Photo caption: The Eyjafjallajökull Volcano erupting in Iceland as seen from NASA’s Earth Observing-1 satellite on May 2, 2010. How dare it interrupt the lives of all those folks on business travel.

This is a Dr. Jeff’s Jeffisms post.

This is crossposted at the Huffington Post HERE.

OK, so I’m a regular on Twitter, and proud of it. I guess that makes me a Tweep, and if you aren’t, I’ve got something to tell you. There are lots of folks that think Twitter is where you go when you’ve got this intense need to broadcast to the world what you had for lunch. Mostly these are folks that stay away from Twitter ’cause they either don’t understand it or its power as a social medium. But there are also a whole bunch of Tweeps out there that do think I’m interested in their lunch today—let’s call them lunchies.

So to Twitter avoiders, and to the lunchies, I’d like to add my two cents. Twitter is a water cooler for the 21st century. At this cooler you can meet fellow human beings from across the planet, and share thoughts about life, our world, and our children—common thoughts that bind us all, regardless of nationality. In an age when as never before humanity faces a perfect storm of global problems, it’s precisely this kind of water cooler you’d like to see, and to frequent.

Twitter allows countless users (yes, the Tweeps) to send their messages (Tweets) into the cyber aether, forming an immense Public Stream. It is a place where all messages are equal, and each is nothing more than a human thought compressed into 140 characters. From the shores of the great Public Stream, you can see the messages flow by. There goes one from a teacher who’s had a tough day. I think I’ll reach out to her with a link, and tell her why her job is so important. There goes a link to an article on nuclear proliferation from a Pakistani perspective. Gee, I wonder what their thinking might be. There’s a thought from the President of the United States. Hey Mr. President, did you see the open letter I wrote to you on the crisis in science education? And that person over there is proposing a regular time on Twitter to have a global conversation about climate change (oh that’s me!) And yes, there goes a message from a guy who says he had a tuna sandwich for lunch.

But to be part of a social community, you can’t just watch the messages flow by. (You could, but that passive trolling for information is the old, dark ages internet experience.) You need to wade into the stream, and find folks with whom you’d like to strike up a conversation, and Tweet your own thoughts into the Public Stream. So Twitter makes it so. You can decide to ‘Follow’ any of the Tweeps in the Twitterverse, and Mr. Twitter will pull all the Tweets of those that you Follow from the Public Stream, and feed them to you as your own continuous thread of human consciousness. You can also create lists of favorites, so the consciousness can be distilled as you see fit. And the sum total of all of those Tweeps you Follow make up your Personal Learning Network (PLN). Conversely, folks might think YOUR thoughts—your Tweets—are deep and insightful, maybe ’cause you are a fellow lunchie, and so they decide to Follow you—these are your ‘Followers’.

The most remarkable experience I have on Twitter, and it’s right up there with the very best learning experiences I’ve EVER had over my lifetime as an educator, an astrophysicist, and a learner, is #edchat. Every Tuesday night at 7:00 pm Eastern Time, I join HUNDREDS of educators from across the planet that get comfortable in front of their computers—a very local and personal experience—and have a global, free-for-all conversation about education. The operation of Twitter as the vehicle for communication quickly recedes into the background, and you enter into a world of rapid-paced vibrant conversations with folks as committed as you to sharing important ideas. You leave with new thoughts, new directions, a reinvigorated sense that the issues of importance to you are also important to others—providing a common bond, and you embrace friends you’ve never met but that you deeply understand.

I am so impressed with #edchat to address diverse topics like education reform, recipes for success and failure in the classroom, implementation of new educational technologies, and assessment, that we (the National Center for Earth and Space Science Education) have decided to launch in early Summer 2010 our own weekly scheduled Twitter chat on Science Education, and maybe a second more specific one dedicated to Climate Change Education. Help me gauge interest! If you think you might want to participate, let me know by leaving a comment below.

