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	<title>Comments on: Distance to the Horizon</title>
	<atom:link href="http://www.erik-rasmussen.com/blog/2008/03/25/distance-to-the-horizon/feed/" rel="self" type="application/rss+xml" />
	<link>http://www.erik-rasmussen.com/blog/2008/03/25/distance-to-the-horizon/</link>
	<description>Thoughts and photos from an American living in Spain.</description>
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		<title>By: Erik R.</title>
		<link>http://www.erik-rasmussen.com/blog/2008/03/25/distance-to-the-horizon/comment-page-1/#comment-5537</link>
		<dc:creator>Erik R.</dc:creator>
		<pubDate>Tue, 26 Jan 2010 21:43:03 +0000</pubDate>
		<guid isPermaLink="false">http://www.erik-rasmussen.com/blog/2008/03/25/distance-to-the-horizon/#comment-5537</guid>
		<description>Most excellent post, Marcos! To everyone reading this, please go check out his &lt;em&gt;gorgeous&lt;/em&gt; graphics, whether you can read Spanish or not.</description>
		<content:encoded><![CDATA[<p>Most excellent post, Marcos! To everyone reading this, please go check out his <em>gorgeous</em> graphics, whether you can read Spanish or not.</p>
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		<title>By: Marcos Molina</title>
		<link>http://www.erik-rasmussen.com/blog/2008/03/25/distance-to-the-horizon/comment-page-1/#comment-5536</link>
		<dc:creator>Marcos Molina</dc:creator>
		<pubDate>Tue, 26 Jan 2010 21:21:16 +0000</pubDate>
		<guid isPermaLink="false">http://www.erik-rasmussen.com/blog/2008/03/25/distance-to-the-horizon/#comment-5536</guid>
		<description>Hello Erik, I am writing you from Mallorca, Spain. I happened to find your website while I was making the last post in my blog. I found extremely interesting the calculator to find out the distance to the horizon. I decided to link this post to my post (today 26-1-2010), in the context of my recent article «Among the horizon: theory and practice» ( http://marcosmolina.wordpress.com/2010/01/26/mas-alla-del-horizonte-y-vii-teoria-y-practica ), about the tops of the mountains in the Iberian peninsula that can be seen from the roof of my dear island Mallorca. Interestingly, these observations allow us to see much farther than the actual horizon thanks to circumstancial atmospheric refraction. I hope it&#039;s ok for you to link your blog. Otherwise please let me know and I&#039;ll delete it.
Congratulations for such an amazing website.
Best regards from Palma de Mallorca.
Marcos.</description>
		<content:encoded><![CDATA[<p>Hello Erik, I am writing you from Mallorca, Spain. I happened to find your website while I was making the last post in my blog. I found extremely interesting the calculator to find out the distance to the horizon. I decided to link this post to my post (today 26-1-2010), in the context of my recent article «Among the horizon: theory and practice» ( <a href="http://marcosmolina.wordpress.com/2010/01/26/mas-alla-del-horizonte-y-vii-teoria-y-practica" rel="nofollow">http://marcosmolina.wordpress.com/2010/01/26/mas-alla-del-horizonte-y-vii-teoria-y-practica</a> ), about the tops of the mountains in the Iberian peninsula that can be seen from the roof of my dear island Mallorca. Interestingly, these observations allow us to see much farther than the actual horizon thanks to circumstancial atmospheric refraction. I hope it&#8217;s ok for you to link your blog. Otherwise please let me know and I&#8217;ll delete it.<br />
Congratulations for such an amazing website.<br />
Best regards from Palma de Mallorca.<br />
Marcos.</p>
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		<title>By: Allan Davidson</title>
		<link>http://www.erik-rasmussen.com/blog/2008/03/25/distance-to-the-horizon/comment-page-1/#comment-5304</link>
		<dc:creator>Allan Davidson</dc:creator>
		<pubDate>Thu, 19 Nov 2009 07:57:22 +0000</pubDate>
		<guid isPermaLink="false">http://www.erik-rasmussen.com/blog/2008/03/25/distance-to-the-horizon/#comment-5304</guid>
		<description>It seems to me that the easiest way to calculate the distance of the horizon is the old sailor&#039;s method, which is:

The Square Root of the Height of Eye (in feet)  x 1.16 = the distance of the visible horizon in Nautical Miles.  

