tag:blogger.com,1999:blog-43528242820462015762024-03-13T02:39:37.197-07:00Zweiback MotelThoughts about matters geographic, mathematical, cultural, adventuresome...Morgan Hitehttp://www.blogger.com/profile/02187274906810012520noreply@blogger.comBlogger32125tag:blogger.com,1999:blog-4352824282046201576.post-6348765406319189182013-12-04T19:21:00.000-08:002013-12-04T19:44:04.950-08:00Ubuntu Precise, QGIS, GRASS and r.denoiseIf you are interested in making your own shaded relief in QGIS, you may want to know about a GRASS module called <b>r.denoise</b>. <br />
<br />
<b>r.denoise</b> (as explained more at length <a href="http://gis.stackexchange.com/questions/12833/how-to-smooth-a-dem">here</a>), removes the random noise from a digital elevation model. As a result, when you generate a shaded relief image from the DEM it doesn't show as many small texture features.<br />
<br />
<table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody>
<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj_PrvwyE0CuQ_tCMdvnKz7AfB9ALyiwhA_sxm4HL3jnAY6-n0STOWVZnrkPaIgVKBamzRBwD3K5IKN5AhdNufXODVX4MFAO3hcSRDMlhppDlxuGezNvfCws-TOWXwW4cIuq546NLiO2sk/s1600/093L14_shaded_relief_detail.jpg" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" height="160" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj_PrvwyE0CuQ_tCMdvnKz7AfB9ALyiwhA_sxm4HL3jnAY6-n0STOWVZnrkPaIgVKBamzRBwD3K5IKN5AhdNufXODVX4MFAO3hcSRDMlhppDlxuGezNvfCws-TOWXwW4cIuq546NLiO2sk/s320/093L14_shaded_relief_detail.jpg" width="320" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">Shaded relief of a portion of Canadian topographic map 093L14 (Smithers) generated with GRASS's module <b>r.shaded.relief</b>. At left, shaded relief from regular CDED DEM, and, at right, from CDED DEM denoised with <b>r.denoise</b>. Denoising parameters in this case were 5 iterations at a tolerance of 0.93.</td></tr>
</tbody></table>
The trick is that, although under Ubuntu Precise it's easy to install QGIS and GRASS (packages <b>qgis</b> and <b>qgis-plugin-grass</b>), r.denoise is not a standard module in GRASS. It's an <i>addon</i>. There are many wonderful GRASS addons (see a list <a href="http://grasswiki.osgeo.org/wiki/GRASS_AddOns">here</a>), but installing a GRASS addon when you did not compile GRASS yourself (i.e., you installed it through a precompiled package, as one tends to do under Ubuntu), requires a few extra steps. It can be done, however!<br />
<br />
I recently struggled through installing r.denoise, and I was unable to find complete instructions on the web, so I thought I would explain here how I did it. <br />
<br />
I'll assume that you are running Ubuntu Precise, and that you already have QGIS 2 and the GRASS plugin installed, and that you know how to use them.<br />
<br />
<h3>
Preparation</h3>
There are four things you will need <i>before</i> you can install r.denoise:<br />
<ul>
<li>package <b>grass-dev</b> (which will in turn require package <b>grass</b>)</li>
<li>package <b>subversion</b></li>
<li>the <b>mdenoise</b> utility</li>
<li>a patch in a makefile that comes as part of <b>grass-dev</b> (apparently you will not need this if you have <b>grass</b> version >=6.4.2, but at this point Ubuntu has 6.4.1)</li>
</ul>
Phase 1: The packages <b>grass-dev</b> and <b>subversion</b> you can install through the synaptic package manager.<br />
<br />
Phase 2: To install <b>mdenoise</b>, <br />
<ol>
<li>go to <a href="http://www.cs.cf.ac.uk/meshfiltering/index_files/Page342.htm">the Cardiff University site on the Filtering and Processing of Irregular Meshes with Uncertainties</a> and downlaod <b>mdsource.zip</b></li>
<li>unzip it into a temporary folder, e.g., on your desktop</li>
<li>open a terminal in that folder and compile mdenoise with:</li>
<blockquote class="tr_bq">
<span style="font-family: "Courier New",Courier,monospace;">$ g++ -o mdenoise mdenoise.cpp triangle.c</span></blockquote>
<li>move (as root or using sudo) the new file that appears, "mdenoise," into /usr/bin:</li>
</ol>
<blockquote class="tr_bq">
<span style="font-family: "Courier New",Courier,monospace;">$ sudo mv mdenoise /usr/bin/</span></blockquote>
<br />
Phase 3: to patch <b>Platform.make</b> file in <b>/usr/lib/grass64/include/Make</b>, run the following command:<br />
<br />
<blockquote class="tr_bq">
<code>
<span style="font-size: x-small;">$ sudo sed -i -e 's+^\(GRASS_HOME[ ]*=\) /build/.*+\1 ${INST_DIR}+' \<br /> -e 's+^\(RUN_GISBASE[ ]*=\) /build/.*+\1 ${INST_DIR}+' \<br /> /usr/lib/grass64/include/Make/Platform.make</span></code></blockquote>
<code> </code>
<br />
OK, now you're ready to install the addon r.denoise.<br />
<br />
<h3>
Installing r.denoise itself</h3>
<ol>
</ol>
1. Start QGIS and make sure the GRASS plugin in loaded. If you haven't already discovered it, the GRASS menu is under the "Plugins" menu.<br />
<br />
2. Open a GRASS mapset, so that the GRASS toolbox will be available: Plugins>GRASS>Open mapset, or the corresponding button on the GRASS toolbar. (If you need to create a GRASS mapset first, a set of getting-started-with-GRASS instructions are <a href="http://www.qgis.org/en/docs/user_manual/grass_integration/grass_integration.html">here</a>.)<br />
<br />
3. Open the GRASS Tools: Plugins>GRASS>Open GRASS Tools, or the corresponding button on the GRASS toolbar.<br />
<br />
4. Open a GRASS shell. You can find this at the top of the Modules Tree ("Modules Tree " tab), or search for it ("shell") on the Modules List tab. A GRASS shell opens as a fourth tab in the GRASS window. In this shell window, Ctrl-Shift-C and Ctrl-Shft-V act as Copy and Paste, just as in a regular terminal window.<br />
<br />
5. In the GRASS shell, type:<br />
<blockquote>
<span style="font-family: "Courier New",Courier,monospace;">$ g.extension extension=r.denoise svnurl=http://svn.osgeo.org/grass/grass-addons/grass6/</span></blockquote>
This will launch a process of downloading the source code for the addon via <b>subversion</b>, compiling it, and then installing the executable.<br />
<br />
Unfortunately, if you're like me, you will get this:<br />
<br />
<blockquote class="tr_bq">
<span style="font-family: "Courier New",Courier,monospace;">Fetching <r .denoise=""> from GRASS-Addons SVN (be patient)...<br />A r.denoise/description.html<br />A r.denoise/r.denoise<br />A r.denoise/Makefile<br /> U r.denoise<br />Checked out revision 58345.<br />Compiling <r .denoise="">...<br />mkdir -p /usr/lib/grass64/bin.x86_64-pc-linux-gnu<br />mkdir: cannot create directory `/usr/lib/grass64/bin.x86_64-pc-linux-gnu': Permission denied<br />make: *** [/usr/lib/grass64/bin.x86_64-pc-linux-gnu] Error 1<br />ERROR: Compilation failed, sorry. Please check above error messages.</r></r></span></blockquote>
<br />
In short, GRASS does not have permission to create this directory it wants (/usr/lib/grass64/bin.x86_64-pc-linux-gnu). I tried a number of workarounds. Running GRASS as root does not help. Attempting to 'sudo' this <b>g.extension</b> command does not work. Finally, I simply created the directory myself from within the GRASS shell by typing:<br />
<br />
<blockquote class="tr_bq">
<span style="font-family: "Courier New",Courier,monospace;">$ sudo mkdir /usr/lib/grass64/bin.x86_64-pc-linux-gnu</span></blockquote>
<br />
I know this looks an ugly and desperate act, but it leads to success just down the road, so bear with me.<br />
<br />
<br />
Note that all I had to do was copy the <code>mkdir</code> line from the output above (with Ctrl-Shift-C), paste it in as the next command (Ctrl-Shift-V), hit the Home key to jump to the front of the command line, type 'sudo' and hit Enter.<br />
<br />
Now run the <b>g.extension</b> command again (tap up-arrow until it reappears as you entered it before), and get a similar error for <i>another</i> directory it can't create:<br />
<br />
<blockquote class="tr_bq">
<span style="font-family: "Courier New",Courier,monospace;">Fetching <r .denoise=""> from GRASS-Addons SVN (be patient)...<br />A r.denoise/description.html<br />A r.denoise/r.denoise<br />A r.denoise/Makefile<br /> U r.denoise<br />Checked out revision 58345.<br />Compiling <r .denoise="">...<br />mkdir -p /usr/lib/grass64/dist.x86_64-pc-linux-gnu/include/grass<br />mkdir: cannot create directory `/usr/lib/grass64/dist.x86_64-pc-linux-gnu': Permission denied<br />make: *** [/usr/lib/grass64/dist.x86_64-pc-linux-gnu/include/grass] Error 1<br />ERROR: Compilation failed, sorry. Please check above error messages.</r></r></span></blockquote>
<br />
Repeat the process of creating the new subdir by hand.<br />
<br />
<blockquote class="tr_bq">
<span style="font-family: "Courier New",Courier,monospace;">$ sudo mkdir -p /usr/lib/grass64/dist.x86_64-pc-linux-gnu/include/grass</span><br />
<br /></blockquote>
However, this time change the permissions to world-writeable on this new subdir. <b>g.extension</b> is going to want to create six more sub-directories under it, so this will save you significant time<b></b>:<br />
<blockquote class="tr_bq">
<span style="font-family: "Courier New",Courier,monospace;">$ sudo chmod -R 777 /usr/lib/grass64/dist.x86_64-pc-linux-gnu/</span> </blockquote>
<br />
Running the <b>g.extension</b> command a third time you will now get a long output:<br />
<br />
<blockquote class="tr_bq">
<span style="font-family: "Courier New",Courier,monospace;">Fetching <r .denoise=""> from GRASS-Addons SVN (be patient)...<br />A r.denoise/description.html<br />A r.denoise/r.denoise<br />A r.denoise/Makefile<br /> U r.denoise<br />Checked out revision 58345.<br />Compiling <r .denoise="">...<br />mkdir -p /usr/lib/grass64/dist.x86_64-pc-linux-gnu/lib<br />mkdir -p /usr/lib/grass64/dist.x86_64-pc-linux-gnu/bin<br />mkdir -p /usr/lib/grass64/dist.x86_64-pc-linux-gnu/etc<br />mkdir -p /usr/lib/grass64/dist.x86_64-pc-linux-gnu/driver<br />mkdir -p /usr/lib/grass64/dist.x86_64-pc-linux-gnu/driver/db<br />mkdir -p /usr/lib/grass64/dist.x86_64-pc-linux-gnu/fonts<br />if [ ! -d /usr/lib/grass64/dist.x86_64-pc-linux-gnu/scripts ]; then mkdir -p /usr/lib/grass64/dist.x86_64-pc-linux-gnu/scripts; fi<br />/usr/bin/install -c r.denoise /usr/lib/grass64/dist.x86_64-pc-linux-gnu/scripts/r.denoise<br />make htmlscript scriptstrings<br />[...and a whole lot of other stuff, including errors...]</r></r></span></blockquote>
<br />
This is good news: your script has been created and it's at <b>/usr/lib/grass64/dist.x86_64-pc-linux-gnu/scripts/r.denoise.</b> (Note: we're not going to get the documentation for the module. That's what all the final errors are about. Haven't been able to solve this part yet.)<b><br /></b><br />
<br />
As a final step, it's up to you (using sudo) to move it to <b>/usr/lib/grass64/scripts</b>:<br />
<br />
<blockquote class="tr_bq">
<span style="font-family: "Courier New",Courier,monospace;">$ sudo mv /usr/lib/grass64/dist.x86_64-pc-linux-gnu/scripts/r.denoise /usr/lib/grass64/scripts/</span></blockquote>
<br />
Make sure it's executable, and if it's not you can make it that way with <br />
<br />
<blockquote class="tr_bq">
<span style="font-family: "Courier New",Courier,monospace;">$ sudo chmod +x /usr/lib/grass64/scripts/r.denoise</span></blockquote>
<br />
r.denoise is now accessible to you through the GRASS shell by typing:<br />
<blockquote class="tr_bq">
<span style="font-family: "Courier New",Courier,monospace;">$ r.denoise</span></blockquote>
<br />
It'll open a nice little GUI and let you get started denoising.<br />
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiQD7Q_7lDj5Prz2ZyItoosNREWzDTdu-1X8crp1L6zDp48MaMOeeq3zyhWvszXXhaNqojcOBoM5g5TUFjCzhjRk0lDievu3bbG18BR5UZUtPVNy4020ps6MUTSF_tzpGwpRb9j_YvdvEQ/s1600/r.denoise_gui.jpg.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="287" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiQD7Q_7lDj5Prz2ZyItoosNREWzDTdu-1X8crp1L6zDp48MaMOeeq3zyhWvszXXhaNqojcOBoM5g5TUFjCzhjRk0lDievu3bbG18BR5UZUtPVNy4020ps6MUTSF_tzpGwpRb9j_YvdvEQ/s320/r.denoise_gui.jpg.png" width="320" /></a></div>
<br />
<br />
One final note, probably unnecessary to seasoned GRASS users. When <b>r.denoise</b> asks you for a raster input map, you can pick from the current mapset using the dropdown. It'll insert the name of the map with an @ sign and then the mapset name, something like "mymap@mymapset". But when it asks for "Denoised raster output map," put in a <i>new</i> filename <i>without</i> the "@mymapset".<br />
<br />
Happy denoising! <br />
<br />
<br />
<br />
<br />
<br />Morgan Hitehttp://www.blogger.com/profile/02187274906810012520noreply@blogger.com2tag:blogger.com,1999:blog-4352824282046201576.post-7881784164227160622013-11-22T16:24:00.001-08:002013-11-22T16:24:13.599-08:00Galera DivisionGalera division is a technique used in the late Medieval and early Renaissance periods in southern Europe. It was a technique of the <i>abbaco</i> schools, popular schools of reckoning that developed to serve the needs of merchants and navigators. For more about abbaco schools I would recommend two excellent articles in <i>Loci</i>: <a href="http://www.maa.org/publications/periodicals/convergence/he-advanced-him-200-lambs-of-gold-the-pamiers-manuscript">Randy Schwartz's article on the Pamiers Manuscript</a>, and <a href="http://www.maa.org/publications/periodicals/convergence/solving-the-cubic-with-cardano">William Branson's article on solving a cubic equation the way Girolamo Cardano would have done it in the 1500s</a>.<br />
<br />
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhyZTzG1yiAqcyUIT9OdXUPJgyikMyHnCg-3sJaM6DFLgF2vIyZycoqWyoxHvGs4dxkYYnN6-_qQoMlCisb17nK-NhBcB7FDJ7onShL-GDn3r97Bovb3PR-ai-xYqL85Z-bp_Q3vWppmqA/s1600/galera+division+treviso+example+F.+37.+r.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhyZTzG1yiAqcyUIT9OdXUPJgyikMyHnCg-3sJaM6DFLgF2vIyZycoqWyoxHvGs4dxkYYnN6-_qQoMlCisb17nK-NhBcB7FDJ7onShL-GDn3r97Bovb3PR-ai-xYqL85Z-bp_Q3vWppmqA/s1600/galera+division+treviso+example+F.+37.+r.png" /></a></div>
<br />
For a bit of background, you must understand that the people doing arithmetic at this time (the 1300s and 1400s) were doing so without the equals sign (=), the plus sign (+), the minus sign (-), the multiplication sign (x), the division sign (\(\div\)) or the decimal point (.). These were all yet to be invented! Problems were expressed in <i>words</i>. Numbers that were not whole numbers were always expressed in fractions. (It's somehow comforting to know that they already did use the fraction notation we use today, a numerator and denominator separated by a bar). Money and weights involved complex non-decimal fractions, like 24 grossi to a ducat and 32 pizoli to the grosso (Venetian coinage), or 12 ounces to the pound and 6 sazi to the ounce.<br />
<br />
For example, here's a problem from the <a href="http://en.wikipedia.org/wiki/Treviso_arithmetic"><i>Treviso Arithmetic</i></a>, a how-to manual of arithmetic written in 1478 in Venetian (rather than Latin -- indicating to us that it was intended for a wide audience outside of universities):<br />
<br />
<blockquote class="tr_bq">
<i>Se lire.100.e \(\frac{1}{4}\) de seda valisseno ducati 42 g 2.e\(\frac{1}{5}\) che valerano lire 9816 onze.3.e \(\frac{1}{6}\)</i>[F. 36, v.] </blockquote>
<br />
<blockquote class="tr_bq">
If 100 and \(\frac{1}{4}\) pounds of silk are valued at 42 ducats, 7 and \(\frac{1}{5}\) grossi, what will 9816 pounds, 3 and \(\frac{1}{6}\) ounces be valued at?</blockquote>
<br />
But reckoners had tools to navigate these complicated numbers and get the right results. They were not afraid of big numbers, and indeed they regularly did calculations that would choke a modern hand calculator. Here's the author of the <i>Treviso Arithmetic</i> dividing 12,030 into 14,350,278,384 in the process of showing us how to solve the problem above.<br />
<br />
<table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody>
<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiiy5_TZblmLB4WK7hrOEYIuZd3563OHHRtmgMymgpTPwLI9UrBDTF7YxTRsjjOk7AD7UWbLXme6hLi_-Drsk1aaHbCpfVTl9CyUIKI_9HHo7KjDUoV0gDmcQ72FdGFiTQ-ct698rbVTZ4/s1600/big+galera+division+Treviso+Arithmetic+F+40.png" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" height="179" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiiy5_TZblmLB4WK7hrOEYIuZd3563OHHRtmgMymgpTPwLI9UrBDTF7YxTRsjjOk7AD7UWbLXme6hLi_-Drsk1aaHbCpfVTl9CyUIKI_9HHo7KjDUoV0gDmcQ72FdGFiTQ-ct698rbVTZ4/s320/big+galera+division+Treviso+Arithmetic+F+40.png" width="320" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;"><i>Treviso Arithmetic</i>, 1478, F. 38, r.</td></tr>
</tbody></table>
<br />
<br />
It's called <i>galera</i> division because the mass of cancelled digits that proliferates above and below the dividend and divisor in the completed problem resembles a galley (<i>galera</i>) sailing directly at you: narrowing to the waterline below, narrowing to the top sails above. In the <i>Treviso Arithmetic</i> it is called <i>batello</i> or "boat" division.<br />
<br />
As Frank Swetz points out in his book <a href="http://books.google.ca/books?id=xu_SVhW9DK0C&dq=capitalism+and+arithmetic&source=gbs_navlinks_s"><i>Capitalism and Arithmetic</i></a>, galera division had the advantage, in an age when paper was expensive, of filling a smaller, more compact space on paper than our modern long division technique would. <br />
<br />
<br />
<table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody>
<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhXhekyOKFWdNdnnOyxsFz1MXE47EB1t2p9KY1T5ymTwZr8153-bj4ez0eCv1oH1fCiDpSvUaZ0e7yphwlgiw1-yN0HCCdyp0kB5D2rfTolVg1uerkzA2Ja-shTT2K8stXa3EYffMohK10/s1600/long+galera+compared.png" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" height="161" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhXhekyOKFWdNdnnOyxsFz1MXE47EB1t2p9KY1T5ymTwZr8153-bj4ez0eCv1oH1fCiDpSvUaZ0e7yphwlgiw1-yN0HCCdyp0kB5D2rfTolVg1uerkzA2Ja-shTT2K8stXa3EYffMohK10/s320/long+galera+compared.png" width="320" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">1607 divided by 42: long division (left) and <i>galera</i> division (right)</td></tr>
</tbody></table>
<br />
<div class="separator" style="clear: both; text-align: center;">
</div>
Galera is intriguing because it's a lost technique used by people centuries ago, but it's also worth noting that it involves acts of multiplication and subtraction that are frequently smaller than those you'll do in long division. In long division, one multiplies the new quotient digit by the <i>whole</i> divisor, and then subtracts the result, however big it is, from the relevant part of the dividend. In galera division, as I'll show below, one multiplies the new quotient digit by <i>each digit of the divisor in turn</i>, subtracting these smaller results individually from the relevant piece of the dividend above.<br />
<br />
Galera division can get away with this because its process is one of constantly adjusting the dividend, crossing out digits and replacing them with others. So, to know your way around a galera division problem, notice that at any given time the current dividend can be assembled from the uncrossed-out digits at the tops of the columns of figures. Similarly, the divisor is crossed out and re-written at the bottom of the columns. Learn to find these with your eye, and you'll be looking at the problem the way a galera divider did.<br />
<br />
<table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody>