Recently I looked back at my archive of Tweets that I’ve sent over the months, and some (at least to me) seem funny, compelling …. why, even thought-provoking. (Feel free to disagree!) Who says you can’t frame really big ideas in 140 characters. But that’s also pretty much the whole idea of my Dr. Jeff’s ‘Jeffisms’ flavor of blog post here at BotU. So I decided that each month I’ll choose some of my Tweets, and bundle them in a post as ‘Tweetisms for the 21st Century”. This is the first such post, and below are a number of recent Tweets selected from conversations I’ve had with friends across my PLN, and as part of that truly remarkable weekly experience #edchat.

And hey, if you don’t do Twitter, maybe you ought to give it a try … and if you are already a Tweep, well cool! But regardless, I’m right here, right now, formally inviting you to Follow me on Twitter at http://twitter.com/doctorjeff (assuming you are not a lunchie), and I’ll Follow you back!

-dj

Some Tweetisms

On the Environment:

BREAKING NEWS: Humans angry that ash from volcano interrupts their lives. Planet apologizes 4 terrible inconvenience.

Fred & Barney? Lived long ago, so must b dumb. They drove rock cars that weighed a ton … we’re smarter now.

DENIAL DAILY NEWS: Earth wanders off axis, heads 4 Sun. #Climate change deniers blame raging inferno on conspiracy by science community.

On Our Existence:

Question: Was Mr. Magoo just lucky? Or did the world conspire to move under his feet in a way that made life joyful … at least for him?

Sometimes the issues that are in plain sight are the hardest to see.

On Education:

If we treat our learners as so many pegs to push thru holes, where is the humanity in that? Where is the joy in learning?

It takes a community to educate a child & a network of communities to reach a generation. http://ncesse.org/about/core-beliefs/

We are teaching to the test because it is the educational path of least resistance for results … & a disgrace to education.

KEY IRONY – you can teach the wrong things really well, get rewarded for teaching it well, and our kids and nation will all suffer.

… because 6 MILLION teachers in the US 1 out of 50 Americans have no coherent voice. Use Social Media for a movement: http://bit.ly/bc7VG8

On Science:

ASTROLOGY DEPT NEWS: “Hey Ralph, what are the #zodiacfacts today?”  “Who cares, let’s use the dart board like we always do.”

Why do I get the feeling there’s an Anti-Science Movement? Hey followers – no more medicine, vaccines, cell phones, TV, computers. 

Does anyone know where Blindfaithyland is? Can’t seem to find it on Google Maps. But it must exist….lots of folks swear by it. 

The Doctorjeff Funnies:

New adage: If we were meant to fly, we’d have …… a brain that could engineer a flying machine.

Help!! A Koala is holding me prisoner and won’t let me go until I get a tweet from an Australian. Anybody down under that can help?

[2 folks from Australia quickly answered my plea and I got out of the clutches of the Koala.]

Photocredit: NASA

This post is a Teachable Moment in the News and a Dr. Jeff’s Jeffism.

It’s been a wonderful year for me here at Blog on the Universe. We launched in May 2009, not knowing if the concept would catch on. It did, and in just 7 months I’ve had the good fortune of reaching and conversing with tens of thousands of educators, science and space enthusiasts, science writers, environmentalists, homeschool moms and dads, ed techs, and scifi fans. The Blog now has a pretty eclectic following … which is very cool.

To all of you that follow the ol’ blog, may you and your families have a healthy, joyous, and prosperous 2010! And my advice is live in the moment.

Now for something completely different (Monty Python?) While I was tweeting to my PLN earlier today I came up with some New Years fun facts and Jeffisms of sorts. Thought I’d collect them all and share them here with you. Teachers and parents, you might want to discuss these with your kids!

Ponder this: From the moment the New Year began to the end of the first day in 2010, YOU on Earth have traveled a whopping 1.6 MILLION miles (2.6 MILLION km) along Earth’s orbit around the Sun.

