Posted by DrJeff on June 15th, 2009
Filed under 1.1. Dr. Jeff's Weekly Challenge, 1.5. Dr. Jeff's Jeffisms, 3. Science Education, 4. The Earth, 5. Space Science, 5.1. Our Solar System, 5.1.1. The Sun, 5.1.2. The Moon, 5.4. Milky Way Galaxy, 5.5. Other Galaxies, 5.6. The Universe
Copyright 2009 | About this blog
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
3. How many folds so the thickness is as tall as:
the Statue of Liberty?
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
4 Responses to “Weekly Challenge 3: What Can You Do With a Humongous Piece of Xerox Paper?”
Michele Arduengo Says:
June 20th, 2009 at 3:13 pm
Thanks for pointing me to this article. I was fortunate enough to teach at a liberal arts college that had both a writing-across-the-curriculum AND a math-across-the-curriculum program. I think one reason that our society is so math-phobic is because we don’t try to integrate math into other subjects beyond the sciences. In the cases where I have seen math come together with history or marketing or visual arts and music, the students have really gained a better understanding of both subjects.
Maria Miller Says:
June 21st, 2009 at 1:40 pm
Answer to 2: For the paper stack to be as tall as me, I’d need 14 foldings. The paper length needed to accomplish this is an enormous 14.06 km!
Please see http://www.pomonahistorical.org/12times.htm
So it isn’t feasible to do! The other challenges even less so. You’d need paper so long you couldn’t handle it.
Chip W Says:
August 19th, 2009 at 11:38 pm
I just read your Challenge #3 about the really big piece of xerox paper. Here’s another answer to the question “What will I ever need this (math) for?”
Math is really good brain exercise. It also teaches a way of thinking that’s good to be good at. Rational thinking is probably innate, but math helps us develop it.
Margaret M-S Says:
September 10th, 2009 at 8:50 am
Well said about the language of mathematics! As a mathematics and biology major and now a STEM educator, I have always held a strong belief that mathematics is foundational to everything, not just in the STEM areas. I knew when I taught that I could not MAKE every student like mathematics, but I knew when they left the classroom they at least appreciated mathematics. As a teacher educator now, this is what I try to instill in my preservice secondary teachers. Our state is moving towards a quantitative literacy in addition to literacy across the content areas. Their idea of quantitative literacy is to have mathematics across the content areas. Stay tuned!