Photo caption: Computer-generated image of the Milky Way galaxy based on real data.

This post is a Dr. Jeff’s Weekly Challenge. It was requested by (teacher extraordinaire) Jami Lupold and her class in the great city of Houston, Texas, USA.

If you’re a teacher and your class has an idea for a blog post, slip me a note!

Last week I gave you a scare. It happened when I told you that you’re really on a spaceship hurtling through space. I was in the midst of describing all of Earth’s motions—it spins, it orbits the Sun, the Sun orbits the center of our galaxy carrying Earth and the Solar System along for the ride—and that’s when I saw panic on your face. You started to get a bit dizzy, so I turned on the “fasten seat belt sign” in light of all the conceptual turbulence ahead. To keep your mind off all the spinnin’ and revolvin’ I gave you an assignment to calculate Earth’s speed—your speed—due to these three motions. Does this all ring a bell? No? Why don’t you go and re-read the original challenge from last week, so you can refocus.

Good. Now that you’re back. Let’s get to the answers. Did I mention this week’s challenge was in our in-flight magazine in the seat pocket in front of you? By the way, I see you dug your fingernails into your seat, and your fingertips seem a bit blue. (Hope the answers don’t send you into a panic.)

And now the answers—

1. The Effect of Earth’s rotation: say you’re just standin’ there on Earth’s equator, all peaceful-like (a shout-out to my favorite class in Texas), minding your own business. How fast are you moving due to Earth’s rotation?

Hint: the Earth rotates once in 24 hours, and think “circumference of Earth.”

Answer: Just STANDING on the equator you are moving about 1,000 mph (nearly 1,700 km/hr)! You’re moving 1 mile every 3 seconds (1 km every 2 seconds)!

See the “How did I come up with those Answers” section below.

2. The Effect of Earth’s revolution (it’s orbit around the Sun):

Now you’re standing on the North Pole. Why? Well it’s a place where we can forget about the speed you’re carried due to Earth’s rotation. Up here (excuse me for a moment …. brrrrr) Earth’s rotation just gently rotates you once in 24 hours on the spin axis you’re standing on. But you’re still movin’ through space, yes you are … ’cause the entire Earth is zipping along in its orbit around the Sun. Your assignment #2 if you choose to accept it: how fast are you moving due to Earth’s motion around the Sun?

Hint: the Sun is 93,000,000 miles or 149,600,000 km (on average) from Earth, and it takes 1 year to go around once. This time think “circumference = 2 x pi x r”

Answer:

STANDING on spaceship Earth, you are being carried around the Sun at a speed of 19 MILES PER SECOND (30 KM PER SECOND)!! Say “one mississippi” …. there, you just moved 19 miles (30 km)!  That’s the same as 67,000 miles/hour (107,000 km/hour)!!  (Maybe you should keep your seat belt on.)

See the “How did I come up with those Answers” section below.

3. The effect of Earth’s revolution around the center of the Milky Way galaxy:

Your assignment #3 is to figure out how fast the Sun (carrying the entire Solar System along for the ride) is moving in its orbit around the center of the Milky Way galaxy.

Hint: assume the Sun is 28,000 light years from the center, and completes 1 orbit in 240 million years

Oh, other needed Hint: 1 light year = 5.9 trillion miles or 9.5 trillion km

And yeah: think “circumference = 2 x pi x r” (again)

Answer:

For you to orbit the center of the Milky Way once in even the unfathomable time of 240 million years still requires you to be moving very, exceedingly, incredibly, *unbelievably* fast. Right now you are cruising through the galaxy at 495,000 MILES/HOUR (795,000 km/hr)!! That’s 140 MILES/SECOND (220 km/second)! Count out 17 seconds. Cool. You just moved the length of the continental United States, from New York to San Francisco. REALLY!

What? You’d like to travel the entire diameter of planet Earth? Wait 1 minute (actually 57 seconds). Done.

See the “How did I come up with those Answers” section below.

