Carl Sagan explains how science works: Eratosthenes and the size of the planet

January 23, 2013

It’s not exactly a hoax.  It started out as just bad reporting of history.

In his search for an easier route from Spain to China, in which he stumbled into the Americas, Christopher Columbus knew with  certainty the Earth is a round ball.  The story that he proved the Earth round, or rather than he laid the foundations for Magellan to prove the Earth round, is only a story, mostly devoid of fact.  Sailors knew something was up just from their having watched things while sailing on the ocean.  One can deduce the ball shape of the planet by watching other ships as they sail away, and sink below the horizon.  Were sailors of a more scientific bent, they could have made much of the fact that the guy in the crow’s nest could see a ship moving away — or an island or a continent — for a time longer than those a few dozen feet below, on the deck of the ship.

Long before that a Greek librarian and polymath, Eratosthenes, figured out that the surface of the Earth is curved, deduced that the planet is basically a ball, and calculated very closely how big the ball is, merely by noting the different shadows cast by the sun at the Spring/Vernal Equinox.  Carl Sagan used this story way back in his famous PBS series, Cosmos.  It’s still interesting, informative and instructive today (surely Texas 9th grade geography teachers use this example all the time, no?  9th grade math teachers?  Say, what?).

You can find this and more Sagan videos at the Carl Sagan Portal on YouTube.

How did he do it?  Wikipedia — as usual — has a good, relatively lay explanation:

Visual representation of Eratosthenes's calculations of the size of the spherical Earth.

Bathtub Art Figure 1:  Eratosthenes’ measurement of the Earth’s circumference.

Eratosthenes calculated the circumference of the Earth without leaving Egypt. Eratosthenes knew that, on the summer solstice, at local noon in the Ancient Egyptian city of Swenet (known in Greek as Syene, and in the modern day as Aswan) on the Tropic of Cancer, the sun would appear at the zenith, directly overhead (he had been told that the shadow of someone looking down a deep well would block the reflection of the Sun at noon). Using a gnomon, he measured the sun’s angle of elevation at noon on the solstice in his hometown of Alexandria, and found it to be 1/50th of a circle (7°12′) south of the zenith. Assuming that the Earth was spherical (360°), and that Alexandria was due north of Syene, he concluded that the meridian arc distance from Alexandria to Syene must therefore be 1/50 = 7°12’/360°, and was therefore 1/50 of the total circumference of the Earth. His knowledge of the size of Egypt after many generations of surveying trips for the Pharaonic bookkeepers gave a distance between the cities of 5,000 stadia (about 500 geographical miles or 927.7 km). This distance was corroborated by inquiring about the time that it takes to travel from Syene to Alexandria by camel. He rounded the result to a final value of 700 stadia per degree, which implies a circumference of 252,000 stadia. The exact size of the stadion he used is frequently argued. The common Attic stadion was about 185 m,[9] which would imply a circumference of 46,620 km, which is off the actual circumference by 16.3%; too large an error to be considered as ‘accurate’. However, if we assume that Eratosthenes used the “Egyptian stadion”[10] of about 157.5 m, his measurement turns out to be 39,690 km, an error of less than 2%.[11]

Description of Bathtub Art Figure 1:

Syene (S) is located on the Tropic of Cancer, so that at summer solstice the sun appears at the zenith, directly overhead. In Alexandria (A) the sun is \varphi south of the zenith at the same time. So the circumference of earth can be calculated being \frac{360^\circ}{\varphi} times the distance \delta between A and S.

Erastothenes measured the angle \varphi to be 1/50 of a circle and his access to knowledge of the size of Egypt gave a north/south distance \delta between Alexandria and Syene of 5000 stadia. His circumference of the Earth was therefore 250 000 stadia. Certain accepted values of the length of the stadia in use at the time give an error of less than 6% for the true value for the polar circumference.

Tropic of Cancer sign in Western Sahara

Tropic of Cancer sign in Western Sahara, placed by trans-Sahara racers, in English and Hungarian Photo: Wikipedia

A fun little exercise, but a remarkable achievement for anyone about 240 years before the birth of of the Biblical Jesus.  Syene, now known as Aswan, is on what we now call the Tropic of Cancer (the “tropics” were named by the Greeks, but I am uncertain whether the line had that name in Eratosthenes’s time).  The date is probably not important, so much as the observation that the sun was vertical at noon on a given date — and then Eratosthenes’s experiment to see whether that were true in Alexandria, and then his understanding of what that might mean and his work to assemble the data to make the calculations.   High school students — heck, junior high school students — should be able to figure all that out today, if they had the basics down.  I suspect that knowing this story would be a spur to students to learn the elements of the mystery and how it was solved, and what it might mean for later navigators of the oceans, land and air, for astronomers, for farmers and for mathematics.

