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	<title>representations &amp;laquo; WordPress.com Tag Feed</title>
	<link>http://en.wordpress.com/tag/representations/</link>
	<description>Feed of posts on WordPress.com tagged "representations"</description>
	<pubDate>Thu, 24 Dec 2009 11:19:17 +0000</pubDate>

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<item>
<title><![CDATA[Groupings, Shopping Lists, Vectors: part 7]]></title>
<link>http://unlearningmath.com/2009/12/23/groupings-shopping-lists-vectors-part-7/</link>
<pubDate>Wed, 23 Dec 2009 11:17:57 +0000</pubDate>
<dc:creator>Bert Speelpenning</dc:creator>
<guid>http://unlearningmath.com/2009/12/23/groupings-shopping-lists-vectors-part-7/</guid>
<description><![CDATA[In part 6 of this series, I introduced an operation called inner product between two vectors, as a w]]></description>
<content:encoded><![CDATA[<div class='snap_preview'><p>In <a href="http://unlearningmath.com/2009/12/20/groupings-shopping-lists-vectors-part-6/">part 6</a> of this series, I introduced an operation called<em> inner product</em> between two vectors, as a way to find the total price of an order using a price list.  In this post, I want to give a bunch of other examples where the same pattern shows up.</p>
<p>But before I do so, I want to &#8216;fess up&#8217; to something.  It&#8217;s the kind of thing that irritates me when I see others do it.  I did something that didn&#8217;t make any particular sense in the context in which I used it &#8211; it only makes sense in a future setting, in this case a setting that is several posts away.  We do this in math class all the time: we put the motivation into the future &#8220;some day this will all make sense.  You need this because of the 9th grade test, or because of graduate school.&#8221;  Instead, I think it is really important that the math makes sense now, always now, not in the future.<br />
Truth is that my displaying the vector inner product using one horizontal vector and one vertical vector was not something that was particularly appropriate in the problem setting that I used.  It may have gotten in the way somewhat.  So let me correct that here and use a representation that is appropriate to the situation at hand.</p>
<p>Instead of this representation:</p>
<table border="0" cellspacing="0" cellpadding="0">
<tbody>
<tr>
<td width="43" valign="top"></td>
<td width="138" valign="top">
<table border="1" cellspacing="0" cellpadding="0">
<tbody>
<tr>
<td width="100" valign="top">cheeseburger</td>
<td width="43" valign="top">$1.50</td>
</tr>
<tr>
<td width="100" valign="top">chickenburger</td>
<td width="43" valign="top">$1.80</td>
</tr>
<tr>
<td width="100" valign="top">coke</td>
<td width="43" valign="top">$1.20</td>
</tr>
<tr>
<td width="100" valign="top">diet coke</td>
<td width="43" valign="top">$1.20</td>
</tr>
<tr>
<td width="100" valign="top">fries</td>
<td width="43" valign="top">$1.50</td>
</tr>
<tr>
<td width="100" valign="top">hamburger</td>
<td width="43" valign="top">$1.40</td>
</tr>
<tr>
<td width="100" valign="top">ice cream treat</td>
<td width="43" valign="top">$1.90</td>
</tr>
<tr>
<td width="100" valign="top">kid meal</td>
<td width="43" valign="top">$3.00</td>
</tr>
</tbody>
</table>
</td>
</tr>
<tr>
<td width="43" valign="top">
<table border="1" cellspacing="0" cellpadding="0">
<tbody>
<tr>
<td width="43" valign="top">coke</td>
<td width="70" valign="top">cheeseburger</td>
<td width="70" valign="top">hamburger</td>
<td width="45" valign="top">fries</td>
</tr>
<tr>
<td valign="top">3</td>
<td valign="top">1</td>
<td valign="top">5</td>
<td valign="top">2</td>
</tr>
</tbody>
</table>
</td>
<td width="138" valign="top">
<table border="0" cellspacing="0" cellpadding="0">
<tbody>
<tr>
<td width="100" valign="top"></td>
<td width="43" valign="top">$</td>
</tr>
<tr>
<td valign="top"></td>
<td valign="top">$15.10</td>
</tr>
</tbody>
</table>
</td>
</tr>
</tbody>
</table>
<p>it would be more natural to use a representation like this (which more closely matches many order forms you may see):</p>
<table border="0" cellspacing="0" cellpadding="0">
<tbody>
<tr>
<td width="100" valign="top"><span style="color:#0000ff;">Item</span></td>
<td width="43" valign="top"><span style="color:#0000ff;">Price</span></td>
<td style="text-align:center;" width="20" valign="top"><span style="color:#0000ff;">×</span></td>
<td style="text-align:center;" width="45" valign="top"><span style="color:#0000ff;">Order</span></td>
<td style="text-align:center;" width="20" valign="top"><span style="color:#0000ff;">=</span></td>
<td width="43" valign="top"><span style="color:#0000ff;">Amount</span></td>
</tr>
<tr>
<td width="100" valign="top">cheeseburger</td>
<td width="43" valign="top">$1.50</td>
<td style="text-align:center;" width="20" valign="top">×</td>
<td style="text-align:center;" width="45" valign="top">1</td>
<td style="text-align:center;" width="20" valign="top">=</td>
<td style="text-align:right;" width="43" valign="top">$1.50</td>
</tr>
<tr>
<td width="100" valign="top">chickenburger</td>
<td width="43" valign="top">$1.80</td>
<td style="text-align:center;" width="20" valign="top">×</td>
<td style="text-align:center;" width="45" valign="top"></td>
<td style="text-align:center;" width="20" valign="top">=</td>
<td width="43" valign="top"></td>
</tr>
<tr>
<td width="100" valign="top">coke</td>
<td width="43" valign="top">$1.20</td>
<td style="text-align:center;" width="20" valign="top">×</td>
<td style="text-align:center;" width="45" valign="top">3</td>
<td style="text-align:center;" width="20" valign="top">=</td>
<td style="text-align:right;" width="43" valign="top">$3.60</td>
</tr>
<tr>
<td width="100" valign="top">diet coke</td>
<td width="43" valign="top">$1.20</td>
<td style="text-align:center;" width="20" valign="top">×</td>
<td style="text-align:center;" width="45" valign="top"></td>
<td style="text-align:center;" width="20" valign="top">=</td>
<td width="43" valign="top"></td>
</tr>
<tr>
<td width="100" valign="top">fries</td>
<td width="43" valign="top">$1.50</td>
<td style="text-align:center;" width="20" valign="top">×</td>
<td style="text-align:center;" width="45" valign="top">2</td>
<td style="text-align:center;" width="20" valign="top">=</td>
<td style="text-align:right;" width="43" valign="top">$3.00</td>
</tr>
<tr>
<td width="100" valign="top">hamburger</td>
<td width="43" valign="top">$1.40</td>
<td style="text-align:center;" width="20" valign="top">×</td>
<td style="text-align:center;" width="45" valign="top">5</td>
<td style="text-align:center;" width="20" valign="top">=</td>
<td style="text-align:right;" width="43" valign="top">$7.00</td>
</tr>
<tr>
<td width="100" valign="top">ice cream treat</td>
<td width="43" valign="top">$1.90</td>
<td style="text-align:center;" width="20" valign="top">×</td>
<td style="text-align:center;" width="45" valign="top"></td>
<td style="text-align:center;" width="20" valign="top">=</td>
<td width="43" valign="top"></td>
</tr>
<tr>
<td width="100" valign="top">kid meal</td>
<td width="43" valign="top">$3.00</td>
<td style="text-align:center;" width="20" valign="top">×</td>
<td style="text-align:center;" width="45" valign="top"></td>
<td style="text-align:center;" width="20" valign="top">=</td>
<td width="43" valign="top"></td>
</tr>
<tr>
<td width="100" valign="top"></td>
<td width="43" valign="top"></td>
<td style="text-align:center;" width="20" valign="top"></td>
<td style="text-align:center;" width="45" valign="top"><span style="color:#993300;">Total</span></td>
<td style="text-align:center;" width="20" valign="top"><span style="color:#993300;">=</span></td>
<td style="text-align:right;" width="43" valign="top"><span style="color:#993300;">$15.10</span></td>
</tr>
</tbody>
</table>
<p>This representation matches more clearly how most of us would think about an order being priced.  The two starting vectors(the order vector and the price vector) can be seen in this arrangement, though they are a bit indistinct.  If you&#8217;d feel better if the blank entries are replaced by zeros, you are welcome to do it that way:</p>
<table border="0" cellspacing="0" cellpadding="0">
<tbody>
<tr>
<td width="100" valign="top"><span style="color:#0000ff;">Item</span></td>
<td width="43" valign="top"><span style="color:#0000ff;">Price</span></td>
<td width="20" valign="top"><span style="color:#0000ff;">×</span></td>
<td style="text-align:center;" width="45" valign="top"><span style="color:#0000ff;">Order</span></td>
<td width="20" valign="top"><span style="color:#0000ff;">=</span></td>
<td width="43" valign="top"><span style="color:#0000ff;">Amount</span></td>
</tr>
<tr>
<td width="100" valign="top">cheeseburger</td>
<td width="43" valign="top">$1.50</td>
<td width="20" valign="top">×</td>
<td style="text-align:center;" width="45" valign="top">1</td>
<td width="20" valign="top">=</td>
<td style="text-align:right;" width="43" valign="top">$1.50</td>
</tr>
<tr>
<td width="100" valign="top">chickenburger</td>
<td width="43" valign="top">$1.80</td>
<td width="20" valign="top">×</td>
<td style="text-align:center;" width="45" valign="top">0</td>
<td width="20" valign="top">=</td>
<td style="text-align:right;" width="43" valign="top">$0.00</td>
</tr>
<tr>
<td width="100" valign="top">coke</td>
<td width="43" valign="top">$1.20</td>
<td width="20" valign="top">×</td>
<td style="text-align:center;" width="45" valign="top">3</td>
<td width="20" valign="top">=</td>
<td style="text-align:right;" width="43" valign="top">$3.60</td>
</tr>
<tr>
<td width="100" valign="top">diet coke</td>
<td width="43" valign="top">$1.20</td>
<td width="20" valign="top">×</td>
<td style="text-align:center;" width="45" valign="top">0</td>
<td width="20" valign="top">=</td>
<td style="text-align:right;" width="43" valign="top">$0.00</td>
</tr>
<tr>
<td width="100" valign="top">fries</td>
<td width="43" valign="top">$1.50</td>
<td width="20" valign="top">×</td>
<td style="text-align:center;" width="45" valign="top">2</td>
<td width="20" valign="top">=</td>
<td style="text-align:right;" width="43" valign="top">$3.00</td>
</tr>
<tr>
<td width="100" valign="top">hamburger</td>
<td width="43" valign="top">$1.40</td>
<td width="20" valign="top">×</td>
<td style="text-align:center;" width="45" valign="top">5</td>
<td width="20" valign="top">=</td>
<td style="text-align:right;" width="43" valign="top">$7.00</td>
</tr>
<tr>
<td width="100" valign="top">ice cream treat</td>
<td width="43" valign="top">$1.90</td>
<td width="20" valign="top">×</td>
<td style="text-align:center;" width="45" valign="top">0</td>
<td width="20" valign="top">=</td>
<td style="text-align:right;" width="43" valign="top">$0.00</td>
</tr>
<tr>
<td width="100" valign="top">kid meal</td>
<td width="43" valign="top">$3.00</td>
<td width="20" valign="top">×</td>
<td style="text-align:center;" width="45" valign="top">0</td>
<td width="20" valign="top">=</td>
<td style="text-align:right;" width="43" valign="top">$0.00</td>
</tr>
<tr>
<td width="100" valign="top"></td>
<td width="43" valign="top"></td>
<td width="20" valign="top"></td>
<td style="text-align:center;" width="45" valign="top"><span style="color:#993300;">Total</span></td>
<td width="20" valign="top"><span style="color:#993300;">=</span></td>
<td style="text-align:right;" width="43" valign="top"><span style="color:#993300;">$15.10</span></td>
</tr>
</tbody>
</table>
<p>OK &#8211; now on to other examples of inner products.</p>
<p><strong>Weighted Average</strong> &#8211; One that most teachers are familiar with is that of computing an average score based on a series of tests, each with its own weight.  So let&#8217;s say there was a test in September, and one in October, and one in November, and a final in December.  Let&#8217;s say the scores on each are in the range from 0 to 100, and that the final is supposed to count twice as heavily as the other tests.</p>
<p>The weights vector would be:</p>
<table border="1" cellspacing="0" cellpadding="0">
<tbody>
<tr>
<td style="text-align:center;" width="80" valign="top">September</td>
<td style="text-align:center;" width="43" valign="top">.20</td>
</tr>
<tr>
<td style="text-align:center;" width="80" valign="top">October</td>
<td style="text-align:center;" width="43" valign="top">.20</td>
</tr>
<tr>
<td style="text-align:center;" width="80" valign="top">November</td>
<td style="text-align:center;" width="43" valign="top">.20</td>
</tr>
<tr>
<td style="text-align:center;" width="80" valign="top">December</td>
<td style="text-align:center;" width="43" valign="top">.40</td>
</tr>
</tbody>
</table>
<p>The weight vector is the same for all students, and is independent of the scores.</p>
<p>A particular student would have a set of scores.  Let&#8217;s assume Jesse&#8217;s scores are like this:</p>
<table border="1" cellspacing="0" cellpadding="0">
<tbody>
<tr style="text-align:center;">
<td width="80" valign="top">September</td>
<td style="text-align:center;" width="43" valign="top">60</td>
</tr>
<tr>
<td style="text-align:center;" width="80" valign="top">October</td>
<td style="text-align:center;" width="43" valign="top">70</td>
</tr>
<tr>
<td style="text-align:center;" width="80" valign="top">November</td>
<td style="text-align:center;" width="43" valign="top">50</td>
</tr>
<tr>
<td style="text-align:center;" width="80" valign="top">December</td>
