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	<title>Comments on: Nautical numeration</title>
	<atom:link href="http://bit-player.org/2009/nautical-numeration/feed" rel="self" type="application/rss+xml" />
	<link>http://bit-player.org/2009/nautical-numeration</link>
	<description>An amateur's outlook on computation and mathematics.</description>
	<pubDate>Fri, 30 Jul 2010 22:22:22 +0000</pubDate>
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		<title>By: Carl Witty</title>
		<link>http://bit-player.org/2009/nautical-numeration#comment-2232</link>
		<dc:creator>Carl Witty</dc:creator>
		<pubDate>Tue, 22 Sep 2009 05:53:58 +0000</pubDate>
		<guid isPermaLink="false">http://bit-player.org/?p=440#comment-2232</guid>
		<description>No, a letter isn't a sequence of numerals; see the bottom paragraph of page 12 of Roscoe's document, where it describes that "All three placed in position at the same time."  So each codeword (representing either a number from 1 to 99, or a character of the alphabet) consists of hoisting some number of disks simultaneously.

I'm guessing that Roscoe's code is an earlier stage in the evolution; note that Roscoe's code has the 10 signal positions in a fairly logical, memorable sequence.  Perhaps they changed the pattern for the Citadel because their codebook (or at least the signals they used often) had more 0's than 6's, or something; so they modified the signal positions to make a 0 easier and a 6 harder.</description>
		<content:encoded><![CDATA[<p>No, a letter isn&#8217;t a sequence of numerals; see the bottom paragraph of page 12 of Roscoe&#8217;s document, where it describes that &#8220;All three placed in position at the same time.&#8221;  So each codeword (representing either a number from 1 to 99, or a character of the alphabet) consists of hoisting some number of disks simultaneously.</p>
<p>I&#8217;m guessing that Roscoe&#8217;s code is an earlier stage in the evolution; note that Roscoe&#8217;s code has the 10 signal positions in a fairly logical, memorable sequence.  Perhaps they changed the pattern for the Citadel because their codebook (or at least the signals they used often) had more 0&#8217;s than 6&#8217;s, or something; so they modified the signal positions to make a 0 easier and a 6 harder.</p>
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		<title>By: Jim Ward</title>
		<link>http://bit-player.org/2009/nautical-numeration#comment-2230</link>
		<dc:creator>Jim Ward</dc:creator>
		<pubDate>Wed, 16 Sep 2009 20:33:28 +0000</pubDate>
		<guid isPermaLink="false">http://bit-player.org/?p=440#comment-2230</guid>
		<description>Or not ..

http://www.coastalradio.org.uk/spud/spud/spud02.pdf</description>
		<content:encoded><![CDATA[<p>Or not ..</p>
<p><a href="http://www.coastalradio.org.uk/spud/spud/spud02.pdf" rel="nofollow">http://www.coastalradio.org.uk/spud/spud/spud02.pdf</a></p>
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		<title>By: Jim Ward</title>
		<link>http://bit-player.org/2009/nautical-numeration#comment-2229</link>
		<dc:creator>Jim Ward</dc:creator>
		<pubDate>Wed, 16 Sep 2009 19:27:37 +0000</pubDate>
		<guid isPermaLink="false">http://bit-player.org/?p=440#comment-2229</guid>
		<description>Could be a clock. How did the Royal Navy mark time in the 1850s?

http://www.navy.mil/navydata/questions/bells.html</description>
		<content:encoded><![CDATA[<p>Could be a clock. How did the Royal Navy mark time in the 1850s?</p>
<p><a href="http://www.navy.mil/navydata/questions/bells.html" rel="nofollow">http://www.navy.mil/navydata/questions/bells.html</a></p>
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		<title>By: Jim Ward</title>
		<link>http://bit-player.org/2009/nautical-numeration#comment-2228</link>
		<dc:creator>Jim Ward</dc:creator>
		<pubDate>Wed, 16 Sep 2009 19:05:35 +0000</pubDate>
		<guid isPermaLink="false">http://bit-player.org/?p=440#comment-2228</guid>
		<description>It's not a  number code, it's a 10 position cyclic signaling system. First you hang the lamp in the 0th  position. Then you add the  lamp in the 1st position, then you add the  lamp in the 2nd position .. when you add add the 5th position lamp, you have 6 lamps hanging from the yardarm. Then you pull lamp 2 up to lamp 1 to make the 6th position, pull lamp 4 up to 3 to make the 7th position, pull lamp 0 to make the 8th position, pull all the lamps down to make the 9th position.  Yarrr!</description>
		<content:encoded><![CDATA[<p>It&#8217;s not a  number code, it&#8217;s a 10 position cyclic signaling system. First you hang the lamp in the 0th  position. Then you add the  lamp in the 1st position, then you add the  lamp in the 2nd position .. when you add add the 5th position lamp, you have 6 lamps hanging from the yardarm. Then you pull lamp 2 up to lamp 1 to make the 6th position, pull lamp 4 up to 3 to make the 7th position, pull lamp 0 to make the 8th position, pull all the lamps down to make the 9th position.  Yarrr!</p>
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		<title>By: Gijs Bruyn</title>
		<link>http://bit-player.org/2009/nautical-numeration#comment-2224</link>
		<dc:creator>Gijs Bruyn</dc:creator>
		<pubDate>Mon, 14 Sep 2009 08:58:35 +0000</pubDate>
		<guid isPermaLink="false">http://bit-player.org/?p=440#comment-2224</guid>
		<description>... in the moving disk interpretation of the diagram, there are three positions {left, middle, right} and two movements {up, down}, giving six combinations. Numbers six and higher need an extra `digit', i.e. an extra movement.