<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhane0666IO3z0XY1xhY1BONjxYBp-BiBQMiO6D1ZDFxYbA1PyF2nsIQJkBAjoG84ZJVegYcP2OVOU3tFj6u16cfttAlNOCLO8HIO1cUozdCcvAW0Ht7XFTJLabhwBLAMJw9tOchIw6Lgw/s1600/galera+division+reading.png" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhane0666IO3z0XY1xhY1BONjxYBp-BiBQMiO6D1ZDFxYbA1PyF2nsIQJkBAjoG84ZJVegYcP2OVOU3tFj6u16cfttAlNOCLO8HIO1cUozdCcvAW0Ht7XFTJLabhwBLAMJw9tOchIw6Lgw/s1600/galera+division+reading.png" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">At this stage in the problem the dividend is 347. </td></tr>
</tbody></table>
<br />
<br />
So let's get started. We'll divide 42 into 1607.<br />
<br />
<h3>
Setup</h3>
Write the divisor under the dividend, much like a fraction, and place a vertical bar to the right of them. Align them so that the first digits of the divisor go into the first digits of the dividend. <br />
<div class="separator" style="clear: both; text-align: center;">
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Let's say however that the problem was 38 into 699. We would observe that 38 is less than 69 – it can go into it – so it would be lined up like this:<br />
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When the first digits of the dividend and divisor are the same, you have to look at the next digit. So, 18 into 1274 would be aligned like this:<br />
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Now, back to dividing 42 into 1607.<br />
<h3>
Step 1</h3>
Consider how many times the divisor (42) will go into just those digits of the dividend that are immediately above and to the left of it (160). The answer is 3 times, so write a 3 to the right of the vertical line. This is the beginning of the quotient.<br />
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<h3>
Step 2</h3>
Multiply this new quotient digit by the leftmost, that is, most significant, digit in the divisor, and hold that number in your head. (3 times 4 makes 12. Hold 12 in your head.) Strike out the portion of the dividend that is above and to the left of this leftmost divisor digit (16), and over it write the difference between it and the number in your head (12 from 16 leaves 4). Also strike out leftmost digit of the divisor (4), to indicate we've “used” it. <br />
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<br />
(Notice that the dividend has been changed now 407, but not all the digits are on the same line.)<br />
<h3>
Step 3</h3>
Now multiply the new quotient digit by the next most significant digit of the divisor, and hold that number in your head. (3 times 2 makes 6. Hold 6 in your head.) Strike out the portion of the dividend that is above and to the left of this digit of the divisor (40), and over it write the difference between it and the number in your head (6 from 40 leaves 34). Also strike out this digit of the divisor (2), to indicate we've “used” it. (The dividend is now 347, with all three digits on different lines.)<br />
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<h3>
Step 4</h3>
Write in a fresh copy of the divisor, but shifted one column right. (The 4 will go under the original 2, and the 2 will go to the left of the original 2.)<br />
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<br />
Now we're ready to guess the next digit of the quotient, and repeat those four steps again.<br />
<h3>
Step 1</h3>
Consider how many times the divisor (42) will go into just those digits of the dividend that are immediately above and to the left of it (347). The answer is 8 times, so write an 8 to the right of the vertical line. <br />
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<h3>
Step 2</h3>
Multiply this new quotient digit by the leftmost, that is, most significant, digit in the divisor, and hold that number in your head. (8 times 4 makes 32. Hold 32 in your head.) Strike out the portion of the dividend that is above and to the left of this leftmost digit of the divisor (34), and over it write the difference between it and the number in your head (32 from 34 leaves 2). Also strike out leftmost digit of the divisor (4), to indicate we've “used” it. (Notice that the dividend has been changed now to 27, but not all the digits are on the same line.) <br />
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<h3>
Step 3</h3>
Now multiply the new quotient digit by the next most significant digit of the divisor, and hold that number in your head. (8 times 2 makes 16. Hold 16 in your head.) Strike out the portion of the dividend that is above and to the left of this digit of the divisor (27), and over it write the difference between it and the number in your head (16 from 27 makes 11). Also strike out this digit of the divisor (2), to indicate we've “used” it. (The dividend is now 11, with digits on different lines.)<br />
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<u>We can't move the divisor any further right, so we're done</u>. We don't have to write the divisor again. The answer is 38 with a remainder of 11. Done!<br />
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<h2>
10's-complement Subtraction</h2>
In doing that galera division we performed a lot of subtraction. It's easy to assume that people in the 1400s did subtraction as we do today, but they did not! In the <i>Treviso Arithmetic</i>, subtraction did not employ the "borrowing" method we use, but used a technique we can call <i>10's-complement subtraction</i>.<br />
<br />
Today, when faced with subtracting a larger digit from a smaller digit, we "borrow." Let's say we are subtracting 16 from 41. We begin with the one's place, and faced with taking 6 from 1 we "borrow" from the ten's place to make 11, decrement the 4 to a 3, take 6 from 11 to get 5, and then move on.<br />
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<br />
In 10's-complement subtraction you also begin with the one's place, but faced with taking 6 from 1, you pause and note the <i>10's complement </i>of 6, that is, the number you would add to 6 to get 10. It's 4.<br />
<br />
This 4 you <i>add</i> to the number above that you were trying to subtract 6 from. Four plus 1 is 5, so you write a 5 below the line as your answer digit for this column. (Note that this means you <b>don't have to have memorized the subtraction tables for numbers larger than 9</b>!)<br />
<br />
Finally, instead of decrementing the next digit of the minuend (upper number), we <i>add one</i> to the next digit of the subtrahend (the lower number). Same result.<br />
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<br />Morgan Hitehttp://www.blogger.com/profile/02187274906810012520noreply@blogger.com0tag:blogger.com,1999:blog-4352824282046201576.post-62678897856670514822013-09-18T15:53:00.002-07:002013-09-19T07:22:56.371-07:00Quick and Dirty Mapping with Geographic Data<div style="text-align: justify;">
Barely a day goes by without seeing a map on the web. And the more eye-catching maps are usually fairly <i>involved</i> productions. Consider, for example, <a href="http://www.bombsight.org/">Bomb Sight</a>, or the <a href="http://aqueduct.wri.org/atlas">World Water Risk Atlas</a>. These maps can be quite beautiful, and offer all sorts of capabilities to explore data. But they aren't the kind of mapping I want to talk about here.<br />
<br />
I'm interested in a much lower-end question: what can a person do to <i>quickly</i> post his or her geographic data onto a map? Let's say I have a
couple of KML files (or GPX, or shapefiles... we'll get to discussing <b>formats</b> in a bit): if I just need to visualize them, what's my best place to go? Let's say that I'm not making a presentation and I don't need to be able to share the data, or let others edit it. Nor do I need visitors to be able to draw on the map.<br />
<br />
For the moment I'll also assume that I don't even want to be able to customize how the data looks, or be able to direct others to this quick and dirty map. I'll cover that in a later post.<br />
<br />
The user should not have to know anything about the world of GIS. He or she should not have to re-project the data, or convert formats. There shouldn't be a need to understand map projections. There is a broad range of people who receive data -- maybe it's downloaded from the web, handed over by a collaborator, sent by a friend or produced by the company -- and they just want to see it.</div>
<div style="text-align: justify;">
<br /></div>
<h3>
GPSVisualizer</h3>
<a href="http://www.gpsvisualizer.com/">GPSVisualizer</a> is probably your best single bet for a quick and dirty map, whether your geographic data is <b>KML, KMZ, CSV</b> or <b>XLS</b>.<br />
<br />
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<br />
<div style="text-align: justify;">
On the home page, where it
says "Get started now," browse for your data file and click "Go!"<br />
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You'll get a small inset map of your data over a Google maps background. If your data included lines, these are summarized in the box in the upper right side of the map.<br />
<br />
There are several nice features available to you now:<br />
<ul>
<li>With one click you can go to a full page view of your map. (Click on "view" in the fine print at the top where it says your map is "also <b>temporarily</b> available to view.") </li>
<li>You can click on your points or lines and see the data embedded within them.</li>
<li>You can change the background of your map, with over 20 backgrounds to choose from. These include Yahoo maps, OpenStreet map, and topographic maps for the US and Canada</li>
<li>You can copy that address for the full-page view of your map and send it to others to visit -- at least for a few hours. (GPSVisualizer says the map is there "temporarily". It's probably good for the rest of the day unless use of the site is heavy.) </li>
</ul>
If you go back a page, back to that "Get started now" box, you can re-generate the map and, instead of getting a Google maps mash-up, receive:<br />
<ul>
<li>a Google Earth (KMZ) version of your data</li>
<li>a JPEG image</li>
<li>a PNG image</li>
<li>an SVG image</li>
<li>an elevation profile</li>
<li>a GPX version of your data</li>
<li>a plain-text</li>
</ul>
Nice. Simple. Effective.<br />
<br />
<ul>
</ul>
<h3>
Hillmap</h3>
If the data you have is in the <b>GPX</b> format, GPSVisualizer will
still work just fine. (GPX is a format that usually comes out of GPS
devices, or software people use to manage their GPSs.) However if you
have GPX data, in many ways <a href="http://www.hillmap.com/">Hillmap</a> is a more delightful site, and even easier to use.<br />
<br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgrVOu7CjvxIu9K_xx3209mBZnUmCnybXyCA8lQqWfjcjqB7ID-5_KfyN0B-jaAerljVKCH3sSBLPsRRGfSAvvg3hsFiAP7N9zRSLxvCRJ2E6_FySABoVbCq9ymbCGyyoB-cm_PSC_m-6I/s1600/hillmap_home.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="136" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgrVOu7CjvxIu9K_xx3209mBZnUmCnybXyCA8lQqWfjcjqB7ID-5_KfyN0B-jaAerljVKCH3sSBLPsRRGfSAvvg3hsFiAP7N9zRSLxvCRJ2E6_FySABoVbCq9ymbCGyyoB-cm_PSC_m-6I/s320/hillmap_home.jpg" width="320" /></a></div>
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With Hillmap, you can drag and drop that GPX file right onto either of their double maps. It will upload the file and move the map to view your data. By default the maps a show "map" and "satellite" views, but there are 14 different backgrounds to choose from.<br />
Now you can:<br />
<ul>
<li>Switch to the <i>Input and Output</i> tab, and use the <i>Link To</i> button to get a link to this map, or an iframe tag to paste into a blog post (example below). (Note: set you preferred background <i>before</i> you get the link or iframe code.)</li>
<li>Also on the <i>Input and Output</i> tab, you can <b>print</b> your map. </li>
</ul>
Hillmap is very clever: they've thought about how awkward most things printed out of web browsers look, and they've created an interface where you can get a decent looking map. You choose the dimensions of the printed map you want, and the dpi. It will then tell you what scaling to apply when sending it to the printer, and open a new tab with just the map image on it.</div>
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In Firefox, for example, you go File - Print Preview, set the scale to the given percentage, and hit Print. Very nice results, and, as a real bonus, <b>it has a scale bar on it!</b><br />
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<ul>
</ul>
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<h3>
A short digression on formats</h3>
There are six common formats that geographic data comes in:<br />
<ul>
<li><b>KML</b> This is the original Google Earth data format. (KML stands for "Keyhole Markup Language".) You might have a KML file if you drew some points, lines or areas in Google Earth. Or you might have downloaded a KML file from the web. KML files can contain points, lines and areas.</li>
<li><b>KMZ</b> This is a zipped version of KML.</li>
<li><b>GPX</b> A format for sharing data among GPSs, as discussed above. GPX files can contain points (which they call "waypoints") and lines (which they call "tracks").</li>
<li><b>shapefile</b> This is a format originally created by a company called ESRI, but now used by most GIS software. It's common in academic and scientific circles. Note that <b>a "shapefile" is actually a set of four files.</b> These files all share the same name but have different extensions, like <i>trail.shp, trail.dbx, trail.shx, </i>and<i> trail.prj. </i>When sites ask you to upload a shapefile, they usually want you to zip the four files together into a .ZIP file first. A shapefile can only contain one kind of data: points, lines OR areas.</li>
<li><b>CSV</b> or "Comma Separated Values." This is a plain text file with columns of data separated by, well, commas. Other variants of this format use tabs or semicolons to separate the fields. These files are generated by spreadsheet programs like Excel or OpenOffice Calc, and they can be displayed by those programs. When a CSV file contains geographic data it typically has columns named <i>latitude</i> and <i>longitude</i>. (It's also possible that instead the columns are <i>northing </i>and <i>easting. </i>This means the data is in a UTM projection, which I won't go into that here.) CSV data is usually just the locations of points.</li>
<li><b>XLS</b> Microsoft Excel's spreadsheet format. Like CSV data, it will have latitude and longitude columns, and represent the locations of points.</li>
</ul>
There are also more obscure ones, like GeoRSS, GeoJSON, and GML, but if you have data in one of those formats you're probably beyond the scope of this post already.<br />
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<h3>
CartoDB </h3>
The format we haven't covered yet is <b>shapefile</b>. If you have this kind of data, neither of the two sites above will work, but <a href="http://cartodb.com/">CartoDB</a> will. <br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjVpw5Kfe3Ahe87pGXBRstBp26t4Ts-eVe9TW6FhEPYUoU-Hl_AozecQhuzGHChpPxetqcgj_zc-dR18t_fnUNW9XANV0086YGqpa8HZGv0i3WRbdFidICTUIk2adQDDVYkMonhl4uikW0/s1600/cartoDB_home.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="144" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjVpw5Kfe3Ahe87pGXBRstBp26t4Ts-eVe9TW6FhEPYUoU-Hl_AozecQhuzGHChpPxetqcgj_zc-dR18t_fnUNW9XANV0086YGqpa8HZGv0i3WRbdFidICTUIk2adQDDVYkMonhl4uikW0/s320/cartoDB_home.jpg" width="320" /></a></div>
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Like other sites that can accept shapefiles (such as <a href="http://www.arcgis.com/home/index.html">ArcGIS Online</a> and <a href="http://geocommons.com/">GeoCommons</a>), CartoDB requires you to get a free account and insists that data you upload be publicly discoverable by other users. But it is simpler and more intuitive than those other services. </div>
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Do note the limitations of the free CartoDB account. It will only let you have five uploaded shapefiles (which it calls "tables") at once, 5 MB of data total, and ten thousand views of your map. For our purposes this is not particularly onerous, but note that because a single shapefile can only hold a single kind of geographic data (points, lines <u>or</u> areas), you will be uploading more than one shapefile if, for example, you have both line <b>and</b> points to view. <br />
<br />
Once you have your free account, log in and upload your shapefile by clicking on the large "New Table" button with the plus sign on it. Click <i>select a file</i>, locate your zipped shapefile, and when the progress bar finishes you're looking at a table of data for the geographic objects in your shapefile. Click on <i>Map View</i>. and you see the map. From upload to map is pretty fast.<br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiWlGHTC6d6KY_TCz4bCfMgFRGmTKbLXqCeboOqNgDBbS4sZZZd9dzpnPscTs6OFm1hAvPONqTuTwu9W4Jmn-ylusM4LTJg5PrJbNr9FlCz0sj81qYl1S3tOrWOnjvOB6CMkh3up-3zGo8/s1600/CartoDB_points_inital_map.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="142" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiWlGHTC6d6KY_TCz4bCfMgFRGmTKbLXqCeboOqNgDBbS4sZZZd9dzpnPscTs6OFm1hAvPONqTuTwu9W4Jmn-ylusM4LTJg5PrJbNr9FlCz0sj81qYl1S3tOrWOnjvOB6CMkh3up-3zGo8/s320/CartoDB_points_inital_map.jpg" width="320" /></a></div>
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Notice that you can change among the seven background maps (Nokia Day; Google terrain, roads, satellite, hybrid, grey roadmap, or dark).<br />
<br />
If you click on one of your features you don't see the data yet, but a <i>select fields</i> link is offered, which pulls a set of toggle switches out from the right side of the map. Toggle "on" all the fields you want to see displayed.<br />
<br />
To add a second shapefile to the map, you have to first convert it to a "Visualization." (Use the "Visualize" button in the upper right.) Once you give your visualization a name, the Visualize button becomes a "Publish" button. Right below it is a small "+" button which will allow you to add another shapefile (that you've already uploaded) to the map.<br />
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Next post: websites of choice for quick styling and sharing of maps. </div>
<h3>
</h3>
<pre> </pre>
<h2>
</h2>
Morgan Hitehttp://www.blogger.com/profile/02187274906810012520noreply@blogger.com1tag:blogger.com,1999:blog-4352824282046201576.post-23886182894609719012013-09-14T12:03:00.000-07:002013-09-14T14:06:25.719-07:00A Geometry Puzzle: Alternating Hexagons and Squares In a Ring<div class="separator" style="clear: both; text-align: center;">
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgfDE_QwbgFiHfwhcUKiAH1anxW-A1Hs9GpBPP9_tBi7REePXT9OV7t5tQzCC5GYNRzzBbHTj5-fSrmnFPQAEAPLJVH6CtiZpx2VnyZMwZ-Xfr1Vsa-TuOccMdw1ZS0fZkiZ_eI2-NPVRw/s1600/09.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="186" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgfDE_QwbgFiHfwhcUKiAH1anxW-A1Hs9GpBPP9_tBi7REePXT9OV7t5tQzCC5GYNRzzBbHTj5-fSrmnFPQAEAPLJVH6CtiZpx2VnyZMwZ-Xfr1Vsa-TuOccMdw1ZS0fZkiZ_eI2-NPVRw/s200/09.jpg" width="200" /></a></div>
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<h3>
Background</h3>
This intriguing pattern is an alternating sequence of six hexagons and six squares. Both basic shapes have the same edge length, and they pack perfectly around a centre.<br />
<br />