<td style="text-align:center;" width="43" valign="top">100</td>
</tr>
</tbody>
</table>
<p>The final score for Jesse would be the inner product of his score vector and the weights vector:<br />
60 × .20 + 70 × .20 + 50 × .20 + 100 × .40 = 12 + 14 + 10 + 40 = 76.</p>
<p>(This matches the result you&#8217;d get if you took the average of 60, 70, 50, 100, 100 where you&#8217;d repeat the December score twice.  That&#8217;s another way to give the December score double the weight of the others.  60 + 70 + 50 + 100 + 100 = 380, and if you divide that by 5 &#8211; which is the number of scores added together &#8211; you get the same 76.)</p>
<p><strong>Total Calories</strong> &#8211; Just like we can price an order by computing the inner product of the order vector with a price vector, we can get the total calories of an order by computing the inner product of the order vector with a calorie vector.</p>
<p><strong>Number of Cups</strong> &#8211; We can keep track of inventory through inner products, too.  A store will typically want to replace the inventory that&#8217;s been sold, and for that it wants to keep track of the total amount sold.  This is probably most useful  when done for a particular period, like a day.  To keep the example simple, let&#8217;s assume we&#8217;re keeping track for each single order (and then add these up for all orders in a day).  The store would want to keep track of the number of hamburger patties used up, the number of slices of pickle used, etc.  In this example, we&#8217;ll keep track of the number of cups used for a particular order.  Again, this can be done by taking the inner product of the order vector with the following vector:</p>
<table border="1" cellspacing="0" cellpadding="0">
<tbody>
<tr>
<td width="100" valign="top">cheeseburger</td>
<td style="text-align:center;" width="43" valign="top">0</td>
</tr>
<tr>
<td width="100" valign="top">chickenburger</td>
<td style="text-align:center;" width="43" valign="top">0</td>
</tr>
<tr>
<td width="100" valign="top">coke</td>
<td style="text-align:center;" width="43" valign="top">1</td>
</tr>
<tr>
<td width="100" valign="top">diet coke</td>
<td style="text-align:center;" width="43" valign="top">1</td>
</tr>
<tr>
<td width="100" valign="top">fries</td>
<td style="text-align:center;" width="43" valign="top">0</td>
</tr>
<tr>
<td width="100" valign="top">hamburger</td>
<td style="text-align:center;" width="43" valign="top">0</td>
</tr>
<tr>
<td width="100" valign="top">ice cream treat</td>
<td style="text-align:center;" width="43" valign="top">0</td>
</tr>
<tr>
<td width="100" valign="top">kid meal</td>
<td style="text-align:center;" width="43" valign="top">1</td>
</tr>
</tbody>
</table>
<p>which we might name the &#8220;cup vector&#8221;.  You can verify for yourself that the inner product of our example order</p>
<table border="1" cellspacing="0" cellpadding="0" width="237">
<tbody>
<tr>
<td width="43" valign="top">coke</td>
<td width="70" valign="top">cheeseburger</td>
<td width="70" valign="top">hamburger</td>
<td width="45" valign="top">fries</td>
</tr>
<tr>
<td valign="top">3</td>
<td valign="top">1</td>
<td valign="top">5</td>
<td valign="top">2</td>
</tr>
</tbody>
</table>
<p>with the cup vector would yield 3 cups.  For (3×1 cup) + (1×0 cups) + (5×0 cups) + (2×0 cups) = 3 cups.</p>
<p>We&#8217;ll see more examples of inner products later, including geometric examples.  I think we&#8217;ve got enough here to gives us a natural introduction to a new topic in the next post: we are going to introduce <em>matrices</em>.</p>
</div>]]></content:encoded>
</item>
<item>
<title><![CDATA[Groupings, Shopping Lists, Vectors: part 6]]></title>
<link>http://unlearningmath.com/2009/12/20/groupings-shopping-lists-vectors-part-6/</link>
<pubDate>Mon, 21 Dec 2009 07:33:07 +0000</pubDate>
<dc:creator>Bert Speelpenning</dc:creator>
<guid>http://unlearningmath.com/2009/12/20/groupings-shopping-lists-vectors-part-6/</guid>
<description><![CDATA[In this series on vectors we showed vector addition in this post, and then took a small excursion to]]></description>
<content:encoded><![CDATA[<div class='snap_preview'><p>In this series on <em>vectors</em> we showed vector addition in <a href="http://unlearningmath.com/2009/12/18/groupings-shopping-lists-vectors-part-4/">this post</a>, and then took a small <a href="http://unlearningmath.com/2009/12/19/groupings-shopping-lists-vectors-part-5/">excursion</a> to show a surprising connection between some vector additions and the distributive property.</p>
<p>In  this post, I will combine vectors with look-up tables and thus introduce an operation usually called <em>inner product</em>.  For this, we will take as our starting point the drive-up window order from a previous post:</p>
<table style="height:32px;" border="1" cellspacing="0" cellpadding="0" width="237">
<tbody>
<tr style="text-align:center;">
<td width="43" valign="top">coke</td>
<td width="70" valign="top">cheeseburger</td>
<td width="70" valign="top">hamburger</td>
<td width="45" valign="top">fries</td>
</tr>
<tr style="text-align:center;">
<td valign="top">3</td>
<td valign="top">1</td>
<td valign="top">5</td>
<td valign="top">2</td>
</tr>
</tbody>
</table>
<p>The box above represents the order, and we have been assuming that this order is specific enough that the fast food folks can get you what you want.  Specifically, that there is an understanding of what an order of &#8220;coke&#8221; is as compared to, say, &#8220;coke, small&#8221;, or &#8220;diet coke, large&#8221;.</p>
<p>Yet serving up your order is not the only concern of the fast food place.  They need to get paid.  They charge you for the items ordered, based on a price list.  (And then, in the USA and some other countries, they compute taxes on top of the total; in yet other countries, the taxes would already be included in the prices shown on the price list.  In this post, I&#8217;ll ignore taxes altogether.)</p>
<p>The price list can also be shown as a vector.  It might look like this:</p>
<table border="1" cellspacing="0" cellpadding="0">
<tbody>
<tr>
<td width="100" valign="top">cheeseburger</td>
<td width="43" valign="top">$1.50</td>
</tr>
<tr>
<td width="100" valign="top">chickenburger</td>
<td width="43" valign="top">$1.80</td>
</tr>
<tr>
<td width="100" valign="top">coke</td>
<td width="43" valign="top">$1.20</td>
</tr>
<tr>
<td width="100" valign="top">diet coke</td>
<td width="43" valign="top">$1.20</td>
</tr>
<tr>
<td width="100" valign="top">fries</td>
<td width="43" valign="top">$1.50</td>
</tr>
<tr>
<td width="100" valign="top">hamburger</td>
<td width="43" valign="top">$1.40</td>
</tr>
<tr>
<td width="100" valign="top">ice cream treat</td>
<td width="43" valign="top">$1.90</td>
</tr>
<tr>
<td width="100" valign="top">kid meal</td>
<td width="43" valign="top">$3.00</td>
</tr>
</tbody>
</table>
<p>The price list will typically contain many items that weren&#8217;t ordered.   Typically, there is an entry in the price list for any item ordered.</p>
<p>To find the total amount (ignoring taxes), it is pretty clear what needs to be done: for each item ordered, you multiply the amount ordered by the price found from the price list vector, and then you add it all up.</p>
<table border="0" cellspacing="0" cellpadding="0">
<tbody>
<tr>
<td width="43" valign="top"></td>
<td width="138" valign="top">
<table border="1" cellspacing="0" cellpadding="0">
<tbody>
<tr>
<td width="100" valign="top">cheeseburger</td>
<td style="text-align:right;" width="43" valign="top">$1.50</td>
</tr>
<tr>
<td width="100" valign="top">chickenburger</td>
<td style="text-align:right;" width="43" valign="top">$1.80</td>
</tr>
<tr>
<td width="100" valign="top">coke</td>
<td style="text-align:right;" width="43" valign="top">$1.20</td>
</tr>
<tr>
<td width="100" valign="top">diet coke</td>
<td style="text-align:right;" width="43" valign="top">$1.20</td>
</tr>
<tr>
<td width="100" valign="top">fries</td>
<td style="text-align:right;" width="43" valign="top">$1.50</td>
</tr>
<tr>
<td width="100" valign="top">hamburger</td>
<td style="text-align:right;" width="43" valign="top">$1.40</td>
</tr>
<tr>
<td width="100" valign="top">ice cream treat</td>
<td style="text-align:right;" width="43" valign="top">$1.90</td>
</tr>
<tr>
<td width="100" valign="top">kid meal</td>
<td style="text-align:right;" width="43" valign="top">$3.00</td>
</tr>
</tbody>
</table>
</td>
</tr>
<tr>
<td width="43" valign="top">
<table border="1" cellspacing="0" cellpadding="0">
<tbody>
<tr style="text-align:center;">
<td width="43" valign="top">coke</td>
<td width="70" valign="top">cheeseburger</td>
<td width="70" valign="top">hamburger</td>
<td width="45" valign="top">fries</td>
</tr>
<tr style="text-align:center;">
<td valign="top">3</td>
<td valign="top">1</td>
<td valign="top">5</td>
<td valign="top">2</td>
</tr>
</tbody>
</table>
</td>
<td style="text-align:left;" width="138" valign="top">
<table border="0" cellspacing="0" cellpadding="0">
<tbody>
<tr style="text-align:center;">
<td width="100" valign="top"></td>
<td width="43" valign="top"><span style="color:#ffffff;">$</span></td>
</tr>
<tr style="text-align:center;">
<td valign="top"></td>
<td style="text-align:right;" valign="top">$15.10</td>
</tr>
</tbody>
</table>
</td>
</tr>
</tbody>
</table>
<p>The $15.10 comes from coke (3 times $1.20) plus cheeseburger (1 times $1.50) plus hamburger (5 times $1.40) plus fries (2 times 1.50).</p>
<p style="text-align:center;"><a href="http://bertspeelpenning.wordpress.com/files/2009/12/inner-product.jpg"><img class="size-full wp-image-1373  aligncenter" title="inner product" src="http://bertspeelpenning.wordpress.com/files/2009/12/inner-product.jpg" alt="" width="480" height="295" /></a></p>
<p>The operation on the order vector and the price list vector that gives us the final price (ignoring taxes) is called <em>inner product</em>.  I don&#8217;t want to go into the significance or the origin of the name (though you would correctly guess that there is also something called an <em>outer product</em>.)  Inner product is also often called the <em>dot product</em>.</p>
<p>You may have noticed that the situation shown is not symmetric with respect to the two vectors.  Yet there are ways to make the similarity between the two vectors more pronounced.  One way to do that is to ignore the parts of the price list that aren&#8217;t being called upon.  We can also reorder the entries to match those of the order.  Doing so might give us something like this:</p>
<p><a href="http://bertspeelpenning.wordpress.com/files/2009/12/inner-product-reduced.jpg"><img class="size-full wp-image-1374  aligncenter" title="inner product, reduced" src="http://bertspeelpenning.wordpress.com/files/2009/12/inner-product-reduced.jpg" alt="" width="420" height="413" /></a>Alternatively, we could expand the order to match the price list, by explicitly  marking zeros for those items on the menu that aren&#8217;t ordered.  This is something we may show later.</p>
<p>For now, I will note that textbooks sometimes show this inner product as follows:</p>
<table border="0" cellspacing="0" cellpadding="0">
<tbody>
<tr>
<td style="text-align:left;" width="100" valign="top"></td>
<td width="43" valign="top">
<table border="1" cellspacing="0" cellpadding="0">
<tbody>
<tr>
<td style="text-align:right;" width="43" valign="top">1.20</td>
</tr>
<tr>
<td style="text-align:right;" width="43" valign="top">1.50</td>
</tr>
<tr>
<td style="text-align:right;" width="43" valign="top">1.40</td>
</tr>
<tr>
<td style="text-align:right;" width="43" valign="top">1.50</td>
</tr>
</tbody>
</table>
</td>
</tr>
<tr>
<td width="100" valign="top">
<table border="1" cellspacing="0" cellpadding="0">
<tbody>
<tr style="text-align:center;">
<td width="25" valign="top">3</td>
<td width="25" valign="top">1</td>
<td width="25" valign="top">5</td>
<td width="25" valign="top">2</td>
</tr>
</tbody>
</table>
</td>
<td style="text-align:right;" width="43" valign="top">
<table style="height:17px;" border="0" cellspacing="0" cellpadding="0" width="43">
<tbody>
<tr style="text-align:center;">
<td valign="top"></td>
<td style="text-align:right;" valign="top">15.10</td>
</tr>
</tbody>
</table>
</td>
</tr>
</tbody>
</table>
<p>where the information that gives us the meaning of the 15.10 is left out, but at least the distinction between the two operands of the operation is maintained.  But since the process of multiplying and adding is itself commutative, there are many textbooks that dispense with the different treatment of the two operands altogether and write the thing as (3,1,5,2) • (1.20,1.50,1.40,1.50) = 15.10 and treat it as a completely symmetric operation: (1.20,1.50,1.40,1.50) • (3,1,5,2) = 15.10.  I will come back to these more subtle points in a later post.  What I hope I have achieved in this post is that you see how the scenario of an order &#8211; written as a vector &#8211; combined with a price list &#8211; also written as a vector &#8211; naturally leads to a process that gives us a single number, and that this process matches what textbooks call inner product.</p>
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<title><![CDATA[Groupings, Shopping Lists, Vectors: part 5]]></title>
<link>http://unlearningmath.com/2009/12/19/groupings-shopping-lists-vectors-part-5/</link>
<pubDate>Sun, 20 Dec 2009 01:37:21 +0000</pubDate>