The full encoding is (where every movement is followed by a return to the baseline): 0 = [left down]; 1 = [right up]; 2 = [right down]; 3 = [middle up]; 4 = [middle down]; 5 = [left up]; 6 = [right up up]; 7 = [middle up up]; 8 = [left up up]; 9 = [{left, middle, right} down down].

In this interpretation the viewer only has to see the disks, not the mast and crossarm, because every halyard has exactly one disk, all the time. Because of the offset of the middle halyard left and right are easily distinguished, and the up and down movements are also easy to distinguish because only one disk is moving up or down relative to the two other disks at the baseline. At night the disks can be replaced by lamps.</description>
		<content:encoded><![CDATA[<p>&#8230; in the moving disk interpretation of the diagram, there are three positions {left, middle, right} and two movements {up, down}, giving six combinations. Numbers six and higher need an extra `digit&#8217;, i.e. an extra movement.</p>
<p>The full encoding is (where every movement is followed by a return to the baseline): 0 = [left down]; 1 = [right up]; 2 = [right down]; 3 = [middle up]; 4 = [middle down]; 5 = [left up]; 6 = [right up up]; 7 = [middle up up]; 8 = [left up up]; 9 = [{left, middle, right} down down].</p>
<p>In this interpretation the viewer only has to see the disks, not the mast and crossarm, because every halyard has exactly one disk, all the time. Because of the offset of the middle halyard left and right are easily distinguished, and the up and down movements are also easy to distinguish because only one disk is moving up or down relative to the two other disks at the baseline. At night the disks can be replaced by lamps.</p>
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		<title>By: gijs</title>
		<link>http://bit-player.org/2009/nautical-numeration#comment-2223</link>
		<dc:creator>gijs</dc:creator>
		<pubDate>Sun, 13 Sep 2009 21:35:08 +0000</pubDate>
		<guid isPermaLink="false">http://bit-player.org/?p=440#comment-2223</guid>
		<description>The coding could be based on the movement of the disks. The start position is one disk on each halyard (left, middle and right), in a position that allows it to move up or down, with the middle offset to the right. The diagram then shows the halyard, direction and count of the movements.  Following the diagram the numbers would be encoded as 0 = (left: down, up); 1 = (right: up, down); ...; 6 = (right: up, down, up, down); etc. 

It's a lot easier to operate than the other encodings, because you don't have to add and remove disks all the time.</description>
		<content:encoded><![CDATA[<p>The coding could be based on the movement of the disks. The start position is one disk on each halyard (left, middle and right), in a position that allows it to move up or down, with the middle offset to the right. The diagram then shows the halyard, direction and count of the movements.  Following the diagram the numbers would be encoded as 0 = (left: down, up); 1 = (right: up, down); &#8230;; 6 = (right: up, down, up, down); etc. </p>
<p>It&#8217;s a lot easier to operate than the other encodings, because you don&#8217;t have to add and remove disks all the time.</p>
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		<title>By: brian</title>
		<link>http://bit-player.org/2009/nautical-numeration#comment-2217</link>
		<dc:creator>brian</dc:creator>
		<pubDate>Thu, 10 Sep 2009 14:27:17 +0000</pubDate>
		<guid isPermaLink="false">http://bit-player.org/?p=440#comment-2217</guid>
		<description>A further comment on Barry's alternative interpretation:

Nemo argued earlier that a distant viewer could not determine absolute vertical position; Barry argues that the viewer cannot determine absolute horizontal position. It seems to me that both of these assertions are true if the viewer can see &lt;em&gt;only&lt;/em&gt; the disks, but both are false if the viewer can also make out the mast and the crossarm. I don't know whether the mast and crossarm were assumed visible or not, but it seems likely that the assumption would be either both or neither.