Look up in the sky! It’s a bird! It’s a plane! It’s superman!  … big deal. Just sittin’ there, [insert your name here] is WAY faster than a speeding bullet.

Teachers and Parents:

You don’t need to do the calculation with your class (or child at home) to use this post as a powerful lesson. The speeds described above are remarkable, and are sure to impress. Some points:

1. The first calculation is the easiest because you don’t need scientific notation, and you don’t need to convert units. So you might want to do this one to demonstrate the geometry of a circle (the path traveled), and the relation: speed = distance / time.

2. Show some examples of speed = distance / time,  e.g., if you travel 100 miles in a car at 50 mph, how long did it take?

3. Have them guess what speeds might be associated with each motion before you tell them the answer.

4. With the answers above in hand, have them calculate how long it would take to travel distances that are familiar to them, e.g., the distance between two cities. Calculate separately the time it would take due to Earth’s rotation, Earth’s orbit around the Sun, and the Solar System’s orbit around the center of the galaxy.

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

Note that calculating answers 2 and 3 below requires an understanding of scientific notation.

There are two key relationships you need for all three questions. In each case the motion you’re investigating carries you once around a circle in a given period of time:

The first is the relationship between a circle’s diameter (d) or radius (r) and the circle’s circumference (c):

circumference = pi x diameter

or

circumference = 2 x pi x radius

where  pi = 3.14

The second relationship provides your speed if you know the distance you’ve traveled in a given time:

speed = distance / time

1. The Effect of Earth’s rotation

The important point: you travel around the circumference of Earth once in 24 hours.

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

Earth’s circumference = pi x diameter:  24,888 miles (40,054 km)

speed = distance / time  =  circumference / time

English units: speed =  24,888 / 24  = 1,037 miles/hr   Or: 0.29 miles/sec

Metric units: speed = 40,054 / 24 = 1,670 km/hr   Or: 0.46 km/sec

2. The Effect of Earth’s revolution (it’s orbit around the Sun):

The important point: you travel the path of Earth’s orbit around the Sun once in 1 year. You can assume the orbit is a circle whose radius is 93,000,000 miles (149,600,000 km), which is the average distance between Earth and the Sun.

Circumference of Earth’s orbit around Sun:

= 2  x pi x radius:  584 million miles (939,5 million km)

Time to orbit Sun once:

= 1 year = 365.25 days = 8,766 hours = 3.16 x 10 ⁷ seconds

speed = distance / time  =  circumference / time

English units: speed =  584 x 10⁶ / 8,766  = 66,600 miles/hr   Or: 18.5 miles/sec

Metric units: speed = 939.5 x 10⁶ / 8,766 = 107,200 km/hr   Or: 29.8 km/sec

3. The effect of Earth’s revolution around the center of the Milky Way galaxy:

The important point: you travel around the center of the Milky Way galaxy once in 240 million years. You can assume the orbit is a circle whose radius is 28,000 light years (each light year is the distance light travels in a year.)

Let’s convert 28,000 light years to meaningful units of miles and km. The hint said that 1 light year = 5.9 trillion miles or 9.5 trillion km

English units: 28,000 light yrs x (5.9 x 10¹² miles /light yr) = 1.65 x 10¹⁷ miles

Metric units: 28,000 light yrs x (9.5 x 10¹² km / light yr) =  2.66 x 10¹⁷ km

Now let’s calculate the circumference of the orbit around the galactic center:

= 2  x pi x radius:

English units: 2 x pi x (1.65 x 10¹⁷ miles) = 1.04 x 10¹⁸ miles

Metric units: 2 x pi x (2.66 x 10¹⁷ km) = 1.67 x 10¹⁸ km

Time to orbit the center of Milky Way once:

240 x 10⁶ years = 8.8 x 10¹⁰ days = 2.1 x 10¹² hours = 7.6 x 10¹⁵ seconds

speed = distance / time  =  circumference / time

English units: speed =  1.04 x 10¹⁸/ 2.1 x 10¹² =  x 495,000 miles/hr

Or: 140 miles/sec

Metric units: speed = 1.67 x 10¹⁸ / 2.1 x10¹² = 795,000 km/hr

Or: 220 km/sec

Photo Credit: National Geographic Society Image Collection, 1999.