I also like this story because it presents a strange conundrum, a paradox about what people know, and what they may reason from the foundation of what they know.  Our friend and frequent commenter Morgan, whose blog he calls the House of Eratosthenes.  I suspect he thinks himself some latter-day Eratosthenian (“Latter-day Erats?”).  He says as much in his blog FAQ:

I’m just like Eratosthenes peeking into a well here, and I don’t know what it means yet.

It’s an entertaining read and more enlightening that one might think from his forays here, so you probably ought to go read the FAQ and the reasons Morgan misbelieves liberals miss out on Eratosthenes’s wisdom.  Morgan has an explanation of Eratosthenes and his discoveries which I find too brief to be accurate (and I’m not sure why Morgan finds the name “Beta” to be dubious; being a polymath was not a small thing then, or now; second best in everything means one is first in the All-Around, first in the academic centathlon or millathlon — no mean set of feats at all).  I find that funny because, while he makes a pretense and some effort to following Eratosthenes and scientific methods, to me he seems to find science and logic things to run away from, as in our recent discussion where he ends up defending Anthony Watts’s erroneous views because Watts’s critics didn’t link to Watts (see comments in “It’s raining crazy,” and see also Morgan’s own post, which defies explanation).  Eratosthenes would find that funny, too, I hope, but not a demonstration of Eratosthenian logic and calculation.

Does anyone doubt where Carl Sagan would be in the debate between the dozen serious scientists and hundreds of political wankers who deny climate change, and the thousands of scientists and good citizens who recognize that it occurs and think we should get on with saving the future?

(Did James Burke cover Eratosthenes in his brilliant series Connections?  Which episode?)

Tip of the old scrub brush to Fred Clark at Slacktivist, whose compilation posts often overflow with stuff you ought to know or see, and whose post today sent me to Joe at It’s Okay to Be Smart and “Top 10 Reasons We Know The Earth Is Round.”

More:


Carl Sagan Day, November 9, 2012

November 9, 2012

Electioneering cut into my planning — didn’t get anything done for Carl Sagan Day, today, November 9.  Here’s the post from last year, with a few links to sources including new sources at the bottom.  “Our species needs, and deserves, a citizenry with minds wide awake and a basic understanding of how the world works,” Sagan said.  Boy, howdy, now more than ever.

Have a happy Carl Sagan Day!

_________________________________________________________________________

Press release from the Center for Inquiry:

Carl Sagan Day: November 9 — Celebrate with us!
Event Ideas & Sagan Day Commemorative Posters

Carl Sagan Day Poster 2011Carl Sagan was a Professor of Astronomy and Space Science and Director of the Laboratory for Planetary Studies at Cornell University, but most of us know him as a Pulitzer Prize winning author and the creator of COSMOS. That Emmy and Peabody award-winning PBS television series transformed educational television and continues to affect the hearts and minds of over a billion people in over sixty countries.

No other scientist has been able to reach and engage so many nonscientists in such a meaningful way, and that is why we honor Dr. Sagan, remember his work, and revel in the cosmos he helped us understand.

Two years ago, CFI–Fort Lauderdale and other groups hostd the first Carl Sagan Day event in Florida.  It was a fantastic success and now individuals and groups around the world are planning their own tributes with science fairs, planetarium shows, teacher workshops, star parties, COSMOS marathons, and more—all to say “Thanks!” to Sagan and to bring his gifts to another generation of “starstuff.”

How can you celebrate Carl Sagan Day?

Whether you’re an independent skeptics group, an astronomy club, a science department, a researcher, a teacher, a student, or just a really big Sagan fan, there are plenty of ways to celebrate Sagan Day:

  • Host a COSMOS marathon—all 13 episodes are available for free at hulu.com.
  • Check out Sagan’s many books at your local library or bookstore using the thorough listings from WorldCat.org.
  • Enjoy the special collection of articles by or about Sagan, previously published in Skeptical Inquirer magazine.
  • Listen to Sagan’s last public address for the Committee for Skeptical Inquiry (formerly CSICOP) as replayed on CFI’s podcast, Point of Inquiry: “Wonder and Skepticism.”
  • Listen to Ann Druyan, writer, producer, and widow of Sagan, discuss life with Carl, his outlook on life, and his famous Gifford Lectures, “The Varieties of Scientific Experience,” also on Point of Inquiry.
  • Host your own apple pie baking contest (from scratch, of course).
  • Dress like Carl for a day!
  • Refresh your skeptic skills with a review of Sagan’s Baloney Detection Kit.
  • Invite your friends over and try to convince them you have a dragon in your garage.
  • Take in a star show at your local planetarium.
  • At the very least, seek out a dark sky, look UP, and reconnect with the grandeur of the cosmos.

Let us know how you’re planning to commemorate Carl Sagan Day 2011 and we’ll add your event to our Carl Sagan Day Event Calendar to help spread the word.  Please email your event information to grassroots@centerforinquiry.net.

Great collection of posters, featuring Sagan, the Very Large Array, and quotes from the good doctor, here.

November 9 is the anniversary of Sagan’s birth, of course.

