as explained by natural variation in the environment over long timescales. No wonder that folks don’t understand the timescales for evolution of species.

So here now is a novel way to look at it. Thanks Jordi! I think this will help lots of folks understand something they’ve never understood before.

Humans and Time

We humans now live on average about 75 years (in the developed world; in Africa the life expectancy is frighteningly low at 32 to 55). I’ll assume that 75 years is the life expectancy of a human in the absence of devastating diseases like AIDS, and with availability to modern medicine.

We humans also like to perceive the passage of time in units of seconds, minutes, hours, days, weeks, months, and years. We’ve created these units because they are comfortable, connected to the rhythms in the sky and in our bodies, and each is used to make sense of events both short and long. Here’s the critical point for the rest of the story—

One of our average humans sees 75 years x 365.25 days/year =

27,394 days in their life

That’s amazing. That’s 27,394 days of getting up in the morning, eating, working, playing, relaxing, and going to bed. Put this way, the length of a single day is absolutely inconsequential relative to a human lifetime. Agreed? Good.

A Really Cool Diary

So let’s say I had this really cool diary with one page for every day of our average human’s life. It’s a single book with 27,394 pages. I could give it to you at birth and ask you to record your life one page—one day—at a time (with some help from a friend in your early and possibly later years). Like I said, one cool diary.

A Day in the Life of the Earth

Let’s say planet Earth was this large cosmic creature. She’s got a life expectancy of about 10 billion years, from her birth with the Sun nearly 5 billion years ago, to her ultimate fate when the Sun is in its waning years some 5 billion years from now (nope not telling).

Earth obviously has a lot to say, and SHE’s been keeping a diary since she was born. But she’s got it in far too many volumes, since each didn’t come with many pages, and they’re all old and worn out. Hey, I think a new diary is a perfect gift for her! I’ll give her one of my really cool diaries with 27,394 pages. I’ll help her move all her old diary entries into the new one so it will truly record her 10 billion year life. Why don’t we call each page a GEOLOGIC DAY (a Dr. Jeff made-up term.) And every Geologic Day is absolutely inconsequential relative to Earth’s lifetime. After all, Earth has 27,394 of them.

Every Geologic Day, Earth will write in her diary the comings and goings for that day. Here’s the next important point—

Every one of the 27,394 pages in Earth’s diary—each Geologic Day—

is 365,000 years long

enough time for 14,600 human generations

How come? Easy: 10 billion years divided by 27,394.

Take a minute to process that.

I hope this gives you a new perspective for spans of time for Earth—called geologic time—relative to the time span for our fleeting lives.

So I give my friend the Earth one of my cool diaries. She likes it—her life all in one book. I also happen to be very close with Earth, and she’s letting me look at her diary. So here we are in the middle of her life and she just now finished her entry for day 13,697. She’s already written the first 13,696 pages (I helped her transfer the entries from her old diary with Apple Time Capsule.) Here now is her page 13,697—

Dear diary-

To Teachers:

You can really make this a powerful visual demonstration in class. The life of Earth recorded on 27,394 sheets of paper is a challenge to demonstrate. But if you can borrow some cartons of xerox paper, with each carton containing typically 10 reams, then here is what I’d do. Each ream contains 500 sheets. So you need 5 full cartons (that’s 50 reams = 25,000 sheets) + 4 reams (another 2,000 sheets) + 394 sheets.

Without telling the class anything about what you are doing, have them take the reams out of the boxes (without opening them) and lay them out on the floor. Have them open one ream to see how many sheets are in it. In fact, have them count the sheets in the ream and take out the 394 sheets you need. Then:

• walk them through the concept of a single diary for an average human lifetime: they should calculate how many diary pages they would need if there is one page per day; then have them calculate how many sheets are on the floor—”oh, the number of days in a human lifetime!  WOW!!  That’s a lot of days for a human!”

• let them in on the idea of giving this diary to Earth, and assuming a lifetime of 10 billion years, have them calculate how many years of history are on EACH sheet—”365.000 years! No way!!” Then have them calculate the equivalent number of human generations on one sheet assuming 25 years per generation (a reasonable time from parent birth to child of parent birth)—”Can that be right? 14,600 generations!?”