<dc:creator>Bert Speelpenning</dc:creator>
<guid>http://unlearningmath.com/2009/12/19/groupings-shopping-lists-vectors-part-5/</guid>
<description><![CDATA[In the previous post, I introduced vector addition in terms of combining two piles of stuff, while k]]></description>
<content:encoded><![CDATA[<div class='snap_preview'><p>In the <a href="http://unlearningmath.com/2009/12/18/groupings-shopping-lists-vectors-part-4/">previous post</a>, I introduced vector addition in terms of combining two piles of stuff, while keeping track of what kind of stuff is in our piles, and how many of each of the stuff we&#8217;ve got.</p>
<p>In this post, I&#8217;m going to take a small excursion from the main path of this series, and show a connection between vector addition and the distributive property.  This excursion is mostly intended for people who are already familiar with the distributive property &#8211; who may even teach it &#8211; but who have noticed how the standard formulation of it: a(b+c)  = ab + ac really never comes alive for the students they work with.</p>
<p>Let&#8217;s take as our starting point the two trips to the gasoline pump from the previous post, and their sum:</p>
<table border="0" cellspacing="0" cellpadding="0">
<tbody>
<tr>
<td>
<table border="1" cellspacing="0" cellpadding="0" width="149">
<tbody>
<tr>
<td width="43" valign="top">9.6</td>
<td width="138" valign="top">gallons</td>
</tr>
<tr>
<td width="43" valign="top">27.84</td>
<td width="138" valign="top">dollars</td>
</tr>
</tbody>
</table>
</td>
<td style="text-align:center;" width="40">+</td>
<td>
<table border="1" cellspacing="0" cellpadding="0" width="149">
<tbody>
<tr>
<td width="43" valign="top">8.1</td>
<td width="138" valign="top">gallons</td>
</tr>
<tr>
<td width="43" valign="top">23.49</td>
<td width="138" valign="top">dollars</td>
</tr>
</tbody>
</table>
</td>
<td style="text-align:center;" width="40">=</td>
<td>
<table border="1" cellspacing="0" cellpadding="0" width="149">
<tbody>
<tr>
<td width="43" valign="top">17.7</td>
<td width="138" valign="top">gallons</td>
</tr>
<tr>
<td width="43" valign="top">51.33</td>
<td width="138" valign="top">dollars</td>
</tr>
</tbody>
</table>
</td>
</tr>
</tbody>
</table>
<p>and recall that the first two vectors indicate how much gas was pumped on each trip and how much was paid for it, and the resulting sum vector indicates how much gas was pumped in total and how much was paid in total for these trips.  The thing I&#8217;d like to emphasize at this point is how general a result this is, and how little it depends on detailed knowledge about each trip.  For example, it really doesn&#8217;t matter if both trips were to the same gas station &#8211; it doesn&#8217;t even matter if both trips were done with the same car.  The first receipt may come from taking your truck to station A, and the second receipt may come from your spouse taking the minivan to station B.  Specifically, I&#8217;d like to emphasize that there&#8217;s nothing about the way we added the two vectors that in any way depends on the price of gas.  The price of gas on the first trip may have been higher, or lower, or the same compared to the price of gas on the second trip.</p>
<p>So now let&#8217;s bring to this very general scenario a very special condition, one that itself has nothing to do with vector addition: let&#8217;s assume that the price of gas was <em>identical </em>between the two trips.  That is, the price of gas per gallon hasn&#8217;t budged, neither up nor down.  In the example above, this condition is met: the price of gas is $2.90 for each gallon on the first trip, and it is also $2.90 per gallon on the second trip.  If that&#8217;s the case, can we then say something interesting about the sum vector?</p>
<p>The sum vector represents the total amount of gas pumped, and the total amount of money paid for it.  We pumped all that gas in two trips, and paid for it in two trips.  How much would we have paid if we had pumped 17.7 gallons of gas in a single trip?  On the one hand, at $2.90 a gallon, we would have paid 17.7 times 2.90 dollars.  On the other hand, we should have paid neither less nor more than we paid in total for the two trips: it&#8217;s the same total amount of gas, and it&#8217;s all at the same price.  The sum vector, when prices stay constant, represents two things at the same time: the sum of the two trips, and the charge for 17.7 gallons of gas.</p>
<p><a href="http://bertspeelpenning.wordpress.com/files/2009/12/distributive-property.jpg"><img class="aligncenter size-full wp-image-1360" title="distributive property" src="http://bertspeelpenning.wordpress.com/files/2009/12/distributive-property.jpg" alt="" width="600" height="231" /></a>This relationship between six quantities, in a 2&#215;3 arrangement, appears to be very natural for seventh and eighth graders: they understand it, use it, bend it to their needs.  Most seventh graders I&#8217;ve worked with don&#8217;t need me to explain this to them in detail, they can invent the critical parts of it on their own.  I&#8217;ve written about that before, e.g. in <a href="http://unlearningmath.com/2009/03/27/relationships-percentages/">this post</a>.  Interestingly, these tend to be the same kids for whom a(b+c)=ab+ac is meaningless alphabet soup.</p>
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<title><![CDATA[Groupings, Shopping Lists, Vectors: part 4]]></title>
<link>http://unlearningmath.com/2009/12/18/groupings-shopping-lists-vectors-part-4/</link>
<pubDate>Sat, 19 Dec 2009 05:13:34 +0000</pubDate>
<dc:creator>Bert Speelpenning</dc:creator>
<guid>http://unlearningmath.com/2009/12/18/groupings-shopping-lists-vectors-part-4/</guid>
<description><![CDATA[Part 1, part 2, and part 3 of this series looked at a particular model for vector algebra, based on ]]></description>
<content:encoded><![CDATA[<div class='snap_preview'><p><a href="http://unlearningmath.com/2009/12/15/groupings-shopping-lists-vectors-part-1/">Part 1</a>, <a href="http://unlearningmath.com/2009/12/16/groupings-shopping-lists-vectors-part-2/">part 2</a>, and <a href="http://unlearningmath.com/2009/12/16/groupings-shopping-lists-vectors-part-3/">part 3</a> of this series looked at a particular model for vector algebra, based on some simple notions such as that of a shopping list.</p>
<p>In this post, I want to play with vector addition and look at the nature of that operation when expressed using the notation developed in the last post.</p>
<p>For a starting point, let&#8217;s look at two of your recent gas station receipts:</p>
<table border="1" cellspacing="0" cellpadding="0" width="149">
<tbody>
<tr>
<td width="43" valign="top">9.6</td>
<td width="138" valign="top">gallons</td>
</tr>
<tr>
<td width="43" valign="top">27.84</td>
<td width="138" valign="top">dollars</td>
</tr>
</tbody>
</table>
<p>- and -</p>
<table border="1" cellspacing="0" cellpadding="0" width="149">
<tbody>
<tr>
<td width="43" valign="top">8.1</td>
<td width="138" valign="top">gallons</td>
</tr>
<tr>
<td width="43" valign="top">23.49</td>
<td width="138" valign="top">dollars</td>
</tr>
</tbody>
</table>
<p>and think about what it would mean to add these up.  The most obvious part of this might be to add up the amounts: $27.84 + $23.49 = $51.33.  What does the amount $51.33 represent?  It represents the total amount of money you paid to the gas station people for gas, in these two trips to the gas station.</p>
<p>We could also look to see how much gas the $51.33 paid for.  We got 9.6 gallons on the first trip, and 8.1 gallons on the second trip, for a total of 17.7 gallons.  We can represent the result of our work as follows:</p>
<table border="1" cellspacing="0" cellpadding="0" width="149">
<tbody>
<tr>
<td width="43" valign="top">17.7</td>
<td width="138" valign="top">gallons</td>
</tr>
<tr>
<td width="43" valign="top">51.33</td>
<td width="138" valign="top">dollars</td>
</tr>
</tbody>
</table>
<p>and we can consider this our first example of vector addition.  You add the gallons, you add the dollars, and get a new vector, and this new vector still represents what got paid for how much gas &#8211; however, this time not through a single purchase, but two purchases combined.</p>
<p>Let&#8217;s look at another situation, one where we will look at coins.  Let&#8217;s assume that in the ashtray of my car I&#8217;ve got the following coins:</p>
<table border="1" cellspacing="0" cellpadding="0" width="149">
<tbody>
<tr>
<td width="43" valign="top">2</td>
<td width="138" valign="top">quarters</td>
</tr>
<tr>
<td width="43" valign="top">7</td>
<td width="138" valign="top">pennies</td>
</tr>
<tr>
<td width="43" valign="top">2</td>
<td width="138" valign="top">nickels</td>
</tr>
</tbody>
</table>
<p>and in my coin purse I&#8217;ve got:</p>
<table border="1" cellspacing="0" cellpadding="0" width="149">
<tbody>
<tr>
<td width="43" valign="top">2</td>
<td width="138" valign="top">dimes</td>
</tr>
<tr>
<td width="43" valign="top">1</td>
<td width="138" valign="top">Kennedy 50ct piece</td>
</tr>
<tr>
<td width="43" valign="top">3</td>
<td width="138" valign="top">nickels</td>
</tr>
</tbody>
</table>
<p>and I move all the coins from the ashtray into my coin purse.  What is in my coin purse now?</p>
<p>There is not a lot of overlap between the two: the only kind of coin present in both the ashtray and the coin purse is nickels.  The other coins only occur in one or in the other.  Keeping track of what will be in the ocin purse after joining them together is relatively simple.  One way to write the result is:</p>
<table border="1" cellspacing="0" cellpadding="0" width="149">
<tbody>
<tr>
<td width="43" valign="top">2</td>
<td width="138" valign="top">quarters</td>
</tr>
<tr>
<td width="43" valign="top">7</td>
<td width="138" valign="top">pennies</td>
</tr>
<tr>
<td width="43" valign="top">5</td>
<td width="138" valign="top">nickels</td>
</tr>
<tr>
<td width="43" valign="top">2</td>
<td width="138" valign="top">dimes</td>
</tr>
<tr>
<td width="43" valign="top">1</td>
<td width="138" valign="top">Kennedy 50ct piece</td>
</tr>
</tbody>
</table>
<p>and you might note that this is a very different answer from <em>$1.52</em>, which is an answer to a very different question: &#8220;what is the <em>value </em>of what is in my coin purse?&#8221;</p>
<p>Combining two piles of coins, and keeping track of the total number of each type of coin, that&#8217;s a perfect example of vector addition.  (If you&#8217;re a math teacher, you might object that my last example isn&#8217;t really an example of vector addition, but rather of &#8220;adding <em>like </em>terms&#8221;.  In response, I&#8217;d say that &#8220;adding like terms&#8221; is a special case of vector addition, and that it is too bad that we usually treat them as completely different and unrelated things.)</p>
<p>Thinking of vectors as piles of stuff where we keep track of what the stuff is and how many of each of the stuff is there &#8211; this leads naturally to thinking of vector addition as combining two piles of stuff into a single pile, and continue to keep track of what is there and how many of each are there.</p>
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<title><![CDATA[Groupings, Shopping lists, Vectors: part 3]]></title>
<link>http://unlearningmath.com/2009/12/16/groupings-shopping-lists-vectors-part-3/</link>
<pubDate>Thu, 17 Dec 2009 05:34:23 +0000</pubDate>
<dc:creator>Bert Speelpenning</dc:creator>
<guid>http://unlearningmath.com/2009/12/16/groupings-shopping-lists-vectors-part-3/</guid>
<description><![CDATA[The previous installments in this series can be found here and here. What I am after is a natural wa]]></description>
<content:encoded><![CDATA[<div class='snap_preview'><p>The previous installments in this series can be found <a href="http://unlearningmath.com/2009/12/15/groupings-shopping-lists-vectors-part-1/">here</a> and <a href="http://unlearningmath.com/2009/12/16/groupings-shopping-lists-vectors-part-2/">here</a>.</p>
<p>What I am after is a natural way to develop the usefulness of the idea of a <em>vector</em>, and in the previous post I suggested that a <em>shopping list</em> gives us a good start.  Here, I want to show some natural notations for that idea, even though that notation will look very different from the standard notation used in typical math class and typical textbooks.</p>
<p>Let&#8217;s start with this:</p>
<table border="1" cellspacing="0" cellpadding="0">
<tbody>
<tr style="text-align:center;">
<td width="49" valign="top">5</td>
<td width="180" valign="top">apple, Gravenstein</td>
</tr>
<tr style="text-align:center;">
<td width="49" valign="top">2</td>
<td width="180" valign="top">six-pack, Coke</td>
</tr>
<tr style="text-align:center;">
<td width="49" valign="top">3</td>
<td width="180" valign="top">bottle, Heineken dark</td>
</tr>
<tr style="text-align:center;">
<td width="49" valign="top">2</td>
<td width="180" valign="top">pound, Russet potatoes</td>
</tr>
</tbody>
</table>