Photo caption: Computer-generated image of the Milky Way galaxy based on real data.

This post is a Dr. Jeff’s Weekly Challenge. It was requested by (teacher extraordinaire) Jami Lupold and her class in the great city of Houston, Texas, USA.

If you’re a teacher and your class has an idea for a blog post, slip me a note!

You wanted to be an astronaut? Poof. Done.

You and your friends are on a spaceship called Earth—with all known life aboard. With you sitting there calmly reading this, and no obvious need to hold on to something for dear life, it might seem that the spaceship under your feet is carrying you on a nice steady trajectory through space. Uh … Nope. Right now you’re being carried along on something more akin to a cosmic-sized amusement park ride. Earth is rotating on its axis, it’s orbiting the Sun, and the whole Solar System (the Sun and its planets, dwarf planets, asteroids, comets, and Trans-Neptunian Objects) is orbiting the center of the Milky Way galaxy. The Milky Way itself is moving relative to other nearby galaxies, the local group of galaxies is moving through a greater space, and all this is set against a backdrop of an expanding fabric of space and time across the entire universe. I know!!!! (© Craig Ferguson) Dizzy?

[Pleasant Ding] The captain has just turned on the seat belt sign. There may be some conceptual turbulence up ahead. But I’ll make the ride as smooth as possible.

OK, I think a Weekly Challenge requesting that you calculate all the spinning, and revolving, and free-flying is a bit much, so let’s concentrate on three things:

Here now the Challenge—

1. The Effect of Earth’s rotation: say you’re just standin’ there on Earth’s equator, all peaceful-like (a shout-out to my favorite class in Texas), minding your own business. How fast are you moving due to Earth’s rotation?

Hint: the Earth rotates once in 24 hours, and think “circumference of Earth.”

2. The Effect of Earth’s revolution (it’s orbit around the Sun):

Now you’re standing on the North Pole. Why? Well it’s a place where we can forget about the speed you’re carried due to Earth’s rotation. Up here (excuse me for a moment …. brrrrr) Earth’s rotation just gently rotates you once in 24 hours on the spin axis you’re standing on. But you’re still movin’ through space, yes you are … ’cause the entire Earth is zipping along in its orbit around the Sun. Your assignment #2 if you choose to accept it: how fast are you moving due to Earth’s motion around the Sun?

Hint: the Sun is 93,000,000 miles or 149,600,000 km (on average) from Earth, and it takes 1 year to go around once. This time think “circumference = 2 x pi x r”

3. The effect of Earth’s revolution around the center of the Milky Way galaxy:

This one is the toughest ’cause now I’ve relocated you to the north pole of … the SUN. Here, you don’t experience effects 1 and 2 above. From here you can just watch the spinning Earth as it orbits you. (Excuse me a minute …. hot, hot, hot!) What? Why did I put you on the NORTH POLE of the Sun? So I would not confuse you with your motion due to the Sun’s ROTATION.  (Hey, get with the program …. everything is in motion.)

Your assignment #3 is to figure out how fast the Sun (carrying the entire Solar System along for the ride) is moving in its orbit around the center of the Milky Way galaxy.

Hint: assume the Sun is 28,000 light years from the center, and completes 1 orbit in 240 million years

Oh, other needed Hint: 1 light year = 5.9 trillion miles or 9.5 trillion km

And yeah: think “circumference = 2 x pi x r” (again)

So get to figurin’, and remember that while you’re sittin’ there, you’re ZOOMING THROUGH SPACE due to those three effects you’re figurin’!

Thanks Jami and Jami’s class! Have a great school year!

—Doctor Jeff (Honorary Texan)

Answer now posted here!

Photo Credit: National Geographic Society Image Collection, 1999.