That’s the same as traveling 200 Earth diameters. Another way to think about it—today you traveled the diameter of Earth every 7 minutes … and you didn’t even feel a breeze.

I actually wrote a blog post about your travels through space aboard Spaceship Earth. If you liked my New Years thought above, you’ll really like this post.

Ponder this too: You may have been standing there watching the clock as it counted down to midnight. But actually … YOU were flying to the location of midnight on Earth at up to 1,000 mph (1,600 km/hr) due to Earth’s rotation. The clock was just keeping track of your flight. Did you remember to buckle up?

Fun fact: It’s 2010. Thank goodness we made it through another 31,557,600 seconds since New Years 2009. (Hummm that’s almost pi x 10⁷ —that’s creepy.)

More pondering: the location in Earth’s orbit where you marked the start of YOUR 2010 orbit of the Sun is different from someone in another time zone.  In other words, someone on the opposite side of Earth from you started their New Year 800,000 miles (1,300,000 km) from where you started yours.

Earth to other planets: hey guys, I must be at that strange, rather non-descript place in my orbit again, ’cause the bipeds are all celebrating.

Other planets to Earth: we know, we saw fireworks sweeping across your surface as their cities and towns moved into midnight. Weird critters you’ve got living on you.

Pluto to Earth: hey if you were more like me, those bipeds would only celebrate every 240 Earth years!

Earth to Pluto: yeah but if I were more like you, there wouldn’t be any bipeds here, and hey, why am I talking to you anyway? You’re not a planet any more.

Pluto to Earth: even I think that’s pretty cold.

Hey gang, ready for another orbit of the Sun here at Blog on the Universe? May it be a safe journey, and I promise I’ll try to be a good guide.

—Doctor Jeff

Photocredit: NASA, ESA and J. Hester (ASU)

Dr. Jeff on Mathematics Education

This is a Dr. Jeff’s Jeffism and a Dr. Jeff Speaks Out.

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

how she operates, you must speak her language.

—Dr. Jeff

I wrote this essay because I needed to get something off my chest. It first appeared as a foreword to a Dr. Jeff’s Weekly Challenge posted on June 15, 2009, but I think it’s so important that I decided to commit it to a formal Resource Page here at Blog on the Universe. My Resource Pages are all found in the right navigation column under the section titled “Pages” and under the subsection titled “Dr. Jeff on Stuff – The BotU Resource Pages” (take a look at right.) I dedicate the Resource Pages to essays on important topics like: the Nature of Our Existence, the Art of Teaching, Scientists and Engineers as Heros and Role Models, and the Crisis in Science and Technology Education. I felt that an important essay on mathematics and mathematics education should be a dedicated Resource Page.

So here now is my sure to be viewed as an outrageous essay:

Dr. Jeff on Mathematics Education

Let me know what you think by leaving a comment on that page. Also—you can read more about this Blog’s Resource Pages HERE.

This post is a Dr. Jeff’s Jeffism.

First a word from our Sponsor—

Come back Thursday August 13, for my take on the White House blue-ribbon panel looking at the future of NASA’s human space flight program.

Come back Monday, August 17, Rod Serling will be posting here on BotU: “Weekly Challenge 6: Today’s Special in the Cosmic Kitchen is …”

There’s no sight like the sky on a cloudless night far from city lights. The heavens filled with seemingly countless stars is overwhelming. At those moments, I cannot help but wonder if on a planet orbiting that star over there might be someone also looking heavenward, and in their sky is our Sun as one star among many. It touches the depths of one’s soul to look up into the night sky and wonder who might be staring back.

All those stars you see are stars of the Milky Way galaxy, our city of stars. But the Milky Way contains far more than those dotting your sky. Many are too dim to be seen with the unaided eye. Yet a vast number of stars can be easily seen—you just need to recognize them. You see that double band of white light that arches from horizon to horizon above you? Those are Milky Way stars so numerous that they combine into a continuum of light stretching across the heavens. It’s as if milk was sprayed in a broad arch across the sky—which is the heart of the Greek creation story for the Milky Way. Why do I single out the Greeks? There’s is just one of many elegant creation stories embraced by human cultures over history and passed down from generation to generation. It’s because the english word ‘galaxy’ derives from the Greek ‘galaktos’ which means ‘milk’.