Furthermore, this fairly complex construction can be done with only a ruler and straightedge. Typically, you start with a circle, within which you construct what will be the dodecagonal centre of the figure above. The alternating hexagons and squares then sit on the sides of this dodecagon.<br />
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Because we will have to create other hexagons along the way, I'll call the hexagons in the final pattern around the outside <i>ring hexagons</i>.<br />
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The construction goes like this. (I will assume you know how to construct a hexagon within a circle, and how to bisect a line segment.)<br />
<table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody>
<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiYnElmg2WbbgB-uE0xIJuiZRFTRX9dG_POzJMmbGK9LsnJ3ZuidkN5YXrYuVZ25ko8wUh0wTbYzPfnVoM9a-di2wT-6kEpjcF7DoC-xs0bn_DtwSwnRUmglIYSesjk0jQhq2t4wjLH_6E/s1600/01.jpg" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" height="200" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiYnElmg2WbbgB-uE0xIJuiZRFTRX9dG_POzJMmbGK9LsnJ3ZuidkN5YXrYuVZ25ko8wUh0wTbYzPfnVoM9a-di2wT-6kEpjcF7DoC-xs0bn_DtwSwnRUmglIYSesjk0jQhq2t4wjLH_6E/s200/01.jpg" width="200" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">1. Draw a circle.</td></tr>
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<table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody>
<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjJYoyIZovLe4RD4RO1GU2nFW0956K8V4oZKWDaY5ZMeGSuN7dKC83sYmwO4t6_LO_mPsEQxqPsXzfDUp_3M7bylJ8oN8THgW1iEJNHhwvrzuZ5XW1JSbUoeARe5BD3TCXYFYIAT6tcqVo/s1600/02.jpg" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" height="200" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjJYoyIZovLe4RD4RO1GU2nFW0956K8V4oZKWDaY5ZMeGSuN7dKC83sYmwO4t6_LO_mPsEQxqPsXzfDUp_3M7bylJ8oN8THgW1iEJNHhwvrzuZ5XW1JSbUoeARe5BD3TCXYFYIAT6tcqVo/s200/02.jpg" width="200" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">2. Construct a hexagon within it.</td></tr>
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<table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody>
<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiP1MlV7-vSZKDbEVJFl4jjAb_W4QHOwJtxxSMqdNo2pTRIfo6s_YCs2On9_Jf-exTRBlKTml9tXWvbjFUADqcCKyTFab68bz3cmVcK-vuEAlD5fSj1LGytFoG8aTgT-0Y3AXydbmWVQ88/s1600/03.jpg" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" height="200" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiP1MlV7-vSZKDbEVJFl4jjAb_W4QHOwJtxxSMqdNo2pTRIfo6s_YCs2On9_Jf-exTRBlKTml9tXWvbjFUADqcCKyTFab68bz3cmVcK-vuEAlD5fSj1LGytFoG8aTgT-0Y3AXydbmWVQ88/s200/03.jpg" width="200" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">3. Bisect one of the sides of the hexagon and draw a ray from the circle's
centre through it. Construct another hexagon beginning with a vertex
that falls where this ray intersects the circle.</td></tr>
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<table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody>
<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEibo2ydJpyrpxUDGKP2FtcSwrrH4GHglmZmLBGU42q2sOwqkxyQPUknHLx1nP5ZIj-isn0-Ahzy4khM1h1pj6wpoF0tmDLY6A4JvHsN9lmL8nMBL0wS77AX9mgZ8cmgZN7eDKL2-2ZK4ME/s1600/04.jpg" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" height="200" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEibo2ydJpyrpxUDGKP2FtcSwrrH4GHglmZmLBGU42q2sOwqkxyQPUknHLx1nP5ZIj-isn0-Ahzy4khM1h1pj6wpoF0tmDLY6A4JvHsN9lmL8nMBL0wS77AX9mgZ8cmgZN7eDKL2-2ZK4ME/s200/04.jpg" width="200" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">4. Connect the successive vertices of the two hexagons to make a dodecagon, a 12-sided regular polygon.</td></tr>
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<table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody>
<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgagzJHRSjJYX9rUaG8vu7gTktg25qdEIyOIrhQYUbqGMy9igdBHaRCe3csSeAo3wv302bbCS999GUwdvuJSGdent4EVlA5hMIo76n4cWemysIZYE8Orvu61OaOdMetoVoCsd3DhT42tQ4/s1600/05.jpg" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" height="320" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgagzJHRSjJYX9rUaG8vu7gTktg25qdEIyOIrhQYUbqGMy9igdBHaRCe3csSeAo3wv302bbCS999GUwdvuJSGdent4EVlA5hMIo76n4cWemysIZYE8Orvu61OaOdMetoVoCsd3DhT42tQ4/s320/05.jpg" width="319" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">5. Using the side length of the dodecagon as radius, draw circles around each vertex of the dodecagon.</td></tr>
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<table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody>
<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiRCYarr3Rc6nx9wga7N6q7j4hJFiMK8Waor-6VRzofQsF-W8ZCBMQTcp8zK9_cihNPIOwphXUjR55LVY4-VU33r4SvJ389l6oWubevDCncbhffS9SMklU0N_9Ch7UspI3HVFzBOgWYr3U/s1600/06.jpg" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" height="319" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiRCYarr3Rc6nx9wga7N6q7j4hJFiMK8Waor-6VRzofQsF-W8ZCBMQTcp8zK9_cihNPIOwphXUjR55LVY4-VU33r4SvJ389l6oWubevDCncbhffS9SMklU0N_9Ch7UspI3HVFzBOgWYr3U/s320/06.jpg" width="320" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">6. Using every other intersection of these circles as a centre, draw six more circles of the same radius.</td></tr>
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<table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody>
<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEikmqNmybLLLghUHML8hAcxKk10EaKdHz6XIxgv4ud5qFOfe3Ms-30Ei8JtVCzcYe0-whSzPoZMPYXZPp_3zf1ZxAVlDAJ86a5oJyy6ShpkD3zQWp60EQMQ-Jgbd_tKT9id3m0UELvrt8M/s1600/07.jpg" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" height="319" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEikmqNmybLLLghUHML8hAcxKk10EaKdHz6XIxgv4ud5qFOfe3Ms-30Ei8JtVCzcYe0-whSzPoZMPYXZPp_3zf1ZxAVlDAJ86a5oJyy6ShpkD3zQWp60EQMQ-Jgbd_tKT9id3m0UELvrt8M/s320/07.jpg" width="320" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">7. Construct hexagons within these last six circles. One side of each will coincide with a side of the dodecagon.</td></tr>
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<table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody>
<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEirU8kYrkZ_ytbLfibsMyBylzc_ZDkEFvEAogSPAgKydCbnlE98U5vTkq2OsCSFM9yfExxowJUladcIomEIk7CZb8NPHI444z-K3HTL-0Yj3reHC7MpZ1UZZ5WcF1AUTgFTUi8QOycHyMg/s1600/08.jpg" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" height="319" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEirU8kYrkZ_ytbLfibsMyBylzc_ZDkEFvEAogSPAgKydCbnlE98U5vTkq2OsCSFM9yfExxowJUladcIomEIk7CZb8NPHI444z-K3HTL-0Yj3reHC7MpZ1UZZ5WcF1AUTgFTUi8QOycHyMg/s320/08.jpg" width="320" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">8. Connect hexagons to form squares.</td></tr>
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<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi_p26VrlPcWmvMn5Z-eqJdmOzkj5sywij3IzHB0w-juuLk5wJddbOZ4zRVbRWq4Kq1s-BcS-dUivcIjTApeP6Wov4tUqXksPyAoEkSOq5S53zl6YC1h7W4IO7DGxk_g1z3VxQRRY7JjMQ/s1600/08a.jpg" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" height="318" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi_p26VrlPcWmvMn5Z-eqJdmOzkj5sywij3IzHB0w-juuLk5wJddbOZ4zRVbRWq4Kq1s-BcS-dUivcIjTApeP6Wov4tUqXksPyAoEkSOq5S53zl6YC1h7W4IO7DGxk_g1z3VxQRRY7JjMQ/s320/08a.jpg" width="320" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">9. The final figure without the construction lines. Rotating it 15°
counterclockwise will make it look like the one at the very top of the
post.</td></tr>
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<h3>
The Puzzle</h3>
OK, now for the puzzle. If we connect the centres of the six hexagons in the ring, we get another, larger hexagon.<br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj6zV0uyWgsjtGmG4LaxnV1L9cqmmMMhkZ85QDs9wo8oTeYlF_TsrRxbahdeoWhrmOKe3AN-6KRRy7mxtYID4ZCzd_jl0d5ZFDkl7ShcNV0O7N75rLM2ISGgfJAVU5N3aiHFSUqlpilXlM/s1600/finished+pattern+with+master+hexagon.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="299" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj6zV0uyWgsjtGmG4LaxnV1L9cqmmMMhkZ85QDs9wo8oTeYlF_TsrRxbahdeoWhrmOKe3AN-6KRRy7mxtYID4ZCzd_jl0d5ZFDkl7ShcNV0O7N75rLM2ISGgfJAVU5N3aiHFSUqlpilXlM/s320/finished+pattern+with+master+hexagon.jpg" width="320" /></a></div>
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This hexagon, which I'll call the <b>master hexagon</b>, can be used as the repeating frame for tiling a larger area with the pattern.<br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiXwFJ4G1htF5J_654xwiGID2Tiakz8PKxYcH8mhIZormTRj7R_y5CF1NcjGi2uRWtXhoi0FopCg5GHSD7omROmNrWAKiKx1-wqcxH2JAbmVvcxMYG6XeA5lPflaj-c3IWF8BFLiAUEM08/s1600/tiled+pattern.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="202" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiXwFJ4G1htF5J_654xwiGID2Tiakz8PKxYcH8mhIZormTRj7R_y5CF1NcjGi2uRWtXhoi0FopCg5GHSD7omROmNrWAKiKx1-wqcxH2JAbmVvcxMYG6XeA5lPflaj-c3IWF8BFLiAUEM08/s320/tiled+pattern.jpg" width="320" /></a></div>
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<br />
But if you were to do this, you would draw the pattern of master hexagons first, and would then construct the ring pattern based on it.<br />
<br />
So here's the puzzle: <b>how do you construct the ring pattern of hexagons and squares, given only the master hexagon?</b><br />
<br />
<h3>
Solution</h3>
The basic problem is to locate the dodecagon that forms the inside of the ring. Once we have that, we can construct the ring, as above. But how do we get from the master hexagon to the dodecagon? <br />
<table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody>
<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh-1AOJK0OfxjCjN9ZVkHKZjDQI-b9sb8bCnovT_2kIOX8Vk8IO9WzOChc8jcPKvgcW_ZZA7u7sZ4NGtGqCJ9RTN21I9oBgzhqX_shmWHJEZbLl5CzZSGDJW_0J5_BivbpR9oo-MXnjrqQ/s1600/01.jpg" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" height="200" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh-1AOJK0OfxjCjN9ZVkHKZjDQI-b9sb8bCnovT_2kIOX8Vk8IO9WzOChc8jcPKvgcW_ZZA7u7sZ4NGtGqCJ9RTN21I9oBgzhqX_shmWHJEZbLl5CzZSGDJW_0J5_BivbpR9oo-MXnjrqQ/s200/01.jpg" width="200" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">10. Begin with the master hexagon.</td></tr>
</tbody></table>
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<table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody>
<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgXgdMccA13Vc-8SxH4Uc4Gs6uFxNr6WXEA67has2v9UwIMS2gUq7je2FzADkFoDvxVh9vbbaHTxQvYXkC26RLrfSjHE6F-Efq7clkzwtQSt9oJFuIFK4sleLC0jf4Nr3batfTV4qMdQ-Y/s1600/02.jpg" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" height="200" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgXgdMccA13Vc-8SxH4Uc4Gs6uFxNr6WXEA67has2v9UwIMS2gUq7je2FzADkFoDvxVh9vbbaHTxQvYXkC26RLrfSjHE6F-Efq7clkzwtQSt9oJFuIFK4sleLC0jf4Nr3batfTV4qMdQ-Y/s200/02.jpg" width="200" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">11. Locate its centre by connecting vertices, and construct the circumscribing circle.</td></tr>
</tbody></table>
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<table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody>
<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgOzxvlbp9IsmeAFxmRyDaxgbpi1u_lpcGYlIyv5EYsAoVDiqBGkkwhyphenhyphenNPX_uXyhrRshcIEBEl1rruq1FTR0QhbPn02V-mIomzEfgM6xbrLHwZvdqyQy0MD1gFQkjGMXHnyL3tE5DMk-N4/s1600/03.jpg" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" height="200" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgOzxvlbp9IsmeAFxmRyDaxgbpi1u_lpcGYlIyv5EYsAoVDiqBGkkwhyphenhyphenNPX_uXyhrRshcIEBEl1rruq1FTR0QhbPn02V-mIomzEfgM6xbrLHwZvdqyQy0MD1gFQkjGMXHnyL3tE5DMk-N4/s200/03.jpg" width="200" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">12. Bisect one side of the hexagon, and construct a second hexagon, much
as you did in step 3 above, starting from the point where this bisector
meets the circle.</td></tr>
</tbody></table>
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<table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody>
<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhggG-t2xnlF31moSpatRS-Gl5i5XtRSe__afKLZcLRJ0LII2DyiIbftxAsUo2ivT1DObf2k2SIDubo6C_Pb5qNW_Av6gOekEXsyXo7NpxjL9PdQC36A8QPuWHJ8bg25hQ3z_rrQw_UmvE/s1600/04.jpg" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" height="200" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhggG-t2xnlF31moSpatRS-Gl5i5XtRSe__afKLZcLRJ0LII2DyiIbftxAsUo2ivT1DObf2k2SIDubo6C_Pb5qNW_Av6gOekEXsyXo7NpxjL9PdQC36A8QPuWHJ8bg25hQ3z_rrQw_UmvE/s200/04.jpg" width="200" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">13. Connect vertices of one hexagon to make a six pointed star.</td></tr>
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<table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody>
<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjhk5LA58-Mg85szc-Gvriq-cUONr8n8Cz1sE969JmKgfRZqxvpekiv4XV-37gwgxN64Nk74f0_yVxPZvdAs2gDvv0ZmpV6oc0hYZ1_OpejP4T7FPqQIDUY0t8ihpJ6hJjLb_ygav2ugjQ/s1600/05.jpg" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" height="200" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjhk5LA58-Mg85szc-Gvriq-cUONr8n8Cz1sE969JmKgfRZqxvpekiv4XV-37gwgxN64Nk74f0_yVxPZvdAs2gDvv0ZmpV6oc0hYZ1_OpejP4T7FPqQIDUY0t8ihpJ6hJjLb_ygav2ugjQ/s200/05.jpg" width="200" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">14. Connect the vertices of the other hexagon in a similar fashion.</td></tr>
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<table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody>
<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEinrHSrvgW9lZDb6W8kFtTwnNcsw4i4x_fhxRZzcq8gY0cIxqHoLC5YhCEFLb-ILZz-DYb6WM87bcKd9xXhgsJv1sy7V9ALxNe09M6NTJQXS2BRcY9cI3jLZn4aDQKS15Kap6JGrF2hHJQ/s1600/06.jpg" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" height="320" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEinrHSrvgW9lZDb6W8kFtTwnNcsw4i4x_fhxRZzcq8gY0cIxqHoLC5YhCEFLb-ILZz-DYb6WM87bcKd9xXhgsJv1sy7V9ALxNe09M6NTJQXS2BRcY9cI3jLZn4aDQKS15Kap6JGrF2hHJQ/s320/06.jpg" width="320" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">15. Connect the intersections of those two six-pointed stars, to make a
dodecagon. This is the dodecagon that will form the inside of the ring.</td></tr>
</tbody></table>
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<table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody>
<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgw0ET45l71JuiTcxDmwa9Na7yngJGnVp8B_2TdlF-tjfZ6hwYciB2VgpE6BHXiz89mPKwOPYo1d21MTqlYSLifwCZFNWLs3hsb97yiU3yFTmWrgtfIzWJwNFaiNGRgkQmfPhTaB-DjYkE/s1600/07.jpg" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" height="299" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgw0ET45l71JuiTcxDmwa9Na7yngJGnVp8B_2TdlF-tjfZ6hwYciB2VgpE6BHXiz89mPKwOPYo1d21MTqlYSLifwCZFNWLs3hsb97yiU3yFTmWrgtfIzWJwNFaiNGRgkQmfPhTaB-DjYkE/s320/07.jpg" width="320" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">16. Using steps 5, 6 and 7 above, construct ring hexagons from the sides of the dodecagon.</td></tr>
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<table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody>
<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgYjgFoLtkpwkYX30X5JvTt_Idaj3iI74lbwWJ0EjcMAzh0fp-q7LeEd0b-A2UkGSu_PiIoDL0aPJjH9EW0wQtc3k80XrC7hfhjwEZAMpx3R2TRrf8C33Fuqn7EDxGZ0YEca3jYjPvhHOo/s1600/08.jpg" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" height="299" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgYjgFoLtkpwkYX30X5JvTt_Idaj3iI74lbwWJ0EjcMAzh0fp-q7LeEd0b-A2UkGSu_PiIoDL0aPJjH9EW0wQtc3k80XrC7hfhjwEZAMpx3R2TRrf8C33Fuqn7EDxGZ0YEca3jYjPvhHOo/s320/08.jpg" width="320" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">17. And, as in step 8 above, connect the ring hexagons to form squares.</td></tr>
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It's interesting to compare the construction lines one uses when beginning with a circle to those drawn when beginning with the master hexagon.<br />
<table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody>
<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjTf7UyTDvRkGdcDGq5kVPQLT6etBkcFmirm1IySwNq0Ts5u-0KkSq6g3zPeiMm8HfCBHBym5v_7zj7q8A1CSZFEBnzh70zE1tW1nQ66mwUiww5Ku3EUrKxg6GL3RuCqweKPfMz0BBE8-k/s1600/forward_and_reverse_lines.jpg" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" height="183" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjTf7UyTDvRkGdcDGq5kVPQLT6etBkcFmirm1IySwNq0Ts5u-0KkSq6g3zPeiMm8HfCBHBym5v_7zj7q8A1CSZFEBnzh70zE1tW1nQ66mwUiww5Ku3EUrKxg6GL3RuCqweKPfMz0BBE8-k/s400/forward_and_reverse_lines.jpg" width="400" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">18. "Forward" construction lines (that is, those beginning from the
circle that circumscribes the dodecagon) are black. "Reverse"
construction lines (beginning with the master hexagon) are blue.</td></tr>
</tbody></table>
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<h3>
Commentary</h3>
Why does using this method to construct the dodecagon within the master hexagon work?<br />
<br />
Well, we know the master hexagon has a concentric dodecagon within it somewhere. But which dodecagon? <br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhSGrrhEm58RD9nAdazVqxRuapa0OtHPBuyORbAigmmt1wSc2aHePCleEaarInkG_gr1rL2_eFUWDWnapeptVJTfk3eGd3k-CQyjhlfo7O12Z1y5Xr3am9IcTl-JxUuFBCfPoLfqPFKR_E/s1600/01.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="277" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhSGrrhEm58RD9nAdazVqxRuapa0OtHPBuyORbAigmmt1wSc2aHePCleEaarInkG_gr1rL2_eFUWDWnapeptVJTfk3eGd3k-CQyjhlfo7O12Z1y5Xr3am9IcTl-JxUuFBCfPoLfqPFKR_E/s320/01.jpg" width="320" /></a></div>
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<br />
Because each dodecagon has a different edge length, each implies a
different size of hexagons arrayed around it. We want the dodecagon
where the hexagon's centre will fall at a vertex of the master hexagon
(the red one, below, in this case).<br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgeSgSR99C4pRFq424PPVbO2uv0ukPqOw95WA0VMR9SiwwZvpXSPsBX01HVBvRmfrKcE4vKVUYlK1nnP6_TXB3woi5bHxzYzZxHMASz4QKRVZmTXtqShx1tQTCr3HhOhrGR37H8wnPuyIA/s1600/02.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="219" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgeSgSR99C4pRFq424PPVbO2uv0ukPqOw95WA0VMR9SiwwZvpXSPsBX01HVBvRmfrKcE4vKVUYlK1nnP6_TXB3woi5bHxzYzZxHMASz4QKRVZmTXtqShx1tQTCr3HhOhrGR37H8wnPuyIA/s320/02.jpg" width="320" /></a></div>
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<br />
The "right" dodecagon will have vertices that are 60° apart when viewed from a vertex of the master hexagon. Necessarily then, these dodecagon vertices will fall somewhere on the sides of equilateral triangles drawn within the master hexagon.
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhdZpYMjNrLHMpNy4WwGDSmfzlYgUXggvKym31S4BVX3mlD88A6u7yHlMSLJOaB1_HT__P7thTxYCmSilRV5ai3RwLNj4okwz3jOe_rEVLztMi8Rax5FVt_dG5Y7wrVB6Ttd8mAxIeUj0g/s1600/03.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="233" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhdZpYMjNrLHMpNy4WwGDSmfzlYgUXggvKym31S4BVX3mlD88A6u7yHlMSLJOaB1_HT__P7thTxYCmSilRV5ai3RwLNj4okwz3jOe_rEVLztMi8Rax5FVt_dG5Y7wrVB6Ttd8mAxIeUj0g/s320/03.jpg" width="320" /></a></div>
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Drawing the other equilateral triangle within this hexagon gives us a
general idea of where these dodecagon vertices will fall, but nothing
precise. As well, this pattern so far only has 6-fold rotational symmetry.
<br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgyIwRq7QzRFrkeEBmAGz-yIGLTmq5cIZLJkHwQTNjKKYDZZ26Zmg1Q2n3oREgZEpuPrnuHwp1ohsXXJxm-ROdqHhRMPzbCV576h_R3SzwuYR4NA1UWVxSBMHKIDwwNjepCUqt5gHdW_QA/s1600/04.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="277" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgyIwRq7QzRFrkeEBmAGz-yIGLTmq5cIZLJkHwQTNjKKYDZZ26Zmg1Q2n3oREgZEpuPrnuHwp1ohsXXJxm-ROdqHhRMPzbCV576h_R3SzwuYR4NA1UWVxSBMHKIDwwNjepCUqt5gHdW_QA/s320/04.jpg" width="320" /></a></div>
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If we add <i>another</i> master hexagon, rotated 15°, and its inner triangles, we get a pattern with the necessary 12-fold rotational symmetry.<br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgLMxCkyehyphenhyphenu6SCXPcIt0fJT4WfM9r0vhj3_6bG8QYu7_ud7zUzhK4-zlm0K23ze5lrlX_GY1pRzbn0nCHGVz0WKOE3gu56TvpNKj6yfkRWgni1UDXs2RR55-_QELHiK-VTOiNZ26zSjZU/s1600/05.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="320" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgLMxCkyehyphenhyphenu6SCXPcIt0fJT4WfM9r0vhj3_6bG8QYu7_ud7zUzhK4-zlm0K23ze5lrlX_GY1pRzbn0nCHGVz0WKOE3gu56TvpNKj6yfkRWgni1UDXs2RR55-_QELHiK-VTOiNZ26zSjZU/s320/05.jpg" width="319" /></a></div>
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<br />
The set of four equilateral triangles has 3 sets of common
intersections, all of which will make dodecagons (red, orange and
yellow, below). But only the outermost set (red) creates dodecagon
sides that subtend a 60° angle when viewed from the vertices of the
master hexagon.<br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh2soou-NDkOPxliZL_jSzi0gnl3l_2MPWUqIhtHgTCRNW_ZsF-T8mxGJNaB2aIYbaEio96j8j-3RKXSvQ-6k7Iib3VkJgAO_MVg4HVWgZxxEyJcnFKHCahpbPKdi0LiUc3xutrMe_iZ2g/s1600/06.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="320" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh2soou-NDkOPxliZL_jSzi0gnl3l_2MPWUqIhtHgTCRNW_ZsF-T8mxGJNaB2aIYbaEio96j8j-3RKXSvQ-6k7Iib3VkJgAO_MVg4HVWgZxxEyJcnFKHCahpbPKdi0LiUc3xutrMe_iZ2g/s320/06.jpg" width="319" /></a></div>
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Morgan Hitehttp://www.blogger.com/profile/02187274906810012520noreply@blogger.com0tag:blogger.com,1999:blog-4352824282046201576.post-32052179307554243112013-08-26T10:56:00.001-07:002013-08-26T10:56:32.905-07:00A Dado from the Alhambra's Hall of Justice, via Owen Jones and Eric Broug<div class="separator" style="clear: both; text-align: center;">
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh3HRCLevVtTnl_QA1ztzZLrvwnncoKJlVnCekJIrootawjB5NKiIBEhy5qpfnFh1KKfGc_kcqRKfGq9U1pRGRWjxqJobwbS22hgtO-CY7OTuLiE7KjCTn7S33BpXDcdJfY9dpwqSldEMc/s1600/finished+pattern+on+shed1.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="161" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh3HRCLevVtTnl_QA1ztzZLrvwnncoKJlVnCekJIrootawjB5NKiIBEhy5qpfnFh1KKfGc_kcqRKfGq9U1pRGRWjxqJobwbS22hgtO-CY7OTuLiE7KjCTn7S33BpXDcdJfY9dpwqSldEMc/s640/finished+pattern+on+shed1.jpg" width="640" /></a></div>
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<div style="text-align: justify;">
This art project, on the doors of my garden shed, began with a pattern in Owen Jones' 1856 <i>Grammar of Ornament.</i></div>
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<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEibXG-7cGgHYOgaX0VmxdPEp2XFR_ovQT8wQcGp-lyXvOGHGppFLcZAyZoMMhPHUaokjemAozRGEAKEP8i5SQ29PcJ7-tWlIj6AVnOFhhCqevxVHSbe-bqRoBAnJqdI118PNRCF5aK6PE8/s1600/XLIII+number+11.jpg" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEibXG-7cGgHYOgaX0VmxdPEp2XFR_ovQT8wQcGp-lyXvOGHGppFLcZAyZoMMhPHUaokjemAozRGEAKEP8i5SQ29PcJ7-tWlIj6AVnOFhhCqevxVHSbe-bqRoBAnJqdI118PNRCF5aK6PE8/s1600/XLIII+number+11.jpg" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">Jones' Plate XLIII, No. 11, as shown in the <a href="http://digicoll.library.wisc.edu/cgi-bin/DLDecArts/DLDecArts-idx?type=header&id=DLDecArts.GramOrnJones&isize=M&pview=hide">online version</a> of the <i>Grammar Of Ornament</i> (rotated 90°)<i><br /></i></td></tr>
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<div style="text-align: justify;">
Jones notes that this pattern is a <i>dado</i>
from the Hall of Justice in the Alhambra, Granada, Spain. I had to look this up: a dado is the lower half of a wall, below a dividing rib called the dado rail. This is a horizontal feature sticking out of the
middle of a wall, something your grandmother might have called the "chair rail."</div>
<div style="text-align: justify;">
<br /></div>
<div style="text-align: justify;">
My project was to paint this pattern on a wall. I wasn't going to paint it on as a dado, however: I would cover the whole the wall of my garden shed with it, using the rotated version shown above.</div>
<div style="text-align: justify;">
<br /></div>
<div style="text-align: justify;">
Although we have wonderful computer software now that allows us to make fabulous patterns and to experiment with colouring them in different ways, and we have copiers and scanners to facilitate this, and indeed we have a cheap and bountiful supply of paper, markers, rulers and compasses, none of this equipment allows us to get a design anywhere other than on <i>paper</i>. What are the challenges involved with getting it onto a <i>wall</i>?</div>
<br />
<h3>
Construction method</h3>
<h3>
</h3>
<div style="text-align: justify;">
If you look at this dado pattern, you will see that it is centred on 12-pointed stars, around which radiate 12 pairs of parallel lines. I had Eric Broug's book <a href="http://books.google.ca/books/about/Islamic_Geometric_Patterns.html?id=Gc0QJQAACAAJ" target="_blank"><i>Islamic Geometric Patterns</i></a>, so I looked through it to see if he reproduced
something like this. As luck would have it, I found the same pattern, without the colouring.</div>
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<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhAYrC_033KjccOsXg9zUphaTcRu05samrFMhubZPYWFe7y99TztKhQkWQCEuP7QUlaOYAXqWZJFGuiiMon5ZTza6cXrRZSFKO4RqAlc0uBrVKYsdireovF7iLFBu-GoUS6O8l9i4odGzI/s1600/Broug+Mosque+al-Nasir+Mohammed+pattern+small.jpeg" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" height="315" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhAYrC_033KjccOsXg9zUphaTcRu05samrFMhubZPYWFe7y99TztKhQkWQCEuP7QUlaOYAXqWZJFGuiiMon5ZTza6cXrRZSFKO4RqAlc0uBrVKYsdireovF7iLFBu-GoUS6O8l9i4odGzI/s320/Broug+Mosque+al-Nasir+Mohammed+pattern+small.jpeg" width="320" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">The same pattern in Broug, Notice the hexagonal symmetry.</td></tr>
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<div style="text-align: justify;">
Broug
gives an elegant method of construction for this pattern
using only a compass and straightedge. In essence, one constructs hexagons within a circle, and then connects
various intersection points. Once the host of <i>construction lines</i> are drawn, a few segments (only a few!) are selected to make the
pattern.</div>
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<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhVMWKwhzWbwyYYwxHDs7ROxesTWZBNiDZWegfV6zpZrEpT4_VgyT-ia415byrRjesXou7szUI_O81BVfxzpLI0hZJhMSqcz7X8Q-xxgRNkMN-V-andlPjQa6VwMnjjNR4qdud2ahOqF9M/s1600/Broug+Mosque+al-Nasir+Mohammed+pattern+final.jpeg" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" height="315" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhVMWKwhzWbwyYYwxHDs7ROxesTWZBNiDZWegfV6zpZrEpT4_VgyT-ia415byrRjesXou7szUI_O81BVfxzpLI0hZJhMSqcz7X8Q-xxgRNkMN-V-andlPjQa6VwMnjjNR4qdud2ahOqF9M/s320/Broug+Mosque+al-Nasir+Mohammed+pattern+final.jpeg" width="320" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">Illustration from Broug showing the construction lines (faint) and the pattern (red). The heavier black line indicates the bounds of the basic hexagonal unit</td></tr>
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<br />
<h3>
Paper Test</h3>
<div style="text-align: justify;">
Doing these things on paper is relatively easy. Following Broug's
instructions, I made the construction lines and then inked in the
pattern on a small sheet of paper. The radius of the master circle was
8.5cm.</div>
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<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgBH-9pm9xwGbtf3Pt8B0HIMkW57zJcVRC2Bu6PSiqbVkJz-FiTBXGXFzy-YvTRAJGU4JeaDoxa-oKhd6NR9Pvx3fNu6JNG16XCxLxYwCzJcvzixQr5UDDsdvQJeZZ-p94ubjHhS1px7A0/s1600/small+proof+small.jpeg" style="margin-left: auto; margin-right: auto;"><img border="0" height="271" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgBH-9pm9xwGbtf3Pt8B0HIMkW57zJcVRC2Bu6PSiqbVkJz-FiTBXGXFzy-YvTRAJGU4JeaDoxa-oKhd6NR9Pvx3fNu6JNG16XCxLxYwCzJcvzixQr5UDDsdvQJeZZ-p94ubjHhS1px7A0/s320/small+proof+small.jpeg" width="320" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">Broug's design
realized on paper with compass and straightedge. Construction lines are
in pencil, with inked-in segments showing the actual pattern.</td></tr>
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<div style="text-align: justify;">
By
tracing, I transferred this hexagonal cell to another sheet, and then traced in a couple of other copies at the edges. I
experimented with colouring it. </div>
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<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh_SwuwSOw2fV3rk-zLB5x0dFRIv1xuciu4qH64_thBzq9VXbjm5XpndNbk5eR8TIugyvfhL1RCe7_7356jPDVylyoZCTu86UmvVa2TT4EZwk1RYJMjsRAUdSwXfAcclYGCQgOiaESdago/s1600/small+colour+proof.png" style="margin-left: auto; margin-right: auto;"><img border="0" height="311" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh_SwuwSOw2fV3rk-zLB5x0dFRIv1xuciu4qH64_thBzq9VXbjm5XpndNbk5eR8TIugyvfhL1RCe7_7356jPDVylyoZCTu86UmvVa2TT4EZwk1RYJMjsRAUdSwXfAcclYGCQgOiaESdago/s320/small+colour+proof.png" width="320" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">Repeated pattern traced onto other paper and coloured with felt tip pen.</td></tr>
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<br />
<div style="text-align: justify;">
One
of the advantages of doing this small-scale proof before going to the wall is that you become
familiar with the various shapes that made up the pattern. There are the
blue <b>stars </b>(A), and connecting them are blue or grey <b>darts</b> (B), pointed shapes with convex backs. Between the lines of darts we have <b>petals</b>
(C), pointed shapes with concave backs,
coloured in trios of orange or green. All other space, including the <b>hexagons</b> (D), the <b>rays</b> (E), and the <b>winged darts</b> (F), is yellow.</div>
<div style="text-align: justify;">
<br /></div>
<div style="text-align: justify;">
The basic repeating unit in both Jones' pattern and Broug's pattern is the hexagonal cell. However, in Jones' pattern the hexagons are packed in horizontal rows, whereas in Broug's they are packing in vertical rows.</div>
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<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg9BwgeAquTQxL5bu-tGy_GIfA7AusDhECyYPxlEHfo9p1WW3xAfW5FabF2LLMq2xSdoHJLnUCywocZPXN0RxFc-NOADmrXdH5C4v2HEdTwepVvgi07p7kfHd3JbrxcH0j5DXwliU2ksYg/s1600/comparing+the+hex+packing+in+Brough+and+Jones.jpg" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" height="111" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg9BwgeAquTQxL5bu-tGy_GIfA7AusDhECyYPxlEHfo9p1WW3xAfW5FabF2LLMq2xSdoHJLnUCywocZPXN0RxFc-NOADmrXdH5C4v2HEdTwepVvgi07p7kfHd3JbrxcH0j5DXwliU2ksYg/s320/comparing+the+hex+packing+in+Brough+and+Jones.jpg" width="320" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">Repetition in Jones' version uses vertical packing (black hexagons), whereas Broug's version uses horizontal packing (red hexagons).</td></tr>
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<div style="text-align: justify;">
So, to build Jones' pattern using Broug's construction method I'd have to rotate it 30°.</div>
<br />
<h3>
Paper master</h3>
<div style="text-align: justify;">
My basic strategy here was to work on the wall using a stencil. The stencil would be made from a paper version that I would draw by hand.</div>
<div style="text-align: justify;">
<br /></div>
<div style="text-align: justify;">
In this full-size pattern, the master circle was 40 cm in radius. The hexagon within it was 35 cm from
centre to mid-side, a measurement that would become important later.</div>
<div style="text-align: justify;">
<br /></div>
<div style="text-align: justify;">
I drew in horizontal and vertical axis lines to remind me how this master hexagon would need to be placed on the wall to create the vertical packing in Jones' pattern. </div>
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<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjFkXPRL-x9jA5d4ELPgLQw6o23xrw0R6z3u9UzlU21bZI_Rrq-ZOZ2x7e0KZJvyXIZeg77CYIyStcKK-zIemwa0TOrsrs_CnbgffVcNHRfcEcnzRF78xoYqFj1N_SIQ5mNi4F1ifPGlRQ/s1600/DSC02449.JPG" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" height="276" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjFkXPRL-x9jA5d4ELPgLQw6o23xrw0R6z3u9UzlU21bZI_Rrq-ZOZ2x7e0KZJvyXIZeg77CYIyStcKK-zIemwa0TOrsrs_CnbgffVcNHRfcEcnzRF78xoYqFj1N_SIQ5mNi4F1ifPGlRQ/s320/DSC02449.JPG" width="320" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">Large pattern on paper: vertical axis in green, horizontal axis in blue.</td></tr>
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</div>
<h3>
</h3>
<h3>
To channel or not to channel</h3>
Before making a stencil, I had to make a decision about
the white channels.<br />
<br />
Are they there between the blocks of colour in Jones's reproduction? They are definitely there, although whoever drew the illustration for the <i>Grammar of Ornament</i> wasn't
consistent about the width of these channels. Broug
suggests that in Islamic design you generally <i>do</i> want channels separating polygons (as opposed to polygons touching one another), and that you strive to have
channels of consistent width.<br />
<br />
I chose a channel width of 16 mm, or 8 mm on either side of each pattern line. The 8 mm was not chosen because of an eye for design, or as the result of a mathematical calculation: it was simply that I had a clear plastic ruler with a second line 8 mm from the edge. <br />
<br />
<h3>
Stencil</h3>
I
transferred the vertices of the pattern lines from paper to foam core using a
pin; then I drew between pin holes to reproduce the pattern on the foam core. I marked channels out around the centrelines with the clear
plastic ruler, and then cut out the stencil.<br />
<br />
This stencil covered only part of the design, one quarter of the figure. Although in many ways it
would be ideal to cut a stencil of the entire hexagonal cell, it would have taken a long time and required a bigger piece of foam core than I
had. Practical considerations!<br />
<br />
By clipping the channels at the outer hexagon and the horizontal and vertical axes running through the figure, I made a stencil that could abut itself and repeat in all directions. It included three full rays, a dart, a petal and three points of the central star. The hexagon and the winged dart were there as partial edge figures. I could flip it over and work with either side, and four repeats should cover an entire figure.<br />
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<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjq_4doYMnRE80b3ABrxQcqD9oBupppv6qV4HCXUZ5Hy4ipKb0pZ_2lH9X8qjUchvDKPBYECBIJLsonlcYL4uXXav9g1NQE0tS9payfrh0kOix7f-OvFZxPI9Nh7TWzxc8cu36baLukj_o/s1600/stencil+against+original+drawing.jpg" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" height="185" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjq_4doYMnRE80b3ABrxQcqD9oBupppv6qV4HCXUZ5Hy4ipKb0pZ_2lH9X8qjUchvDKPBYECBIJLsonlcYL4uXXav9g1NQE0tS9payfrh0kOix7f-OvFZxPI9Nh7TWzxc8cu36baLukj_o/s320/stencil+against+original+drawing.jpg" width="320" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">The one-quarter pattern stencil. Yellow lines indicate where stencil was trimmed to both the outer hexagon and the quartering lines.</td></tr>
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<div class="separator" style="clear: both; text-align: center;">
</div>
<div style="text-align: justify;">
I also cut a flexible stencil out of cardstock. This is useful where walls meet ceilings and floors. You can press this kind of stencil into corners. </div>
<br />
<h3>
Notations on the stencil</h3>
<div style="text-align: justify;">
A
stencil is a remarkable tool, and it can carry all sorts of extra
information. Before I got to drawing on the wall, I added two kinds of notations to my stencil: matching zones, and alignment marks.</div>
<div style="text-align: justify;">
<br /></div>
<div style="text-align: justify;">
<b>Matching
zones</b> were places where the stencil would abut against another repeat of itself. When drawing along the edge of the stencil, you can skip these zones. I flagged them with felt tip pen on both sides of the
stencil. </div>
<div style="text-align: justify;">
<br /></div>
<div style="text-align: justify;">
<b>Alignment marks</b> showed where I could expect the stencil to align with horizontal and vertical lines drawn through the centre of central star.</div>
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<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiJ2E31VevTPHjVUNH_EoSXghCfx2JaCk9jS6WJDiHF-LsUXj9H7k6vSsdpxlMQxIgZ2kDjtxVLASGkCBP2tNZNKIv3i0GNM_euVg2aDVTInt8upHTDqD33R80QvXjfIIBcpN4UCQjMu_g/s1600/stencil+showing+alignment+marks.jpg" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" height="240" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiJ2E31VevTPHjVUNH_EoSXghCfx2JaCk9jS6WJDiHF-LsUXj9H7k6vSsdpxlMQxIgZ2kDjtxVLASGkCBP2tNZNKIv3i0GNM_euVg2aDVTInt8upHTDqD33R80QvXjfIIBcpN4UCQjMu_g/s320/stencil+showing+alignment+marks.jpg" width="320" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">A's indicates matching zones; line B-B connects alignment marks</td></tr>
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<br />
<h3>
Picking Colours</h3>
<div style="text-align: justify;">
At
this point I was curious about the colours in the original pattern, not in Jones but in the Alhambra. I was suspicious about Jones' reproduction because all the patterns on that plate had the
same four or five colours. As well, the image from his book online was
somewhat different in colour from the Dorling Kindersley reprint of the <i>Grammar of Ornament</i> that I owned. I went searching on the web for pictures of
the Hall of Justice at the Alhambra, pictures that might show the dado.</div>
<div style="text-align: justify;">
<br /></div>
<div style="text-align: justify;">
It turns out this room is
known by several different names: the Hall of Justice, the Hall of
Kings, Sala de Justicia, and Sala de Reyes. Detailed large images of the
lower walls are not very common, because people are mostly photographing
the ceiling. However on Wikimedia Commons I found a <a href="https://commons.wikimedia.org/wiki/File:Hall_of_Kings_-_Alhambra.JPG">nice large high-res image showing the dado,</a> taken by José Luiz Ribeiro in 2013 and released under a Creative Commons attrubution share-alike license.</div>
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<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgWkZQl0VkTRDP8pXMQ8KuW4SH0CYCscxNQSpWih6ZPQ0OIBbHCHQ26-wNGTjfwsfXrns4B0VRl2kAtXgQnchvf8FSAk-8BDonY9cPP5HxT6YpUocymVLdoBA4sr-GGu9g6XonMvq05axc/s1600/Hall_of_Kings_-_Alhambra_sm.JPG" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" height="320" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgWkZQl0VkTRDP8pXMQ8KuW4SH0CYCscxNQSpWih6ZPQ0OIBbHCHQ26-wNGTjfwsfXrns4B0VRl2kAtXgQnchvf8FSAk-8BDonY9cPP5HxT6YpUocymVLdoBA4sr-GGu9g6XonMvq05axc/s320/Hall_of_Kings_-_Alhambra_sm.JPG" width="205" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">Hall of Kings, Alhambra. © José Luiz Bernardes Ribeiro </td></tr>
</tbody></table>
<div style="text-align: justify;">
Let's zoom in on the dado on the left side of the photograph and compare it with the image in Jones.</div>
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<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiCyIcSwvEU-Ts_IGgOsnghXNFhf0FqMi8hxlLZcbp8ydatuz4dCFTj1ltezyFStI7rXrgeX3GElXbibH2N4O3HdlMKtAjd76sBiCyh4GkrITgBsEMtdllfuOXGoxZMsdTYln4QDv5EiYE/s1600/Hall_of_Kings_-_Alhambra_detail_dado_2+versions.JPG" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" height="320" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiCyIcSwvEU-Ts_IGgOsnghXNFhf0FqMi8hxlLZcbp8ydatuz4dCFTj1ltezyFStI7rXrgeX3GElXbibH2N4O3HdlMKtAjd76sBiCyh4GkrITgBsEMtdllfuOXGoxZMsdTYln4QDv5EiYE/s320/Hall_of_Kings_-_Alhambra_detail_dado_2+versions.JPG" width="249" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">Photograph of the dado from the Alhambra (left) and Plate XLIII #11 from the present Dorling Kindersley edition of Jones's <i>Grammar of Ornament</i> (right)</td></tr>
</tbody></table>
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</div>
<br />
<div style="text-align: justify;">
Although the pattern is
recognizably the one that Jones reproduced, the differences in colour
are appalling. Where the original has black stars and darts, Jones's were blue. Where light blue darts ran across the pattern, Jones used a warm grey. Dark, jade-green petals in the original became a leaf green in Jones. The pale orange petals in the Alhambra were changed into rich orange petals. A white background in the original became gold.</div>
<div style="text-align: justify;">
<br /></div>
<div style="text-align: justify;">
And importantly, here are <u>no channels</u> in the original. There are simply tiles placed next to each other. (Although it's not clear what the material is: it could be semi-precious stones or it could be tiles. I haven't been there.)</div>
<div style="text-align: justify;">
<br /></div>
<div style="text-align: justify;">
So my wall painting was not going to be a reproduction of this dado in any sense. It would be a pattern inspired (distantly) by a dado in the Alhambra, recoloured and presented to the English-speaking world by Owen Jones in the nineteenth century, and then further altered by that idea that I got from Eric Broug's book, of having channels between the shapes.</div>
<br />
<h3>
Final result</h3>
<div style="text-align: justify;">
Using the stencil I sketched the outlines of all shapes on the wall. The flexible stencil was indeed handy where the wall met the ceiling and floor.</div>
<div style="text-align: justify;">
<br /></div>
<div style="text-align: justify;">
I painted it using leftover house paint we had, but trying to approximate the colours in Jones's plate.</div>
<br />
<table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody>
<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgTIegIyh2LPO6o3Dx_IzvRvKm1XNWx-b1NWwfDx4ieMPZVy4nQ8ogMX5lb5VgToAudJz_5Vhd8gHFC_Fn0W_RkGZX6oNW_jeK5L76Z53FwROh_eQ5K_72diFi9oDoDvzvpllU_om5vXpM/s1600/DSC02540_small.JPG" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" height="300" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgTIegIyh2LPO6o3Dx_IzvRvKm1XNWx-b1NWwfDx4ieMPZVy4nQ8ogMX5lb5VgToAudJz_5Vhd8gHFC_Fn0W_RkGZX6oNW_jeK5L76Z53FwROh_eQ5K_72diFi9oDoDvzvpllU_om5vXpM/s400/DSC02540_small.JPG" width="400" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">It is in fact even difficult to see where the doors are now.</td></tr>
</tbody></table>
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<br />Morgan Hitehttp://www.blogger.com/profile/02187274906810012520noreply@blogger.com0tag:blogger.com,1999:blog-4352824282046201576.post-53464852142434468272013-05-03T09:38:00.003-07:002013-09-14T12:04:15.394-07:00The bounds of Oregon Country<span style="font-size: small;"><span style="font-family: inherit;"><span data-mce-style="font-size: small;"><i>Recently, I made a a series of maps of the historical Oregon Country. This was for an online exhibit at the Osoyoos & District Museum, which can be seen here:<a href="http://www.osoyoosmuseum.ca/1812/1812.html" target="_blank"> http://www.osoyoosmuseum.ca/1812/1812.html</a></i></span></span></span><br />
<span style="font-size: small;"><span style="font-family: inherit;"><br /></span></span>
<span style="font-size: small;"><span style="font-family: inherit;"><span data-mce-style="font-size: small;"><i>The Oregon Country was jointly occupied by the U.S. and Great Britain from 1818, when the two countries signed a treaty formalizing relations after the War of 1812, until 1846, when they divided the Oregon Country along the 49th parallel. In the course of producing these maps, the museum's curator, Ken Favrholdt, and I determined that there was no clear idea of where the Oregon Country ended to the north, and that today Oregon Country is often misrepresented as having ending at 54° 40' north.</i></span></span></span><br />
<span style="font-size: small;"><span style="font-family: inherit;"><br /></span></span>
<span style="font-size: small;"><span style="font-family: inherit;"><span data-mce-style="font-size: small;"><i>What would the actual north bound of Oregon Country have been? </i></span></span></span><br />
<h2>
</h2>
The
lands the U.S. and Britain were negotiating over had large regions that
were poorly explored (that is, poorly explored by Europeans and by
those from back east). Representatives of both countries relied on maps
that, the farther north one went, were less and less accurate, as well
as being essentially unchecked. When diplomats defined the Oregon
Country, they were assuming the maps reflected something more or less
accurate.<br />
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<table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="float: right; margin-left: 1em; text-align: right;"><tbody>
<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiaDYIwzGopDeeC6gaZ8P29ew4C0ryBZvdSa06WWne8dwpieqX0LNn8YCQ9szZazp3cEnNLSaZLtFRpQ1E36tCsJuifnTr28k-Fid4LckdXHQ5J88TNRNxz_R3dzhC_RG7Mpc3KkhdX41Y/s1600/01-Hooker+and+Brown+from+US+Ex+Ex+map+of+Oregon+COuntry,+1841.jpg" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" height="252" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiaDYIwzGopDeeC6gaZ8P29ew4C0ryBZvdSa06WWne8dwpieqX0LNn8YCQ9szZazp3cEnNLSaZLtFRpQ1E36tCsJuifnTr28k-Fid4LckdXHQ5J88TNRNxz_R3dzhC_RG7Mpc3KkhdX41Y/s320/01-Hooker+and+Brown+from+US+Ex+Ex+map+of+Oregon+COuntry,+1841.jpg" width="320" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">Hooker and Brown from US Ex. Ex. map of Oregon Country, 1841</td></tr>
</tbody></table>
One
nice illustration of how little knowledge there was is the case of
Mounts Hooker and Brown. These two 16,000' peaks were said to lie on
either side of Athabasca Pass, the route through the Rockies pioneered
by David Thompson in 1811. They appear authoritatively presented on the
1841 map of Oregon Territory by the U.S. Exploratory Expedition, the
1844 map of the Oregon Territory by the French diplomat Eugene Duflot de
Mofras, and the 1844 map of North American by John Arrowsmith in
London.<br />
<br />
And this was only at 52° north. What other unchecked assumptions lay further north?<br />
<br />
Even
though there were strong sentiments in both Britain and the U.S. that
as little as possible of the Oregon Country should be ceded to the other
party, the exact bounds of Oregon Country were never well defined. The
Treaty text (the Anglo-American Convention of 1818) stipulates that it
is the "North West Coast of America, Westward of the Stony Mountains."