The same formula would have to be applied to any object which the observer wished to see, and then added to the first distance above to obtain the theoretical maximum distance that the top of the object to be viewed would become visible.</description>
		<content:encoded><![CDATA[<p>It seems to me that the easiest way to calculate the distance of the horizon is the old sailor&#8217;s method, which is:</p>
<p>The Square Root of the Height of Eye (in feet)  x 1.16 = the distance of the visible horizon in Nautical Miles.  </p>
<p>The same formula would have to be applied to any object which the observer wished to see, and then added to the first distance above to obtain the theoretical maximum distance that the top of the object to be viewed would become visible.</p>
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		<title>By: Lance</title>
		<link>http://www.erik-rasmussen.com/blog/2008/03/25/distance-to-the-horizon/comment-page-1/#comment-4570</link>
		<dc:creator>Lance</dc:creator>
		<pubDate>Tue, 04 Aug 2009 13:15:09 +0000</pubDate>
		<guid isPermaLink="false">http://www.erik-rasmussen.com/blog/2008/03/25/distance-to-the-horizon/#comment-4570</guid>
		<description>Of course JT is trolling. Why else pretend to take offense at the statement that Americans are &quot;metrically ignorant&quot;? Of course we are. And, on a whole, we speak Spanish worse than Spaniards and Columbians. The average American also spends less time in Russia than the average Russian. And our turnout in the latest Japanese national elections was abysmal!

I would likewise challenge JT&#039;s seriousness if he were to take offense (on behalf of, say, Spaniards) at my statement that Spaniards are relatively ignorant of US customary units.

Look, when it&#039;s just Myanmar and Liberia who are refusing to adopt the metric system, the phrase &quot;metrically ignorant&quot; might sting. But when the world&#039;s last superpower wants to use another system of measure, then it&#039;s hardly a niche system. And one would hope that U.S. citizens would be better at the U.S. system than at others. There&#039;s nothing offensive about saying so.</description>
		<content:encoded><![CDATA[<p>Of course JT is trolling. Why else pretend to take offense at the statement that Americans are &#8220;metrically ignorant&#8221;? Of course we are. And, on a whole, we speak Spanish worse than Spaniards and Columbians. The average American also spends less time in Russia than the average Russian. And our turnout in the latest Japanese national elections was abysmal!</p>
<p>I would likewise challenge JT&#8217;s seriousness if he were to take offense (on behalf of, say, Spaniards) at my statement that Spaniards are relatively ignorant of US customary units.</p>
<p>Look, when it&#8217;s just Myanmar and Liberia who are refusing to adopt the metric system, the phrase &#8220;metrically ignorant&#8221; might sting. But when the world&#8217;s last superpower wants to use another system of measure, then it&#8217;s hardly a niche system. And one would hope that U.S. citizens would be better at the U.S. system than at others. There&#8217;s nothing offensive about saying so.</p>
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		<title>By: Josh</title>
		<link>http://www.erik-rasmussen.com/blog/2008/03/25/distance-to-the-horizon/comment-page-1/#comment-4568</link>
		<dc:creator>Josh</dc:creator>
		<pubDate>Tue, 04 Aug 2009 10:07:30 +0000</pubDate>
		<guid isPermaLink="false">http://www.erik-rasmussen.com/blog/2008/03/25/distance-to-the-horizon/#comment-4568</guid>
		<description>JT, you&#039;re trolling, right?  If you read the post carefully, you&#039;ll see another opportunity to take &quot;personal offense&quot; -- the assumption that the readers are trigonometrically ignorant.  Obviously, most people old enough and sophisticated enough to be reading something like this blog are aware that there is no need to take personal offense when something does not allude to them personally.  If, as you say, you have a &quot;perfectly good mathematical sense of metric computing&quot; then the &quot;metrically ignorant&quot; label doesn&#039;t apply to you.  See, no need to feel offended.  [My guess is that Erik bothered with the polemic conversion table for the convenience of people like his mother (and in the case that his mother is actually comfortable with the metric system, than with my mother, and people like her).]

If what you really wanted to say is that you are offended that anybody would dare comment on the average American&#039;s lack of knowledge of the metric system -- a system of measurement which has been an international standard since the early 1960&#039;s -- than you might have a bone to pick more with the Secretary of Education than with Erik or any other stater of the obvious.  

In short, the internet is such that you will waste far too much of your life getting offended by off-the-cuff comments which don&#039;t even apply to you.  Spend some time in NYC, or any other major urban center, and you&#039;ll quickly harden your skin to such inconsequential offenses.  

If my neither my ramble nor Erik&#039;s more rational explication soothe your abused feelings, maybe the Bard&#039;s words will:

&quot;If we shadows have offended, think but this, and all is mended, that you have but slumber&#039;d here while these visions did appear.  And this weak and idle theme, no more yielding but a dream...&quot;</description>
		<content:encoded><![CDATA[<p>JT, you&#8217;re trolling, right?  If you read the post carefully, you&#8217;ll see another opportunity to take &#8220;personal offense&#8221; &#8212; the assumption that the readers are trigonometrically ignorant.  Obviously, most people old enough and sophisticated enough to be reading something like this blog are aware that there is no need to take personal offense when something does not allude to them personally.  If, as you say, you have a &#8220;perfectly good mathematical sense of metric computing&#8221; then the &#8220;metrically ignorant&#8221; label doesn&#8217;t apply to you.  See, no need to feel offended.  [My guess is that Erik bothered with the polemic conversion table for the convenience of people like his mother (and in the case that his mother is actually comfortable with the metric system, than with my mother, and people like her).]</p>
<p>If what you really wanted to say is that you are offended that anybody would dare comment on the average American&#8217;s lack of knowledge of the metric system &#8212; a system of measurement which has been an international standard since the early 1960&#8217;s &#8212; than you might have a bone to pick more with the Secretary of Education than with Erik or any other stater of the obvious.  </p>
<p>In short, the internet is such that you will waste far too much of your life getting offended by off-the-cuff comments which don&#8217;t even apply to you.  Spend some time in NYC, or any other major urban center, and you&#8217;ll quickly harden your skin to such inconsequential offenses.  </p>
<p>If my neither my ramble nor Erik&#8217;s more rational explication soothe your abused feelings, maybe the Bard&#8217;s words will:</p>
<p>&#8220;If we shadows have offended, think but this, and all is mended, that you have but slumber&#8217;d here while these visions did appear.  And this weak and idle theme, no more yielding but a dream&#8230;&#8221;</p>
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		<title>By: Erik R.</title>
		<link>http://www.erik-rasmussen.com/blog/2008/03/25/distance-to-the-horizon/comment-page-1/#comment-4567</link>
		<dc:creator>Erik R.</dc:creator>
		<pubDate>Tue, 04 Aug 2009 09:13:01 +0000</pubDate>
		<guid isPermaLink="false">http://www.erik-rasmussen.com/blog/2008/03/25/distance-to-the-horizon/#comment-4567</guid>
		<description>JT, first of all, I&#039;d like to thank you for reporting the bug in the calculator.  My blog has been through some database migration lately, and the calculator was a casualty.  It&#039;s fixed now.

I strongly suspect that you are naively optimistic about our fellow countrymen&#039;s knowledge of the metric system.  If you gave the following test to random Americans on the street (not just 13-year-old science students) I&#039;d be very surprised if more than 10% got them all correct.

1) Which is longer, a centimeter or a kilometer?

2) How many centimeters are there in a meter?

3) How much does a liter of water weigh in kilograms?

4) Which is bigger, a liter or a gallon?

Most Europeans wouldn&#039;t get #4 of course, because they have no concept of what a US gallon is.  And I suspect that only the scientifically minded might get #3.  But every single European would know the more practical question of, &quot;Is 100 kph too slow or too fast to drive on the motorway (interstate to Americans)?&quot;  Only Americans that had spent some time abroad would have any clue about that question.

Keep in mind that ignorant doesn&#039;t mean stupid; it means lacking in knowledge.</description>
		<content:encoded><![CDATA[<p>JT, first of all, I&#8217;d like to thank you for reporting the bug in the calculator.  My blog has been through some database migration lately, and the calculator was a casualty.  It&#8217;s fixed now.</p>
<p>I strongly suspect that you are naively optimistic about our fellow countrymen&#8217;s knowledge of the metric system.  If you gave the following test to random Americans on the street (not just 13-year-old science students) I&#8217;d be very surprised if more than 10% got them all correct.</p>
<p>1) Which is longer, a centimeter or a kilometer?</p>
<p>2) How many centimeters are there in a meter?</p>
<p>3) How much does a liter of water weigh in kilograms?</p>
<p>4) Which is bigger, a liter or a gallon?</p>
<p>Most Europeans wouldn&#8217;t get #4 of course, because they have no concept of what a US gallon is.  And I suspect that only the scientifically minded might get #3.  But every single European would know the more practical question of, &#8220;Is 100 kph too slow or too fast to drive on the motorway (interstate to Americans)?&#8221;  Only Americans that had spent some time abroad would have any clue about that question.</p>
<p>Keep in mind that ignorant doesn&#8217;t mean stupid; it means lacking in knowledge.</p>
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		<title>By: JT</title>
		<link>http://www.erik-rasmussen.com/blog/2008/03/25/distance-to-the-horizon/comment-page-1/#comment-4563</link>
		<dc:creator>JT</dc:creator>
		<pubDate>Tue, 04 Aug 2009 03:39:04 +0000</pubDate>
		<guid isPermaLink="false">http://www.erik-rasmussen.com/blog/2008/03/25/distance-to-the-horizon/#comment-4563</guid>
		<description>I take personal offense to this line in your otherwise informative treatise:

&quot;For the metrically ignorant Americans&quot;

for I am an &#039;American&#039; with a perfectly good mathematical sense of metric computing and can do it &#039;in my head&#039;, as I imagine most &#039;Americans&#039; who stumble on this blog can, as well.