Take a look at the impressive photograph above. Those dots are all stars—stars of the Milky Way. (I hope you just said “WOW.”) It was taken by the Hubble Space Telescope in 1998. It’s the Sagittarius Star Cloud in the direction of our galaxy’s center. Yet the photo is of a tiny patch of sky. If you want to know how tiny, give a dime to a friend, have them walk 75 feet (23 meters) away from you and lift the dime over their head. Then see how much of the sky the dime covers up from where you’re standing. That’s the amount of sky in the photograph. Go ahead and try it with friends, with your child, or with your class.

You’ll notice I’ve drawn a white rectangle on the photo. The photo is big enough to contain about 175 of these rectangles. That’s the number of students in about 7 classrooms (if there are 25 students per class.)

The rectangle is special. It contains about 50 visible stars. How do I know? I zoomed in on the photograph, drew the rectangle, and adjusted its size so it contained 50 stars as best I could count them.

So in the photograph there are enough visible stars to give 50 to every one of the 175 students in the seven classes. That’s a lot of stars—about 8,750.

Now here’s the BIG question. How many stars are in the Milky Way Galaxy? And here’s the answer as a Dr. Jeff’s Jeffism:

There are likely enough stars in the Milky Way to give 50

to every human being on Earth.

Just think about that for a moment, and let it soak in.  Now think about this—I’ve only handed out the stars of a single galaxy.

How did I calculate my Jeffism you ask?

I needed two pieces of information—the human population of Earth, and the number of stars in the Milky Way. I can get the first by going to the always handy World Population Clock that we’ve used here and here on BotU before. From the clock I see Earth now supports 6.78 BILLION humans!

There are a number of references for the number of stars in the Milky Way, for example: 1, 2, 3.  The number ranges from 200-400 BILLION!

So if there are 50 stars for every person on Earth, I’d have 50 x 6.78 billion stars total, or 339 BILLION stars—well within the predicted range for the number of Milky Way stars. Pretty cool huh.

Teachers and parents:

Have fun with your child or students by calculating how many Milky Way stars there are for everyone in their: school, city or town. state (if in the US), and nation. Assume there are 335 billion stars in the Milky Way.

Have you child or students research how many galaxies are estimated to be in the observable universe, and see if they can come up with a way to easily picture the total number of STARS in the observable universe. I have. It will be the subject of a future blog post. Promise.

Photo credit: NASA., ESA. and the Hubble Heritage Team (STScI/AURA). Note: the photo was taken using Hubble’s Wide Field Planetary Camera (WFPC) 2, with a field-of-view of 2.7 arc-minutes or 0.045 degrees.

This post is a Dr. Jeff’s Jeffism.

Last week on BotU, I used boat-loads of wrapping paper to gift wrap the Moon. I can’t believe that I actually bought TOO MUCH of the stuff! What to do with the leftovers, what to do. Hey, I know! I’ll wrap the largest asteroid Ceres! (Oops … can I say that? Are the IAU police listening?)

What? You don’t know what I’m talking about? Don’t you remember the whole ‘Is Pluto a Planet’ thing in 2006? Well it spilled over to poor old Ceres. In its infinite wisdom, the International Astronomical Union—the IAU—renamed Ceres a “Dwarf Planet” ’cause what they did to Pluto had a ripple effect across the Solar System. BUT they forgot to let the rest of us know if we should still call Ceres an asteroid. Or maybe they just don’t write very well (see below.)

So you know what? I’m going to call it a dwarf planet AND the largest asteroid. “Now, now kids, don’t fight …Shimmer … it’s a floor wax AND a dessert topping (SNL.)”

