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	<title>The Why Files &#187; mathematics</title>
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		<title>New math mavens = pigeons?</title>
		<link>http://whyfiles.org/2011/new-math-mavens-pigeons/</link>
		<comments>http://whyfiles.org/2011/new-math-mavens-pigeons/#comments</comments>
		<pubDate>Thu, 22 Dec 2011 21:42:53 +0000</pubDate>
		<dc:creator>svmedaristwf</dc:creator>
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		<category><![CDATA[bird ornithology]]></category>
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		<category><![CDATA[Damian Scarf]]></category>
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		<category><![CDATA[numbers]]></category>
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		<guid isPermaLink="false">http://whyfiles.org/?p=21420</guid>
		<description><![CDATA[Can pigeons learn an abstract mathematical rule? Apparently, according to a new study, which asked pigeons to place, five blue dots and eight green squares, in ascending order. Now we know birds and primates can both do this, but where and why did this ability originate?]]></description>
			<content:encoded><![CDATA[<h3>Count on me</h3>
<p>
  If you&#8217;ve hung around a big-city park, you may think that pigeons are countless &#8212; or uncountable. But according to scientists from New Zealand, pigeons now join the short list of animals that can count &#8212; or at least, can places images containing two countable items in numerical order. </p>
<div class="box300">
<a id="rollover1" href="#" title="rollover_pigeon"></a></p>
<div class="attrib">Courtesy William van der Vliet</div>
<div class="caption">Testing time for the birds: pigeons got the right answer by pecking the image with the smaller number of items first. (That green square showed up briefly after a peck.) The results showed that pigeons can learn an abstract rule related to numbers &#8212; even though they cannot count.</div>
</div>
<p>
 It&#8217;s blue news for those who think only humans deserve human capacities.  From empathy and altruism to murder and war, animals seem to have caught on to some of our best &#8212; and worst &#8212; tricks. </p>
<p>
  Now Damian Scarf, a post-doctoral researcher at the University of Otago, with his colleagues, has taught three pigeons to order pairs of  numbers in the range from one through nine.</p>
<p>
  This is not exactly counting, but it certainly is a sign of numerical awareness in birds.</p>
<p>
  More important, the researchers  have taught these retired racing pigeons the concept of smaller-to-larger, Scarf says. &#8220;Previously, this number abstraction was only known in primates, and now we have shown that it is not unique to primates.&#8221;</p>
<h3>Serious screen-time serves science</h3>
<p>
  The experiment began with a year-long training period, during which the birds were shown pairs of images, each containing one, two or three countable items. If the birds pecked at both images, smaller number first, they were rewarded with some wheat. (Although the images never contained a numeral, we refer to the &#8220;number&#8221; they contain for brevity.) </p>
<p>
  To prevent the birds from focusing on color, shape or other non-numerical details, the images showed a range of items, so that the only correct answer would reflect their number rather than other distinctions.</p>
<p>
  &#8220;The training time reflects how difficult it is for them to abstract,&#8221; Scarf says. &#8220;It&#8217;s such a foreign situation, number is not the first port of call when presented with a stimulus to discriminate. That&#8217;s why we had so many shapes, colors, surface areas.&#8221; </p>
<p>
  Even if the birds originally made their judgments based on color, &#8220;we pushed them to use a different strategy, to break away from that. Number is not the default discrimination mechanism&#8221; for pigeons, says Scarf, who worked under advisor Michael Colombo of Otago. </p>
<div class="imgBigClear">
<a href="http://whyfiles.org/wp-content/uploads/2011/12/scarf1hr.jpg">
<div class="enlarge">ENLARGE</div>
<p><img src="http://whyfiles.org/wp-content/uploads/2011/12/scarf1hr.jpg" alt="Seven pigeons sit atop seven computer screens, each screen displays a set of different shapes in different colors" title="Pigeon repose with monitors" width="620" height="auto" class="alignnone size-full wp-image-21428" /></a></p>
<div class="attrib">Courtesy Damian Scarf</div>