<p>You can recognize it as a shopping list for a grocery store.  We want 5 apples, 2 six-packs of Coke, etc.  For each item, we say what it is we want, and how many of those we want.  Though it looks like a bunch of different things that are only loosely connected, it is essential for our purposes here that we can also look at it as a single whole.  That single whole is the shopping list, and it corresponds to a single trip to the grocery store, a single shopping cart, and a single grocery receipt.  The single whole is what we are calling a <em>vector</em>, here represented as a box with two columns, one column for the things and one column to indicate how many of each of these things.</p>
<p>Sometimes, we will find it useful to turn the whole thing on its side:</p>
<table border="1" cellspacing="0" cellpadding="0">
<tbody>
<tr style="text-align:center;">
<td width="91" valign="top">apples,<br />
Gravenstein</td>
<td width="72" valign="top">six-packs,<br />
Coke</td>
<td width="72" valign="top">bottles,<br />
Heineken dark</td>
<td width="72" valign="top">pounds,<br />
Russet potatoes</td>
</tr>
<tr style="text-align:center;">
<td width="91" valign="top">5</td>
<td width="72" valign="top">2</td>
<td width="72" valign="top">3</td>
<td width="72" valign="top">2</td>
</tr>
</tbody>
</table>
<p>The standard notation for vectors in textbooks would show this as (5,2,3,2), which leaves out the very things that allows us to see what the numbers are supposed to mean.  The good thing about the standard notation, of course, is that it is really really compact.  But sometimes being too concise can remove all the flavor.  (There is the famous joke from Woody Allen where he describes <em>War and Peace</em> after speed-reading it: &#8220;It&#8217;s about some Russians.&#8221;)</p>
<p>Of course, there are other situations than shopping lists that could be modeled in the same way.  Here, as an example, is a stock portfolio:</p>
<table border="1" cellspacing="0" cellpadding="0">
<tbody>
<tr style="text-align:center;">
<td width="43" valign="top">200</td>
<td width="138" valign="top">shares Coca Cola</td>
</tr>
<tr style="text-align:center;">
<td width="43" valign="top">100</td>
<td width="138" valign="top">shares Toyota</td>
</tr>
<tr style="text-align:center;">
<td width="43" valign="top">100</td>
<td width="138" valign="top">shares Honda</td>
</tr>
</tbody>
</table>
<p>The box above represents a single portfolio, consisting of three different stocks.  It isn&#8217;t enough to know which stocks you own, it also matters how many shares of each.</p>
<p>And the &#8220;X&#8221; on the pirate&#8217;s treasure map may indicate the location of the treasure like so:</p>
<table style="height:32px;" border="1" cellspacing="0" cellpadding="0" width="173">
<tbody>
<tr style="text-align:center;">
<td width="43" valign="top">400</td>
<td width="138" valign="top">paces East</td>
</tr>
<tr style="text-align:center;">
<td width="43" valign="top">600</td>
<td width="138" valign="top">paces North</td>
</tr>
</tbody>
</table>
<p>and the readout on the gasoline pump (and on your receipt) might say:</p>
<table style="height:32px;" border="1" cellspacing="0" cellpadding="0" width="149">
<tbody>
<tr style="text-align:center;">
<td width="43" valign="top">9.6</td>
<td width="138" valign="top">gallons</td>
</tr>
<tr style="text-align:center;">
<td width="43" valign="top">27.84</td>
<td width="138" valign="top">dollars</td>
</tr>
</tbody>
</table>
<p>The position of a ball dropped from a height on a graph might be recorded as:</p>
<table style="height:46px;" border="1" cellspacing="0" cellpadding="0" width="215">
<tbody>
<tr style="text-align:center;">
<td style="text-align:center;" width="43" valign="top">3</td>
<td width="138" valign="top">seconds after drop</td>
</tr>
<tr style="text-align:center;">
<td width="43" valign="top">144</td>
<td width="138" valign="top">feet below starting point</td>
</tr>
</tbody>
</table>
<p>So what&#8217;s the big deal?  We haven&#8217;t done anything yet, we have just recorded some data in a consistent format.  All I can suggest at this point is that this consistent format is convenient and somewhat self-contained.  In the next post I will introduce simple operations on vectors, such as vector addition.</p>
<p>Coming Attractions: soon, we&#8217;ll even make sense out of vector inner products and show how those arise in a natural way.</p>
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<title><![CDATA[Groupings, Shopping Lists, Vectors: part 2]]></title>
<link>http://unlearningmath.com/2009/12/16/groupings-shopping-lists-vectors-part-2/</link>
<pubDate>Wed, 16 Dec 2009 08:45:56 +0000</pubDate>
<dc:creator>Bert Speelpenning</dc:creator>
<guid>http://unlearningmath.com/2009/12/16/groupings-shopping-lists-vectors-part-2/</guid>
<description><![CDATA[For an introduction to this series of posts, see here. Imagine Joe going up to the drive-through, to]]></description>
<content:encoded><![CDATA[<div class='snap_preview'><p>For an introduction to this series of posts, see <a href="http://unlearningmath.com/2009/12/15/groupings-shopping-lists-vectors-part-1/">here</a>.</p>
<p>Imagine Joe going up to the drive-through, to order for himself and his room mates.  Their orders are all combined on a piece of paper.  He reads it at the order window: &#8220;2 hamburgers, 1 fries, 1 coke, 1 cheeseburger, 1 fries, 3 hamburgers, 2 cokes.&#8221;  At the pick up window, he pays and gets the stuff.  Before driving away, he checks to make sure everything is there.  He counts 3 cokes, 1 cheeseburger, 2 fries, 4 hamburgers.  Does this match his order?</p>
<p>There is nothing particularly complicated about this scenario, and I trust you can quickly determine the answer.  What&#8217;s interesting in this scenario is all the things we tend to take for granted when we think about this situation.</p>
<p>Let&#8217;s compare the original shopping list with Joe&#8217;s count after receiving the order:</p>
<p style="padding-left:30px;"><span style="color:#000080;"><span style="text-decoration:underline;">Shopping List</span><br />
2 hamburgers<br />
1 fries<br />
1 coke<br />
1 cheeseburger<br />
1 fries<br />
3 hamburgers<br />
2 cokes</span></p>
<p style="padding-left:210px;"><span style="color:#008000;"><span style="text-decoration:underline;">Joe&#8217;s original Count</span><br />
3 cokes<br />
1 cheeseburger<br />
4 hamburgers<br />
2 fries</span></p>
<p>In the shopping list, hamburgers come first, whereas in Joe&#8217;s count, cokes come first.  The shopping list has seven entries, and Joe&#8217;s count has only four.  Yet we don&#8217;t fault Joe&#8217;s count on those grounds, but rather that one hamburger is missing.  If it wasn&#8217;t for the one hamburger, we&#8217;d think of Joe&#8217;s count as equivalent to the shopping list.  The fact that the shopping list has two separate entries with fries doesn&#8217;t seem to be critical; what&#8217;s critical to Joe is that the totals match.  What does that mean?  It means that there is the right number of hamburgers, as well as the right number of fries, as well as the right number of everything else.  For Joe, extra fries wouldn&#8217;t necessarily compensate for missing hamburgers, and cheeseburgers wouldn&#8217;t work as substitutes for missing cokes.  What Joe expects is that the count shows the right stuff, and in the right amount for each of the stuff.</p>
<p>After Joe gets an additional hamburger, he is ready to head home.  His count is updated as follows:</p>
<p style="padding-left:210px;"><span style="color:#008000;"><span style="text-decoration:underline;">Joe&#8217;s updated Count</span><br />
3 cokes<br />
1 cheeseburger<br />
4 hamburgers<br />
2 fries<br />
1 hamburger</span></p>
<p><span style="color:#008000;"><span style="color:#000000;">If you are thinking that his updated count should really look like this:</span></span></p>
<p style="padding-left:210px;"><span style="color:#333300;"><span style="text-decoration:underline;">Your Count</span><br />
3 cokes<br />
1 cheeseburger<br />
5 hamburgers<br />
2 fries</span></p>
<p><span style="color:#008000;"><span style="color:#000000;">then we are partially in agreement.  Yes, your count shows the same totals as the original shopping list.  Yes, your version of the count seems particularly clean and lean: there is only one line that pertains to hamburgers, and only one line that pertains to cokes, etc.  In contrast, the following count seems to lose vital information:</span></span></p>
<p style="padding-left:210px;"><span style="color:#008000;"><span style="color:#000000;"><span style="color:#ff6600;"><span style="text-decoration:underline;">Counting Gone Overboard</span><br />
11 items</span></span></span></p>
<p><span style="color:#008000;"><span style="color:#000000;"><span style="color:#ff6600;"><span style="color:#000000;">There is something that the original Shopping List, Joe&#8217;s updated Count and Your Count have in common, which is not shared by Joe&#8217;s Original Count nor the Counting Gone Overboard.  What those three have in common is that they are really all talking about the same order.  In contrast, Joe&#8217;s Original Count is missing a hamburger, and the Counting Gone Overboard doesn&#8217;t distinguish between hamburgers and cokes (it could refer to an order of 11 hamburgers just as easily).</span></span></span></span></p>
<p><span style="color:#008000;"><span style="color:#000000;"><span style="color:#ff6600;"><span style="color:#000000;">To constitute a clear order, our piece of paper must have numbers on it, but numbers alone are insufficient: it must be clear for each number exactly what is being counted: it isn&#8217;t just &#8220;3&#8243;, but &#8220;3 cokes&#8221;.  So, more precisely, the order isn&#8217;t just a bunch of numbers, but rather a bunch of <em>entries</em>, where each entry combines a number with the thing that is being counted.  In this bunch of entries, the order of entries is not important, and we don&#8217;t particularly mind if there are multiple entries for hamburgers, or multiple entries for coke.  What we do care about is that we end up with the right total amount of coke, and the right total amount of hamburgers, and the right total amount of fries, etc.</span></span></span></span></p>
<p><span style="color:#008000;"><span style="color:#000000;"><span style="color:#ff6600;"><span style="color:#000000;">In this series of posts, I&#8217;m going to use the name <em>vector </em>for these kinds of shopping lists.  What is important at this point is that you can look at the shopping list as a single thing, as a whole, and not merely as a collection of parts (entries).  Just as the shopping lists, a vector can be written in a number of equivalent ways.  As long as Joe comes home with the right stuff, it doesn&#8217;t particularly matter how the order was written.</span></span></span></span></p>
<p><span style="color:#008000;"><span style="color:#000000;"><span style="color:#ff6600;"><span style="color:#000000;">In the next post in this series, I will play with this notion so you can see its usefulness, and introduce a useful notation to go with it.<br />
</span></span></span></span></p>
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<title><![CDATA[Groupings, Shopping Lists, Vectors: part 1]]></title>
<link>http://unlearningmath.com/2009/12/15/groupings-shopping-lists-vectors-part-1/</link>
<pubDate>Tue, 15 Dec 2009 08:18:42 +0000</pubDate>
<dc:creator>Bert Speelpenning</dc:creator>
<guid>http://unlearningmath.com/2009/12/15/groupings-shopping-lists-vectors-part-1/</guid>
<description><![CDATA[There is a surprisingly versatile part of mathematics that deals with groupings and collections of t]]></description>
<content:encoded><![CDATA[<div class='snap_preview'><p>There is a surprisingly versatile part of mathematics that deals with groupings and collections of things.  The main ideas involved are really quite easy and practical.  If you can make sense of a shopping list written by a spouse or parent, or if you can make sense of the paper cash register slip that the checkout person puts in your bag, you can make sense of this part of mathematics.  It is really too bad that the way textbooks and schools talk about this part of mathematics tends to abstract out all the sense-making parts and then hides even further behind fancy but rather forbidding names like vectors and matrices.  The part of mathematics I&#8217;m referring to is usually called vector algebra, or matrix algebra, or linear algebra.</p>
<p>I want to do a series of blog posts aimed at resurrecting the natural simplicity of the concept of a vector, by avoiding the straitjacket of the standard vector notation(s) for quite a while.  Of course I&#8217;ll connect up the work presented here with the standard notations and terminology, but there are other useful notations &#8211; I like a very flexible notation that is more &#8216;verbose&#8217; than the standard one and that allows you to see what is going on.  This flexible notation looks more like a cash register receipt or like the shopping cart from Amazon.com or like a database table.</p>