• re-arrange the paper with half of it on one side of the floor to represent Earth’s history that is already recorded,and the other half on the other side of the floor representing Earth’s future history.

• then pick the single sheet of paper that represents the last 365,000 years of history, so that on this sheet, the final diary entry is the present. Lay it between the two groups of paper representing the past and future history of Earth.

Ask the class to think about this sheet of paper as a 24-hour clock. So at time 0:00:00, you’re at the beginning of the sheet, 365,000 years ago. At time 12:00:00 you’re in the middle of the sheet 182,500 years ago. At time 24:00:00 you’re in the present moment, where you all happen to be sitting in class.

Ask them to calculate the time on the clock when human civilization began (10,000 years ago, answer: at time 23:20:19); when the industrial age began (the age of fossil fuels; 150 years ago, answer: at time 23:59:25).

Have them look at world population growth noting what’s happened during the age of fossil fuels, the carbon dioxide level over the last 650,000 years, and the world temperature over the last 2,000 years. What is the data telling you?

• have them figure out how many sheets ago the dinosaur extinction took place.

• have them research Earth’s geological history, and figure out which sheets contain other milestones or important intervals in Earth’s history.

This should be MIND BLOWING! It is an experience your students will likely remember for a lifetime.

Photo caption: Earth from MESSENGER spacecraft as it flew by Earth on August 2, 2005. MESSENGER goes into orbit around Mercury on March 18, 2011.

Image courtesy NASA, Johns Hopkins University Applied Physics Laboratory, and Carnegie Institution of Washington.

This post is a Driving with Jordi, and a Dr. Jeff’s Jeffism.

“Daddy, how long would it take to drive around the Sun?”

So there we were on the Washington, DC, beltway heading for his elementary school. We were cruising at 60 mph—yes, on the beltway, I know!! (© Craig Ferguson, CBS).  Jordi said, “daddy, how far has this car gone since you and mommy got it?” I looked down at the odometer and read 249,000 and some odd miles. Cool! The ’95 Camry was doing just fine. Besides getting close to the 250,000-mile mark, the space guy in me knew that the Earth’s circumference is about 24,900 miles. “Jordi! This car could just have gone around the entire planet Earth 10 times!” He wasn’t expecting that answer. He thought that was … way cool. Cars aren’t supposed to be able to go around an entire planet are they?

But before we get to the rest of the story, first a detour at a Jeffism—

Science Education is about conceptual understanding

at an emotional level.

The learning wasn’t about the 249,000 miles. It was about relating that distance to something familiar or concrete or impressive—which caused an emotional reaction

in … both of us. The trick is to build a bridge to the familiar. (Want more on this? Read my Power of Models page.)

Then the discussion really took off. “You know, it took mommy and daddy 14 YEARS to drive that far. We’re not on the road all day as part of our jobs, but we’re still driving 18,000 miles a year.”  (For you cross-country U.S. drivers, that’s 7 New York to California trips a year.)

That’s when he hit me with the question. “Daddy, how long would it take to drive around the Sun?”  “Uuugh, you mean drive along the path the Earth takes around the Sun?”  “No daddy, if the Sun were a solid ball and we were driving on it, how long would it take to drive around it once?” I’m not kidding, that’s what my first grader asked. So I started figuring it out aloud so he could follow along, and even do the math with me.

The Sun is about 100 times the diameter of the Earth (actually 109, but 100 is a nice round number and close enough), so its circumference is about 100 times that of Earth. Our little-Camry-that-could made it 10 times around the Earth, which is only ONE TENTH THE WAY AROUND THE SUN. “Jordi, to drive around the Sun just once, we’d need to have ten Camrys, each with 249,000 miles on them. Or … drive this Camry for 140 years!  He said woooaah! We got to school. He told his friends.  

Isn’t science an adventure? So is life with Jordi. Hope you can share this with your kids. 

Teachers and parents:

1. How long it takes for a  trip is a good way to get a feel for a distance, as long as your audience is familiar with the vehicle you’re using, and they’ve got a good feel for its typical speed.  