By The Way:  Your tantalizing calculator at the bottom of the article doesn&#039;t work for me on Firefox 3.5 or Safari 3.2

Cheers,

Jt</description>
		<content:encoded><![CDATA[<p>I take personal offense to this line in your otherwise informative treatise:</p>
<p>&#8220;For the metrically ignorant Americans&#8221;</p>
<p>for I am an &#8216;American&#8217; with a perfectly good mathematical sense of metric computing and can do it &#8216;in my head&#8217;, as I imagine most &#8216;Americans&#8217; who stumble on this blog can, as well.</p>
<p>By The Way:  Your tantalizing calculator at the bottom of the article doesn&#8217;t work for me on Firefox 3.5 or Safari 3.2</p>
<p>Cheers,</p>
<p>Jt</p>
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		<title>By: Ray Tibbitts</title>
		<link>http://www.erik-rasmussen.com/blog/2008/03/25/distance-to-the-horizon/comment-page-1/#comment-3648</link>
		<dc:creator>Ray Tibbitts</dc:creator>
		<pubDate>Fri, 16 Jan 2009 22:41:03 +0000</pubDate>
		<guid isPermaLink="false">http://www.erik-rasmussen.com/blog/2008/03/25/distance-to-the-horizon/#comment-3648</guid>
		<description>Cool.
Thanks again.
Now what do you do in THIS situation?
http://www.flickr.com/photos/aparejador/2603131352/</description>
		<content:encoded><![CDATA[<p>Cool.<br />
Thanks again.<br />
Now what do you do in THIS situation?<br />
<a href="http://www.flickr.com/photos/aparejador/2603131352/" rel="nofollow">http://www.flickr.com/photos/aparejador/2603131352/</a></p>
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		<title>By: Erik R.</title>
		<link>http://www.erik-rasmussen.com/blog/2008/03/25/distance-to-the-horizon/comment-page-1/#comment-3644</link>
		<dc:creator>Erik R.</dc:creator>
		<pubDate>Fri, 16 Jan 2009 17:09:48 +0000</pubDate>
		<guid isPermaLink="false">http://www.erik-rasmussen.com/blog/2008/03/25/distance-to-the-horizon/#comment-3644</guid>
		<description>Ray, in the &lt;a href=&quot;http://forums.fark.com/cgi/fark/comments.pl?IDLink=4147995&quot; rel=&quot;nofollow&quot;&gt;lively discussion about this over on Fark&lt;/a&gt;, someone has posted this nice sketch that answers your question pretty well.

&lt;img src=&quot;http://img.photobucket.com/albums/v736/jj71/horizon.jpg&quot; border=&quot;0&quot; width=&quot;445&quot; height=&quot;292&quot; alt=&quot;horizon sketch&quot;/&gt;</description>
		<content:encoded><![CDATA[<p>Ray, in the <a href="http://forums.fark.com/cgi/fark/comments.pl?IDLink=4147995" rel="nofollow">lively discussion about this over on Fark</a>, someone has posted this nice sketch that answers your question pretty well.</p>
<p><img src="http://img.photobucket.com/albums/v736/jj71/horizon.jpg" border="0" width="445" height="292" alt="horizon sketch"/></p>
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		<title>By: Erik R.</title>
		<link>http://www.erik-rasmussen.com/blog/2008/03/25/distance-to-the-horizon/comment-page-1/#comment-3639</link>
		<dc:creator>Erik R.</dc:creator>
		<pubDate>Fri, 16 Jan 2009 10:47:58 +0000</pubDate>
		<guid isPermaLink="false">http://www.erik-rasmussen.com/blog/2008/03/25/distance-to-the-horizon/#comment-3639</guid>
		<description>This post was assuming a perfectly smooth sphere, simplified to a circle.  Obviously things are a little different when you&#039;ve got jagged mountains jutting up.  Actually, it might be interesting to do another calculation of how far away point A and B could be given their altitudes H&lt;sub&gt;A&lt;/sub&gt; and H&lt;sub&gt;B&lt;/sub&gt; above sea level.  Some of the commenters over on &lt;a href=&quot;http://blogs.discovermagazine.com/badastronomy/2009/01/15/how-far-away-is-the-horizon/&quot; rel=&quot;nofollow&quot;&gt;Bad Astronomy&lt;/a&gt; had the same questions as you, Ray.</description>
		<content:encoded><![CDATA[<p>This post was assuming a perfectly smooth sphere, simplified to a circle.  Obviously things are a little different when you&#8217;ve got jagged mountains jutting up.  Actually, it might be interesting to do another calculation of how far away point A and B could be given their altitudes H<sub>A</sub> and H<sub>B</sub> above sea level.  Some of the commenters over on <a href="http://blogs.discovermagazine.com/badastronomy/2009/01/15/how-far-away-is-the-horizon/" rel="nofollow">Bad Astronomy</a> had the same questions as you, Ray.</p>
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