<p>Traditionally, we first encounter vectors in physics class, where velocity and force are said to have a direction, not just an amount.  We learn to draw an arrow with a length equal to the amount of force, and with a direction that&#8217;s the direction in which the force is applied, and we learn to call this arrow a <em>vector</em>.  At this time we may even learn about the combined effect of two forces acting together but each in a different direction (e.g. a model airplane held by a string).  When we later learn in math class about vectors, what we learn may feel completely different: we may now be told that a vector is a sequence of numbers, written in this form: (3,2,10,1) and you may be shown rules for adding, subtracting and multiplying these sequences without having any idea where these rules came from.  If you are shown these completely arbitrary-looking rules, you may not even realize that something strange is going on &#8211; for this may not look any different from other parts of your secondary school math education.   When they say that (3,2,10,1) + (1,2,3,4) equals (4,5,13,5) this may appear innocent enough, and when they say that (3,2,10,1)-(1,2,3,4) equals (2,0,7,-3) this may not look too strange either, but if you then were to guess that (3,2,10,1) times (1,2,3,4) would be (3,6,30,4) you may hear instead: &#8220;no, (3,2,10,1) times (1,2,3,4) equals 41, and this is called an inner product.&#8221;  The teacher may show you how the inner product is computed, but the odds are that from the description you will still have no idea as to what real-life question &#8220;41&#8243; is the answer to, let alone why you should care.</p>
<p>My promise to you is that this series will be easy and fun and sensible, ; that by the end, you&#8217;ll see what the big deal is, and why the textbook people think it is so important, and you will get to see how the standard way of presenting the material loses everything that made it easy, fun and sensible to start with but ended up with an extremely compact notation.  At that point you will be in a very good place to judge if the trade-off was worth it.</p>
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<title><![CDATA[Equalizer fun: representing voices]]></title>
<link>http://vaidehipatil.wordpress.com/2009/12/11/equalizer-fun-representing-voices/</link>
<pubDate>Fri, 11 Dec 2009 14:59:43 +0000</pubDate>
<dc:creator>vaidehipatil</dc:creator>
<guid>http://vaidehipatil.wordpress.com/2009/12/11/equalizer-fun-representing-voices/</guid>
<description><![CDATA[I sincerely hope that the friends featured below do not see the post]]></description>
<content:encoded><![CDATA[<div class='snap_preview'><p><a href="http://vaidehipatil.wordpress.com/files/2009/12/geetikaeq1.jpg">I sincerely hope that the friends featured below do not see the post <img src='http://s.wordpress.com/wp-includes/images/smilies/icon_wink.gif' alt=';)' class='wp-smiley' /> </a></p>
<p><img class="alignnone size-full wp-image-519" title="Treble" src="http://vaidehipatil.wordpress.com/files/2009/12/geetikaeq1.jpg" alt="" width="402" height="567" /></p>
<p><a href="http://vaidehipatil.wordpress.com/files/2009/12/wayloneq.jpg"><img class="alignnone size-full wp-image-520" title="Bass" src="http://vaidehipatil.wordpress.com/files/2009/12/wayloneq.jpg" alt="" width="379" height="562" /></a></p>
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<title><![CDATA[Night of the Living Dead: Zombies and Minstrelsy]]></title>
<link>http://pietothemediaecologist.wordpress.com/2009/12/10/night-of-the-living-dead-zombies-and-minstrelsy/</link>
<pubDate>Thu, 10 Dec 2009 19:06:32 +0000</pubDate>
<dc:creator>pietothemediaecologist</dc:creator>
<guid>http://pietothemediaecologist.wordpress.com/2009/12/10/night-of-the-living-dead-zombies-and-minstrelsy/</guid>
<description><![CDATA[If we think about Night of the Living Dead (1968) playing in theaters and drive-ins in the midst of ]]></description>
<content:encoded><![CDATA[<div class='snap_preview'><p><a href="http://pietothemediaecologist.wordpress.com/files/2009/12/196820la20noche20de20los20muertos20vivientes20ing20lc2001.jpg"><img class="aligncenter size-full wp-image-42" title="1968%20La%20noche%20de%20los%20muertos%20vivientes%20(ing)%20(lc)%2001" src="http://pietothemediaecologist.wordpress.com/files/2009/12/196820la20noche20de20los20muertos20vivientes20ing20lc2001.jpg" alt="" width="600" height="469" /></a></p>
<p>If we think about <em><a href="http://www.imdb.com/title/tt0063350/" target="_blank">Night of the Living Dead</a></em> (1968) playing in theaters and drive-ins in the midst of the racial conflict of the civil rights movement then we can glimpse some of the power of this film.  With the main character Ben being African-American the film can be read not only as a zombie film but as an allegory on race and the meaning of “blackness” in a white world.  Although <em>NotLD</em> relates to the social and political upheavals of the sixties, for Ben whiteness signifies a social order based on white dominance and how it positions him as a non-white outsider;  there is little difference between the whiteness of the zombies and the whiteness of the humans;</p>
<p>First in the matter of race we can connect the film with images prevalent within the historical context of the sixties.  The images in <em>NotLD</em> of German Shepherds with police would be recognized from news footage and press photos as the dog of choice to suppress and disperse civil rights protesters.  Furthermore images of zombie-hunting police officers and non-uniformed deputies side-by-side strongly resembles images of police and civilian conspiracies against civil rights workers that occurred in the South during the civil rights movement. </p>
<p>This intertextual dimension applies to the set of still images that appear at the end of the film.  Certainly the black and white photographs of the disposal of Ben’s body by an all white gang both fit the low budget nature of <em>NotLD</em> and add a visually striking and dramatic element to the death of Ben.  However the grainy, dot matrix quality to the photos connote a certain type of image; they have a documentary and journalistic feel as though they were snatched from a <em>Life</em> magazine or a newspaper.  The journalistic realism of the images seems to suggest, on the level of the horror narrative, a chilling sense that these events are possible thus adding to the horror of the film;  but the journalistically styled photos of an all white mob gathered around a slain African-American connects the scene with the <em>historical reality</em> of racist acts such as beatings, lynching and burnings.  Also the manner in which the film frames the group is important; the white men of the group are shot from a low angle to give them a feeling of dominance over Ben.  White dominance is further connoted as one photo shows a sinister “meat hook” that one of the vigilantes wields which reads as a “removal” tool, but also as a vigilante weapon to be used against Ben.  The whole sequence has a menacing feel that goes beyond the denotation of the scene as merely gruesome thrills of the “zombie” genre to a place where the viewer feels as though she is witnessing through news photos the racist brutalization of Ben’s body. </p>
<p> The ending is highly ambivalent as it breaks off a narrative that portrays Ben as the most dominant character. In the politics of representation Ben’s character runs counter to the racist stereotypes found in Hollywood films.  Ben comprises “traditional” characteristics of whiteness: rationality, courage, resourcefulness.  When compared to Harry Cooper, the white father of the family featured in the film, Ben displays a confident authority that violently ends with Ben wrestling a gun from Harry and later shooting him. </p>
<p>Beyond its intertextuality and prescient progressive politics of representation <em>NotLD</em> engages with racial discourses in another way.  Romero has stated in <a href="http://www.avclub.com/articles/george-romero,14198/" target="_blank">interviews</a>, “In the script, his race is never mentioned. In my mind, when I wrote that initial scene, he was a white guy”.  The casting of Duane Jones as Ben was a matter of convenience..  But as stated above to have an African-American actor cast in a lead role regardless of the director’s original intent within the historical context of the civil rights struggles automatically engages with racist discourses and practices.</p>
<p>What I suggest is that Romero’s original vision of Ben as white and then casting a black actor deftly plays with the racist tradition of black-face minstrelsy and turns it on its head.  Traditionally black-face minstrelsy was the racist practice of white performers donning black face to gain access to African-American personae and then reproducing racist stereotypes. This twist on minstrelsy permits Ben to carry the burden of racial meaning as a signifier of blackness while also escaping any restrictions based on race as a textual and  racial category.  Romero unconsciously created in Ben a character that resides inside and outside of racial discourses. </p>
<p>This relates to <a href="http://www.amazon.com/White-Richard-Dyer/dp/0415095379" target="_blank">Richard Dyer’s</a> insight into the compelling paradox at the heart of whiteness as a racial category.  Dyer states that whiteness as a racial category is both visible and invisible. One thing Dyer seems to be suggesting is that as a visible category, or signifier, whiteness is granted, ideologically and socially, a position of power.  At the same time whiteness as a racial category is invisible; that is whites are never marked or viewed as being determined by their race.  On the other hand Dyer suggests that other races however are defined in racial terms; each individual who is a member of a “non-white” race has his or her nature defined by their race, furthermore they are defined in relation to the “universality” and “normality” of whiteness.</p>
<p>Dyer’s insight resides at the heart of Ben’s minstrelsy; as a signifier Ben is encoded as racial, as being African-American, as non-white; but as a signified Ben connotes all of the traditional meanings associated with whiteness.   In <em>NotLD</em> race becomes, in Stuart Halls’ words, a “floating signifier” that confounds and counters the traditionally oppressive representations of race.</p>
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<title><![CDATA[Melinda Hawtin's Research: French Prison Photography ]]></title>
<link>http://prisonphotography.wordpress.com/2009/12/06/melinda-hawtins-research-french-prison-photography/</link>
<pubDate>Sun, 06 Dec 2009 20:22:17 +0000</pubDate>
<dc:creator>petebrook</dc:creator>
<guid>http://prisonphotography.wordpress.com/2009/12/06/melinda-hawtins-research-french-prison-photography/</guid>
<description><![CDATA[© Philippe Bazin Last month, Melinda Hawtin contacted me about her interest and graduate research in]]></description>
<content:encoded><![CDATA[<div class='snap_preview'><div id="attachment_4827" class="wp-caption aligncenter" style="width: 330px"><img class="size-full wp-image-4827" title="© Phillipe Bazin" src="http://prisonphotography.wordpress.com/files/2009/12/bazin.jpg" alt="" width="320" height="318" /><p class="wp-caption-text">© Philippe Bazin</p></div>
<p>Last month, <a href="http://frenchprisonphotography.blogspot.com/" target="_blank"><strong>Melinda Hawtin</strong></a> contacted me about her interest and graduate research into the representations of prisons in French contemporary photography.</p>
<p>My position in the world is a little more comfortable knowing that another human has the niche commitment to prison photography!</p>
<p>Hawtin&#8217;s geography-specific project is even more narrowly defined as mine. She humbly referred to her blog as &#8220;yet a vessel for my (mostly) unresearched musings but I am hoping that in time it will take on a more coherent form&#8221;. Martin&#8217;s posts are far more than her modesty suggests &#8211; they are important introductions to academics, works and points of analysis.</p>
<p>Hawtin introduced me to the work of <strong><a href="http://www.galerieannebarrault.com/philippe_bazin/index.html" target="_blank">Philippe Bazin</a></strong>, whose series <a href="http://www.galerieannebarrault.com/philippe_bazin/detenus.html" target="_blank"><strong><em>Détenus</em></strong></a> is a straight photographic study of French prisoners. Hawtin is discomforted somewhat by Bazin&#8217;s <a href="http://frenchprisonphotography.blogspot.com/2009/10/times-ran-recent-article-that-discussed.html" target="_blank">sentimentalisation</a> of prisoners, &#8220;it seems strange and rather naive that artists like Bazin are so keen to portray the humanity of inmates. I’m not suggesting that they demonise them instead but monochrome, close-up images of prisoners could be seen to be over-romanticising the prisoner&#8221;.</p>
<div id="attachment_4828" class="wp-caption aligncenter" style="width: 330px"><a href="http://prisonphotography.wordpress.com/files/2009/12/bazin2.jpg"><img class="size-full wp-image-4828" title="© Philippe Bazin" src="http://prisonphotography.wordpress.com/files/2009/12/bazin2.jpg" alt="" width="320" height="319" /></a><p class="wp-caption-text">© Philippe Bazin</p></div>
<p>My take? Intimate shots do not automatically translate to sentimentalisation or captures of &#8220;true&#8221; humanity. It is always hazardous to prescribe the reaction of an audience to a photographic style. I would step back (possibly cowardly) and suggest that Bazin&#8217;s portraits are worthwhile simply because they differ in tone from the vast majority of other photographic studies of prisoners.</p>