Now for the cool part—

If I gift wrapped Ceres the largest asteroid, I’d need a piece of wrapping

paper 4 TIMES THE AREA OF TEXAS!

Certainly Texans can appreciate that. Another way to say it (and here’s the Jeffism)—

If I wanted to explore the entire surface of the largest asteroid Ceres,

it would be like exploring an area 4 times the size of Texas.

That’s a BIG rock.

To teachers:

1. Have your class check my calculation. See if the surface area of Ceres is approximately 4 times the size of Texas.

Hint: the surface area of a sphere = 4 x pi x r² where r is the radius of the sphere

2. Discuss with the class why precise definitions in science (or any subject) are important. You can use my “Frustrations with the IAU” section below to explore the specific problem with the definition for Ceres.

Dr. Jeff’s frustration with the IAU:

Here it is, the ‘official’ FAQ taken directly from the International Astronomical Union web site. As you all know, FAQ stands for FREQUENTLY asked question. So the IAU felt it very important to clarify their position on the FREQUENTLY asked question “What is Ceres?” And now, the IAU rersponse—

Q: What is Ceres?
A: Ceres is (or now we can say it was) the largest asteroid, about 1000 km across, orbiting in the asteroid belt between Mars and Jupiter. Ceres now qualifies as a dwarf planet because it is now known to be large enough (massive enough) to have self-gravity pulling itself into a nearly round shape. [Published reference for shape of Ceres: P. Thomas et al. (2005), Nature 437, 224-227. Dr. Peter Thomas is at Cornell University.] Ceres orbits within the asteroid belt and is an example of a case of an object that does not orbit in a clear path. There are many other asteroids that can cross the orbital path of Ceres.

Dr. Jeff pondering: Hmmm, now that’s what I call a really crisp answer. I’m no longer puzzled. “Ceres is (or now we can say it was) the largest asteroid …” certainly seems very consistent with “There are many OTHER asteroids …” Hey IAU, do you guys really read what you write? Here, I’ll help you with a rewrite, and just say you’re going with Answer 1 or Answer 2, so we can all know how to have a conversation about Ceres:

Q: What is Ceres?

Answer 1: Ceres has been reclassified as a dwarf planet because … [fill in dwarf planet definition here.] Note it is no longer considered an asteroid.

or

Answer 2: Ceres has been reclassified as a dwarf planet because … [fill in dwarf planet definition here.]  It is, however, still considered an asteroid. Other objects in the Solar System have dual, even triple status (because we the IAU say so). Pluto is now a dwarf planet AND a Trans-Neptunian Object AND a Plutoid.

(Would you put trust in definitions concerning your Solar System from an organization that cannot write simple FAQs? I don’t.)

IAU—Intentionally Against Understanding.

Photo credit: NASA, ESA, and J. Parker (Southwest Research Institute)

This post is a Teachable Moment in the News and a Dr. Jeff’s Jeffism.

Have you ever just stopped on a cloudless night and stared at the Moon? And I’m not talking about a 2 second passing glance, and a smile. A jewel in the night, it is a sight many of us learn to ignore. Yet it is ANOTHER WORLD, and we can see it clearly from our backyards. That to me seems like a gift.

Now for my gift to you. If you’ve never done it, or you haven’t recently, PLEASE just take out a simple pair of binoculars (forget the telescope) and look at the Moon. Do it with your children. Teach them an appreciation for what’s in their sky. It is a stunning site.

When you do, let them know there’s a brand new spacecraft orbiting the Moon. The Lunar Reconnaissance Orbiter (LRO), built at NASA’s Goddard Space Flight Center here in Greenbelt Maryland, went into lunar orbit on June 23. Today the first pictures of the Moon by LRO were released.

It looks so close, yet you would need 30 Earths side-by-side to span the distance from Earth to the Moon. Thus far, 27 humans have made the trip—12 humans have walked on the lunar surface.