Let's look at what these words might mean.<br />
<br />
<table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="float: right; margin-left: 1em; text-align: right;"><tbody>
<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjVj8wdKh6ZhXc1pdnWTCc1ml1DW86Jyq1hK3zIBIropM375nfSt9jYgQvko-gAjAYOUmLEon1aPXZEXi40t3QSy2qjy5zDrELB5hUmwuz5O9MUfCtDO9nPXo_Wspi19K_Ncu_pp5PMVuM/s1600/02a-Oregon+Country+with+watersheds,+latitudes+and+crest.jpg" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" height="320" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjVj8wdKh6ZhXc1pdnWTCc1ml1DW86Jyq1hK3zIBIropM375nfSt9jYgQvko-gAjAYOUmLEon1aPXZEXi40t3QSy2qjy5zDrELB5hUmwuz5O9MUfCtDO9nPXo_Wspi19K_Ncu_pp5PMVuM/s320/02a-Oregon+Country+with+watersheds,+latitudes+and+crest.jpg" width="247" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">Watersheds, latitudes and the crest of the Rockies in Oregon Country</td></tr>
</tbody></table>
The <b>West</b> bound is pretty clear: it's the Pacific Ocean.<br />
<br />
The <b>South</b> bound is pretty clear: it's the 42<sup>nd</sup>parallel, agreed to be the northern limit of Spanish claims in the 1818 Adams–On<span data-mce-style="font-family: Times New Roman,serif;" style="font-family: Times New Roman,serif;">í</span>s Treaty.<br />
<br />
The <b>East </b>bound
relies on there being a feature called the Stony Mountains. Most maps
of the period show the Stony Mountains as a thin band of peaks running
north-south, which would have made a precise boundary.<br />
<br />
<table cellpadding="0" cellspacing="0" class="tr-caption-container" style="float: right; margin-left: 1em; text-align: right;"><tbody>
<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjWVIQNBVKAaJbHXFeLnjEDW81D-pI2mA8O69XRF2lH9zufX-67mQPvQRN-HLn1BcuXuEph7avwfy0mgeMIh5D8SuMR6o5WgGHnkAx1GXCXR95V81mkmfkge9ys0_F96Vz9e-PFm5xBLXk/s1600/03-Arrowsmith+1844+North+America+detail.jpg" imageanchor="1" style="clear: right; margin-bottom: 1em; margin-left: auto; margin-right: auto;"><img border="0" height="320" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjWVIQNBVKAaJbHXFeLnjEDW81D-pI2mA8O69XRF2lH9zufX-67mQPvQRN-HLn1BcuXuEph7avwfy0mgeMIh5D8SuMR6o5WgGHnkAx1GXCXR95V81mkmfkge9ys0_F96Vz9e-PFm5xBLXk/s320/03-Arrowsmith+1844+North+America+detail.jpg" width="219" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">The Arrowsmith map from 1844, showing the Rockies as a single chain</td><td class="tr-caption" style="text-align: center;"></td></tr>
</tbody></table>
But the
reality is that the Rockies are a fairly fat range. In practice, we
generally look to the watershed divide to define where "Westward of the
Stony Mountains" might begin. But the farther north one goes, the more
the watershed divide begins to play with your mind.<br />
<br />
South
of 52°, it's a simple choice of the Atlantic watershed on one side, and
the Pacific watershed on the other. But north of 52° one has to choose
between the Atlantic-Arctic divide, which wanders off across the high
plains to the northeast, or the Pacific-Arctic divide, which continues
to follow the core of the range. Assuming you choose the latter, your
next conundrum occurs at about 54° 30', where the Pacific-Arctic divide
diverges from the Rockies and heads northwest. At this point, large
rivers of the Peace River system are rising west of the crest of the
range and flowing through it. Here the range has no meaning as a
watershed divide at all.<br />
<br />
If we stick by the words of the treaty,
we are bound to continue following the crest of the Rockies. So Oregon
Country north of 54° 30' includes some eastward flowing rivers. And
indeed, cartographers of the time, if they ever mapped Oregon Country
this far north, drew there line as we have, along the crest of the
Rockies.<br />
<br />
The <b>North</b> bound is the big mystery. The
Treaty did not address it, and here we get into territory that was
little travelled and little reported.<br />
<br />
Nowadays it's not uncommon
for a history map to show Oregon Country as ending at 54° 40' north.
They either show this as a line drawn from the Pacific Ocean to the
Rocky Mountains by the 1824 treaty between the U.S. and Russia, which is
wrong, or they show it as the northern limit of American claims, which
is right, but in neither case does this mean that Oregon Country ended
here.<br />
<br />
54° 40' was not a number that meant anything when the Oregon
Country was set up in 1818. It arises for the first time six years
later when the Americans and the Russians sign the St. Petersburg
Convention of 1824. This treaty mentions 54° 40' as a latitude to
separate their respective spheres of influence regarding<b> coastal establishments</b>. The wording of the treaty is <i>“there
shall not be formed by the citizens of the United States ... any
establishment upon the Northwest Coast of America, nor in any of the
Islands adjacent, to the north of fifty-four degrees and forty minutes
of north latitude ; and that, in the same manner, there shall be none
formed by Russian subjects... south of the same parallel.” </i><br />
<br />
<table cellpadding="0" cellspacing="0" class="tr-caption-container" style="float: left; margin-right: 1em; text-align: left;"><tbody>
<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhsEq0TnB8ufjkv2cXPUQfyD61Dhlq3zf5Qc46CsfbvHCW5FGscu_KQ1yq53ZOiOV_hUAj3wdcSAMqVx_gdH4UTAmGIZJbGdTZpQyTcmQgMAt1vGI__Dd-LAzRx8pFWklJXR34_vbeN6A0/s1600/06a-Eugene+Duflot+de+Mofras+1844+American+Coast+on+the+Pacific+Rumsey.jpg" imageanchor="1" style="clear: right; margin-bottom: 1em; margin-left: auto; margin-right: auto;"><img border="0" height="200" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhsEq0TnB8ufjkv2cXPUQfyD61Dhlq3zf5Qc46CsfbvHCW5FGscu_KQ1yq53ZOiOV_hUAj3wdcSAMqVx_gdH4UTAmGIZJbGdTZpQyTcmQgMAt1vGI__Dd-LAzRx8pFWklJXR34_vbeN6A0/s200/06a-Eugene+Duflot+de+Mofras+1844+American+Coast+on+the+Pacific+Rumsey.jpg" width="154" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">Eugene Duflot de Mofras's map, 1844</td></tr>
</tbody></table>
<table cellpadding="0" cellspacing="0" class="tr-caption-container" style="float: left; margin-right: 1em; text-align: left;"><tbody>
<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjoRL8L7KreYvh_7eoE69FXzIyjM9ehCzIyCYz7M2pIJbrAbi7wBIWEM2hO1cQAQ7_7sGHiDTeQeBwatPAtjOINrxMKLCJzzPwYnD71GO8g-YH2A5-J4wRd2AXdsaw38YIJCvdtazEow_0/s1600/06b-Eugene+Duflot+de+Mofras+1844+detail+line+at+54+40.jpg" imageanchor="1" style="clear: left; margin-bottom: 1em; margin-left: auto; margin-right: auto;"><img border="0" height="98" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjoRL8L7KreYvh_7eoE69FXzIyjM9ehCzIyCYz7M2pIJbrAbi7wBIWEM2hO1cQAQ7_7sGHiDTeQeBwatPAtjOINrxMKLCJzzPwYnD71GO8g-YH2A5-J4wRd2AXdsaw38YIJCvdtazEow_0/s200/06b-Eugene+Duflot+de+Mofras+1844+detail+line+at+54+40.jpg" width="200" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">Line at 54° 40' on the Duflot de Mofras map </td></tr>
</tbody></table>
Nonetheless,
this begins the practice of cartographers drawing a line at 54° 40' all
the way from the coast to the crest of the Stony Mountains, a distance
of about 700 km. Some, like Duflot
de Mofras in 1844, claim this line merely represents something defined
in the treaty, and leave either side of it the same colour. In other
words, there's no implication that this was the end of Oregon.<br />
<br />
<table cellpadding="0" cellspacing="0" class="tr-caption-container" style="float: left; margin-right: 1em; text-align: left;"><tbody>
<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjzVh5AnJ0gGCvO3HByOQOh6-ydw2XJihJnKKM4MWiqa8hYVOR7fMEz_rnv80iufolt4raAjGWkrPHbWUHQC7AzO5fwk17Z6B0UyWNitrlEgxGLiZegHqv-20T6NSB9M3xCLGTug-_muWk/s1600/07a-1841+Wilkes+Expedition+Oregon+Territory+Rumsey.jpg" imageanchor="1" style="clear: left; margin-bottom: 1em; margin-left: auto; margin-right: auto;"><img border="0" height="188" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjzVh5AnJ0gGCvO3HByOQOh6-ydw2XJihJnKKM4MWiqa8hYVOR7fMEz_rnv80iufolt4raAjGWkrPHbWUHQC7AzO5fwk17Z6B0UyWNitrlEgxGLiZegHqv-20T6NSB9M3xCLGTug-_muWk/s200/07a-1841+Wilkes+Expedition+Oregon+Territory+Rumsey.jpg" width="200" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">Map of Oregon Territory, 1841, Wilkes Expedition</td></tr>
</tbody></table>
<table cellpadding="0" cellspacing="0" class="tr-caption-container" style="float: right; margin-left: 1em; text-align: right;"><tbody>
<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh_oRANB_WZp-JF7mVV3Qx4ffafbJQlJIdEtHfAmnxbA_Op5bIrdRvUUjlpG-TBuVNWADPuOmplR1_uz3jUW8s3z0IqUhvJ_mJARQU52SnYbmSUIqClKg1ImXzXSY1nk9pbpUYWBbDBCvs/s1600/07b-1841+Wilkes+Expedition+Oregon+Territory+Rumsey+detail.jpg" imageanchor="1" style="clear: right; margin-bottom: 1em; margin-left: auto; margin-right: auto;"><img border="0" height="46" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh_oRANB_WZp-JF7mVV3Qx4ffafbJQlJIdEtHfAmnxbA_Op5bIrdRvUUjlpG-TBuVNWADPuOmplR1_uz3jUW8s3z0IqUhvJ_mJARQU52SnYbmSUIqClKg1ImXzXSY1nk9pbpUYWBbDBCvs/s200/07b-1841+Wilkes+Expedition+Oregon+Territory+Rumsey+detail.jpg" width="200" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">Detail of 54° 40' line on Wilkes Expedition map</td></tr>
</tbody></table>
<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
Others
are more ambiguous. The American "Wilkes Expedition" of 1841 produced an
authoritative-looking "Map of the Oregon Territory" on which the Oregon
Country ended, at 54° 40', with an unlabelled line in the same style as
other international boundaries on the map.<br />
<br />
<table cellpadding="0" cellspacing="0" class="tr-caption-container" style="float: right; margin-left: 1em; text-align: right;"><tbody>
<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhRrX0bfGicFxM7uFmQybJaUqyzjex8LCewbYsfvI3AgtfuK7P0_oCwcucxv2CKObUpHWva91m34b8N9Z9mM8cBpo45KVyRdEeNillfrhxHybDjpWZeGDjqGcvJRJEYtmhXOhGs035_muM/s1600/09a-Jeremiah+Greenleaf.,+1840+Oregon,+Brattleboro,+Rumsey.jpg" imageanchor="1" style="clear: right; margin-bottom: 1em; margin-left: auto; margin-right: auto;"><img border="0" height="173" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhRrX0bfGicFxM7uFmQybJaUqyzjex8LCewbYsfvI3AgtfuK7P0_oCwcucxv2CKObUpHWva91m34b8N9Z9mM8cBpo45KVyRdEeNillfrhxHybDjpWZeGDjqGcvJRJEYtmhXOhGs035_muM/s200/09a-Jeremiah+Greenleaf.,+1840+Oregon,+Brattleboro,+Rumsey.jpg" width="200" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">Jeremiah Greenleaf, 1840, Brattleboro</td></tr>
</tbody></table>
<br />
<br />
<br />
<br />
<br />
<br />
<br />
American commercial map-makers go further: they colour the land
differently on either side of 54° 40', and label the line as "Boundary
of Russian Possessions Settled by Convention in 1824" (Jeremiah
Greenleaf, Brattleboro, in 1840) or "Boundary of 1824" (Henry Tanner,
Philadelphia, in 1833).<br />
<table cellpadding="0" cellspacing="0" class="tr-caption-container" style="float: left; margin-right: 1em; text-align: left;"><tbody>
<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg3YMC5JB0BaE51vlCWwPQLBeAloSJxX6X5TuShiySTgNhAHLgliI6k8ykDyo1sulLc1xjbCmJP71JuopqkqmmFQ7dfHGZN9tDwrc2s8ZbBZuRo3Ph4oDvzXg4WF8F01VRR9FUzergrqd8/s1600/08a-Henry+Tanner+Phildelphia+1833+North+America+NW+Rumsey+detail.jpg" imageanchor="1" style="clear: left; margin-bottom: 1em; margin-left: auto; margin-right: auto;"><img border="0" height="188" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg3YMC5JB0BaE51vlCWwPQLBeAloSJxX6X5TuShiySTgNhAHLgliI6k8ykDyo1sulLc1xjbCmJP71JuopqkqmmFQ7dfHGZN9tDwrc2s8ZbBZuRo3Ph4oDvzXg4WF8F01VRR9FUzergrqd8/s200/08a-Henry+Tanner+Phildelphia+1833+North+America+NW+Rumsey+detail.jpg" width="200" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">Henry's Tanner's 1833 map of Oregon</td></tr>
</tbody></table>
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<table cellpadding="0" cellspacing="0" class="tr-caption-container" style="float: right; margin-left: 1em; text-align: right;"><tbody>
<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjEVbnMzQJCaEkyTn9b68gW-rXY3RIW7ZZyedN_iAzAUGv4k_9xIRlFE01pPjW25GIBoQs2FYGvLjyxD7IkngctY5ykRCIfec1lVpL6bUeHfQXt0iUUlSe-cmSer-S7UNFTW2Jj7nJkuvY/s1600/10-Oregon_Boundary_1846+From+Burpee+Historical+Atlas+of+Canada.jpg" imageanchor="1" style="clear: right; margin-bottom: 1em; margin-left: auto; margin-right: auto;"><img border="0" height="200" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjEVbnMzQJCaEkyTn9b68gW-rXY3RIW7ZZyedN_iAzAUGv4k_9xIRlFE01pPjW25GIBoQs2FYGvLjyxD7IkngctY5ykRCIfec1lVpL6bUeHfQXt0iUUlSe-cmSer-S7UNFTW2Jj7nJkuvY/s200/10-Oregon_Boundary_1846+From+Burpee+Historical+Atlas+of+Canada.jpg" width="155" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">From Lawrence J. Burpee, editor, AN HISTORICAL ATLAS OF CANADA, Toronto, Thomas Nelson and Sons, 1927</td></tr>
</tbody></table>
<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
So
the myth grows that the disputed Oregon Country somehow stopped at 54°
40', and in the 20th century you have maps like one from Burpee's
Historical Atlas of Canada, 1927, that shows the Oregon boundary running
along 54° 40', or this <br />
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<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEibSH538kVKUfkuQE5s2RlhiLyLS1CPYYA8A7jpttZSzTmcoI3q7thZFtgTD84W43bFu4g9pcBKLX008_mA8qODW-cAJZjNzji8o3pWwUOCmroDa88pZfkuNm6Bc8uTS3IzlxVpwngB1ts/s1600/11-Denoyer-Geppert+Oregon+Country2.JPG" imageanchor="1" style="clear: left; margin-bottom: 1em; margin-left: auto; margin-right: auto;"><img border="0" height="150" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEibSH538kVKUfkuQE5s2RlhiLyLS1CPYYA8A7jpttZSzTmcoI3q7thZFtgTD84W43bFu4g9pcBKLX008_mA8qODW-cAJZjNzji8o3pWwUOCmroDa88pZfkuNm6Bc8uTS3IzlxVpwngB1ts/s200/11-Denoyer-Geppert+Oregon+Country2.JPG" width="200" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">Denoyer-Geppert 1941 Historical Oregon Country</td></tr>
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Denoyer-Geppert 1941 school room map of the Historic Oregon Country,
where 54° 40' is labelled both as the treaty line of 1824 and as the
limit of American claims. But the yellow colour says something else:
that north of 54° 40' is not Oregon Country.<br />
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Our
question was, how did people on the ground on this side of the Rockies,
think of Oregon Country? We decided to resolve this problem by looking
to the Hudson's Bay Company. They had an administrative unit here,
called the Columbia Department, which represented the scope of
fur-trading activities throughout the Oregon Territory. It began at the
crest of the Rockies, and it went as far south as the Spanish border;
what did they take to be the northern limit of this Department?<br />
<br />
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<tr><td class="tr-caption" style="text-align: center;">Oregon Country as we mapped it</td></tr>
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These
lands had fallen under HBC control in 1827 when they bought the North
West Company and its operations. The north half of what the HBC
eventually called the Columbia Department had been called New Caledonia
by the NWC. and its northern limits were basically as far north as its
northernmost posts, Fort McLeod and Stuart's Lake Fort, could trade.
Practically, this was the headwaters of the Nass and Skeena Rivers
(which closely parallel each other west of the divide) and the
headwaters of the Finlay River (east of the divide; effectively the
headwaters of the Peace). These areas, incidentally, are north of 54°
40'.<br />
<br />
This being the practical limits of Oregon Country for the fur
traders at the time, we decided to use the Nass and Finlay Rivers as
our boundary. Note that these two rivers do not meet at the divide.
Their respective headwaters are about 50 km apart, and occur in close
proximity to the headwaters of the Stikine, another Pacific river that
reaches the coast farther north. A connecting line had to be drawn using
the watershed boundaries, first the Finlay-Skeena, then the
Stikine-Skeena, then the Nass-Stikine.Morgan Hitehttp://www.blogger.com/profile/02187274906810012520noreply@blogger.com3tag:blogger.com,1999:blog-4352824282046201576.post-17960445424512086002011-05-10T10:43:00.000-07:002011-05-10T13:46:35.445-07:00Passby Creek 1<style type="text/css">
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<div style="margin-bottom: 0in;">I gave the Passby Creek Trail a try yesterday. This trail is pretty weak on references: all I had was a recommendation from S---, who had snowshoed it, and a verbal description from the bcnorth.ca website dated was pre-2005. There was no entry in the original <i>Trails To Timberline, </i>and no entry on followyourpath.ca. I set out to follow the verbal description and see if I could just find the roadhead. I took snowshoes because on north-facing sloes the snowline seems to be still down around 2000'</div><div style="margin-bottom: 0in;"><br />
</div><div style="margin-bottom: 0in;">I've been thinking about mapping trails without a GPS—a sort of variant on “Games Climbers Play” that I'm calling “Games Map-makers Play.” It's about going back to the technology of 1990: no computer, no Google Earth, no GPS. Just map and compass. So I took a compass, and the 1971 topo map.</div><div style="margin-bottom: 0in;"><br />
</div><div style="margin-bottom: 0in;">Here was the verbal description:</div><div style="margin-bottom: 0in;"><br />
</div><div style="margin-bottom: 0.2in; margin-left: 0.5in;">Drive north from Smithers on Highway 16 for 24.4 kms and turn left on the Kitseguecla Lake Road. Turn left again after .7 km and cross the railway tracks on the 6000 Forest Service Road. About 1/2 km past the 6008 sign, turn left on the small Forestry Road. After driving 2.3 km past some fields, bear right at the "Y" onto the 608 Road, drive across a small bridge and turn left at the 4 km sign on a small road behind a corral to an overgrown landing in the cut block. The trail starts from the southwest corner of the landing and follows the creek bank south to the edge of the timber. After about an 1-1/2 hours hike, turn left on the beaten track. The old main trail goes straight ahead down the hill to Passby Lake. </div><div style="margin-bottom: 0.2in;">You'll notice it sounds like you somehow get from the Kitseguecla Lake Road to the 6000 Forest Service Road, but in fact they're the same thing. It's marked with the little yellow kilometre signs: “6001,” “6002,” etc. Four tenths of a km past the 6008 signs (yes, this road seems to have been posted twice, and there are two signs in slightly different places for many of the kilometres) was the left turn described, but it turned out also to be the turn posted “Hankin-Evelyn Backcountry Trails Parking, 9km.” I'd noticed this last fall and wanted to check it out: it's the gladed, skins-only, backcountry ski area developed over the past few years by the Bulkley Backcountry Ski Society. </div><div style="margin-bottom: 0.2in;">45 minutes from the house at this point.</div><div style="margin-bottom: 0.2in;">This turn-off was already signed from here as the 608 Road, and right off it had one of those scary yellow signs giving a radio frequency: “608 Road; Call Empty; 159.42”. At if that wasn't going to give me enough of a pause--picturing a head-on collision with a a logging truck because I have no such radio--there was also another sign close to the ground on the same post, red one, saying “Road Temporarily Closed To Recreation Traffic.” Oh, Geez.</div><div style="margin-bottom: 0.2in;">I went down there anyway, slowly, watching and listening for logging trucks. (Some doubt if this actually works.) Partly it was me being indignant that recreation sites should not be limited to people with forestry radios; partly it was me impatient to know what was down there. I met no one. I crossed Trout Creek, passed through some fields, and ascended through snowy forest. Snowline is at something like 2000' on these north-facing slopes. It was unclear where the “Y” was, but I did pass a turn-off to the left for a “602 Road” and that might have been it.</div><div style="margin-bottom: 0.2in;">At 4 km there was the mentioned bridge and small corral. Leading up behind the corral, which was mired in snow, was what was probably an old road between young (maybe 20 year old) pine and spruce. It was unplowed and certainly undrivable. (The snow was about two feet deep here.) I decided that, for today, <i>this</i> was the roadhead, and parked on the road margin, leaving plenty of room for the hurtling logging trucks of my imagination. I donned snowshoes, shouldered pack, and set out to explore “a small road behind a corral to an overgrown landing in the cut block.” </div><div style="margin-bottom: 0.2in;">There was an old track of snowshoes going up there, perhaps from a week before, and I followed these. I passed a yellow “deactivated road” sign, and after about ½ km I came to what might have been, seven years ago, a “overgrown landing:” it was full of aspen rather than coniferous trees. Here I shot a bearing to the Nipples and to the highest point on the ridge across the valley, so I could figure out later where the “landing” was.</div><div style="margin-bottom: 0.2in;">From here, “the trail starts from the southwest corner of the landing and follows the creek bank south to the edge of the timber.” I poked around in the far southwest corner, but the place was only about the size of a small parking lot, and the snowshoe tracks continued confidently up a narrower corridor between trees a bit more at what I would call the “mid-point” in the south side of the landing. Oh well. I followed the tracks, and found myself in a distinct corridor between trees, narrower than a road but about the right size for what would have been a pack trail 70 years ago. I looked for blazes but found none. The trees were still “recently” planted, but a little bigger now, maybe 30 years old. There was no creek in evidence, but I thought I could hear one off to my left. </div><div style="margin-bottom: 0.2in;">One piece of evidence that would help in figuring this all out would be a map showing cut blocks and the years they were cut.</div><div style="margin-bottom: 0.2in;">Varied thrushes and some kind of warbler were calling. I saw a hare ahead, already gone brown. After a while the snowshoe prints left the corridor between trees and forked through denser pine right up a little ridge nose. I followed them for a hundred metres or so and got a view out over the basin I was walking through. I could see I had indeed been following a stream, and that I was in a big area of light green (a <i>warm </i>green) trees, but on the edges there were taller, dark green trees: “the edge of timber.” I'm pretty sure that in the local lingo of forestry, “timber” specifically means the uncut, mature trees, rather than trees period.</div><div style="margin-bottom: 0.2in;">It looked like a long way to <i>the edge of timber. </i> I'd accomplished what I came for, and I'd forgot my gaiters, ski poles, and dark glasses, so I turned around. But first I went a bit further up what appeared to be the trail corridor and found I did come out on the creek itself. It was melted open and made a lovely, inspiring Spring sound.</div><div style="margin-bottom: 0.2in;">Descending, I was struck by how much the place was like the canyonlands at that moment. Across from me to the north, the ridge seemed sere, bare and melted out, like something you might see above White Canyon, or the Escalante Road. The whole area was unnaturally quiet, as if I was a long way from civilization. I was standing on two feet of snow, but life was surging up all around. My hands smelled of pine and cottonwood where they'd brushed branches, and it was just about enough to make me feel good about having survived Winter.</div><div style="margin-bottom: 0.2in;">At home I called the BC Rec guys, Kevin and Ben, and found out the 608 road is temporarily closed for the melt (they call it “break-up” ), so vehicles don't tear up the steep section near the Hankin-Evelyn Parking lot, which was 5 km beyond where I went. They don't know of any logging planned on the 608 Road in the next few years, so that's good news. </div><div style="margin-bottom: 0.2in;">The triangulation proved totally inaccurate to locate the “landing.” I was off by kilometres. Instead I located it using (embarrassed!) a GPS track of this trail I found on my server, perhaps donated originally by a colleague at BC Parks. Do I need a better compass? A plane table? A sextant? Must work on this.<br />
Here's what I knew at the end of this first day: <br />
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</div>Morgan Hitehttp://www.blogger.com/profile/02187274906810012520noreply@blogger.com0tag:blogger.com,1999:blog-4352824282046201576.post-32215266282329460892011-05-05T10:50:00.000-07:002011-05-05T10:50:44.592-07:00Winter River<style type="text/css">
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<div align="JUSTIFY" style="margin-bottom: 0in;"><span style="font-family: Palatino Linotype,serif;"><span style="font-size: x-small;">Although it's covered in snow, you can see that no trees or bushes grow in that strange, long, thin, wandering field that goes down the centre of the valley. After your car has warmed up and the heat is working, you can relax as you drive from Smithers to Quick, and notice that no fences cross that field. If you have lived in Winter all your life you might wonder about it. And by March it sometimes feels like we have lived in Winter all our lives.</span></span></div><div align="JUSTIFY" style="margin-bottom: 0in;"><br />
</div><div align="JUSTIFY" style="margin-bottom: 0in;"><span style="font-family: Palatino Linotype,serif;"><span style="font-size: x-small;">Rivers get closed down in winter. Like an amusement park where the rides are boarded up, silent and still, the river goes under its white tarp for the whole season. The employees are gone, the children are gone, there's no noise or light. We drive past put-ins or over bridges and pay no attention, as if there were a sign saying “Closed until Spring.”</span></span></div><div align="JUSTIFY" style="margin-bottom: 0in;"><br />
</div><div align="JUSTIFY" style="margin-bottom: 0in;"><span style="font-family: Palatino Linotype,serif;"><span style="font-size: x-small;">You won't learn that the river is there in the winter by listening to people tell stories about it. You hear that flow went up quite fast one week on May, that a certain rapid got washed out, that it took four hours one September to go from Walcott to Telkwa by canoe. Someone talks about coho making it past Moricetown, or which hole always contains a steelhead; another tells a story about going from Morice Lake to the Skeena in a kayak. There are guides to paddling, books about fishing... Perhaps the river is </span></span><span style="font-family: Palatino Linotype,serif;"><span style="font-size: x-small;"><i>just</i></span></span><span style="font-family: Palatino Linotype,serif;"><span style="font-size: x-small;"> a summer phenomenon.</span></span></div><div align="JUSTIFY" style="margin-bottom: 0in;"><br />
</div><div align="JUSTIFY" style="margin-bottom: 0in;"><span style="font-family: Palatino Linotype,serif;"><span style="font-size: x-small;">Come examine the winter river. It's quite silent here. The ice is lumpy and jumbled along the river edge. It piles up in strange shapes which, like snowflakes, never repeat and don't last long. The air is cold and a slight breeze blows from the south. Snow is moving in. Like the curving back of a big beast, water surfaces briefly in the centre of the channel, grey and muscly. It rides along in the air for a few metres, then dives again beneath the ice.</span></span></div><div align="JUSTIFY" style="margin-bottom: 0in;"><br />
</div><div align="JUSTIFY" style="margin-bottom: 0in;"><span style="font-family: Palatino Linotype,serif;"><span style="font-size: x-small;">You shouldn't go down there in the dark water, but someone has; and we know that down in the gravels, steelhead are waiting out the winter silently, holding their territories. Salmon eggs are hatching. The nearby Lake Kathlyn elementary school sets up a tank to hatch salmon eggs, and it is completely covered from light, a refrigeration tube inserted into it to keep the water frigidly cold. Quietly bubbling outside a classroom for months, it reminds us what it's like on the bottom of the river. </span></span> </div><div align="JUSTIFY" style="margin-bottom: 0in;"><br />
</div><div align="JUSTIFY" style="margin-bottom: 0in;"><span style="font-family: Palatino Linotype,serif;"><span style="font-size: x-small;">Up on the surface people are skiing on the ice, or perhaps just meandering down the edge of the river, cautiously avoiding the uncertain centre when ice can be thin. In Telkwa a snowmobile trail gets set up on the ice of the Telkwa River, and the village has a new trail for a few months. When it's solidly frozen, the river could be the ideal highway for dog sleds or foot travellers because, as I said before, there are no fences.</span></span></div><div align="JUSTIFY" style="margin-bottom: 0in;"><br />
</div><div align="JUSTIFY" style="margin-bottom: 0in;"><span style="font-family: Palatino Linotype,serif;"><span style="font-size: x-small;">You might think that the size of the river is the same in winter, but don't be fooled. In winter, the river is a much different size. It's not smaller. It's bigger. Because what is a river? It's the contiguous waterbody as far as it stretches. In summer it stretches merely from bank to bank; but in winter, water, in some form or another, frozen or liquid, continues contiguously far beyond the bank. Sure, there's liquid water in the riverbed, and then ice on top; but there's snow above that, and the unbroken blanket of snow continues, climbing the banks and setting off across the fields and through the forest. It's all river now, all river water, getting ready to flow downhill, sagging downhill already. There's nowhere you can draw a line and say, “This is river and that is not.” We are inundated: the snow and ice in turn stretch up the hill, around your house, over your car, across the road, up the mountains, over the pass, down to other rivers. It's all river now. And the summer river is a mere remnant of the real river, the Winter river.</span></span></div><div align="JUSTIFY" style="margin-bottom: 0in;"><br />
</div>Morgan Hitehttp://www.blogger.com/profile/02187274906810012520noreply@blogger.com0tag:blogger.com,1999:blog-4352824282046201576.post-54497698032488914662011-04-22T16:19:00.001-07:002011-04-22T16:19:22.184-07:00Vignette April 21Paso Robles looks like a ranching town trying to re-brand itself as a wine region, with western wear stores and wine tasting shops. Downtown, trim shops ring a grassy square with the old public library building in the centre. A small newspaper box on the corner advertises for a Tea Party convention: "Our government is trying to redesign our society by redistributing our income."<br />
<br />
Trying to redesign our society. This is indeed the prerogative of government. Redistributing our income. Indeed, this is why government exists. Perhaps the Tea Party members, alarmed by the change they see, imagine that they could never need government services, neither welfare nor emergency services nor medical treatment. Such a position surely springs from a belief that one is in control of one's life: in control of whether one gets fired, or ill, or lost. But life experience suggests this is not so true (although it's an obviously appealing idea). <br />
<br />
Buddhism suggests that the apparent coherence of the narrative of our lives is an illusion. It seems as though our lives unfold as a story; but in fact that's a trick of the mind. We seem to be in control, but there is no 'we.' We're good at interpreting the events of our lives as the fruit of cause and effect; we're not so good at exerting coherent control. Morgan Hitehttp://www.blogger.com/profile/02187274906810012520noreply@blogger.com0tag:blogger.com,1999:blog-4352824282046201576.post-54892416866068909182011-04-22T16:17:00.001-07:002011-04-22T16:19:48.554-07:00Vignette April 20It's Saturday morning at Morro Rock, and three birders are set up in the big dirt parking area under the east face of the Rock. They're looking at peregrine falcons; specifically at a female with a nest; and one of them assiduously takes me through the process of locating her on the vast face of the Rock, crowded as it is with gulls and cormorants, and towering some 200' above us. "See that cave with a gull in it; now go left, across the green area, and there are three little holes: two conjoined and one separate. Now go up at 11 o'clock about ten feet and she's sitting on a little knob, and her nest is in is the hole beside her." And there she is indeed, small and brown, but with the distinctive cheek patches of a peregrine.<br />
<br />
Morro Rock is signed with "Ecological Reserve: do not climb," otherwise it would be covered with climbers. The crack systems and overhangs are textbook rock route stuff, and the rock, a dark grey matrix with phenocrysts in it's, looks hard, strong and clean. But the rock, the last of a series of intrusive volcanic plugs along the coast here (neatly arranged in descending size), is reserved for the many species of nesting birds. <br />
<br />
A surfing class for kids (it's Spring Break week here), is being held on the beach next to the base of the Rock. Ten small boys in red shirts are organized by four you g men and women in green shirts,Morgan Hitehttp://www.blogger.com/profile/02187274906810012520noreply@blogger.com0tag:blogger.com,1999:blog-4352824282046201576.post-89121316663199497232011-04-20T14:04:00.000-07:002011-04-20T14:04:10.923-07:00Vignette April 18M vignette 18 April<br />
<br />
Bedrock swirls crazily in the cliffs along the beach, pitching this way and that, both white and brown. At low tide, thick sheets of rock are exposed with tide pools between them. some of these rocks are drilled with even round holes, some pencil-sized, some big enough to admit a finger. some contain shells, and in fact the holes are being made by these mussels, who excavate their own shelter in rock. Once the mussel is gone, pebbles fill them: red, orange, brown, white and blue. some are like crystal, some like shell.<br />
<br />
The sea is green offshore today, although if you look far enough it goes blue, and then, just before the horizon, an even deeper blue. along the coast to the right, to the north, is the land of Vandenberg Air Force Base, lush green hills today sloping down to the final cliffs that back the beach. It looks as though you could drop a ball at the top and it would roll down and shoot out over the sea, launched like from a ski jump.<br />
<br />
The sky has been clear from dawn, except for the bank of fog out at sea, which had not moved since we arrived 18 hours ago. the wind died during the night, and began the morning as a steady breeze from the land. later it swings to the north but remains a mere wind rather than a gale. In the campground they have a starred and striped wind indicator, and it is standing out straight all day. The waves roll in steadily.Morgan Hitehttp://www.blogger.com/profile/02187274906810012520noreply@blogger.com0tag:blogger.com,1999:blog-4352824282046201576.post-27088786720197508702011-04-17T10:12:00.000-07:002011-04-17T10:12:54.102-07:00Vignette April 17In Buellton at the Flying Flags RV Resort a calendar of Ronald Reagan hangs on the wall of the office. There's something odd in Buellton. The RV park itself is a little town within the town, with named streets and shady trees. People seem to be here to socialize, and a large outdoor table is spread with lunch for ten at one RV near us. At 7:00 a.m. Dog walkers are out, although the large field where we have parked (sold as "dry camping" because it lacks hookups) is mostly empty. The sun rises and you need your dark glasses immediately.<br />
<br />
This is RV park taken to the corporate level. There is an 800 number answered by "reservations agents". Inside the office there are cashier stations. They take your name and address as you register, although mine is tossed out once its Canadian nature is discovered. The place feels conservative, although on this Sunday morning I can't quite put my finger on why.Morgan Hitehttp://www.blogger.com/profile/02187274906810012520noreply@blogger.com0tag:blogger.com,1999:blog-4352824282046201576.post-45564813535466063652011-04-17T10:02:00.000-07:002011-04-17T10:02:12.432-07:00Vignette April 9M April 9<br />
<br />
In Merced we stop at an enormous Home Depot by the highway to buy a pair of pliers to fix a sleeping bag zipper. actually, all Home Depots in California seem to be enormous, and this one was the same as all the others, so perhaps I should say 'at a Home Depot.' <br />
<br />
Inside, the cavernous building I hear a cashier saying to a customer, "¿Y el número de telefono?" Spanish is ubiquitous in California, and so is bilingualism. In the grocery store in Lancaster the cashier deals in Spanish with the previous customer (who greets her with "Hola") and then in English with Kate. although she tells Kate the total is vente y ocho and then corrects herself to twenty-eight. <br />
<br />
Spanish is on the move here. It's not just migrant workers; it's the whole middle class. And the creative fertility of bilingualism is also everywhere. In a state park I hear a man in a pickup ask a ranger the way to the exit. "Right out that way," says the ranger, and then I hear the man in the pickup begin joking with his friend in Spanish: we are such chowderheads not be able to find our way out of here; didn't we drive past this firewood shack twice before; yeah, but it was your fault! At least that's what I think they were saying: my Spanish is pretty poor. If I lived here though I'd be working on it: it's where things are going.Morgan Hitehttp://www.blogger.com/profile/02187274906810012520noreply@blogger.com1tag:blogger.com,1999:blog-4352824282046201576.post-63935084517771081372011-04-17T10:00:00.000-07:002011-04-17T10:00:33.339-07:00Vignette april16In the men's room at McGrath State Beach, the stall doors hang wrong on their hinges, so you have to lift the door with your foot to slide home the bolt, which Galen does handily. We have been told twice by different people that this campground will be closed at the end of this summer because of the state's budget crisis: no money to fix the ailing bathrooms. It seems ironic that bathrooms should dictate the demise of the facility, but that's how the decline of government services looks up close.<br />
<br />
At Antelope Valley Poppy Reserve, the volunteers told me that budget crises are a way of life for California: that when she was young her father was emploed by the state and he would periodically say, "Yep, there's no money this week." And then the state rebounds. It's unclear if this will be the case again. But if so then McGrath campground will be revived in a couple years I would predict. As travelers here we are catching the wave of the moment, enjoying the facilities still open as the state slides into poverty.Morgan Hitehttp://www.blogger.com/profile/02187274906810012520noreply@blogger.com0tag:blogger.com,1999:blog-4352824282046201576.post-24107421947181184112011-04-08T16:00:00.000-07:002011-04-09T16:03:09.388-07:00Vignette 8 April 2011A mile up Minturn Road from the freeway that runs the length of the San Joaquin Valley we come to the Buchanan Hollow Nut Company. We pull into a small yard with a warehouse on one side, an organic certification sign over its closed door. There is a store on the other, and row upon row of nut trees out the back.<br />
<br />
Inside, a small round lady is bagging pisotacios into 1 lb bags, and bowls of free samples are set out for us: ordinary pistacios, garlic pistacios, hot chili pistacious, choclate covered almods, apricot bits, cashews and so on. A rakish fellow dressed in a hat that never comes off encourages us to interrupt him if we needed anything, and says we are welcome to wander the orchards if we wish.<br />
<br />