<p>Hawtin and I swapped resources and names including the excellent <a href="http://www.lemonde.fr/societe/visuel/2009/06/22/le-corps-incarcere_1209087_3224.html" target="_blank">Visa pour L&#8217;Image web documentary winner</a>, <strong><a href="/2009/02/06/jean-gaumy-les-incarceres/" target="_blank">Jean Gaumy</a></strong> and <strong><a href="http://www.lizzie-sadin.com/" target="_blank">Lizzie Sadin</a></strong>, whose photography focuses on juveniles in prisons across the globe, including her own nation of France.</p>
<p>Investigations into the portrayal of French prisoners could not be more timely:</p>
<blockquote><p><a href="http://www.france24.com/en/20090915-french-lawmakers-examine-prison-reform-bill" target="_blank">French President <strong>Nicolas Sarkozy</strong> has called French prisons <strong>&#8220;the shame of the nation&#8221;</strong>, and the European Union has demanded that France improve the detention conditions of its inmates to meet minimum European standards.</a></p></blockquote>
<p>I&#8217;ll be sure to check in with Hawtin&#8217;s <a href="http://frenchprisonphotography.blogspot.com/" target="_blank">blog</a> regularly.</p>
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<title><![CDATA[Blitzen Trapper Embrace Their Inner Wolf]]></title>
<link>http://animalinventory.net/2009/11/24/blitzen-trapper-embrace-their-inner-wolf/</link>
<pubDate>Tue, 24 Nov 2009 14:51:06 +0000</pubDate>
<dc:creator>lisagbrown</dc:creator>
<guid>http://animalinventory.net/2009/11/24/blitzen-trapper-embrace-their-inner-wolf/</guid>
<description><![CDATA[On Blitzen Trapper&#8217;s new album Furr, the band draws on the storytelling tradition of shapeshif]]></description>
<content:encoded><![CDATA[<div class='snap_preview'><p><a href="http://www.amazon.com/Furr/dp/B001GD5KDM/ref=sr_1_1?ie=UTF8&#38;s=dmusic&#38;qid=1259073298&#38;sr=8-1"><img class="alignright size-full wp-image-962" title="blitzen trapper" src="http://animalinventory.wordpress.com/files/2009/11/blitzen-trapper1.jpg" alt="" width="658" height="801" /></a><a href="http://www.amazon.com/Furr/dp/B001GD5KDM/ref=sr_1_1?ie=UTF8&#38;s=dmusic&#38;qid=1259073298&#38;sr=8-1"></a></p>
<p>On <a href="http://blitzentrapper.net">Blitzen Trapper&#8217;s </a>new album <em>Furr</em>, the band draws on the storytelling tradition of shapeshifters: humans and animals who can shift between forms. The band embraces their inner wolf on the title track, &#8220;Furr.&#8221; Read the fantastic lyrics below:</p>
<p>&#8220;Furr&#8221;</p>
<p>Yeah, when I was only 17,<br />
I could hear the angels whispering<br />
So I droned into the words and<br />
wondered aimlessly about till<br />
I heard my mother shouting through the fog<br />
It turned out to be the howling of a dog<br />
or a wolf to be exact.<br />
The sound sent shivers down my back<br />
but I was drawn into the pack.<br />
And before long, they allowed me<br />
to join in and sing their song.<br />
So from the cliffs and highest hill, yeah<br />
we would gladly get our fill,<br />
howling endlessly and shrilly at the dawn.<br />
And I lost the taste for judging right from wrong.<br />
For my flesh had turned to fur, yeah<br />
And my thoughts, they surely were turned to<br />
instinct and obedience to God.</p>
<p>You can wear your fur<br />
like the river on fire.<br />
But you better be sure<br />
if you&#8217;re makin&#8217; God a liar.<br />
I&#8217;m a rattlesnake, babe,<br />
I&#8217;m like fuel on fire.<br />
So if you&#8217;re gonna&#8217; get made,<br />
don&#8217;t be afraid of what you&#8217;ve learned.</p>
<p>On the day that I turned 23,<br />
I was curled up underneath a dogwood tree.<br />
When suddenly a girl<br />
with skin the color of a pearl,<br />
wandered aimlessly,<br />
but she didn&#8217;t seem to see.<br />
She was listenin&#8217; for the angels just like me.<br />
So I stood and looked about.<br />
I brushed the leaves off of my snout.<br />
And then I heard my mother shouting through the trees.<br />
You should have seen that girl go shaky at the knees.<br />
So I took her by the arm<br />
we settled down upon a farm.<br />
And raised our children up as<br />
gently as you please.</p>
<p>And now my fur has turned to skin.<br />
And I&#8217;ve been quickly ushered in<br />
to a world that I confess I do not know.<br />
But I still dream of running careless through the snow.<br />
An&#8217; through the howlin&#8217; winds that blow,<br />
across the ancient distant flow,<br />
it fill our bodies up like water till we know.</p>
<p>You can wear your fur<br />
like the river on fire.<br />
But you better be sure<br />
if you&#8217;re makin&#8217; God a liar.<br />
I&#8217;m a rattlesnake, babe,<br />
I&#8217;m like fuel on fire.<br />
So if you&#8217;re gonna&#8217; get made,<br />
don&#8217;t be afraid of what you&#8217;ve learned.</p>
<p>Listen to the song on <a href="http://blitzentrapper.net/rexx.html">Blitzen Trapper&#8217;s website</a></p>
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<title><![CDATA[Samedi 21 et dimanche 22 novembre 2009, aux Halles de Sierre - impressions]]></title>
<link>http://cieopale.wordpress.com/2009/11/22/novembre-21-et-22-aux-halles-de-sierre/</link>
<pubDate>Sun, 22 Nov 2009 11:22:43 +0000</pubDate>
<dc:creator>Erika</dc:creator>
<guid>http://cieopale.wordpress.com/2009/11/22/novembre-21-et-22-aux-halles-de-sierre/</guid>
<description><![CDATA[Chers spectateurs du week-end, Tout d&#8217;abord merci pour votre présence, sans elle nous n&#8217;]]></description>
<content:encoded><![CDATA[<div class='snap_preview'><p>Chers spectateurs du week-end,</p>
<p>Tout d&#8217;abord merci pour votre présence, sans elle nous n&#8217;existerions pas&#8230; car le théâtre c&#8217;est aussi la présence du public !!! et quels spectateurs samedi soir&#8230;</p>
<p>Sans aucun doute, le spectacle se crée en communion avec la présence de son parterre et  samedi, de même que dimanche, l&#8217;expérience fût fort belle.</p>
<p>Mille mercis ! Nous attendons donc vos impressions, en réponse à ce message. A vos plumes !!!</p>
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<title><![CDATA[Something new - Introduction]]></title>
<link>http://laverymedia.wordpress.com/2009/11/22/something-new-introduction/</link>
<pubDate>Sun, 22 Nov 2009 04:22:11 +0000</pubDate>
<dc:creator>laverymedia</dc:creator>
<guid>http://laverymedia.wordpress.com/2009/11/22/something-new-introduction/</guid>
<description><![CDATA[For something new this year I&#8217;ve decided to add a blogging component to the year 11 media cour]]></description>
<content:encoded><![CDATA[<div class='snap_preview'><h3>For something new this year I&#8217;ve decided to add a blogging component to the year 11 media course. The basis for this is twofold:</h3>
<h4>1. To give you a chance to interact with each other, me and the wide world of media through an avenue of the media</h4>
<h4>2. To give you a place to explore your thoughts and views of the media saturated world in which we live</h4>
<p>&#160;</p>
<p><strong>There are a few simple things to keep in mind:</strong></p>
<p>* <strong><span style="text-decoration:underline;">you have to blog at least once a week</span></strong> (from today November 23 2009 until the end of the year next year &#8211; sometime in early November)</p>
<p>* <span style="text-decoration:underline;"><strong>you have to respond to another class member&#8217;s blog at least once a week</strong></span> (in a positive way)</p>
<p>* you can blog about anything that relates to media:</p>
<ul>
<li>changes in technology</li>
<li>changes in methods of presentation or messages in a variety of different media</li>
<li>foreign media (i always find it interesting to see how television shows and films are adapted in different countries &#8211; for example <em>The Nanny </em>VS. <em>Dadi</em>, <em>Infernal Affairs</em> VS. <em>The Departed</em>  [or any number of American remakes - especially the horrid failures]: this is especially interesting if the cultures are very different)</li>
<li>aspects of the media you love</li>
<li>aspects of the media you take issue with</li>
<li>cool stuff</li>
<li>a response to the work we are doing in class</li>
<li>things you have created</li>
<li>media laws (both foreign and domestic)</li>
</ul>
<p>Basically anything that relates to media (and this course). Anything you have any view about whatsoever. </p>
<p>You need to blog<span style="text-decoration:underline;"><strong> </strong></span><span style="text-decoration:underline;"><strong>at least</strong></span><span style="text-decoration:underline;"><strong> 100 words</strong></span> (but feel free to go way over that) &#8211; obviously this changes with the use of images you have created yourself.</p>
<p>&#160;</p>
<p>You can make your blog as basic or complicated as you like &#8211; change the <strong><span style="color:#ff0000;"><em><span style="text-decoration:underline;">appearance</span></em></span></strong> and whatever else to personalise it to what you are about and how you relate to the media.</p>
<p>Be sure to tag your blogs so you can categorise your musings and make your blog easier to navigate.</p>
<p>&#160;</p>
<p>Don&#8217;t be shy &#8211; state your opinions (make sure they are informed)</p>
<p>Provide links to things you find interesting &#8211; <a class="wp-oembed" title="Sitcom Wives: A Plague on Mankind" href="http://www.bipolarnation.com/2007/02/22/sitcom-wives-a-plague-on-mankind/" target="_blank">here</a> is an article on the same topic as we have already talked about today to do with representations</p>
<p>&#160;</p>
<p>Add images to help demonstrate your points:</p>
<p><a href="http://laverymedia.wordpress.com/files/2009/11/the_nanny.jpg"><img class="alignleft size-medium wp-image-4" title="the_nanny" src="http://laverymedia.wordpress.com/files/2009/11/the_nanny.jpg?w=271" alt="" width="271" height="300" /></a><a href="http://laverymedia.wordpress.com/files/2009/11/dadii6xw4.jpg"><img class="alignleft size-medium wp-image-5" title="dadii6xw4" src="http://laverymedia.wordpress.com/files/2009/11/dadii6xw4.jpg?w=204" alt="" width="204" height="300" /></a></p>
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<p>&#160;</p>
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<p>&#160;</p>
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<p>&#160;</p>
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<h2>Have fun!</h2>
<p><em>Once you have created your blog send me the address and i&#8217;ll provide links to everyone&#8217;s blogs</em></p>
<p>Lavery</p>
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<title><![CDATA[ATELIER 13/12/2009 de 13h à 17h - BRUXELLES]]></title>
<link>http://troupesapristi.wordpress.com/2009/11/16/atelier/</link>
<pubDate>Mon, 16 Nov 2009 13:53:17 +0000</pubDate>
<dc:creator>Angeles Hernandez</dc:creator>
<guid>http://troupesapristi.wordpress.com/2009/11/16/atelier/</guid>
<description><![CDATA[Nous vous accueillons pour une après-midi d’initiation au Playback Théâtre. Le dimanche 13 décembre ]]></description>
<content:encoded><![CDATA[<div class='snap_preview'><p>Nous vous accueillons pour une après-midi d’initiation au Playback Théâtre.</p>
<p><span id="more-46"> </span></p>
<p><span style="color:#0000ff;"><strong>Le dimanche 13 décembre</strong> </span></p>
<p><span style="color:#000000;">LIEU – Rue Louis Ernotte 62 à 1170 BRUXELLES</span></p>
<p><span style="color:#000080;"><span style="color:#000000;">Pour l’itinéraire, cliquez  “<a href="../ateliers-initiations/">ATELIERS</a><a href="../ateliers-initiations/">“</a></span></span></p>
<p>&#160;</p>
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<title><![CDATA[REPRESENTATION 13/12/09 de 16H à 17H – BRUXELLES]]></title>
<link>http://troupesapristi.wordpress.com/2009/11/16/representations-131209-a-16h-%e2%80%93-bruxelles/</link>
<pubDate>Mon, 16 Nov 2009 13:47:09 +0000</pubDate>
<dc:creator>Angeles Hernandez</dc:creator>
<guid>http://troupesapristi.wordpress.com/2009/11/16/representations-131209-a-16h-%e2%80%93-bruxelles/</guid>
<description><![CDATA[La troupe accueille le public qui désire découvrir ou redécouvrir le Playback théâtre et la troupe S]]></description>
<content:encoded><![CDATA[<div class='snap_preview'><p><span style="color:#000000;"><strong>La troupe accueille le public qui désire découvrir ou redécouvrir le Playback théâtre et la troupe Sapristi</strong></span></p>
<p><span style="color:#000000;">LIEU – Rue Louis Ernotte 62 à 1170 BRUXELLES</span></p>
<p><span style="color:#000080;"><span style="color:#000000;">Pour l’itinéraire, cliquez  “<a href="../ateliers-initiations/">ATELIERS</a><a href="../ateliers-initiations/">“</a></span></span></p>
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<title><![CDATA[Cogito ergo I am right #8:  Lazy Philosophical Nitpicker]]></title>
<link>http://carlsagansdanceparty.wordpress.com/2009/11/14/cogito-ergo-i-am-right-8-lazy-philosopher/</link>
<pubDate>Sat, 14 Nov 2009 22:09:31 +0000</pubDate>
<dc:creator>logicmania</dc:creator>
<guid>http://carlsagansdanceparty.wordpress.com/2009/11/14/cogito-ergo-i-am-right-8-lazy-philosopher/</guid>
<description><![CDATA[By Amateur Philosopher Penny Ham I was thinking just the other day. You can still be a great philoso]]></description>
<content:encoded><![CDATA[<div class='snap_preview'><p>By Amateur Philosopher Penny Ham</p>