Here’s a thought—maybe if I treated the Moon as a gift, and gave it the respect it deserves, it wouldn’t be taken for granted quite so much. So let me gift wrap it before presenting it to you anew. First, I’d need a piece of wrapping paper the size of—Africa. You don’t believe me? Look at the picture.

Here’s another way to say it—

If you wanted to explore the entire surface of the Moon it would

be equivalent to exploring the entire continent of Africa.

Now doesn’t that make you think of the Moon a little differently? Maybe like it really is another world? Maybe even a little in awe of that jewel in your sky?

Now do me a favor and find those binoculars, take out some lawn chairs, get a friend, your wife, your husband, the kids, and take a look tonight. I’ll even help. Here is a web site at the US Naval Observatory that will allow you to get times for Moonrise and Moonset in your area.

To Teachers:

1. Can you really wrap the Moon with Africa? The Moon is slightly more than 1/4 the diameter of Earth (0.27 x Earth’s diameter). Get a classroom globe of Earth, have your students measure its diameter, and then have them find a ball about 1/4 the diameter to represent the Moon. Have them trace the continent of Africa on the globe onto a piece of paper. Then have them cut out Africa on their paper and see if it can just wrap the ball representing the Moon.

Note: have them propose how to accurately measure the diameter of the Earth globe.

Hint: to measure the diameter (D) of the globe, they might measure the circumference (C) and divide by pi, since C = D x pi

2. Build a physical model of the Earth-Moon System: Next, have the students place the ball representing the Moon 30 Earth diameters away from the globe of Earth. They have just created a physical model of the Earth-Moon system. See if they are shocked at the distance between Earth and Moon (they will be.)

3. Interdisciplinary connections to human exploration: With your Earth-Moon model set up, remind your class that humans ventured from Earth … and WALKED on the surface of the Moon. You can have them read about it in three of my Blog posts: 1, 2, 3. To place the achievements of the Apollo missions in the broader interdisciplinary context of human exploration, have them read and discuss The Nature of Our Existence.

4. Check Dr. Jeff’s math: Have your class check my calculation to see if the surface area of the Moon is approximately equal to the area of Africa.

Hint: the surface area of a sphere = 4 x pi x r² where r is the radius of the sphere

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

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 ‘Jeffism’ by Dr. Jeff and a Dr. Jeff Speaks Out.

Last time on the blog, I used astronaut John Grunsfeld’s recent Business Trip to the Hubble Space Telescope to show you that the perceived limitless ocean of air we live under is really not limitless. At an altitude of 62 miles (100 km) above Earth’s surface, you’re effectively at the top of the atmosphere (since 99.99% of it is beneath you.) So let’s really put this in perspective with a Dr. Jeff Jeffism:

Earth’s atmosphere compared to Earth is thinner than

the skin of an apple compared to an apple.

I truly hope that makes an impression on you. Read it again and let it sink in. Then take a moment and reflect on what you are thinking.

Now … for the rest of the story—

Our atmosphere is nothing more than a slender veil surrounding our planet. It supports all life on spaceship Earth. It is fragile. It is clearly changing at a frightening pace. Next time you’re in a discussion about global warming, pull this Jeffism out of your pocket—regardless of which side of the debate you might be on (is it induced by human activity or not). It speaks to what we ALL have to lose—’we’ the human race; and ‘we’ the other countless species of Earth.

My view? We humans are the agents of global change, and all of humanity needs to consider the consequences head-on and collectively define a response RIGHT NOW. And all those countless other species—their future is in our hands. Look to the birds in flight. Look to the diversity of life on the savannas of Africa, in the rain forests of Central and South America, and in the worlds’ oceans. They are voiceless in this debate, and powerless to intervene.

Look deeply into your children’s eyes and ask what is our responsibility to them, to their children—and to Earth. I have—and when Jordi and Jada look back at me, I get a sense of purpose and a deep resolve—to educate. This blog is one result.