The magic equation: trip time = total distance / speed

A more concrete approach to this Driving with Jordi is to have your kids figure out how long it would take to drive the distance in a car at a speed of 60 mph (97 km/hr) IF YOU DRIVE NON-STOP.

So we also need: circumference = diameter x pi    where  pi = 3.14 

Earth 

equatorial diameter: 7,926 miles (12,756 km)

so circumference is: 24,888 miles (40,054 km)

time to drive around once at 60 mph (97 km/hr): 415 hours = 17.3 days

That’s living in your car—not stopping—for 17.3 days!

Sun

Sun diameter: 865,000 miles (1,392,000 km)

so circumference is: 2,716,000 (4,371,000 km)

time to drive around once at 60 mph (97 km/hr): 45,270 hours = 5.2 YEARS!

Now try the drive between Earth and the Moon:

average Earth-Moon distance: 238,900 miles (384,400 km)

time to drive at 60 mph (97 km/hr): 3,980 hours = 166 DAYS!  

How long did it take the Apollo spacecraft?

Can’t finish without a drive to the Sun:

average Earth-Sun distance: 93,000,000 miles (149,600,000 km)

time to drive at 60 mph (97 km/hr): 1,550,000 hours = 64,580 days = 176 YEARS!!

2. If you want to use this Driving with Jordi to introduce your kids (and you) to the scale of the Solar System, you can download one of the many lessons we developed for the Voyage scale model Solar System in Washington, DC, and are now installing around the nation. This particular lesson allows you to lay out a one to 10-billion scale model Solar System in your local park. It includes the relative sizes of Sun, Earth, and Moon, and the distances between them—on the same scale. 

Parents, here’s the family version of the lesson: Voyage! (PDF, 500 KB)

Teachers, here’s the lesson (written for grades 5-8): Voyage of Discovery (PDF, 870 KB). You might want to do the lesson Our Solar System (PDF, 900 KB) first, which develops a concrete understanding of what we mean by the Solar System.

I think you’ll be blown away. 

Photo credit: Courtesy of SOHO/[instrument] consortium. SOHO is a project of international cooperation between ESA and NASA. 

This post is a solution to a Dr. Jeff’s Weekly Challenge.

For those of you that read last week’s Weekly Challenge 1 and are now waiting on the edge of your seats for the answers, well here they are. For those of you that haven’t yet read Weekly Challenge 1, DON’T LOOK! Go directly to the challenge and read it first, do not pass go, and do not collect $200.

And now the answers—

1. How many ants in a pound of ants?

Hint: there is no single answer because there are lots of different species of ants. So do some research on ants, figure out an answer, and see if your answer falls in the range I’ll give you next week.

The answer:

1.5 MILLION ants in a pound of ants! (Great question Jordi—it stunned your daddy.) This assumes an average-sized species of ant, and that we’re talking about worker ants. (Isn’t there always a disclaimer for an answer to a simple question?)

Depending on the ant species, there are anywhere from 190,000 to 7.5 MILLION ants in a pound of ants! See the ”How did I come up with the answers?” section below.

2. How much does the human race weigh?

Hint: you’ll need to know how many humans are on the planet. Here you go, courtesy of the U.S. Census Bureau.

The answer:

With about 6.8 billion of us on Earth, here is the weight of the human race—

english system: 440 million tons (1 ton = 2,000 lbs)

metric system:  410 million metric tons (1 metric ton = 1,000 kg)

See the “How did I come up with the answers?” section below.

WOW!!  I think I’m impressed. But … wait a second. That’s just a BIG number. I have NO CLUE what that big number means. If I’m to truly understand it (you too in cyberspace), then I need to build a bridge to the familiar. So let’s go on to the third part of our challenge.

3. Wait, I hear Ellen in Detroit saying, “but Dr. Jeff, I’d rather know the total volume of the human race, in other words, how big a volume of space would you need to just fit the entire human race?” Good thinking Ellen! That’s another great way to look at it. So let’s make this a third part of the challenge. Once you calculate 2 above, figure out the total volume of the human race.