More, for 2012:


Make plans now: Carl Sagan Day, November 9

October 25, 2011

Press release from the Center for Inquiry:

Carl Sagan Day: November 9 — Celebrate with us!
Event Ideas & Sagan Day Commemorative Posters

Carl Sagan Day Poster 2011Carl Sagan was a Professor of Astronomy and Space Science and Director of the Laboratory for Planetary Studies at Cornell University, but most of us know him as a Pulitzer Prize winning author and the creator of COSMOS. That Emmy and Peabody award-winning PBS television series transformed educational television and continues to affect the hearts and minds of over a billion people in over sixty countries.

No other scientist has been able to reach and engage so many nonscientists in such a meaningful way, and that is why we honor Dr. Sagan, remember his work, and revel in the cosmos he helped us understand.

Two years ago, CFI–Fort Lauderdale and other groups hostd the first Carl Sagan Day event in Florida.  It was a fantastic success and now individuals and groups around the world are planning their own tributes with science fairs, planetarium shows, teacher workshops, star parties, COSMOS marathons, and more—all to say “Thanks!” to Sagan and to bring his gifts to another generation of “starstuff.”

How can you celebrate Carl Sagan Day?

Whether you’re an independent skeptics group, an astronomy club, a science department, a researcher, a teacher, a student, or just a really big Sagan fan, there are plenty of ways to celebrate Sagan Day:

  • Host a COSMOS marathon—all 13 episodes are available for free at hulu.com.
  • Check out Sagan’s many books at your local library or bookstore using the thorough listings from WorldCat.org.
  • Enjoy the special collection of articles by or about Sagan, previously published in Skeptical Inquirer magazine.
  • Listen to Sagan’s last public address for the Committee for Skeptical Inquiry (formerly CSICOP) as replayed on CFI’s podcast, Point of Inquiry: “Wonder and Skepticism.”
  • Listen to Ann Druyan, writer, producer, and widow of Sagan, discuss life with Carl, his outlook on life, and his famous Gifford Lectures, “The Varieties of Scientific Experience,” also on Point of Inquiry.
  • Host your own apple pie baking contest (from scratch, of course).
  • Dress like Carl for a day!
  • Refresh your skeptic skills with a review of Sagan’s Baloney Detection Kit.
  • Invite your friends over and try to convince them you have a dragon in your garage.
  • Take in a star show at your local planetarium.
  • At the very least, seek out a dark sky, look UP, and reconnect with the grandeur of the cosmos.

Let us know how you’re planning to commemorate Carl Sagan Day 2011 and we’ll add your event to our Carl Sagan Day Event Calendar to help spread the word.  Please email your event information to grassroots@centerforinquiry.net.

Great collection of posters, featuring Sagan, the Very Large Array, and quotes from the good doctor, here.

November 9 is the anniversary of Sagan’s birth, of course.


NASA needs eyewitnesses: Were you at the intersection of Milky Way and Bootës on the evening of March 19?

March 21, 2008

No kidding. Our Italian physicist friend Dorigo passed along the note on his blog, Quantum Diaries Survivor. George Gliba at NASA (gliba@milkyway.gsfc.nasa.gov) hopes someone was watching Bootës at about 6:10 UT (which would be about 1:10 a.m. Central Daylight Time (CDT), if I’m calculating that correctly).

Gliba said:

Last night the NASA SWIFT spacecraft saw the most extrinsically luminous Gamma-ray Burst ever known. Some ground based telescopes recorded the visual optical afterglow to be 5th magnitude!

Here’s your chance to make science history: If you may have seen the thing, or better, if you have a videotape of the incident (which may have lasted a few minutes), scientists would sure love to see it.

Here’s what the Swift telescope captured:

Gamma Ray burst in Bootes, GRB 080319B
The extremely luminous afterglow of GRB 080319B was imaged by Swift’s X-ray Telescope (left) and Optical/Ultraviolet Telescope (right). This was by far the brightest gamma-ray burst afterglow ever seen. Credit: NASA/Swift/Stefan Immler, et al.

So, did you see it? Call George Gliba; details, Gliba’s note to physicists and astronomers below the fold.

What is a gamma ray burst?

Most gamma ray bursts occur when massive stars run out of nuclear fuel. Their cores collapse to form black holes or neutron stars, releasing an intense burst of high-energy gamma rays and ejecting particle jets that rip through space at nearly the speed of light like turbocharged cosmic blowtorches. When the jets plow into surrounding interstellar clouds, they heat the gas, often generating bright afterglows. Gamma ray bursts are the most luminous explosions in the universe since the big bang.

“This burst was a whopper,” said Swift principal investigator Neil Gehrels of NASA’s Goddard Space Flight Center in Greenbelt, Md. “It blows away every gamma ray burst we’ve seen so far.”

Calculations show this one was 7 billion light years away. Cool!

Read the rest of this entry »


Follow

Get every new post delivered to your Inbox.

Join 2,194 other followers

%d bloggers like this: