Cecil’s Great Wall Classic Column
Ignorance amazes me, as I am sure Cecil is amazed almost every day. What amazes me even more is the difficulty in squashing it. People just really don’t like knowing they are wrong. Even when they are forced to accept it, they come-up with some valid, or often invalid, defense for having thought that way.
The last response of his article struck me in just that way, though Cecil was much kinder than I could be, I must give him credit for admitting he was wrong on a small point. However that doesn’t mean you have to let the guy go, believing he was right. Because he was FAR from right.
Below is a modified version of an e-mail I sent Cecil regarding my thoughts, but then I realized I should have posted them here.
Cecil,
Amazing isn’t it how strongly a myth that fascinates can grab on to the imagination and defends itself, even with science. What’s more amazing is its ability to cloud our reasoning when we want a certain result.
I am writing to tell you I think you went too easy on the guy who criticized you for trusting a “NASA goofball.” His claim was that the NASA guy couldn’t work a simple math problem, yet he couldn’t either.
Using both his examples, he made himself a fool. Indeed as you admitted the Earth is larger than one arc degree. However, this information could have been a misquote on the NASA site, indicating the relative size of the moon from the Earth. Moreover, simply stating the size of the Earth relative to the moon does not establish visual acuity. The angular diameter of the moon is 1,870 arc seconds (from the formula, [angular dia / 206,265 = linear dia / distance] , the 206,265 being a conversion # from radians to arc seconds). In relation to actual diameter this means the distances we see on the moon vary from 1.18 miles/arc second on up, averaging 1.8 mi/arc sec overall. Considering in addition, one arcsec is the relative size of the ball tip of a ball point pen as viewed from a football field away [Seeds, 15], I hardly call what we see when we look at the moon, “a large amount of detail on the lunar surface.”
When you reverse the direction the same math breaks down to the following information about viewing the Earth from the moon. The angular diameter of the Earth would be 6,852 arc second. Because the distance is the same, compared to the actual diameter, we find that each arc second represents the same distances as we found for the moon from 1.18 miles/arc second on up, averaging 1.8 mi/arc sec. Assuming the Great Wall presents itself dead on center of the Earth’s visual diameter we can thus calculate its angular size based on our ratio and knowledge of its width. The Badaling Section of Great wall is one of the better-known sections we envision when we think of the Wall. Built in the grandeur of the Ming dynasty the wall measures 5.8 meters wide at the top (Citation 2), arguably one of the wider sections of the wall. For the benefit of the doubt, let us say 10 meters, which converts to .0062 miles. Apply this measure to our ratio or miles/arc seconds, and you will find the angular measure of the Great Wall from the moon to be roughly 1/200th of an arc second. This is about the size of a speck of dust as compared to the ball tip mentioned earlier. Could you see that from a football field away, even if it was bright white on a black background? No way!!!
Needless to say his “eye science” explanation is faulted as well. The information he provides was for visual acuity of a line on a uniform background. The surface of the Earth is NOT a uniform background, there is changing terrain, changing altitudes, changing foliage, scattered bodies of water, snow fields, clouds, and the list goes on. So based on his data, visual acuity falls back to 20 seconds of arc with one eye, according to his data. This equates to an average of 36 miles. And that means an ability to see a single uniform object on a non-uniform background, such as a lake. A city has no uniformity of appearance from high above, trees mix with houses, buildings with roads, parks with parking lots, etc. So not even cities could be visible in daylight. Perhaps a night view during a lunar eclipse (Earth blocking the Sun from the moon) you could see the lights of the major cities, but even that is doubtful given the calculations for distance and luminosity.
On a final note, I could not find confirming information on his numbers for visual acuity. I think claims of being able to see roughly .5 arc seconds is extreme. Consider the following a person with 6/3 metric or 20/10 English vision sees only as fine as .5 arc minutes or 30 arc seconds, this of course is a monocular test (Citation 3). Aside form the fact he claimed average is 20 arc secs, even with a squaring bonus for binocular vision and a uniform background, I can hardly believe it reduces to only .5 arc sec, a factor of 60 less.
Just wanted to share my piece.
Citations:
1] Seeds, Michael A. Horizons: Exploring the Universe. 5th Ed. Albany, New York: ITP, 1998.
2] http://abe.www.ecn.purdue.edu/~agenhtml/agenmc/china/scengw.html
3] Scroll down and you will find a chart http://www.webvision.med.utah.edu/KallSpatial.html
[End of E-Mail]
Even from LEO (low Earth Orbit, 150-300 miles above the Earth), the Great Wall is not capable of being spotted with the unaided eye. Using similar math, one can derive the width of the wall to be a maximum of only 8.4 arc sec at 150 mi. and half that at 300 mi. Again this formula assumes the Wall to be 10 meters at it’s widest.
Also remember, the Great Wall was built by several Dynasties and over varied terrain and, most, if not all the sections, were built out of materials found local to the area the wall was built. Hence, the Great Wall does not appear distinctly different than the terrain surrounding it. Somewhat like a chameleon, up close it is obviously not same as its environment, but from any appreciable distance you can’t see it.
The main reason I share all this is my hope that some will read it an finally quit believing all the farcical information they have been feed in the past regarding the Great Wall of China and it’s visibility from space.