Outside, the pistachio trees are just beginning to leaf out, barely a leaf showing, each tree only about 8 feet high. Jumping across an irrigatrion ditch I find the almonds are the trees fully in leaf, with small fuzzy pouches growing on them. Kate loads her arms with bags of cahsews and almonds and pistachios and finds that pistachios are only about $6 a pound.<br />
<br />
The boys and I use the rest room, where two enormous stuffed heads of wild boar are mounted with weirdly taxidermic expressions on their faces. In the office, the man is excited to find we are from Canada: Canadian mining stocks are going to enable him to retire, he says.Morgan Hitehttp://www.blogger.com/profile/02187274906810012520noreply@blogger.com0tag:blogger.com,1999:blog-4352824282046201576.post-79241507324667718402011-04-07T15:58:00.000-07:002011-04-09T16:00:07.299-07:00Vignette 7 April 2011The San Joaquin and Merced rivers are in flood, and as we arrive at the San Luis National Wildlife Refuge parking lot, just off the two-lane California highway 38, there are lakes and pools of water extending in every direction. The refuge seems closed, but closer reading of an informational sign reveals that it is open to foot traffic alone, So, donning binoculars and bird book, we lock the camper and set out. Great egrets beckon from the water, and clouds of swallows wheel overhead.<br />
<br />
There are astonishing swarms of bugs on the dirt road, some of them so thick they seem to be single entities. Galen whips at them with his sweatshirt, but it soon becomes clear that this does nothing but fill his hood with bugs. He rants and raves that we shoudld head back, that the bugs are driving him crazy, but the bugs are hardly interested in us, and soon Will gets the hang up ignoring them, as Kate and I begin eagerly identifying the birds in sight: western Kingbirds sitting atop bushes and jumping up for flies; red tailed hawks soaring; song sparrows; coots swimming in the water; mockingbirds flying from high point to high point. In the distance we can hear Canada Geese. None of these are unusual or exotic species (except the egrets) but the palpable chatter of life around us in itself exciting.Morgan Hitehttp://www.blogger.com/profile/02187274906810012520noreply@blogger.com0tag:blogger.com,1999:blog-4352824282046201576.post-56783382226899845082011-04-03T21:13:00.000-07:002011-04-03T21:13:41.862-07:00Bodega Bay, April 2nd, 2010On the north California Coast, picture an 'A' where one leg is on the main coast, and the other leg sticks out into the North Pacific. The top of the A points north, and a spit of sand closes off the mouth and crosses the A. But it's not an A with a pointy top: it's more of a nicely curved wishbone shape. In the middle is a calm expanse of water even when a hell of a north wind is blowing, as it was yesterday.<br />
<br />
Near the top is the town of Bodega Bay itself, where we arrived from the north, windblown, hopeful of finding gas and propane for our little stove. We followed signs to a marina on the west side of the bay, and found to my surprise that the gas pumps were of a kind I thought gone for years: pumps without any kind of credit card reader where you always pump before you pay, where you remove the nozzle from the recess in the side of the pump, flip down the metal handle, the numbers reset, and you're ready to go. I told the guy inside how much I liked his pumps. "Ah, he said, "some things never change."<br />
<br />
"Oh, wait," I said, as he rang me up. "I need to get some propane as well. <br />
<br />
"Let's get some gas, dude!" he bellowed. And then, as if to explain himself, he added, "As they used to say. I mean, since you've got the VW and all." He was a jolly bull-necked fellow, with a shaven head and a tattoo on his arm, and as he lay down on the pavement to get at the tiny propane tank under the vehicle, he swore and delivered a constant commentary about how it was going.<br />
<br />
I remembered Gabriel the Romanian saying to me during my orientation to the camper, "When you refill the propane tank, you take it to a place that does propane and you let them do it. This is not a do-it-yourself thing." As I looked at the special coupler this guy was preparing to put on, the strange double hose, and the way he was grunting over some tiny valve out of sight up beneath the vehicle (I lay down on my stomach on the pavement to look and still couldn't see it) I had to agree.<br />
<br />
"I can't budge this thing," he said, pulling out a pair of pliers. "Don't tell me it's..."<br />
<br />
"Aw, no..."<br />
<br />
"Come on..."<br />
<br />
"Hmm, OK." Getting up and turning to the main pump, he said, "Now let's see if you're going to work today," and hit a switch. It hummed to life and propane began moving.<br />
<br />
At 2.4 gallons on the meter it went KLUNK and shut off -- which jibed well with the 2.5 gallon tank Gabriel said we had. Our man disconnected the main hose, and again fiddled with the relief valve. As he got more distressed I got down again and I could see he had it munched in the jaws of his leatherman and was either grinding it or turning it. I can't tell if it's moving," he grunted. "This is not right," he said ominously. And then: "Aw, no!"<br />
<br />
Lying on his back he explained to me that we were at an impasse. He was unable to close the relief valve, propane was leaking out, he was pretty sure an o-ring had blown and the system would be unusable. Soon it would be empty. The pliers were not working! It was frozen: it was busted. And he was mystified why he had found plumbers tape on the base of the valve. "You would never put plumbers tape on one of these!" he said.<br />
<br />
"And get me a pillow, will you?" he joked, since he'd been lying on the ground for so long.<br />
<br />
For the next half hour I was on the phone to Gabriel, and, to his credit, our friendly gas attendant was on the phone to two RV repair places in Petaluma -- an hour's drive away. He was quite distressed that we had come all the way from BC and this had happened to us. But in the end Gabriel, mystified, could only suggest we buy ourselves a two-burner butane stove, which he would pay for. The gas man could find no one capable of repairing the valve on a Saturday. He bid us farewell and gave us two free postcards.<br />
<br />
We drove away, bought some groceries while processing it all, and decided that repairing the stove was NOT our priority. (*Not driving too much* was, that day, our greatest priority.) So we drove north out of Bodega Bay, a short distance to the first park beach, North Salmon Beach, (the wind increased dramatically as we left Bodega Bay), and ate our lunch inside our camper with the window just cracked, which made everything *just* the right temperature. The steady north wind blew away the gas smell hissing from below the camper. Then we donned wind shirts and went down the path (typical California path: a steep, eroding trench through the ice plant) and walked the beach.<br />
<br />
As at Wright's Beach, there were elaborate driftwood constructions on North Salmon Beach, and lots of hardy Californians enjoying them as shelters. There were a number of little forts built by urban castaways (one was roofed over) and the driftwood beams and posts were fabulous. One family was draping their with fabric on the upwind side to protect the children. It was so windy that each time a wave broke up the beach, leaving a pile of foam at its furthest extent, the foam would detach itself from the wave and go tearing up the beach.<br />
<br />
We headed back into Bodega Bay to solve our most pressing problem: where to camp on a Saturday night. Bodega Dune campground was full. We tried a county park over on the west side of the A called (fittingly) Westside Regional park, and there was a site sheltered by trees. It was a great relief to know we had somewhere to sleep for the night and would not have to go a-roving over creation looking for a campsite. We parked and decided we would drive no further that day.<br />
<br />
I got down under the camper to check the gas leak and it was still going. I decided to see what this relief valve felt like with my own hands. I found a little knurled knob. I turned it and the hissing stopped.<br />
<br />
Huh?<br />
<br />
Had I fixed it?<br />
<br />
Gradually it became clear that I *had* fixed it, but not clear what had been the problem before. Once I had a pot of water on the boil to make tea and cocoa I called Gabriel and told him what had happened. He was very happy. "That is a great weight off my shoulders," He said in his endearing Romanian accent.<br />
<br />
Off we went for a walk. There were snowy egrets in the trees by the roadside, looking at us suspiciously.Morgan Hitehttp://www.blogger.com/profile/02187274906810012520noreply@blogger.com0tag:blogger.com,1999:blog-4352824282046201576.post-36954699849886956422011-04-01T15:57:00.000-07:002011-04-09T15:58:32.139-07:00Vignette 1 April 2011At the Simi winery, simply alongside the road from the north into the Sonoma County town of Healdsburg, there is a courtyard with a fountain: water, as always in California, making at once the twin statements of wealth and hospitality. Steve stops into the office for a moment to tell them he is taking some special people through on a tour, and then leads us across a small bridge.<br />
<br />
There is a railway line here, just outside the building, and we admire the two styles of stonework on the winery building: the left half constructed by Chinese railway workers and the right half constructed some years later by Italian immigrants.<br />
<br />
Above that building on the hill are giant stainless steel tanks and crushing machines. ("You mean the grapes are no longer crushed by feet?" says Kate. "Oh no!" laughs Steve: "Have I burst that bubble?") The fermentation vats are open-topped (although under rooves): the red wines fermenting at the ambient temperature, the wine wines fermenting at a chill. The grape skins and seeds for the white wines are collected and taken back to the vinyards to be spread as compost; the skins for the red wines kept int during fermentaiton.<br />
<br />
Inside the building are long rows of oak barrels imported from Franch in immaculate cool rooms that smell sweet with the wood scent. Each has a barcode on it for meticulous tracking.Morgan Hitehttp://www.blogger.com/profile/02187274906810012520noreply@blogger.com0tag:blogger.com,1999:blog-4352824282046201576.post-84898360262449459932011-03-31T15:55:00.000-07:002011-04-09T15:57:22.198-07:00Vignette 31 March 2011After driving through the hot grassy valleys around Fairfax, we suddenly drive into a forest that is unmistakably redwoods: dark green and grey shadows everywhere, and as we twisted and turned through it small houses hidden behind giant ferns bespoke of a people who liked to live in this gloom.<br />
<br />
Soon we arrive at Samulel P Taylor Park, named for a lumberman who found this patch of redwoods to log for the rebuilding of San Francisco after the 1906 earthquake. Now well into its second growth, the trees are not 10' in diameter, but a humbler 5'. We ascend to our campsite, up a mossy hill where silence is all that persists under the trees is silence. The logs are mossy. The ferns grow every where. A small creek trickles below our site. Ther eis only one other camper. Will says the place is creepy.Morgan Hitehttp://www.blogger.com/profile/02187274906810012520noreply@blogger.com0tag:blogger.com,1999:blog-4352824282046201576.post-63456525902990510572011-03-30T15:53:00.000-07:002011-04-09T15:55:36.139-07:00Vignette 30 March 2011Gabriel the Romanian rented us our camper. He was a friendly man who looked like a bust of Caesar Augustus: a round head, white hair, blue eyes and a thin nose. His camper renting outfit was based in what was essentially an oversize storage locker in the back of an alley leading off a one-block street, backing up against a freeway. The taxi dropped us in that unpropitious spot, but Gabriel came out and welcomed us in, our baggage announcing us as not there for business with any of the other little units in the building, where things like welding seemed to be going on.<br />
<br />
Gabriel made us comfortable on an overly soft sofa in the depths of his "office" and introduced us to Christina, at once perhaps his wife and his assistant. They provided us with stacks of maps of different regions of California, plus a guide to camping, and then our orientation to the camper began. In a carefully choreographed order, Gabriel led me around the details of the camper: how to put up the pop-top and how to take it down; how to make the beds and fold them away; where to check the oil and the coolant; how to light the stove and refill the propane tank; how to lock the doors and not lock your keys in. The camper, freshly washed, was dripping with water in the California morning sunshine.Morgan Hitehttp://www.blogger.com/profile/02187274906810012520noreply@blogger.com0tag:blogger.com,1999:blog-4352824282046201576.post-52722566494674987502010-09-29T16:27:00.000-07:002010-09-29T16:27:18.936-07:00The North Circumpolar Maps<table cellpadding="0" cellspacing="0" class="tr-caption-container" style="float: left; text-align: left;"><tbody>
<tr><td style="text-align: center;"><img border="0" height="175" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiO4TuTN8XQxuv5x9KhkcROV77fZ4mB_b93Lw51yOkJcNNtCRbbZSwyemFonh5ivzpLlShKfz1JFCkRtS5UTAduk6n15oXv7KZRJkp1QY9lgFO8kJN2_p0fAnjqcqkCTj0HH1qM6ltwFVs/s200/mcr_0198small.jpg" style="margin-left: auto; margin-right: auto;" width="200" /></td></tr>
<tr><td class="tr-caption" style="text-align: center;">NRCan, 1990 "North Circumpolar Region" MCR 198</td></tr>
</tbody></table>An interesting pair of maps that recently came to my attention (through an article in <a href="http://www.utpjournals.com/carto/carto.html"><i>Cartographica</i></a>) are the 1990 and 2008 versions of the Canadian government's "North Circumpolar Region." High-resolution images for both are available online free from Natural Resource Canada (NRCan), so I'll just post some thumbnails here and details.<br />
<br />
<div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiO4TuTN8XQxuv5x9KhkcROV77fZ4mB_b93Lw51yOkJcNNtCRbbZSwyemFonh5ivzpLlShKfz1JFCkRtS5UTAduk6n15oXv7KZRJkp1QY9lgFO8kJN2_p0fAnjqcqkCTj0HH1qM6ltwFVs/s1600/mcr_0198small.jpg" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"></a></div><table cellpadding="0" cellspacing="0" class="tr-caption-container" style="float: left; text-align: left;"><tbody>
<tr><td style="text-align: center;"><img border="0" height="168" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiCAGj1ILya6huGS2cEWkkK_lr3UZ-wh9EtrZOv2C3XnEhOR0Ccrs-KPSq5w33bcvP-ENlR1VVLdDlZIq7-ulXnUTNgjosvfEC-UIYVJkWajJHqUv8SK1BvT5pO4ZPOCr3QMIVmCTXuOC4/s200/MCR0001_sm.jpg" style="margin-left: auto; margin-right: auto;" width="200" /></td></tr>
<tr><td class="tr-caption" style="text-align: center;">NRCan, 2008 "North Circumpolar Region" MCR 0001</td></tr>
</tbody></table>The original map, <a href="http://atlas.nrcan.gc.ca/site/english/maps/archives/reference/circumpolar/mcr_0198">MCR 198</a>, was a tremendous success in 1990, and <a href="http://atlas.nrcan.gc.ca/site/english/maps/archives/reference/circumpolar/MCR0001_circumpolar_2008">MCR 0001</a> (2008) is an attempt to revise, update, and of course improve it. It is at a slightly smaller scale (1:9,000,000 instead of 1:7,500,000) but many things have been added: international date line, additional arctic ocean floor detail, current pack ice limits, and so on.<br />
<br />
But, which would I rather have hanging on my wall? Hands down it's the older version. It <i>looks</i> better. So what can we learn here?<br />
<br />
<div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiCAGj1ILya6huGS2cEWkkK_lr3UZ-wh9EtrZOv2C3XnEhOR0Ccrs-KPSq5w33bcvP-ENlR1VVLdDlZIq7-ulXnUTNgjosvfEC-UIYVJkWajJHqUv8SK1BvT5pO4ZPOCr3QMIVmCTXuOC4/s1600/MCR0001_sm.jpg" imageanchor="1" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"></a></div>What's striking about the more recent version is the difference in the shaded relief. The first map was done with conventional cartographic tools, and an artist rendered the shaded relief. The second map was done with current GIS technology, the shaded relief being computed.<br />
<br />
<div class="separator" style="clear: both; text-align: center;"></div>According to the article by the authors (<i>Mapping The North,</i> R. Eric Kramers and Andrew Murray, <i>Cartographica</i>, vol 45, No. 3, p.201), the new shaded relief was generated from a DEM using GIS software. However, it didn't look right until it was "tempered with the less-detailed, manually-drawn, 1990 relief." The two were blended in Photoshop to give the right balance of the high-resolution (computer generated) and low-resolution (hand-painted) components.<br />
<br />
It's not the first time I've read this: computer-generated shaded relief is too accurate for the big view: although each peak and ridge is there, the overall impression of a <i>mountain chain</i> is lacking something. Tom Patterson (<i>DEM Manipulation and 3-D Terrain Visualization</i>, Catographica vol. 38, # 1&2 Spring/Summer 2001, p.92) wrote that high-resolution DEMs give the wrong effect at small scales. <br />
<blockquote>Especially problematic are glaciated northern mountains comprising tightly packed ridges and valleys...which often appear as an irregular texture rather than a recognizable topography. </blockquote>And here are Anna Leonowicz, Bernhard Jenny and Lorenz Hurni (<i>Automated Reduction of Visual Complexity In Small-Scale Relief Shading</i>, Cartographica vol. 45, No. 1, Spring 2010, p.73) pointing out that, at present, hand-painted relief is simply better:<br />
<blockquote>Cartographers currently lack advanced methods for using [DEMs] to produce relief visualizations at a level of quality comparable to traditional, manually-executed relief representations.</blockquote>Patterson recommended that you could at least get <i>closer</i> to a hand-painted result by manufacturing a low-resolution DEM (i.e., down-sampling the original), and merging a shaded relief version of that with the shaded relief from the high-resolution data. In a sense this is just what the authors of the 2008 map did. <br />
<br />
Nonetheless the hand-painted relief, for my money, on the original 1990 map still looks better. A circumpolar map is a very grand overview. No one is going to refer to it for details, and it is designed to hang on a wall or adorn a floor. It gives an overall impression of planetary scale; so here I prefer the old style of shaded relief, where the mountain ranges stand out so strongly.<br />
<br />
<table cellpadding="0" cellspacing="0" class="tr-caption-container" style="float: left; text-align: left;"><tbody>
<tr><td style="text-align: center;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhxi3l-GWKWTA4Tg7OK8ZhixpLElZ_idYraHulC9Vx5v2UusSHarjIHLJVe-qtXNugTnrk8gX6MVUwtk2aR1b-zN2U6twDjwslAmqY_D_ZdnV82qCvTujxSUOd62iEs1pjaijAtqYJTR7w/s1600/MCR0001_WCanada.jpg" style="margin-left: auto; margin-right: auto;" /></td></tr>
<tr><td class="tr-caption" style="text-align: center;">Western Canada, 2008-style</td></tr>
</tbody></table><table cellpadding="0" cellspacing="0" class="tr-caption-container" style="float: left; text-align: left;"><tbody>
<tr><td style="text-align: center;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgSJ8eB4tq870-V-YzJemvwqJNZQwB4nu6uN5GED51p2UaPZeRO5rXyCC9apW4iFA8smFNdD_MZ7EGE2Mm3OxGmLv6EV7J7QQrrMVA3I_q1OHPEREpiwlYJ-YnsLP816EFUuTBGY8ezHMc/s1600/MCR0198_WCanada.jpg" style="margin-left: auto; margin-right: auto;" /></td></tr>
<tr><td class="tr-caption" style="text-align: center;">Western Canada, 1990-style</td></tr>
</tbody></table>Compare Western Canada: the bold and well-muscled 1990 version, and the wrinkly (and pink!) 2008 version.<br />
<br />
<div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjzoSEu4nJ-zBm0dHJkFQoRAdWbKh-UsQSIX6ZWiZa7CQPVvwhfrAx7MJ4L7QVAy1TLjdP38x7BGwZq8CoKlaxEAYsAgZh2mUVhOds-bhrwWJhVJJRMDttiEc6MX39SqennV5WI-X6PTck/s1600/MCR0198_Scandinavia.jpg" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"></a></div>Yes, I'm not fond of the colour fill introduced on the more recent version to show national boundaries. It just seems distracting to me and I have a sense that they added it because the GIS software made it easy to do so. I want this to be a map of the physical landscape, not political landscape. The brightly coloured Scandinavian countries are like confetti over in the corner of the map, whereas in the former verison they were deliciously dark and complex entity.<br />
<br />
<div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhdOxtRQ9OFQOqCRoR0rghcXLxEXi9lFnT980DdXzo5gysP01iTbjxlc4vNDvkGH09FR9hQ6xqOvQfW3VUfv7dsuyh1vVzkhk9MhPng5PdeKunn9Esw9ThZ4vCnamNBu9snd98lh-GF83k/s1600/MCR0001_Scandinavia.jpg" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"></a></div><table cellpadding="0" cellspacing="0" class="tr-caption-container" style="float: left; text-align: left;"><tbody>
<tr><td style="text-align: center;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjzoSEu4nJ-zBm0dHJkFQoRAdWbKh-UsQSIX6ZWiZa7CQPVvwhfrAx7MJ4L7QVAy1TLjdP38x7BGwZq8CoKlaxEAYsAgZh2mUVhOds-bhrwWJhVJJRMDttiEc6MX39SqennV5WI-X6PTck/s1600/MCR0198_Scandinavia.jpg" style="margin-left: auto; margin-right: auto;" /></td></tr>
<tr><td class="tr-caption" style="text-align: center;">Scandinavia, 1990-style</td></tr>
</tbody></table><table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: right;"><tbody>
<tr><td style="text-align: center;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhdOxtRQ9OFQOqCRoR0rghcXLxEXi9lFnT980DdXzo5gysP01iTbjxlc4vNDvkGH09FR9hQ6xqOvQfW3VUfv7dsuyh1vVzkhk9MhPng5PdeKunn9Esw9ThZ4vCnamNBu9snd98lh-GF83k/s1600/MCR0001_Scandinavia.jpg" style="margin-left: auto; margin-right: auto;" /></td></tr>
<tr><td class="tr-caption" style="text-align: center;">Scandinavia, 2008-style</td></tr>
</tbody></table>I do appreciate the extension, below the 55 degrees north, of basemap features in the 2008 edition. On the 1990 edition nothing was shown south of that latitude but the water/land division. Now, the highway I live near, at 54<style type="text/css">
p { margin-bottom: 0.21cm; }
</style>º 40', is actually there, on the map.<br />
<br />
However, something was thrown away! Kamchatka, the Sakhalin Islands and the Aleutian Islands, which the artist gave shaded relief to in 1990 throughout their full extents, now have it cut off! Russia <i>needs</i> the full extent of Kamchatka, to emphasize Siberia's size and the way it overhangs the Pacific Ocean. Rendered this way, it just looks silly.<br />
<br />
<table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="float: left; margin-right: 1em; text-align: left;"><tbody>
<tr><td style="text-align: center;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiqsuS4DANRWO7pfGyQ8rwEPkQHrUvmaK_kDmSNF8qD7Y0zU5rOkMT2aA-yuNqIiWCmodhJUbuEn3YlpbRr3mhdJiumtspZm7rj3FpiUVUhY8-0w3dZopvbjEAARXc5ZPPceTsq6XKQD1o/s1600/MCR0198_Kamchatka.jpg" style="margin-left: auto; margin-right: auto;" /></td></tr>
<tr><td class="tr-caption" style="text-align: center;">Kamchatka, 1990-style</td></tr>
</tbody></table><table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: left;"><tbody>
<tr><td style="text-align: center;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgqS7qCeMCXZtOuVQ2ZZpl6ur4r2oX6vWfCI33vQyp3sAQVQKAF7_Uo5SljdHq-Ev1dlagGhg8eOeHw-XANUAeXJ7j6w07aTFll3ekoqb8D3UD1iCKUTJu9mmCtBA3S-1ijEhwullw-q8c/s1600/MCR0001_Kamchatka.jpg" style="margin-left: auto; margin-right: auto;" /></td></tr>
<tr><td class="tr-caption" style="text-align: center;">Kamchatka, 2008-style</td></tr>