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

Welcome humans nice folks. We have assumed you are here for the answer to Weekly Challenge 6. Men in black team #26,342 is therefore now en route to your home. If you don’t know why, before reading any further we recommend (with great strength) that you read Weekly Challenge 6. Our team is rolling (very fast).

And now the answer—

Last week in the Cosmic Kitchen, Chef Jeff pushed the green button on the pasta press, and a single strand of Earth spaghetti was created that just stretched across the 93 billion light-year diameter of the observable universe.

What was the diameter of the spaghetti required?  1 millimeter (0.04 inches)

It is not microscopically thin. It is not the diameter of a fire hose. It is precisely the diameter of—angel hair pasta, a thin spaghetti. Go to your local store buy a box and measure it for yourself. By the way, help support us by purchasing our sponsor’s brand of angel hair. Look for Cosmic Kitchen Pasta #42 available in most supermarkets.

We also submit for your consideration that this was not magic, or some remarkable coincidence. In the Cosmic Kitchen we have the ability to realign the laws of nature. In this case, we have ensured that the Earth, when squeezed into a single strand of Earth spaghetti capable of spanning the observable universe, has the thickness of  … spaghetti. We hope you humans nice folks appreciate the effort. We wanted your planet to still be recognizable to you, at least as today’s special entree.

We also hope you have enjoyed your visit to the Cosmic Kitchen. Its existence is a closely guarded secret, and we are honored to have shared it with you. The men in black will be knocking on your door at any moment. Won’t you please help them fill out our survey? And remember that you can receive a special gift if you answer their final question correctly. Since we have spent this last week together, I now consider us friends, and I want to see you receive your special gift. So remember I gave you the answer to the question last week. Just say “cheese.”

How did Chef Jeff come up with the answer?

The volume of the Earth, a sphere, is to be transformed into the volume of a strand of spaghetti, a cylinder. Recognizing that the volumes are equal, here is how it is done:

1. The volume of a sphere is: 4/3 x pi  x R³ where:

pi = 3.14

R is the radius of the sphere, in this case the radius of Earth:

6,378 km = 6.378 x 10⁶ meters

2. The volume of a cylinder is: pi x r² x h   where:

r is the radius of the cylinder, here the radius of the spaghetti, which is to be calculated

h is the height of the cylinder, here the length of the spaghetti:

93 billion light-years  = 9.3 x 10¹⁰ light-years

converting to meters (see hint last week):

9.3 x 10¹⁰ light-years  x  9.46 x 10¹⁵ meters / light-year  =  8.8 x 10²⁶ meters

3. Setting the two volumes equal yields the equation (note the pi cancels out):

4/3 x R³ =  r² x h

4. Now enter the following data into the equation and solve for r, the radius of the spaghetti:

R = 6.378 x 10⁶ meters

h = 8.8 x 10 ²⁶ meters

You will find r =  0.00063 meters = 0.63 millimeters

Thus the diameter of the spaghetti =  2 x r  =  1.2 millimeters, which is the diameter of angel hair pasta.

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

On a recent tour of CBS, I got separated from my group, got pretty lost, and ended up in a dusty storage room filled with nightmarish props that really creeped me out. In the corner I found an old envelope marked “Rod Serling’ with a script inside. Wow. I decided to turn it into a BotU Weekly Challenge and introduce a new character kinda like, well, me. (It is my Blog.)

First a word from our Sponsor—

Come back Monday, August 24. for the solution to this Weekly Challenge.

Come back Friday, August 21, for a new post “The Scale of the Solar System—A Voyage in Corpus Christi”

Submitted for your consideration, I invite you to accompany me to a Cosmic Kitchen where each entree is of galactic proportions, and ingredients are folded together with forces both unimaginable and seemingly limitless. As we enter the infinite spaces allocated for baking, a solar-system-sized pasta press has just been loaded with planet Earth, and an ejector plate has been inserted which has but a single hole in the center with an adjustable diameter. Chef Jeff has closed the massive door behind the planet, and now the only way out for Earth is through that small opening—for today’s special in the Cosmic Kitchen is Earth spaghetti.

Before pushing the unassumingly small green start button on the pasta press, the diameter of the spaghetti must be set. Once the hydraulics are engaged no adjustments can be made—for the forces at work could result in a catastrophic accident. It has happened in the past. 350,550 years ago the pasta press exploded, planet was everywhere, and the kitchen had to be closed down for cleaning by precisely 10,000,042 workers. (Note that in the Cosmic Kitchen, 42 must be included in the solution to everything).

Given the potential consequences, setting the diameter of the spaghetti required Chef Jeff to consult Cosmic Kitchen’s head chef. Her reply—adjust the diameter so that the single strand of Earth spaghetti could just stretch across the entire observable universe.

Back in the Cosmic Kitchen’s research library, with rows of workstations extending to the horizon, Chef Jeff goes on line to determine the size of the observable universe. He’s come across this before. It came up when he was asked to keep folding a humongous sheet of paper until its thickness could extend to the edge of the observable universe. He remembered the link to the web site with the answer. The diameter of the observable universe is 93 billion light-years.

Chef Jeff (originally trained as an astrophysicist, but thought cooking was more lucrative) now knows that the entire volume of Earth is to be stretched into the volume of a single strand of spaghetti that just spans the 93 billion light-year diameter of the observable universe. A quick calculation gives him the required diameter for the spaghetti.

Back at the pasta press, he transports to the ejector plate, sets the spaghetti’s diameter, and transports back to the control room where he stands ready to push the green button.

Here now the challenge—

By reading this, you have accepted an invitation to be one of the spectators in the Cosmic Kitchen’s gallery. Before Chef Jeff pushes the button, you are asked to submit your guess for the diameter of the spaghetti he will be making today. Leave your guess as a comment below.

If you are in fact brave enough to undertake the calculation before submitting your guess (and you know how to use scientific notation) then here is your hint:

What is the volume of a sphere?

What is the volume of a cylinder?

1 light-year = 9.46 x 10¹⁵ meters

After the answer is posted next week, please wait by your door for my colleagues to arrive. You will easily recognize them. They will be men in black. They will be interviewing you on the quality of this post, and will be taking notes with a rather interesting pen. Please take a close look at their pen. They will also ask you a question to see if you should receive a special gift for taking the survey. Let me help. I know what they will likely ask: “what milk product is often aged before being brought to market.” You should say “cheese.”

Answer now posted here!

This post is a Dr. Jeff’s Weekly Challenge and a Dr. Jeff’s Jeffism.

Last week on BotU, your challenge was to take an imaginary, truly humongous piece of xerox paper—but with normal xerox paper thickness—and figure out how many times you’d need to fold it in half so the folded thickness is the height of you, the Statue of Liberty, the Empire State Building, and Mount Everest. For those that really wanted to challenge themselves, I invited you to keep folding so it would be thick enough to reach the Moon, the Sun, the nearest star, and beyond.

How’d you do?

BUT WAIT! If you haven’t yet read Weekly Challenge 3, DON’T LOOK AT THE SOLUTION HERE JUST YET! First read Weekly Challenge 3, or I’ll take back my paper.

First, a word from our sponsor—

You Want Me To Do What With a Bathroom Scale?

Weekly Challenge 4 to be posted Monday, June 29, 2009

Other Posts coming soon:

A Voyage in Corpus Christi

Twinkle Twinkle Little Star, History Tells How Far You Are

Lessons of Earth

MESSENGER: Target Mercury

And now the answers—

Remember that I began Weekly Challenge 3 by asking you to imagine a humongous piece of paper that, when standing in the middle of it, seemingly extends to the horizon in all directions. This is clearly NOT a real piece of paper. What I posed is called a Thought Experiment—an experiment done on the landscape of your mind. It’s a flavor of experiment that has been done by the likes of Einstein to revolutionize our understanding of space and time. A Thought Experiment often poses a problem that cannot be addressed with a real experiment because doing so is either impossible (as in this case) or clearly beyond current technology, or for that matter beyond any interest in doing it in the real world (e.g., where would you come out if you dug a hole right through the center of the Earth?) And this is precisely why it’s such a powerful type of experiment. It uses critical thinking coupled with what you think you know about the world, to hopefully produce a real conclusion—which often leads to a change in perception.