For a powerful educational essay on global warming as an outgrowth of human activity, read A Day in the Life of the Earth here at Blog on the Universe, or at the Huffington Post.  It includes a foreword by Dr. James Hansen, Director of NASA’s Goddard Institute for Space Studies in New York.

Teachers and parents:

Before reading the Jeffism above to your class or children, use a familiar model to identify preconceptions and misconceptions about the atmosphere. Get a classroom globe of the Earth and ask them how high above the Earth globe they think the atmosphere extends. You’ll be amazed (or maybe not) at the depth of the misconceptions. Then read them the Jeffism, and see if they are shocked. Ask them to reflect on the difference between their perception of the atmosphere and reality.

Here’s more to consider:

• Have a thoughtful and interdisciplinary discussion as a class or as a family considering the larger and inter-connected issues we face on global warming in terms of: science, technology, politics, economics, funding, the need for global partnerships, ethics, and morality. Science should not be taught in isolation from all other manner of human considerations. The world is interdisciplinary, so why would we want to teach about the world only subject by subject?

• Visit my Favorite Quotes page and read the quotes by astronaut Ulf Merbold and cosmonaut Yuri Artyukhin. How are their words relevant to the discussion?

• The Jeffism above is so effective because it builds a bridge to the familiar using a model—in this case using an apple as a conceptual model to understand Earth. Read my Power of Models page to gain deeper insight into how to use modeling in learning environments, and to realize that YOU surround yourself with countless models every day to make the world understandable.

The Experiment

Don’t let your students and children just assume my Jeffism is correct. Help them to insist on testing it. That’s what science is all about. Scientists (your kids) should put ideas to the torture test—and own the process. So assume my Jeffism is a hypothesis, and have them test it for themselves. And let them frame the experiment with guidance from you.

Here’s the concept: the atmosphere is 62 miles (100 km) thick and the Earth’s diameter is 7,900 miles (12,700 km). So how does Earth’s diameter compare to the thickness of the atmosphere? That’s just the ratio: 12,700 / 100 = 127. So the diameter of Earth is 127 times the thickness of the atmosphere!

What about the apple? The skin of the apple is what I’m going to define as the peeling you get when you peel an apple with a good potato peeler (one that does not dig deeply into the apple). Here’s the creative thinking part of the experiment—your students/children need to propose how to measure the thickness of an apple skin. One of a bunch of approaches is to use a peeler and carefully peel a really long strip from an apple. Then tear off reasonably sized pieces and stack them in layers until you have a thickness you can measure with a ruler with millimeter divisions. Measure the thickness of the stack, then count the layers, and divide the thickness of the stack by the number of layers to get the thickness of a single layer. That’s the thickness of the apple skin!

Finally, measure the diameter of the apple and calculate the ratio of apple diameter to skin thickness. This ratio is what you compare to the 127 we got for the ratio of Earth’s diameter to the thickness of the atmosphere.

I just did it with a trusty golden delicious apple. My stack of 10 layers had a measured thickness of 11 mm, corresponding to 1.1 mm for a single layer–which is the thickness of the apple skin. The apple has a diameter of 80 mm. So the diameter of the apple is only 80 / 1.1 = 72 times the thickness of the skin! Comparing that to Earth’s diameter being 127 times the thickness of the atmoshere means—the Jeffism (at least with my apple) is confirmed!

A final thought—you can ask your students or children to go back to the classroom globe of Earth and calculate the thickness of the atmosphere on the globe. It’s just the diameter of the globe divided by 127.

Science—it’s fun, it’s a team effort, it’s eye-opening.

-Dr. Jeff

A word from our sponsor:

• I have the title for next Monday’s Weekly Challenge that is sure to intrigue: A Pound of Ants and the Capabilities of Intelligent Biomass (how do I come up with this stuff). It is a powerful post on how we humans are affecting Earth’s environment.

• Hey, it’s a brand new blog. If you like what you read, leave a comment on the bottom of any of the Posts or Resource Pages. It will help get more teachers and parents aboard!

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