<p>I was thinking just the other day.  You can still be a great philosopher without having to create some great philosophical worldview. Basically, you can be a great philosopher and simply be a nitpicker.</p>
<p>In fact, I enjoy roaming worldviewless just critiquing philosophical ideas all the time. I think maybe someday I will get bored with philosophy and just retire with some worldview.  Maybe great philosophers build worldviews because they need a worldview to retire on. Typical great philosophers build their own worldviews but I&#8217;m not going to be a typical great philosopher.  I&#8217;m most likely just going to retire on some other great philosopher&#8217;s worldview. In that sense, I&#8217;ll just be some great philosophical freeloader.</p>
<p>Picking a philosophical worldview can be quite difficult.  For instance, I find myself arguing for positions that I&#8217;m not necessarily certain about because I just want to see how far I can stretch my position until it snaps.  Let me tell you, for a while I was really liking universals and it felt like I almost found a philosophical dream-home.  I was really considering Leibnizian Rationalism there for a few minutes. But Quine&#8217;s holism is really speaking out to me. Also Putnam has a paper specifically on destroying the distinction between facts and values. I think that is really neat in itself. I would recommend that essay to anyone. The name of it is simply Fact and Value. I seem to be pretty comfortable with an analytic school inspired pragmatism. I&#8217;m not sure though. I&#8217;ve had too much fun lately trying to go a day without the law of non-contradiction. Too many uses of the word &#8216;not&#8217;. Let me tell you.</p>
<p>My indecisiveness about my philosophical position has increased almost as much as my dogmatic way of arguing about some position that I&#8217;m really just underneath indecisive about.  Wow, what a sentence, but that&#8217;s just the way I feel.</p>
<p>My firm beliefs only go this far.</p>
<p>I believe induction to be quite reliable.<br />
I pretty much just hold causality to be true on the macroscopic level.<br />
I believe in the law of non-contradiction. Otherwise I&#8217;d be using a bunch of is and is nots, now wouldn&#8217;t I?<br />
I don&#8217;t think we can know that our representations match the external world. (from my understanding of problems with the correspondence theory)</p>
<p>What I&#8217;m trying to get at is that it&#8217;s very easy to be a lazy philosophical nitpicker.  But I think you can be a great philosopher and be a lazy one at the same time.</p>
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<title><![CDATA[The Design (Purpose) of The Internet?]]></title>
<link>http://imonad.wordpress.com/2009/11/08/the-design-purpose-of-the-internet/</link>
<pubDate>Sun, 08 Nov 2009 23:59:03 +0000</pubDate>
<dc:creator>JohnBrian</dc:creator>
<guid>http://imonad.wordpress.com/2009/11/08/the-design-purpose-of-the-internet/</guid>
<description><![CDATA[I found this (&#8230;while looking for a semi-gift-resonant way to make some money) and had to add m]]></description>
<content:encoded><![CDATA[<div class='snap_preview'><p>I found this (&#8230;while looking for a semi-gift-resonant way to make some money) and had to add my $0.02.</p>
<p><a title="New window will open" href="http://www.linkedin.com/redirect?url=http%3A%2F%2Fbaris%2Etypepad%2Ecom%2Fventure_capitalist%2F2009%2F10%2Fthe-internet-was-designed-for-the-pc%2Ehtml&#38;urlhash=RBNW" target="_blank">http://baris.typepad.com/venture_capitalist/2009/10/the-internet-was-designed-for-the-pc.html</a></p>
<p>My Comment:</p>
<p>&#8220;I live’n’breathe in the &#8220;why” and the “design/purpose&#8221; and the technology space – I love it here.</p>
<p>My work and writing speaks to essential and magical pragmatism (Yes, pragmatics can be magical, ask Williams James) of the “why” of the internet” as a function of an innate and unstoppable, although seemingly detour prone, process of individual, innate and gift-based human evolution… and whole human-systems gift-based or gift-centric social evolution, and more specifically, the evolution of 1) an individual and naturally disposed and gifted human mind, and 2) all of these human minds doing that same thing.</p>
<p>… and a “why the internet exists” design/purpose founded on the innate NEED of all these evolving and inherently gift-driven-at-the-core human minds finding fuller and better and more synergy-rich “connecting” along the way.</p>
<p>My innately disposed preference is to think of the internet as simply a mind-mirror and interactive functional projection and manifestation thereof, the human mind. And over time, guess what, it actually looks more and more like a human cortex, this felt-work of connective tissue, of fibrils, like glial cells and dendridic networks, enmeshed and encapsulating directly, and indirectly and over time, all minds on the planet. And these minds “connected” &#8211; consciously, most not &#8211; are trying really, really hard &#8211; as it is what they are designed to do… is their ultimate and pre-ordained purpose &#8211; to be all they can be&#8230; to be innately and naturally gift-driven and along the way, trying very, very hard to more effectively resonate (socnet) and connect (socnet) to optimizing “partners” along the way, and over generations of our humanity.</p>
<p>It is this fundamental process and direction of human evolving that feeds the evolution of da’Net itSelf, and reciprocally, the further evolution of the natural and innately disposed and gifted human Self.</p>
<p>Nice that the internet helps in all this, and was mirror-designed in fact, for that express purpose, whether we see it as such or not, i.e. it’s purpose within and without and pertaining to the unknown.</p>
<p>Okay, done spewing.</p>
<p>Thanks<br />
Brian&#8221;</p>
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<title><![CDATA[Claude Lévi-Strauss, différence et liberté]]></title>
<link>http://ecriposoph.wordpress.com/2009/11/05/claude-levi-strauss-difference-et-liberte/</link>
<pubDate>Thu, 05 Nov 2009 17:49:10 +0000</pubDate>
<dc:creator>francis lepioufle</dc:creator>
<guid>http://ecriposoph.wordpress.com/2009/11/05/claude-levi-strauss-difference-et-liberte/</guid>
<description><![CDATA[Le grand Lévi-Strauss est décédé le 30 octobre dernier. Un grand monsieur âgé ; surtout un expérimen]]></description>
<content:encoded><![CDATA[<div class='snap_preview'><p><a href="http://ecriposoph.wordpress.com/files/2009/11/p1010398.jpg"><img class="aligncenter size-medium wp-image-996" title="P1010398" src="http://ecriposoph.wordpress.com/files/2009/11/p1010398.jpg?w=300" alt="P1010398" width="300" height="168" /></a>Le grand Lévi-Strauss est décédé le 30 octobre dernier. Un grand monsieur âgé ; surtout un expérimenté des cultures diverses, un chercheur, un savant méthodique. Comme beaucoup d&#8217;entre vous, j&#8217;ai regardé l&#8217;émission sur Arte ce mercredi  4 novembre 2009. Avec quelle clarté et méthode, il faisait découvrir à partir de portées musicales la nécessité de lire transversalement, verticalement les indices pour enfin atteindre le sens des signes ainsi inscrit dans les &#8220;petites histoires&#8221; racontées par les &#8220;tribus&#8221; que nous sommes. Toujours avec cet esprit amusé, jouant de phrases enchâssées, il projetait sa réponse argumentée après des détours de description et de méthode, le tout posé calmement et recouvrant deux dimensions que d&#8217;aucuns pensaient contradictoires : la raison et la sensibilité.</p>
<p>On a beaucoup parlé de &#8220;Tristes Tropiques&#8221;; l<a href="http://www.lemonde.fr/carnet/article/2009/11/04/claude-levi-strauss-est-un-passeur-exceptionnel_1262544">e monde du jeudi 5 novembre </a>fait référence &#8220;Au regard éloigné&#8221;; j&#8217;ai aimé cet ouvrage et si j&#8217;en fais référence aujourd&#8217;hui, c&#8221;est qu&#8217;il fait en quelque sorte l&#8217;éloge de la diversité. &#8220;L&#8217;autre s&#8217;il est différent n&#8217;est pas inférieur&#8221;, une belle phrase à méditer pour nous tous, citoyens, gouvernants, élus( petits et grands ) et non élus , chacun de sa place et de sa responsabilité. Et il cite &#8221; le barbare, c&#8217;est d&#8217;abord l&#8217;homme qui croit à la barbarie.&#8221;</p>
<p>Lévi-Strauss a aussi écrit par rapport  &#8220;au caractère relatif de la liberté&#8221; . Je reprendrai demain quelques lignes de ce maître extraites de &#8220;le regard éloigné&#8221;paru en 1983 chez Plon.</p>
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<title><![CDATA[Animals in Graphic Novels]]></title>
<link>http://animalinventory.net/2009/10/19/animals-in-graphic-novels/</link>
<pubDate>Mon, 19 Oct 2009 10:52:19 +0000</pubDate>
<dc:creator>lisagbrown</dc:creator>
<guid>http://animalinventory.net/2009/10/19/animals-in-graphic-novels/</guid>
<description><![CDATA[If you&#8217;re wondering why Animal Inventory is a little slow these days, let me assure that it]]></description>
<content:encoded><![CDATA[<div class='snap_preview'><p>If you&#8217;re wondering why Animal Inventory is a little slow these days, let me assure that it&#8217;s for good reason. I&#8217;m hard at work on lots of exciting projects, and I&#8217;d like to share one of them with you: I&#8217;m guest-editing the June 2010 issue of <a href="http://www.antennae.org.uk/">Antennae: The Journal of Nature in Visual Culture</a>. The theme of the issue puts my favorite topic in the context of one of my favorite artistic mediums: animals in graphic novels.</p>
<p><img class="aligncenter size-full wp-image-950" title="buddhacover" src="http://animalinventory.wordpress.com/files/2009/10/buddhacover.jpg" alt="buddhacover" width="661" height="588" /><em>Cover art from Osamu Tezuka&#8217;s</em> <a href="http://www.amazon.com/Buddha-1-Kapilavastu-Osamu-Tezuka/dp/193223456X/ref=sr_1_2?ie=UTF8&#38;s=books&#38;qid=1255906434&#38;sr=1-2">Buddha</a></p>
<p>Here in Boston we just had our first snow, so it may seem odd to busy myself with something that&#8217;s debuting in June. Yet, for those of us who are working on the issue, June is right around the corner! If you or someone you know may be interested in contributing to this issue, please take a look at the call for papers below.</p>
<blockquote><p>Antennae: The Journal of Nature in Visual Culture (<a href="http://www.antennae.org.uk/" target="_blank"><span style="color:#0066cc;">www.antennae.org.uk</span></a>) is seeking submission for its June 2010 issue devoted to the subject of &#8220;animals in graphic novels.&#8221;</p>
<p>The issue will primarily focus on papers that examine contemporary graphic novels; examples of these might include Pride of Baghdad (Brian K. Vaughan), First in Space (James Vining), the works of Osamu Tezuka, Animal Man (Grant Morrison), Rabbi&#8217;s Cat (Joann Sfar), Fables (Bill Willingham), and Maus (Art Spiegelman), among others. Papers that examine the subjects of comics for children and comic strips that appear in newspapers may also be considered, depending on the originality of the contextualisation through which they may be presented.</p>
<p>We are looking at gathering a wide range of perspectives, themes and ideas within the broad scope of &#8220;animals in graphic novels.&#8221; These may include, but are not limited to, the following:</p>
<p>- Exploring animality in the graphic novel medium<br />
- Representing the human/animal divide<br />
- Positive and negative aspects of anthropomorphism<br />
- Becoming animal<br />
- Links between sexism, racism and speciesism<br />
- Non-western graphic novels<br />
- The challenges of animal first-person narratives<br />
- Ecocriticism and nature in graphic novels</p>
<p>As per usual Antennae is open to consideration of academic essays as well as fiction and experimental writing. Submission of abstracts and proposals is 1st of December 2009. Final deadline for submissions is 1st of March 2010. For any questions please contact Giovanni Aloi and Lisa Brown (Guest Editor of the <em>Animals in Graphic Novels Issue</em>) at <a href="mailto:antennaeproject@gmail.com"><span style="color:#0068cf;">antennaeproject@gmail.com</span></a></p></blockquote>
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<title><![CDATA[A business professional recently asked me to define "Ecology-of-Mind"...]]></title>
<link>http://imonad.wordpress.com/2009/10/15/i-was-recently-asked-me-to-define-ecology-of-mind-here-is-what-i-said/</link>
<pubDate>Thu, 15 Oct 2009 19:08:32 +0000</pubDate>
<dc:creator>JohnBrian</dc:creator>
<guid>http://imonad.wordpress.com/2009/10/15/i-was-recently-asked-me-to-define-ecology-of-mind-here-is-what-i-said/</guid>
<description><![CDATA[Hi Brian, Nice blog comment. I am not familiar with Google wave yet but it sounds interesting. I am ]]></description>
<content:encoded><![CDATA[<div class='snap_preview'><h3>Hi Brian,</h3>
<h3>Nice blog comment. I am not familiar with Google wave yet but it sounds interesting. I am very interested in further understanding your thoughts about how we can work with technology that helps us to realize and represent our true self more effectively to others while helping us in the &#8220;yearning&#8221; area to work and communicate more effectively with others on our team or that have a common interest or goal. Many of today&#8217;s social networking site like facebook and myspace currently fall short in this key department but I&#8217;m sure they will all evolve based on user feedback.</h3>