<div class="caption">The profusion of colors and shapes was intended to prevent the birds from focusing on anything except number, in a set-up photo that was not taken during the actual experiment.</div>
</div>
<h3>A genius for abstraction?</h3>
<p>
  This does not mean that  the birds are counting, says Scarf. &#8220;It&#8217;s more a fuzzy representation in the brain of what &#8216;three&#8217; is. We can apply this verbal label to three, but they cannot. Pigeons, and animals in general, don&#8217;t have a definite idea of a number, that&#8217;s why they don’t perform perfectly, and why we see the distance effect.&#8221;</p>
<p>
  When the numbers on the test pair are further apart, Scarf found, &#8220;the fuzziness overlaps a little less.&#8221;</p>
<p>
  A greater distance between the numbers produced a quicker response and greater accuracy. For adjacent numbers, like four and five, the birds scored about 66 percent accuracy, compared to more than 95 percent for numbers separated by at least six.  Once the difference rose to at least three, the pigeons did as well as monkeys in a path-breaking 1998 study that opened the field of numerical &#8220;thinking&#8221; in animals.</p>
<p>
  Scarf stresses that the birds were not just regurgitating what they had learned, but were learning numerical rules. &#8220;The goal was to find out whether they could acquire an abstract rule. We were just training for one through three, but they learned some flexibility, an abstract, ascending rule for ordering numbers&#8221; that would apply to other numbers on the screen. </p>
<div class="imgBigClear">
<a href="http://whyfiles.org/wp-content/uploads/2011/12/feeding1.jpg">
<div class="enlarge">ENLARGE</div>
<p><img src="http://whyfiles.org/wp-content/uploads/2011/12/feeding1.jpg" alt="Old man throws seeds to a flock hundreds of pigeons, some on the ground and some flying&lt;" title="Feeding pigeons" width="620" height="auto" class="alignnone size-full wp-image-21430" /></a></p>
<div class="attrib">2011, <a href="http://www.flickr.com/photos/photonquantique/6033350394/">PhOtOnQuAnTiQuE</a></div>
<div class="caption">Feeding countless pigeons in front of the National Museum of Modern Art, Paris.</div>
</div>
<h3>Rooted in evolution, but where?</h3>
<div class="box350">
<a href="http://whyfiles.org/wp-content/uploads/2011/12/capuchincount1.jpg">
<div class="enlarge">ENLARGE</div>
<p><img src="http://whyfiles.org/wp-content/uploads/2011/12/capuchincount1.jpg" alt="Monkey points at square in the upper left corner of a computer screen, two other squares at lower right corner" title="Capuchin counting" width="350" height="auto" class="alignnone size-full wp-image-21429" /></a></p>
<div class="attrib">Photo: <a href="http://www.bucknell.edu/x30370.xml">Peter Judge</a>, Bucknell University</div>
<div class="caption">A brown capuchin monkey also has some mathematical ability.</div>
</div>
<p>
  Being able to recognize that one thing is more numerous than another could help an animal survive, Scarf says. &#8220;When food is available in multiple places, an animal has to develop an optimal strategy for figuring out where the most food is, and I think we have subverted that capacity for this task.&#8221;</p>
<p>
  Where this capacity arose is anybody&#8217;s guess at this point. The <a href="http://en.wikipedia.org/wiki/Evolution_of_mammals">evolutionary lineage</a> of mammals and birds divided about 300 million year ago, Scarf says. &#8220;If this derived from a common ancestor, it&#8217;s very old. It&#8217;s also possible that primates and birds have evolved this independently.&#8221;</p>
<p>
  &#8220;I do think it&#8217;s important, just as our study of mirror self-recognition in monkeys, from the fundamental standpoint of how these abilities come about,&#8221; says Luis Populin, a professor of anatomy at the University of Wisconsin-Madison, who has found that, under certain conditions, monkeys can <a href=" http://www.news.wisc.edu/18469">recognize themselves</a> in a mirror. &#8220;It&#8217;s very nice and is yet another step toward understanding how our cognitive functions develop.&#8221;</p>
<p>
  You have to hand it to these birds, which have set a new standard for avian aptitude. &#8220;The new part is the idea that this abstraction of numbers is not tied to training,&#8221; says Scarf. &#8220;Most numerical tests with animals involve  training and testing with the same numbers, but we were training with a limited set of numbers and testing them with numbers outside the range. They learned an abstract rule, and that&#8217;s what makes this study unique.&#8221;</p>