</tbody></table><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiqsuS4DANRWO7pfGyQ8rwEPkQHrUvmaK_kDmSNF8qD7Y0zU5rOkMT2aA-yuNqIiWCmodhJUbuEn3YlpbRr3mhdJiumtspZm7rj3FpiUVUhY8-0w3dZopvbjEAARXc5ZPPceTsq6XKQD1o/s1600/MCR0198_Kamchatka.jpg" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"></a>And, as you can see in these details, the blues that represent ocean depth were deeper and darker in 1990, which also provided a better overall effect.<br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgqS7qCeMCXZtOuVQ2ZZpl6ur4r2oX6vWfCI33vQyp3sAQVQKAF7_Uo5SljdHq-Ev1dlagGhg8eOeHw-XANUAeXJ7j6w07aTFll3ekoqb8D3UD1iCKUTJu9mmCtBA3S-1ijEhwullw-q8c/s1600/MCR0001_Kamchatka.jpg" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"></a>I don't want to go on ranting here, because I'm not that great a map designer myself. But for GIS people designing maps, the 2008 map is a good lesson. Sometimes it's <i>harder</i> to achieve the effect you want using the latest tools.Morgan Hitehttp://www.blogger.com/profile/02187274906810012520noreply@blogger.com0tag:blogger.com,1999:blog-4352824282046201576.post-89449223810788452212010-07-30T13:56:00.000-07:002010-07-30T14:22:03.955-07:00Searching for Lareipel<a onblur="try {parent.deselectBloggerImageGracefully();} catch(e) {}" href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg-PcE3zdrfrp5msU9X888scvcN3v4Fj4GWzyIZZKSpk2QooGIMJLph-11Ap1ASHL494mKdD6viBItpuiGhUKPVqChcjZYjjPZp8n7WR0EMHN1BkJZVEAjw-fOSP95sXF1w1jxcr9FZK7U/s1600/Desceliers_Original_High.gif.jpg"><img style="float: right; margin: 0pt 0pt 10px 10px; cursor: pointer; width: 400px; height: 307px;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg-PcE3zdrfrp5msU9X888scvcN3v4Fj4GWzyIZZKSpk2QooGIMJLph-11Ap1ASHL494mKdD6viBItpuiGhUKPVqChcjZYjjPZp8n7WR0EMHN1BkJZVEAjw-fOSP95sXF1w1jxcr9FZK7U/s400/Desceliers_Original_High.gif.jpg" alt="" id="BLOGGER_PHOTO_ID_5499807084517701970" border="0" /></a> <style type="text/css"> <!-- @page { margin: 2cm } P { margin-bottom: 0.21cm } --> </style> <p style="margin-bottom: 0cm;"><span style="font-size:100%;">This is an image of a portion of the 1550 Desceliers map, courtesy of the Library and Archives Canada through the <a href="http://www.historicalatlas.ca/website/hacolp/national_perspectives/exploration/unit_05/images/Desceliers_Original_High.gif">Historical Atlas of Canada site</a>.</span></p> <style type="text/css"> <!-- @page { margin: 2cm } P { margin-bottom: 0.21cm } --> </style> <p style="margin-bottom: 0cm;"><span style="font-size:100%;">Pretty quickly you can recognize what's being depicted: with Florida and the Gulf of Mexico at the top, and “Canada” at the bottom, this is an upside down map of North America, drawn to the best of their knowledge mid-sixteenth century. Various places are recognizable. There's Newfoundland out at the mouth of the Gulf of St. Lawrence, labelled something like </span><span style="font-size:100%;"><i>Terre Nevfve, </i></span><span style="font-size:100%;">and the St. Lawrence River itself coming from a big lake inland.<br /></span></p><p style="margin-bottom: 0cm;"><span style="font-size:100%;"><br /></span> </p> <p style="margin-bottom: 0cm;"><span style="font-size:100%;">It's intriguing to see if you can find, on old maps, landmarks with recognizable place names that we use today. <a onblur="try {parent.deselectBloggerImageGracefully();} catch(e) {}" href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhEd1T-vXZoStJGy94SH1_xn4eIMaU-WcCxxHtZtlhAssG4jLPNQCFxQruWHxC1iDs5t10INoXw_DAAURjlufwiX0WO7YtxXZBufpX0WZIvuFNH95REjqsjEj2bGH-6DEYj7XXMhOKYl2Q/s1600/Desceliers+Newfoundland.jpg"><img style="float: right; margin: 0pt 0pt 10px 10px; cursor: pointer; width: 400px; height: 234px;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhEd1T-vXZoStJGy94SH1_xn4eIMaU-WcCxxHtZtlhAssG4jLPNQCFxQruWHxC1iDs5t10INoXw_DAAURjlufwiX0WO7YtxXZBufpX0WZIvuFNH95REjqsjEj2bGH-6DEYj7XXMhOKYl2Q/s400/Desceliers+Newfoundland.jpg" alt="" id="BLOGGER_PHOTO_ID_5499809267291598434" border="0" /></a>For example, Cape Race, at the southeast corner of Newfoundland, is there in the Desceliers map as </span><span style="font-size:100%;"><i>C: de Raz</i></span><span style="font-size:100%;">. Just west of it along Newfoundland's south shore is Cape St. Mary, as </span><span style="font-size:100%;"><i>C: S</i></span><sup><span style="font-size:100%;"><i>t</i></span></sup><span style="font-size:100%;"><i> M</i></span><sup><span style="font-size:100%;"><i>e</i></span></sup><span style="font-size:100%;">.<br /></span></p><p style="margin-bottom: 0cm;"><span style="font-size:100%;"><br /></span> </p> <p style="margin-bottom: 0cm;"><span style="font-size:100%;">But some of the place names on this map are different. For example Prince Edward Island, the bright red island west of Newfoundland in the Gulf of St. Lawrence, easily recognizable by its crescent shape, is </span><span style="font-size:100%;"><i>Y</i></span><sup><span style="font-size:100%;"><i>e</i></span></sup><span style="font-size:100%;"> </span><span style="font-size:100%;"><i>des avenes</i></span><span style="font-size:100%;"> </span><span style="font-family:Liberation Serif,serif;"><span style="font-size:100%;">(Île </span></span><span style="font-size:100%;">des avenes, meaning Isle of the Birds?). It's a common story in eastern Canada that names given by the French when it was </span><span style="font-size:100%;"><i>Nouvelle France</i></span><span style="font-size:100%;"> were overwritten later by the British when they expelled the French in the eighteenth century. So seeing these early French names is like peeling back the wallpaper to uncover how the room was decorated by the previous owners.<br /></span></p><p style="margin-bottom: 0cm;"><span style="font-size:100%;"><br /></span> </p><br /><style type="text/css"> <!-- @page { margin: 2cm } P { margin-bottom: 0.21cm } --></style> <span style="font-size:100%;">However, this replacement of names is generally not the case in Quebec, which retains most of the original French names. And in fact, looking over at the area up the <a onblur="try {parent.deselectBloggerImageGracefully();} catch(e) {}" href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiIp2ca84oDawqsDOwh-bWw-f91Q2H5f0gbwJ2VhxDpjQKpMmay5sM84CRAHnKIMdBYFVnC13owDvX451is1Wer8ASXm8K2pX9gYEqRUCpu1oJsngCGPAK7S0tXQ6yHyxM2U0KjMgGeSuc/s1600/Desceliers+St+Lawrence.jpg"><img style="float: right; margin: 0pt 0pt 10px 10px; cursor: pointer; width: 400px; height: 293px;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiIp2ca84oDawqsDOwh-bWw-f91Q2H5f0gbwJ2VhxDpjQKpMmay5sM84CRAHnKIMdBYFVnC13owDvX451is1Wer8ASXm8K2pX9gYEqRUCpu1oJsngCGPAK7S0tXQ6yHyxM2U0KjMgGeSuc/s400/Desceliers+St+Lawrence.jpg" alt="" id="BLOGGER_PHOTO_ID_5499810042648477234" border="0" /></a>St. Lawrence, you can see a red island where the river narrows, labelled</span><span style="font-size:100%;"> </span><span style="font-size:100%;"><i>Y</i></span><sup><span style="font-size:100%;"><i>e</i></span></sup><span style="font-size:100%;"><i> dorle, </i></span><span style="font-size:100%;">probably today's</span><span style="font-size:100%;"><i> </i></span><span style="font-size:100%;"> </span><span style="font-family:Liberation Serif,serif;"><span style="font-size:100%;">Île</span></span><span style="font-size:100%;"> d'Orleans, next to the city of Quebec. The big river flowing into the St. Lawrence just downstream, labelled </span><span style="font-size:100%;"><i>R. de saqnay,</i></span><span style="font-size:100%;"> and coming from a region labelled </span><span style="font-size:100%;"><i>Sagne</i></span><span style="font-size:100%;"> must be the Saguenay River. These are easy connections to make, but they are satisfying.<br /><br /></span><p style="margin-bottom: 0cm;"> </p> <p style="margin-bottom: 0cm;"><span style="font-size:100%;">What really sticks out like a sore thumb here is that big gold island at the mouth of the St. Lawrence. That can only be the </span><span style="font-size:100%;"><span style="font-style: normal;">Île d'Anticosti, but it's labelled </span></span><span style="font-size:100%;"><i>Y</i></span><sup><span style="font-size:100%;"><i>e </i></span></sup><span style="font-size:100%;"><i>de Taveipel,</i></span><span style="font-size:100%;"><span style="font-style: normal;"> or </span></span><span style="font-size:100%;"><i>Laveipel. </i></span><span style="font-size:100%;"><span style="font-style: normal;">What is that? And the lake upstream , perhaps Lake Ontario, or even the smaller Lac de St. Pierre (which his halfway between Montreal and Quebec City) seems to be labelled </span></span><span style="font-size:100%;"><i>Le</i></span><span style="font-size:100%;"><span style="font-style: normal;"> </span></span><span style="font-size:100%;"><i>Lac daugonlusme</i></span><span style="font-size:100%;"><span style="font-style: normal;">. What is that?</span></span></p><p style="margin-bottom: 0cm;"><span style="font-size:100%;"><span style="font-style: normal;"><br /></span></span></p> <p style="margin-bottom: 0cm;"><span style="font-size:100%;">As I started to look further afield for some record of these old names, my interest was sharpened by the discovery that Google returns </span><span style="font-size:100%;"><b>no</b></span><span style="font-size:100%;"> results for</span><span style="font-size:100%;"><span style="font-style: normal;"> Taveipel, Laveipel or daugonlusme. I have still not found the answers of what these names meant, but I have learned more.</span></span></p><p style="margin-bottom: 0cm;"><span style="font-size:100%;"><span style="font-style: normal;"><br /></span></span></p><p style="margin-bottom: 0cm;"><span style="font-size:100%;">The Desceliers map, in the St. Lawrence area, had to have been based on information gathered during the voyages of Jacques Cartier. Cartier travelled to New France in 1534, 1535 and 1536. Although he was a successor to Columbus, Cabot, Verrazano, Gomez and others, he was the first European explorer to push up a big river in North America. All of the others had noted rivers, and named them, but had sailed past them, looking only for the large sea passage that would lead to the Orient. Cartier's exploration around the Gulf of St. Lawrence (the water between Newfoundland and the mouth of the St. Lawrence) and up the St. Lawrence River itself marks, in effect, Europeans finally letting go of the dream of a shortcut to China, and taking a closer look at the new world they had on their hands. Exploration of the St. Lawrence, then, predates exploration up the Hudson, or into Chesapeake Bay.</span></p><p style="margin-bottom: 0cm;"><span style="font-size:100%;"><br /></span> </p> <p style="margin-bottom: 0cm;"><span style="font-size:100%;"><span style="font-style: normal;"><a onblur="try {parent.deselectBloggerImageGracefully();} catch(e) {}" href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjb_4xpLB8m7oU9D3wtDeQA406TLHLm-yI0-e_r93IAMr9imv1IJlHwXI1IZrJfGZrInmmO9wuOwDqkRE2wR6uErkm4XkJAwcb6vigXXP9SW3BnW3GU1UimLfNNSRYLFMVHD-zT8BWZC6E/s1600/Montreal+to+Newfoundland.png"><img style="float: right; margin: 0pt 0pt 10px 10px; cursor: pointer; width: 400px; height: 171px;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjb_4xpLB8m7oU9D3wtDeQA406TLHLm-yI0-e_r93IAMr9imv1IJlHwXI1IZrJfGZrInmmO9wuOwDqkRE2wR6uErkm4XkJAwcb6vigXXP9SW3BnW3GU1UimLfNNSRYLFMVHD-zT8BWZC6E/s400/Montreal+to+Newfoundland.png" alt="" id="BLOGGER_PHOTO_ID_5499810619644960690" border="0" /></a>When Cartier went up the St. Lawrence he found two native Iroquois communities: the Stadaconans, who lived near present day Quebec (the narrowing of the river above the red island) , and the Hochlagans, who lived on the island where today's city of Montreal sits. He wintered with the Stadaconans. Both Stadacona and Hochelaga appear on the map repeatedly around the St. Lawrence as </span></span><span style="font-size:100%;"><i>ochelaga </i></span><span style="font-size:100%;"><span style="font-style: normal;">and</span></span><span style="font-size:100%;"><i> estadacone, </i></span><span style="font-size:100%;"><span style="font-style: normal;">but not in any one specific place. What seems to read </span></span><span style="font-size:100%;"><i>Totunagi</i></span><span style="font-size:100%;"><span style="font-style: normal;">, deep inland where another big river joins the St. Lawrence, could be Tutonaguy, which was one of two villages Cartier mentions at Hochelaga. (The Ottawa River joins the St. Lawrence at Montreal.)</span></span></p><p style="margin-bottom: 0cm;"><span style="font-size:100%;"><span style="font-style: normal;"><br /></span></span></p> <p style="margin-bottom: 0cm;"><span style="font-size:100%;">A couple days after I began studying this map, I noticed that, on the Desceliers map, on the north shore of the St. Lawrence, across from the gold island, there is a </span><span style="font-size:100%;"><i>R: de Lareipel. </i></span><span style="font-size:100%;"><span style="font-style: normal;">This has to be the same name as the island, but being printed more clearly reveals that </span></span><span style="font-size:100%;">I had been reading the island's name wrong: it is </span><span style="font-size:100%;"><i>Île</i></span><span style="font-size:100%;"><i> de Lareipel</i></span><span style="font-size:100%;">. Still no Google results though.</span></p><p style="margin-bottom: 0cm;"><span style="font-size:100%;"><br /></span></p> <p style="margin-top: 0.21cm;"><span style="font-size:100%;"><a onblur="try {parent.deselectBloggerImageGracefully();} catch(e) {}" href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjrXvLqACKLY0bF_3sQjNgQvzBZD6JdJPN5OfU4E-mBaL47N3lNOQIlr0y0snWIBgku8xXjY77IHPrzk1VmmW9GTtjhUcgRQ8uHIcjr8cvcQJepM5ntgSC8OdROJcOTtnBaSpsOqNmvAPM/s1600/Montreal+to+Quebec.png"><img style="float: right; margin: 0pt 0pt 10px 10px; cursor: pointer; width: 400px; height: 171px;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjrXvLqACKLY0bF_3sQjNgQvzBZD6JdJPN5OfU4E-mBaL47N3lNOQIlr0y0snWIBgku8xXjY77IHPrzk1VmmW9GTtjhUcgRQ8uHIcjr8cvcQJepM5ntgSC8OdROJcOTtnBaSpsOqNmvAPM/s400/Montreal+to+Quebec.png" alt="" id="BLOGGER_PHOTO_ID_5499811318446209762" border="0" /></a>The lake up the St. Lawrence (Le Lac daugonlusme) is most likely Lac Saint-Pierre for several reasons. Cartier never made it to Lake Ontario. The splitting of the river at Totunagi corresponds to the way the Ottawa river comes in from the northwest at Montreal. Lac Saint-Pierre is the only lake along the river downstream from Montreal, and, just as on the Desceliers map, there is a major river entering the lake from the south: we call it now the Saint Francois.</span></p><p style="margin-top: 0.21cm;"><span style="font-size:100%;"><br /></span></p><span style="font-size:100%;">Other named features along the St. Lawrence to Saguenay include </span><span style="font-size:100%;"><i>R[ivier]: de toues </i></span><span style="font-size:100%;"><span style="font-style: normal;"> and </span></span><span style="font-size:100%;"><i>B[aie]: de Lisler</i></span><span style="font-size:100%;"><span style="font-style: normal;">. </span></span><span style="font-size:100%;"><i>R: de toues </i></span><span style="font-size:100%;"><span style="font-style: normal;">must be today's Rivier Saint Maurice. </span></span><span style="font-size:100%;"><i> (Toues</i></span><span style="font-size:100%;"><span style="font-style: normal;"> appear to be a kind of boat.) But Lisler, like Lareipel, does not show up on an internet search.<br /><br /></span></span> <p style="margin-bottom: 0cm;"><span style="font-style: normal;">In the end, this map gives up some names, but others it withholds. It's an intriguing and ongoing puzzle.</span></p>Morgan Hitehttp://www.blogger.com/profile/02187274906810012520noreply@blogger.com0tag:blogger.com,1999:blog-4352824282046201576.post-91597540872450548572010-07-23T16:32:00.000-07:002010-07-23T16:38:11.275-07:00Collective NounsI saw these enjoyable examples of <span style="font-weight: bold;">collective nouns with plural verbs</span> in England:<p></p> <p style="margin-bottom: 0cm; text-align: center;"><span style="font-weight: bold;"></span></p><blockquote><span style="font-weight: bold;">We are an agency that become excitable when...</span> (an ad for an advertising agency)</blockquote><p></p> <p style="margin-bottom: 0cm; text-align: center;"><span style="font-weight: bold;"></span></p><blockquote><span style="font-weight: bold;">When England win, you win....</span> (a billboard ad for some kind of deal whereby when England would win a game in the World Cup, you'd win a ...?)</blockquote><p></p> <p style="margin-bottom: 0cm;">So what is the deal with collective nouns and plural verbs? Why do these sound so wrong to us, yet, find their way past proofreaders and editors in the UK?<br /></p><p style="margin-bottom: 0cm;">In North American we tend to use a singular<span style="font-style: normal;"> verb with collective nouns. We would write, “The school board says...” or “Parliament is sitting.” However in England the preference is to use plural verbs, as in the examples above.</span></p> <p style="margin-bottom: 0cm;"><span style="font-style: normal;">Alan Garner is, as always, pithy on this subject:</span></p> <p style="margin-bottom: 0cm;"><span style="font-style: normal;"></span></p><blockquote><span style="font-style: normal;">The main consideration in handling [collective nouns] skillfuly is consistency in the use of a singlular or plural verb. If, in the beginning of an essay, the phrasing is </span><i>the faculty was</i><span style="font-style: normal;">, then every reference to </span><i>faculty</i><span style="font-style: normal;"> as a noun should be singluar throughout the whole. On the other hand, a writer who wishes to emphasize the individual persons more than the body of persons may decide to write </span><i>the faculty were</i><span style="font-style: normal;">, although </span><i> members of the faculty were</i><span style="font-style: normal;"> is prefereable because it's more accurate. [</span><i>A Dictionary of Modern American Usage</i><span style="font-style: normal;">, p. 133]</span></blockquote><span style="font-style: normal;"></span><p></p> <p style="margin-bottom: 0cm;"><br /></p> <p style="margin-bottom: 0cm;"><br /></p>Morgan Hitehttp://www.blogger.com/profile/02187274906810012520noreply@blogger.com0tag:blogger.com,1999:blog-4352824282046201576.post-55116871267328113492010-05-17T15:00:00.000-07:002010-05-18T11:37:03.727-07:00Letter to the Safety Committee: Speedwell CavernDear Safety Committee;<br /><br />I had the pleasure today of visiting Speedwell Cavern. Despite its name it is not a cavern at all, but rather an old mine: its claim to fame is that you travel through it by boat in a flooded mining tunnel. Quite exotic. But what was really interesting about it in the end (for the tunnel was monotonous and the small cavern at its end offered nothing to write about) was how the tour was done. It was, if you will, Safety, The Old Way.<br /><br />This was a lead mine in the late eighteenth century, and the method devised to get the ore out was to flood one of the tunnels and hand a boat along it. Dry, the tunnel was about 6 feet high; flooded its arched, uneven roof of stone is about four feet high <span style="font-style: italic;">in the centre</span>. The modern boat (four feet wide in a five foot wide tunnel) has an electric motor at each end, and seats for the tourists.<br /><br />Before you descend to the underground artificial river, they pass out hard hats. I have to say I have been jaded by the Corporate Safety Culture, which makes unnecessary gestures to lull the visitor into a sense of security. I thought, "Oh, yes, the usual safety equipment: probably overkill, but it protects the odd visitor who's accident prone." But no! As I descended the 106 wet, slippery stairs, I found myself, like an idiot, checking with my head the contours of the remarkably low ceiling many times. Gee, I thought, I can't believe the ceiling is this low... this is like going down in the real thing.<br /><br />At the bottom our young guide, James, straddled the boat and held it in place by leaning against the tunnel wall while we boarded. Then he walked deftly up the edge of the boat to the bow, and, after telling us some good jokes and warning us to keep our hands inside the gunwales, switched on the motor. Then he, with <span style="font-style: italic;">no</span> hard hat on, sat facing <span style="font-style: italic;">backwards</span> in the bow talking to us. It was truly an impressive feat of skill: using his hands against the tunnel walls to steer the boat in a direction that was behind him, he kept up a steady patter of facts and stories while the tunnel roof whizzed over our protected (and his unprotected) heads.<br /><br />And this was when I realized I had left the realm of Corporate Safety. Because, as you know, safe operations are never based on the skill and bravado of the guide, nor on common sense. I had found a gem that has somehow survived from the past. Safe operations are today always based on redundant systems. Instead of one guide there are two. Everyone wears safety equipment, <span style="font-style: italic;">especially</span> the guides. In the even of engine failure, a second engine stands by or a handline along the tunnel walls provides a way to get back. It was quite apparent that in this case, engine failure would mean we all simply hand-pushed the boat back. I felt valued.<br /><br />As we motored along through the tunnel a direct hit from one of the outcrops whizzing my head would have knocked me out without that hat. Furthermore, as I looked at James in the front of the boat there, jovially regaling us with tales, and the uneven tunnel roof zooming over his head from behind, I realized that he pretty much knew exactly how high he could raise his head. But there was no overhead hoop on the boat to cue him, no safety system in place. I was watching skill at work, not a well-designed system.<br /><br />At various points of interest he would reach down and switch off the electric motor. As the boat glided quietly along he'd tell us the tale of some mining mishap or another, and that done, he'd reach down and turn the switch on again. Oh-ho, I though: no deadman switch! Had the Corporate Safety philosophy been at work here, the motor would only be on only as long as he was there to hold down a spring-loaded switch; if he miscalculated and was whacked by an overhead outcrop, if he tumbled over backwards and fell out in front of the oncoming boat, the motor would cut out. But not in this case. It was a case of safety being based on someone's strength, balance and grace. Don't our analysts always see that as a safety weakness?<br /><br />And it just got better. We reached the far cavern and all got out to view it. After five minutes it was time to reload. James got into the boat first, and launched off when when we had all got in. Yep, you guessed it: whether we left someone behind was dependent on his good counting, or the good shouting of the forgotten passenger--not on having a sweep person, or a rule that the guide is the last one off the wharf.<br /><br />The bottom line here is that I so admire his employers because they <span style="font-style: italic;"><span style="font-weight: bold;">trust</span></span><span style="font-weight: bold; font-style: italic;"></span> him. It is evident that if something goes wrong , they trust he'll be able to figure out what to do, and the passengers might be involved in solving it too. In fact they trust people in general: not to stick their heads up too high in the boat, not to stick their hands out where they can be chopped off.<br /><br />Just thought you guys should know: your reach is mighty, but it does not yet go everywhere.Morgan Hitehttp://www.blogger.com/profile/02187274906810012520noreply@blogger.com0tag:blogger.com,1999:blog-4352824282046201576.post-42634905743588239342010-04-07T07:45:00.000-07:002010-05-03T07:50:47.781-07:00The laying of a nickel on the train trackThe laying of a nickel on the train track has its origins in me, as a<br />five year-old, standing with my mom in Pasadena, California, where my<br />grandmother lived, watching the "Santa Fe Super Chief" roll in to the<br />station.<br /><br />The Super Chief was one of these iconic American trains with a<br />special paint job, and I can just imagine my mom thinking, "Oh, I'll take<br />my little boy down to see the train come in [it would roll right through<br />town and cross several streets]: he'll like that." She puts a penny on<br />the tracks, which are right at street level and I watch with delight as<br />it gets squashed by the giant engine into an oval, coppery smear. I keep<br />it for years after.<br /><br />So it actually has nothing to do with good luck or a safe journey.<br /><br />The last few years, when I would suggest to Galen and Will that we put a<br />penny on the tracks they would howl at me with horror: something about<br />not squashing the queen. Anyway, it was forbidden. So it was with<br />surprise this week that I heard them say, "Sure!" and then proceed to<br />contend over who would get to KEEP the squashed nickel.<br /><br />Well, a nickel, it turns out, does not squash as well as an old, soft,<br />copper penny. What you get is more of a "bent nickel," the result of<br />it being churned and flipped by the engine wheels.<br /><br />We're looking now for older, all-copper pennies. The current issue<br />Canadian penny is a steel blank with copper electroplating. We have to go back to 1996 for real copper pennies.Morgan Hitehttp://www.blogger.com/profile/02187274906810012520noreply@blogger.com0