A note about trying to do this in the real world: You CAN’T actually fold a sheet of paper more than a few times because it quickly gets too small and all the paper is taken up in the curvature of the folds. Try it. If you want to increase the number of folds, you need a larger sheet of paper. But just a few more folds quickly requires a sheet that’s longer than your street, your city, your nation, and, in fact far longer than planet Earth is wide.

This problem was pointed out in the great comment by Maria Miller (see Weekly Challenger 3 page.)  She has a link to a story that made news a few years ago. In 2001, Britney Gallivan a high school student set out to understand the limitations imposed by folding as part of an extra credit problem in math class. She even came up with a limiting equation that defines the minimum size of the paper sheet you’d need in order to fold it a specific number of times. Here are more links to this very cool story about curiosity and drive: 1, 2, 3.

SO … IMAGINE a truly humongous sheet of paper—as long and wide as you need, and let’s explore what would happen to its thickness as you keep folding it.

The answers below are based on a very simple rule. You start with a single sheet that has the thickness of a regular sheet of xerox paper (0.1 mm for those that want to know), and every time you fold the sheet in half:

you double the thickness of the paper

No big thing right? You’d think that you’d need A LOT of folds to get a thickness equal to these large distances. Here you go—

1. How many folds would you need so the thickness is as tall as a ream of xerox

paper (500 sheets)?

just fold it in half 9 times and thickness is 512 sheets

2. How many folds so the thickness is as tall as you?

just fold it in half 14 times and thickness is 5 feet 5 inches (166.5 cm)

3. How many folds so the thickness is as tall as:

the Statue of Liberty?

Height is 305 feet (93 m)

just fold it in half 20 times and thickness is 350 feet (106 m)

the Empire State Building?

Height is 1,472 feet (448.7 meters)

just fold it in half 22 times and thickness is slightly short at 1,398 feet (426 m)

Mount Everest?

The summit is at 29,029 feet or 5.5 miles (8.8 km) altitude

just fold it in half 27 times and thickness is 8.5 miles (13.6 km)

4. How many folds so the thickness is equal to:

the distance from Earth to the Moon?

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

just fold it in half 42 times and thickness is 277,650 miles (446,840 km)

the distance from Earth to the Sun?

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

just fold it in half 51 times and thickness is 142,159,000 miles (228,780,000 km)

the distance to the nearest star Proxima Centauri?

distance of 4.2 light years

just fold it in half 69 times and thickness is 6.3 light years

the width of our Milky Way Galaxy?

diameter: 100,000 light years

just fold it in half 83 times and thickness is 104,000 light years

the distance to the Andromeda Galaxy—nearest large galaxy to the Milky Way?

distance: 2.5 million light years

just fold it in half 88 times and thickness is 3.3 million light years

the distance from Earth to the edge of the observable universe?

distance: 78 billion light years

just fold it in half 103 times and thickness is 109 billion light years

YOU DON’T BELIEVE ME? I KNEW you were going to say that. So I created two Tables that show you how I got these answers really easily. One Table is in English units (inches, feet, miles), and the other Table is in Metric units (cm, km). Choose your system of units and be amazed!

Teachers:

Here’s a way to really do the challenge in the classroom by removing the pesky folding issue. Remember that the basic rule is each fold doubles the thickness of the paper. So instead of folding, just create a pile of paper using this rule, so you’re ‘simulating’ the effect that folding has on the pile’s thickness.

Remember the cartons of xerox paper we used for the post A Day in the Life of the Earth? Go get them out again!! I hope you know the person in charge of the copy room, or you’ll be banned.