<div id="writer">
<p>  &#8212; David J. Tenenbaum</p></div>
<div class="relateds">
<div style="display: none;">
  <a class="simple-footnote" title="Pigeons on Par with Primates in Numerical Competence, Damian Scarf, et al, Science, 23 December 2011." id="return-note-21420-1" href="#note-21420-1"><sup>1</sup></a><br />
<a class="simple-footnote" title="Pigeons: Smarter than people?" id="return-note-21420-2" href="#note-21420-2"><sup>2</sup></a><br />
<a class="simple-footnote" title="Or should we poison some pigeons in the park?" id="return-note-21420-3" href="#note-21420-3"><sup>3</sup></a><br />
<a class="simple-footnote" title="Other signs of pigeon intelligence." id="return-note-21420-4" href="#note-21420-4"><sup>4</sup></a><br />
<a class="simple-footnote" title="What do pigeons and three-year-old children have in common?" id="return-note-21420-5" href="#note-21420-5"><sup>5</sup></a><br />
<a class="simple-footnote" title="Quirky pigeon facts." id="return-note-21420-6" href="#note-21420-6"><sup>6</sup></a><br />
<a class="simple-footnote" title="Other intelligent animals." id="return-note-21420-7" href="#note-21420-7"><sup>7</sup></a><br />
<a class="simple-footnote" title="Spy pigeons." id="return-note-21420-8" href="#note-21420-8"><sup>8</sup></a><br />
<a class="simple-footnote" title="What clever birds." id="return-note-21420-9" href="#note-21420-9"><sup>9</sup></a><br />
<a class="simple-footnote" title="Monkeys count too." id="return-note-21420-10" href="#note-21420-10"><sup>10</sup></a><br />
<a class="simple-footnote" title="And so do hyenas." id="return-note-21420-11" href="#note-21420-11"><sup>11</sup></a>
</div>
</div>
<div id="relateds"><h3>Terry Devitt, editor; S.V. Medaris, designer/illustrator; David J. Tenenbaum, feature writer; Amy Toburen, content development executive; Molly Simis, project assistant</h3></div>
<div class="simple-footnotes"><h3>Bibliography</h3><ol><li id="note-21420-1">Pigeons on Par with Primates in Numerical Competence, Damian Scarf, et al, Science, 23 December 2011. <a href="#return-note-21420-1">&#8617;</a></li><li id="note-21420-2">Pigeons: Smarter than <a href="http://psycnet.apa.org/?&#038;fa=main.doiLanding&#038;doi=10.1037/a0017703">people</a>? <a href="#return-note-21420-2">&#8617;</a></li><li id="note-21420-3">Or should we <a href="http://www.youtube.com/watch?v=yhuMLpdnOjY">poison</a> some pigeons in the park? <a href="#return-note-21420-3">&#8617;</a></li><li id="note-21420-4"><a href="http://www.sciencedaily.com/articles/p/pigeon_intelligence.htm">Other signs</a> of pigeon intelligence. <a href="#return-note-21420-4">&#8617;</a></li><li id="note-21420-5">What do pigeons and <a href="http://www.sciencedaily.com/releases/2008/06/080613145535.htm">three-year-old children</a> have in common? <a href="#return-note-21420-5">&#8617;</a></li><li id="note-21420-6"><a href="http://www.urbanwildlifesociety.org/UWS/GeeWhizQuizAnswers.htm">Quirky pigeon facts</a>. <a href="#return-note-21420-6">&#8617;</a></li><li id="note-21420-7">Other <a href="http://ngm.nationalgeographic.com/2008/03/animal-minds/virginia-morell-text/4">intelligent</a> animals. <a href="#return-note-21420-7">&#8617;</a></li><li id="note-21420-8"><a href="http://www.wired.com/dangerroom/2008/10/stop-that-spy-p/">Spy pigeons</a>. <a href="#return-note-21420-8">&#8617;</a></li><li id="note-21420-9">What <a href="http://www.dailymail.co.uk/news/article-1206608/Birds-feather-drink-The-pigeons-help-sup-water-fountain.html">clever birds</a>. <a href="#return-note-21420-9">&#8617;</a></li><li id="note-21420-10"><a href="http://www.newscientist.com/article/dn14231-counting-monkeys-tick-off-yet-another-human-ability.html">Monkeys</a> count too. <a href="#return-note-21420-10">&#8617;</a></li><li id="note-21420-11">And so do <a href="http://www.scientificamerican.com/article.cfm?id=hyenas-can-count-like-monkeys">hyenas</a>. <a href="#return-note-21420-11">&#8617;</a></li></ol></div>]]></content:encoded>
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		<title>Gecko!</title>
		<link>http://whyfiles.org/2009/gecko/</link>
		<comments>http://whyfiles.org/2009/gecko/#comments</comments>
		<pubDate>Fri, 24 Apr 2009 02:13:30 +0000</pubDate>
		<dc:creator>admin</dc:creator>
				<category><![CDATA[Cool Science Images]]></category>
		<category><![CDATA[electrostatic]]></category>
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		<category><![CDATA[van der Waals forces]]></category>