Hint: you can assume that we humans are made mostly of water, and every 1,000 kg of water takes up 1 cubic meter of space. For those of you who like to conceptualize using the English system of units, 1 ton of water (2,000 lbs) takes up 32 cubic feet of space.

The answer:

The entire human race—the species that can change the environment on a planetary scale—can comfortably fit into a box just 1/2 mile on a side (0.75 km on a side). See the ”How did I come up with the answers?” section below.

If you know Washington, DC, that’s about the volume of space equivalent to the size of the National Mall filled to the top of the Washington Monument.

If you know New York City, that’s a about the volume of space equivalent to the size of Central Park filled to the top of the Flatiron Building.

Isn’t this just so unbelievable SMALL? Can you figure out an equivalent volume in a city near you?

THE IMPORTANT LESSON THIS WEEK

In this box of humanity is—mostly water. Also in this box is a species that is self-aware, intelligent, and driven to know and do anything and everything, and a species that has the capability to imagine, design, and BUILD tools. How does such a small box of intelligent biomass change the planet? TECHNOLOGY. With hydraulics and explosives we can move mountains. With power plants and engines to create energy from fossil fuels we can heat the entire planet, raise the oceans, and change weather on a global scale. I CANNOT think of a better argument for the need for science and technology education. We as a nation, we as a world must make informed decisions about how we use our technology so that we can be good stewards of the planet.

And now—how did I come up with those answers?

The secret piece of information is the weight of a single ant. You might do your standard google search and find an answers-to-everything web site. This is probably how you got your answer. Let’s compare it to mine.

I’m always careful to make sure information I research is accurate. I usually don’t even trust Wikipedia, but often use it to point me in the right direction. At the bottom of a Wiki page there are often references to formal publications by scientists and engineers that have been reviewed by …. other scientists and engineers. We call these “reviewed” or “refereed” publications, and are where you typically find the best available information on a subject.

So here is the magic publication I found by Michael Kaspari, published in 2005 in the Proceedings of the National Academy of Sciences of the United States of America. Michael carefully studied ant colonies at 49 different sites with different climates, and found 434 species of ants. I think we can assume he is an ant expert. He wrote this article to tell other scientists about what he found. If you look at what he wrote it seems pretty technical, but it’s amazing that he describes the breadth of his research in beautiful detail using two very powerful languages–english and mathematics. Scientists and engineers need to be great communicators if their research is to be known by others. But no need to read the article, I’ll translate for you.

Michael found that the weight of a worker ant was anywhere from 0.06 milligrams to 2.34 milligrams. (A milligram is one thousandth of a gram, and a gram is one thousandth of a kilogram. A kilogram is 2.2 pounds.) The worker ant for the largest species he studied was 40 times the weight of the worker ant for the smallest species! The average was about 0.3 mg, which is what I’ll use. So here we go—

Weight of a single ant is 0.3 mg

The number of ants in a pound of ants = 1 pound divided by the weight of a single ant

To divide you need to use the same units: since we have the weight of an ant in milligrams, let’s do the math in milligrams.

Convert 1 pound to milligrams: 1 pound = 0.45 kilograms = 450 grams = 450,000 milligrams

Now divide: 450,000 milligrams / 0.3 milligrams = 1.5 MILLION ants!

But WAIT! Let’s do this for the species he studied with:

• the smallest worker ant, only weighing 0.06 milligrams.

You get 7.5 MILLION ants in a pound of ants!

• the largest worker ant, weighing 2.34 milligrams.

You still get 190,000 ants in a pound of ants!

Here’s a cool question to lead us to the next part of the challenge. If you had as many ants as human beings on Earth, how much would all those ants weigh?

(6.8 billion ants) x (0.3 milligrams per ant) = 2,000 kg (or if you like the English system, about 2 tons)

2. How much does the human race weigh?

Courtesy of the U.S. Census Bureau I see that right now there are about 6.8 BILLION humans on the planet. Now for the guess—I’m going to assume the average human being weighs about 130 lbs (60 kg). It sounds reasonable when I consider children, the difference in weight between men and women, and that most humans live in impoverished conditions.