Start by placing a single sheet of xerox paper on the floor. Then ask students in your class, one by one, to simulate each fold by doubling the number of sheets in the pile. Here’s the way it ‘unfolds’ (no pun intended)—

• First student sees 1 sheet on the floor, so places 1 new sheet on top: pile

thickness is now 2 sheets; they’ve simulated the effect of fold 1

• Second student sees 2 sheets in the pile so places 2 new sheets on top:

thickness is now 4 sheets; they’ve simulated the effect of fold 2

• Third student sees 4 sheets in the pile so places 4 new sheets on top:

thickness is now 8 sheets; they’ve simulated the effect of fold 3

Have them keep going and see how far they get. You already have detailed notes on how it will turn out. It’s my write-up in the two Tables, one for English units and the other for Metric units.

Important note: once you get up to 512 sheets, you can start using whole reams of 500 sheets (so again no need to open more than 1 ream of paper.)

Another note about how to start the lesson: pose the original challenge to the class, and have them see how many times they can fold a sheet of paper. After they quickly see the insurmountable hurdle that the folding requirement imposes, see if they can come up with this way to do the experiment by ‘simulating’ each fold.

Photo credit: NASA and STScI

This post is a Dr. Jeff’s Weekly Challenge and a Dr. Jeff’s Jeffism.

Math is the language of nature. If you yearn to know

how she operates, you must speak her language.

Before getting to the awesome challenge this week, I need to get something off my chest. It’s something very relevant to the challenge, but you might not think so at first—

My first language is English. I have very strong beliefs about how English should be taught in schools. I guess I’m a traditionalist. I also think that my views apply to how any language should be taught in schools around the world.

I think English belongs in English class. Period. You want to speak and read and write English, well do it in an English class. It doesn’t belong in a history class, or a science class, or for that matter a class on economics, art, sociology, psychology, or the law. Let’s keep English where it belongs. It’s just a language. So no English in those other classes. Just sit there and learn the concepts, nuances, big ideas, and emotional content of those subjects through …. osmosis. Think your thoughts toward other members of the class and share brain waves. And please, please … when you do this—DO NOT THINK YOUR THOUGHTS IN ENGLISH!

Am I losing my Twitter and Facebook fans? Is this finally the real Dr. Jeff? What? You think what I said is just absurd? (Good.) You think that English, like any language, is the means by which we express and communicate the richness of our thoughts on all the subjects that address the human condition? Wow, that’s a mouthful. You’ve got me thinking. And please—don’t leave! In my defense, I just thought that English should be treated like we traditionally treat MATH in school. Addition, subtraction, long division, algebra, trigonometry, geometry, calculus, statistics … it often feels like the unwritten decree is “let’s only keep it in the math classes where it belongs!” Why isn’t MATH a natural part of all the subjects taught—as in the case of say …. English?! And the result? Kid to parent, or kid to teacher, or kid to friend: “What will I ever need this for?”

Answer: because without an understanding of and appreciation for MATH you’ll deny yourself the ability to see the richness and majesty of the world around you. A language like English serves as the foundation for our conversations about anything and everything—and so does math. And if that’s not a sufficient answer (it’s sad when it isn’t) then more practically speaking, without math skills, effectively competing in the job markets of the 21st century will be very difficult—because math is everywhere.

This blog is a good example. I’m trying to get across powerful concepts with a seamless fusion of English and math, and for many readers I bet the injection of math is jarring. But the math provides the insight into HOW I’m getting the high impact, “Oh Wow” answers. The math gives you the chance to take OWNERSHIP of the story at a deeper level—because I’m not asking you to take the conclusions on faith. We’re reaching the conclusions together. And the math should be embraced at the same subconscious level as is the English you’re now reading. Why? Because math and English have a great deal in common—

Mathematics is a language. It is the language of nature. If you yearn to know how she operates, you must speak her language. And nature isn’t just found in science class. A human being is a biological entity, and human society is a biological system. All of humanity is part of nature, so all those subjects of importance to human beings are richer if their study includes mathematics. And I’m convinced that our capacity for mathematics is an outgrowth of nature developing the means to understand itself.

