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!