<h3>What is your definition of &#8220;Ecology of Mind&#8221;? </h3>
<h3>Grant,</h3>
<h3>In a complex nutshell (sorry) my interpretation of “Ecology-of-Mind” as a movement that affects each of us personally, our families, society, why and how we make money in the future, etc… concerns a framework bounded by three synergistic assumptions-as-realities:</h3>
<h3>1) The design and the development of technology is innately motivated by the design and function of the human brain.</h3>
<h3>2) This motivation is founded on our innate and natural need for a certain Mind-to-Mind and Minds-to-Minds and Mind-to-Minds quality of human connection and working and life relationships&#8230; that “quality” that motivates the mind to create technology to better connect each of us to the other as potent partnerships and collectives thereof.   A “naturally harmonic ecological system of minds”, a certain optimal global connectivity as human tapestry exists today, everyday and right now. This “EcoMind potential” is constantly and innately motivated to discover and produce fuller and more amazing human synergies &#8211; sooner, with less friction or barrier, more often, and maintain each for its fullest natural time.</h3>
<h3>3) The only element of the equation gone under-developed is us, our innate Self. The idea of a human being living their natural gifts from the get go. Not what we have done or do now but what we are born to do. This is the question we are considering now as a system of minds, led unknowingly by a world of minds, as we create technologies and software that helps us better known and see our innate, natural, real or TruSelf. A scary proposition really. Imagine if you failed at being all of you?</h3>
<h3>This is &#8220;The Great Yearning&#8221; we all have as a sentient a species. To be part of a potent web of meaningful work and people to do it with… to be unique and make a significant difference with our gifts, our nature, our Self.</h3>
<h3>This is, I believe, the most fundamental of all forces of human nature &#8211; outside of more essential human needs for food and shelter &#8211; to YOUniquely create and to do so with others. To evolve. The path is not without curves or obstacle.</h3>
<h3>An Ecology-of-Mind, if it were real, would demand the discovery, creation, nurturing, effective management and quality of human synergy founded on the clarity of each gifted human Self within the system.</h3>
<h3>It is the technology, software really, that moves us to insights and action about our Self that is my work&#8230;</h3>
<h3>We haven&#8217;t a clue really because we have yet to see this quality of human resonance and human connectivity and purposeful work output in action.</h3>
<h3>Those of us that have been on great teams know&#8230; they have been searching for the fix ever since, but it is more than this. Our awareness of our gifts is a huge step. Heck, an awareness of the fact that we have insights at the moment of insight itself is a huge shift in consciousness.</h3>
<h3>The proof of novelty. If I asked you to describe your innate and natural Gifts… you would be stuck.</h3>
<h3>The day you can and everyone else can &#8211; and we find that this way of objectively defining our innate Self’s is the new foundation of our dynamic and evolving online Profile &#8211; is the day we are connecting in ways we could not even imagine. And I imagine, it is this same day that we are all, as a world of people, resting a bit easier.</h3>
<h3>To date we have focused on all the various forms of ecology in the last 30 years, especially the last 10 years, all but the one most important to a truly self-sustaining and prosperous humanity. The Ecology-of-Mind is that last undiscovered country, natural resource gone unmanaged, fully developed, smartly maintained and fully funded.</h3>
<h3>It has been coming and will be coming now more like a Tsunami… big huge swells of evolving change.</h3>
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<title><![CDATA[Grande soirée musicale des Troup'Adour]]></title>
<link>http://lestroupadour.wordpress.com/2009/10/08/grande-soiree-musicale-des-troupadour/</link>
<pubDate>Thu, 08 Oct 2009 10:11:53 +0000</pubDate>
<dc:creator>troupadour</dc:creator>
<guid>http://lestroupadour.wordpress.com/2009/10/08/grande-soiree-musicale-des-troupadour/</guid>
<description><![CDATA[De l’amateur passionné à l’artiste de très haut niveau, l’excellence sera au rendez-vous tout au lon]]></description>
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<p style="margin-bottom:0;" align="justify">De l’amateur passionné à l’artiste de très haut niveau, l’excellence sera au rendez-vous tout au long de cette soirée exceptionnelle. Chanteurs ou instrumentistes, ces musiciens de très grand talent ont répondu présent à l’invitation des Troup’Adour pour offrir au public un concert de grande qualité.</p>
<p style="margin-bottom:0;" align="justify">Lors de cette soirée unique,  chaque ensemble se produira 20 à 25 minutes sur la scène de l’Auditorium Dispan de Floran pour offrir au public une rencontre musicale insolite pendant laquelle classique, romantique, jazz, traditionnel, populaire se succèderont à merveille.</p>
<p style="margin-bottom:0;" align="justify">Tour à tour, se produiront un jeune pianiste qui a remporté en mars dernier à Paris le prix de la presse<span style="color:#000000;"> du Concours International des Grands Amateurs de piano</span>, le trio de jazz groove « Goud » en quartet, un quatuor vocal composé de 4 chanteurs du chœur « Accentus » de renommée internationale, le jeune quatuor à cordes français « Zaïde » très prometteur issu du Conservatoire National Supérieur de Musique de Paris. Les Troup’Adour clôtureront la soirée par un voyage polyphonique en français, anglais, espagnol et arménien.</p>
<p style="margin-bottom:0;" align="justify">Un véritable cocktail musical à déguster sans modération  pour le plus grand bonheur de chacun, petits ou grands.</p>
<p style="margin-bottom:0;"><strong>Le programme:</strong></p>
<p style="margin-left:1.27cm;margin-bottom:0;">Vahan Basmadjian : 2 airs au Doudouk, instrument traditionnel arménien</p>
<p style="margin-left:1.27cm;margin-bottom:0;"><span style="color:#000000;">Romain Coharde  au piano : Ondine de Ravel, la leggerezza de Liszt, valse de Chopin</span></p>
<p style="margin-left:1.27cm;margin-bottom:0;">Le quartet Goud : jazz groove  (<a title="Le trio Goud en Quartet" href="http://goudtrio.free.fr">http://goudtrio.free.fr</a>)</p>
<p style="margin-left:1.27cm;margin-bottom:0;">Le quatuor vocal : Schubert et  Brahms</p>
<p style="margin-left:1.27cm;margin-bottom:0;"><span style="color:#000000;">Le quatuor à cordes Zaïde : quatuor de Haydn et Komitas</span></p>
<p style="margin-left:1.27cm;margin-bottom:0;">Les Troup&#8217;Adour : chants polyphoniques, direction O. Adourian, au piano D. Guiguet</p>
<p style="margin-bottom:0;"><strong>Tarif unique : 5€</strong></p>
<p style="margin-bottom:0;">Réservation fortement conseillée au 01 46 86 31 73 ou à l&#8217;adresse <a href="troupadour@wanadoo.fr">troupadour@wanadoo.fr</a></p>
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<title><![CDATA[Antennae, Issue 11: Insecta]]></title>
<link>http://animalinventory.net/2009/09/27/antennae-issue-11-insecta/</link>
<pubDate>Sun, 27 Sep 2009 18:30:08 +0000</pubDate>
<dc:creator>lisagbrown</dc:creator>
<guid>http://animalinventory.net/2009/09/27/antennae-issue-11-insecta/</guid>
<description><![CDATA[The newest issue of Antennae: The Journal of Nature in Visual Culture is now available for download.]]></description>
<content:encoded><![CDATA[<div class='snap_preview'><p>The newest issue of <a href="http://www.antennae.org.uk/"><em>Antennae: The Journal of Nature in Visual Culture</em></a> is now available for download. The theme of the issue is insects &#8212; namely, our uncomfortable relationship with them and how we can come to see beauty in creepy crawlies. The issue was inspired by Pestival, a week-long festival in London celebrating insects. As Giovanni Aloi, editor-in-chief of <em>Antennae</em>, says:</p>
<blockquote><p>&#8230;this issue of <em>Antennae</em> looks at some of the most challenging and interesting contemporary artists working with insects. The “excuse” for ‘Insecta’ to be released right now is Pestival 2009, “A festival celebrating insects in art, and the art of being an insect” which took place at London’s Southbank Centre this September. Pestival’s aim is to examine insect-human interactivity in bioscience through paradigms of contemporary art, cinema, music and comedy as well as through direct scientific demonstration and educational projects.</p></blockquote>
<p><a href="http://www.antennae.org.uk"><img class="aligncenter size-full wp-image-943" title="Antennae Issue 11" src="http://animalinventory.wordpress.com/files/2009/09/antennae-issue-11.jpg" alt="Antennae Issue 11" width="654" height="926" /></a></p>
<p>Click on the image above to be redirected to the Antennae homepage.</p>
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<title><![CDATA[FTC Guides Suggest Social Media Policies and Procedures Might Reduce Liability Risks]]></title>
<link>http://socialfrequency.wordpress.com/1902/10/09/ftc-guides-suggest-social-media-policies-and-procedures-might-reduce-liability-risks/</link>
<pubDate>Thu, 09 Oct 1902 17:29:44 +0000</pubDate>
<dc:creator>naperville</dc:creator>
<guid>http://socialfrequency.wordpress.com/1902/10/09/ftc-guides-suggest-social-media-policies-and-procedures-might-reduce-liability-risks/</guid>
<description><![CDATA[At the onset of this post, I want to be very clear that I am not intending to send fear coursing thr]]></description>
<content:encoded><![CDATA[<div class='snap_preview'><p><img class="alignright size-medium wp-image-202" title="100_2987" src="http://socialfrequency.wordpress.com/files/2009/10/100_2987.jpg?w=300" alt="100_2987" width="300" height="224" />At the onset of this post, I want to be very clear that I am not intending to send fear coursing through the veins of senior management nor should this be construed as a &#8220;<em>let&#8217;s all find another reason to fear social media&#8221;</em>.</p>
<p>Quite conversely, part of leveraging a strong social media business strategy is ensuring the appropriate operational controls are in place.  Policies, standardized practices and process are a responsible part of any business strategy and the business strategy of social media should be no exception.</p>
<p>This week, potential liability regarding the use of social media hit home as the Federal Trade Commission (FTC) released new Guides concerning the use of endorsements and testimonials in advertising.  Essentially, the new guides will work to ensure a higher level of honesty and transparency in the use of the social web for the purpose of marketing in terms of &#8220;pay to say&#8221; disclosure and factual representations.</p>
<p>Though I am not  a lawyer (nor have I ever played one on TV) and always encourage consultation with legal counsel, I did read through the 81 page FTC document yesterday and came across an important consideration which I don&#8217;t believe has been adequately highlighted.  That consideration is the liability an employer faces for the actions of employees engaging in social media activities either within or outside the scope of their work responsibilities.   The FTC addresses this scenario in response to a question which appears to have arisen during an open comment period relating to employer liability.  Below is a verbatim excerpt from the FTC&#8217;s response:</p>
<p><em>&#8220;&#8230;although the Commission has brought law enforcement actions against companies whose failure to establish or maintain appropriate internal procedures resulted in consumer injury, it is not aware of any instance in which an enforcement action was brought against a company for the actions of a single “rogue” employee who violated established company policy that adequately covered the conduct in question&#8230;  The Commission does not believe, however, that it needs to spell out the procedures that companies should put in place to monitor compliance with the principles set forth in the Guides; these are appropriate subjects for advertisers to determine for themselves, because they have the best knowledge of their business practices, and thus of the processes that would best fulfill their responsibilities.&#8221; <a href="http://www.ftc.gov/os/2009/10/091005endorsementguidesfnnotice.pdf">see page 48 of the complete FTC document for full text</a></em></p>
<p>What this means is it is time to create social media policies and practices within your organization which carefully balance innovative business uses of social media with clear lines drawn on unacceptable practices.</p>
<p>Social Frequency Media Communications can help your organization develop custom internal policies and procedures relating to the appropriate use of social media.  If you are interested in learning more, please contact me directly at stuart@socialfrequency.net.</p>
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