English or Estonian or Japanese or any other spoken/written language models our very thoughts. That’s the point of creating them. Mathematics as a language provides a powerful means by which we can model the world around us so that we can understand it and navigate it successfully. (See The Power of Models page.) Imagine the power you have when you master a spoken/written language AND math!

Finally, math is the only language I know that transcends societies and cultures. It is the language that binds all humanity. So why do we teach our children to treat math as something that is difficult, disconnected, irrelevant, and something to be avoided?

I’ll have many blog posts that do a shout out to mathematics, and this is the first. For this week’s challenge I thought a math problem that coupled the size of you to the size and scale of everything else might be interesting. And it starts with something strangely familiar—a piece of xerox paper, albeit a humongous one.

Here now the challenge—

A friend gave me this sheet of xerox paper. It’s a bit unusual. It’s the same thickness as standard xerox paper, but it’s really long and wide. When I stand in the middle of it, the edge of the paper seems to extend to the horizon in all directions.

I needed to fold it in half. So I got the grounds crew at the nearby baseball stadium and asked them to pretend the rain just stopped and fold the paper the way they fold the tarp used to cover the ball field.

It took some time but they did it. Now the paper was twice the original thickness. This seemed like fun, so I decided to have them fold it again. After the second fold, the paper was 4 times its original thickness. Try it at home with a piece of paper. Fold it twice, and see how thick it is. Then fold it a few more times and you’ll see that—

every fold doubles the thickness of the paper

So here are the official challenge questions. But before setting out to really answer them, read them and take a wild guess for each.

1. How many folds would you need so the thickness is as tall as a ream of xerox

paper (500 sheets)?

2. How many folds so the thickness is as tall as you?

Hint: a ream of standard xerox paper has a thickness of 2 inches (5 cm.) I just

measured one.

3. How many folds so the thickness is as tall as:

the Statue of Liberty?

the Empire State Building?

Mount Everest?

And now, for those that really like a challenge, I dare you to keep folding and leave Earth. First read my The Nature of Our Existence page to get a sense of what lies beyond, and be sure to click on the photos for the captions.

4. How many folds so the thickness is equal to:

the distance from Earth to the Moon?

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

the distance from Earth to the Sun?

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

for the next questions you’ll need that: 1 light year = 5.9 trillion miles or 9.5 trillion kilometers

the distance to the nearest star Proxima Centauri?

distance of 4.2 light years

the width of our Milky Way Galaxy?

diameter: 100,000 light years

the distance to the Andromeda Galaxy—nearest large galaxy to the Milky Way?

distance: 2.5 million light years

the distance from Earth to the edge of the observable universe?

distance: 78 billion light years

I bet you didn’t think THIS is what I was going to do with my piece of humongous xerox paper. (I promise to keep surprising you.)

Answer now posted here!

Photo credit: NASA and STScI

I started this blog to share exciting stories of exploration with those that teach the next generation—parents and teachers. I hope it can help you inspire our children. More generally, these stories are for anyone who gets joy from learning, and aspires to know.

If you really want to get a sense of where I”m coming from, read my Resource Page The Nature of Our Existence. I hope it moves you. And if it does, share it by leaving a comment on the bottom of the page.

It’s a story—a philosophy—reflecting programs developed and delivered over 19 years at the Smithsonian’s National Air and Space Museum, and across the nation—to families, teachers, and the public.

I’d like to see this blog continue for quite a long time. I’ve got lots to share. But that requires us to build an audience. So please let parents, teachers, and friends know about this blog so we can make a difference together. Send out a tweet or some emails!

You might also like to read other Resource Pages in the section called Dr. Jeff on Stuff (see the column at right.) And subscribe for e-mail notification to stay up-to-date with new Posts.

To all those teachers finishing their year and feeling exhausted, you could probably use a reaffirmation right now about why you went into teaching! I think reading The Nature of Our Existence might help. It’s a good way to start your summer!

—Dr. Jeff