The weight of the human race is then:

english system:   6.8 billion x 130 lbs = 880 billion pounds =

440 million tons (1 ton = 2,000 lbs)

metric system:    6.8 billion x 60 kg = 410 billion kg =

410 million metric tons (1 metric ton = 1,000 kg)

WOW!!!!  Or maybe not.

3. How big a volume of space would you need to just fit the entire human race?

Hint: you can assume that we humans are made mostly of water, and every 1,000 kg of water takes up 1 cubic meter of space. For those of you who like to conceptualize using the English system of units, 1 ton of water (2,000 lbs) takes up 32 cubic feet of space.

Yup, we are mostly water. In fact even water treats us like water. If we’re in a pool and we go underwater, we’re pretty close to neutral buoyant—which means we don’t sink too fast or rise too fast. We’re about the density of water.

So here is the volume of the human race:

english system:   440 million tons x 32 cubic feet /ton = 14.1 billion cubic feet

metric system:    410 million metric tons x 1 cubic meter per metric ton= 410 million cubic meters

NOW FOR THE FUN PART.

Let’s assume that we put the human race in a box with the volume above. And let’s assume that the box is a cube where the length = height = width. How big a box would contain the volume above?

Volume of a cube = (length of side) x  (length of side) x (length of side)

= (length of side) ³

To get the length of a side you therefore take the cube root of the volume, and you get:

• english system:  cube root of 14.1 billion cubic feet

length of side = about 2,400 feet = 0.45 miles!!!

• metric system: cube root of 410 millio cubic meters

length of side = about 750 meter = 0.75 kilometers!!

This post is a Dr. Jeff’s Weekly Challenge and a Driving with Jordi.

A day late because of Memorial Day in the U.S.

I’m proud to post my first Driving with Jordi, so here we go!

Two weeks ago I was driving Jordi to school. We started down the road with 5 minutes of quiet contemplation, both of us just getting our heads wrapped around the new day, me with a cup of coffee in hand. Then, out of the blue came the question, “daddy, how many ants in a pound of ants?” I had to ask, “where did that come from?” So he explained that the day before he was hanging out in our big vegetable garden (he loves doing that), picked up a rock, and found lots of ants scurrying for cover. They were really small, and there were lots and lots of them. So he came up with this question to help him get a sense of their scale relative to a familiar ‘ruler’. He picked a pound. He came to me for the answer. I had no clue. So I decided to post this as part of this week’s challenge (see below.) You’ll be happy to know that I now have the answer and have already shared it with Jordi. But he promised not to tell.

Every time we drive together, his question launches a whole conversation. This time was no different. I remembered that in my presentations I sometimes liken the human race to a colony of ants scurrying around the surface of the planet. It’s a great teaching tool given kids know ants, and know ants are part of a ‘society’ in which each ant has a job.

So we talked about the human race as a colony of ants. We humans are all over the planet. We’re changing the environment on a global scale. I told Jordi about the term “biomass” which is the mass (equivalently the weight) of living things. You can imagine the biomass of all living things on the planet—the Earth’s biomass. You can also imagine the biomass of the entire human race. Surely with humanity’s ability to change the entire planet, its biomass must be huge!  Let’s see. Let’s make this the second part of your challenge this week, though this one is a little tougher (for, e.g., good for middle and high school students.)

Here now the challenge—

1.  How many ants in a pound of ants?

Hint: there is no single answer because there are lots of different species of ants. So do some research on ants, figure out an answer, and see if your answer falls in the range I’ll give you next week.

2.  How much does the human race weigh?

Hint: you’ll need to know how many humans are on the planet. Here you go, courtesy of the U.S. Census Bureau.

3. Wait, I hear Ellen in Detroit saying, “but Dr. Jeff, I’d rather know the total volume of the human race, in other words, how big a volume of space would you need to just fit the entire human race?” Good thinking Ellen! That’s another great way to look at it. So let’s make this a third part of the challenge. Once you calculate 2 above, figure out the total volume of the human race.

Hint: you can assume that we humans are made mostly of water, and every 1,000 kg of water takes up 1 cubic meter of space. For those of you who like to conceptualize using the English system of units, 1 ton of water (2,000 lbs) takes up 32 cubic feet of space.

Ok, get to work!

Answers are now posted here!