I'm going to add a photo of the signal mast to the post.</description>
		<content:encoded><![CDATA[<p>A further comment on Barry&#8217;s alternative interpretation:</p>
<p>Nemo argued earlier that a distant viewer could not determine absolute vertical position; Barry argues that the viewer cannot determine absolute horizontal position. It seems to me that both of these assertions are true if the viewer can see <em>only</em> the disks, but both are false if the viewer can also make out the mast and the crossarm. I don&#8217;t know whether the mast and crossarm were assumed visible or not, but it seems likely that the assumption would be either both or neither.</p>
<p>I&#8217;m going to add a photo of the signal mast to the post.</p>
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		<title>By: brian</title>
		<link>http://bit-player.org/2009/nautical-numeration#comment-2216</link>
		<dc:creator>brian</dc:creator>
		<pubDate>Wed, 09 Sep 2009 15:55:45 +0000</pubDate>
		<guid isPermaLink="false">http://bit-player.org/?p=440#comment-2216</guid>
		<description>@Derek Ross: There was doubtless much more to the signaling code than numerals. In particular, there must have been a full alphabet. And, yes, there were canned phrases --- the display at the Citadel showed a few of them.

@Nemo: Good point about relative vs. absolute position. Possibly the crossarm (yard?) on the mast is visible enough to provide a reference level. I just don't know.

@Barry: Oops. Who am I to be telling the Royal Navy how to count?</description>
		<content:encoded><![CDATA[<p>@Derek Ross: There was doubtless much more to the signaling code than numerals. In particular, there must have been a full alphabet. And, yes, there were canned phrases &#8212; the display at the Citadel showed a few of them.</p>
<p>@Nemo: Good point about relative vs. absolute position. Possibly the crossarm (yard?) on the mast is visible enough to provide a reference level. I just don&#8217;t know.</p>
<p>@Barry: Oops. Who am I to be telling the Royal Navy how to count?</p>
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		<title>By: Barry Cipra</title>
		<link>http://bit-player.org/2009/nautical-numeration#comment-2215</link>
		<dc:creator>Barry Cipra</dc:creator>
		<pubDate>Wed, 09 Sep 2009 14:57:15 +0000</pubDate>
		<guid isPermaLink="false">http://bit-player.org/?p=440#comment-2215</guid>
		<description>You write, "Each halyard could display zero or one or two disks, and each displayed disk could be in either an upper or a lower position. That comes to five possible patterns per halyard, and thus 53 = 125 patterns in all."  (Oops, the superscript for 5-cubed didn't seem to copy through.)

I think you mean six, rather than five, hence 6-cubed = 216 patterns in all.  For each halyard, there is one pattern with zero disks, two with one disk, and three with two disks.</description>
		<content:encoded><![CDATA[<p>You write, &#8220;Each halyard could display zero or one or two disks, and each displayed disk could be in either an upper or a lower position. That comes to five possible patterns per halyard, and thus 53 = 125 patterns in all.&#8221;  (Oops, the superscript for 5-cubed didn&#8217;t seem to copy through.)</p>
<p>I think you mean six, rather than five, hence 6-cubed = 216 patterns in all.  For each halyard, there is one pattern with zero disks, two with one disk, and three with two disks.</p>
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		<title>By: Nemo</title>
		<link>http://bit-player.org/2009/nautical-numeration#comment-2214</link>
		<dc:creator>Nemo</dc:creator>
		<pubDate>Wed, 09 Sep 2009 14:43:14 +0000</pubDate>
		<guid isPermaLink="false">http://bit-player.org/?p=440#comment-2214</guid>
		<description>Yeah, OK, my diagrams would be better, too.

But I really do not believe 8 and 9 could only differ in whether the six discs are crowded near the top or near the bottom.  These would be among the harder patterns to distinguish from a distance.  Imagine viewing a ship, off on the horizon...  And you have to tell whether the discs are closer to the top or to the bottom of her mast?

So my proposal is that the code is unary, with N discs representing the number N-1, except that 9 discs can be 8 or 9 depending on position.  With this code, you can distinguish 8 from 9 by the &lt;i&gt;relative&lt;/i&gt; positions of the discs; i.e., are the middle discs nearer the top discs or the bottom discs?

For the code to require identifying the &lt;i&gt;absolute&lt;/i&gt; position of any disc would seem like a design flaw...</description>
		<content:encoded><![CDATA[<p>Yeah, OK, my diagrams would be better, too.</p>
<p>But I really do not believe 8 and 9 could only differ in whether the six discs are crowded near the top or near the bottom.  These would be among the harder patterns to distinguish from a distance.  Imagine viewing a ship, off on the horizon&#8230;  And you have to tell whether the discs are closer to the top or to the bottom of her mast?</p>
<p>So my proposal is that the code is unary, with N discs representing the number N-1, except that 9 discs can be 8 or 9 depending on position.  With this code, you can distinguish 8 from 9 by the <i>relative</i> positions of the discs; i.e., are the middle discs nearer the top discs or the bottom discs?</p>
<p>For the code to require identifying the <i>absolute</i> position of any disc would seem like a design flaw&#8230;</p>
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		<title>By: Nemo</title>
		<link>http://bit-player.org/2009/nautical-numeration#comment-2213</link>
		<dc:creator>Nemo</dc:creator>
		<pubDate>Wed, 09 Sep 2009 14:10:19 +0000</pubDate>
		<guid isPermaLink="false">http://bit-player.org/?p=440#comment-2213</guid>
		<description>I like your second theory for the code (unary for 1-5).  In fact, I like it so much...

Perhaps nearly the entire code is unary, and the difference between 8 and 9 is whether the three middle disks are closer to the top than to the bottom of the masts?   I think such a code would be pretty easy to read, even from a distance, with very little chance for confusion between numbers.

If this were the code and you were assigned the task of generating a small set of mnemonic diagrams, what would your diagrams look like?</description>
		<content:encoded><![CDATA[<p>I like your second theory for the code (unary for 1-5).  In fact, I like it so much&#8230;</p>
<p>Perhaps nearly the entire code is unary, and the difference between 8 and 9 is whether the three middle disks are closer to the top than to the bottom of the masts?   I think such a code would be pretty easy to read, even from a distance, with very little chance for confusion between numbers.</p>
<p>If this were the code and you were assigned the task of generating a small set of mnemonic diagrams, what would your diagrams look like?</p>
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		<title>By: Joseph Gutierrez</title>
		<link>http://bit-player.org/2009/nautical-numeration#comment-2212</link>
		<dc:creator>Joseph Gutierrez</dc:creator>
		<pubDate>Wed, 09 Sep 2009 04:03:50 +0000</pubDate>
		<guid isPermaLink="false">http://bit-player.org/?p=440#comment-2212</guid>
		<description>Ahoy Shipmate,

Thanks for this bit of trivia. Just googling around led me to my old ship USS Mount Whitney.

After leaving the Navy. I had a chance to visit Halifax on business.

Some trivia: 
The most eastern-northern deep water port open all season.
Ammunition ship explosion during WWI?

I believe that you could use it for individual letters/numbers and code words/groups.

Fair Seas</description>
		<content:encoded><![CDATA[<p>Ahoy Shipmate,</p>
<p>Thanks for this bit of trivia. Just googling around led me to my old ship USS Mount Whitney.</p>
<p>After leaving the Navy. I had a chance to visit Halifax on business.</p>
<p>Some trivia:<br />
The most eastern-northern deep water port open all season.<br />
Ammunition ship explosion during WWI?</p>
<p>I believe that you could use it for individual letters/numbers and code words/groups.</p>
<p>Fair Seas</p>
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		<title>By: Derek Ross</title>
		<link>http://bit-player.org/2009/nautical-numeration#comment-2211</link>
		<dc:creator>Derek Ross</dc:creator>
		<pubDate>Wed, 09 Sep 2009 03:09:20 +0000</pubDate>
		<guid isPermaLink="false">http://bit-player.org/?p=440#comment-2211</guid>
		<description>...Or maybe the numbers represented code words as described on page 48 in "The Manual of Signals."  I.e., they weren't trying to transmit numeric information such as latitude, but rather generalities like "lost an anchor."</description>
		<content:encoded><![CDATA[<p>&#8230;Or maybe the numbers represented code words as described on page 48 in &#8220;The Manual of Signals.&#8221;  I.e., they weren&#8217;t trying to transmit numeric information such as latitude, but rather generalities like &#8220;lost an anchor.&#8221;</p>
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		<title>By: Derek Ross</title>
		<link>http://bit-player.org/2009/nautical-numeration#comment-2210</link>
		<dc:creator>Derek Ross</dc:creator>
		<pubDate>Wed, 09 Sep 2009 02:23:16 +0000</pubDate>
		<guid isPermaLink="false">http://bit-player.org/?p=440#comment-2210</guid>
		<description>Were there lots of other codes? Maybe the numbers were an afterthought, and had to be fit into the "gaps" of the code.</description>
		<content:encoded><![CDATA[<p>Were there lots of other codes? Maybe the numbers were an afterthought, and had to be fit into the &#8220;gaps&#8221; of the code.</p>
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