		<guid isPermaLink="false">http://whyfiles.org/?p=1891</guid>
		<description><![CDATA[In an experiment that could only have come out of California, UC Berkeley researchers decided to see what would happen if they chucked a gecko into a wind tunnel. Who says science can’t be fun? Looking for inspiration for building more maneuverable robots, the researchers pointed a powerful fan straight up to simulate freefall conditions [...]]]></description>
			<content:encoded><![CDATA[<div id="attachment_1892" class="wp-caption aligncenter" style="width: 335px"><a href="http://whyfiles.org/wp-content/uploads/2009/04/gecko_flight325.jpg"><img class="size-full wp-image-1892" title="Gecko in flight" src="http://whyfiles.org/wp-content/uploads/2009/04/gecko_flight325.jpg" alt="A flat-tailed house gecko skydiving" width="325" height="292" /></a><p class="wp-caption-text">A flat-tailed house gecko skydiving</p></div>
<p>In an experiment that could only have come out of California, UC Berkeley researchers decided to see what would happen if they chucked a gecko into a wind tunnel. Who says science can’t be fun?</p>
<p>Looking for inspiration for building more maneuverable robots, the researchers pointed a powerful fan straight up to simulate freefall conditions and used a high-speed camera to watch the gecko’s in-flight acrobatics.</p>
<p>What they discovered is that the gecko hardly moves its feet at all in the air.  Instead, it uses its fat-filled tail to control its pitch and yaw, which leaves its bulbous toes to act as drag shoots!  In this way the gecko was able to precisely navigate its way to a perch at the bottom.</p>
<p>With all the leaping around they do geckos need to be sure-footed to survive, so it helps that their feet are stickier than our strongest super glue.  Every square millimeter of their footpads contains about 14,000 superfine hair-like structures, and each one of them is tipped with between 100 and 1000 even finer bristles (see second photo).  The gecko is able to tap into powerful electrostatic forces that surge in the narrow gaps between the hairs. It’s these van der Waals forces that lend the gecko’s feet their near-supernatural tackiness. So forget nails, the mathematics of these forces indicates that &#8212; and we stress that this is purely speculation &#8212; a full-sized gecko on your ceiling could support the weight of a 290-pound chandelier!</p>
<div id="attachment_1895" class="wp-caption aligncenter" style="width: 394px"><a href="http://whyfiles.org/wp-content/uploads/2009/04/mgeckotoes.jpg"><img class="size-full wp-image-1895" title="Gecko toes" src="http://whyfiles.org/wp-content/uploads/2009/04/mgeckotoes.jpg" alt="Every square millimeter of gecko footpads contain about 14,000 superfine hair-like structures." width="384" height="288" /></a><p class="wp-caption-text">Every square millimeter of gecko footpads contain about 14,000 superfine hair-like structures.</p></div>
<p>Credit: Robert Full/UC Berkeley, copyright <a href="http://www.eurekalert.org/pub_releases/2008-03/uoc--gt031408.php">PNAS/NAS 2008</a></p>
<p>Original photo caption: This photo of a flat-tailed house gecko skydiving in a wind tunnel was selected for the cover of the March 18, 2008, issue of PNAS. Geckos use their fat-filled tail to right themselves in midair and maneuver to a secure perch.</p>
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		<title>Math-mangled: Better Way To Teach Math?</title>
		<link>http://whyfiles.org/2006/math-mangled-better-way-to-teach-math/</link>
		<comments>http://whyfiles.org/2006/math-mangled-better-way-to-teach-math/#comments</comments>
		<pubDate>Thu, 09 Mar 2006 15:55:44 +0000</pubDate>
		<dc:creator>schulte</dc:creator>
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		<description><![CDATA[Test shows horrific math performance by U.S. students. What do mathematicians and educators say about teaching math? Are we near a resolution of the math wars? Is there one optimal way to teach math?]]></description>
			<content:encoded><![CDATA[<p>International test shows horrific math performance among U.S. students. What do mathematicians and educators say about teaching math? Are we near a resolution of the &#8220;math wars&#8221;?<span id="more-877"></span></p>
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		<title>Science Matters, Tom Siegfried: Failure at math is a disaster for society</title>
		<link>http://whyfiles.org/2005/failure-at-math-is-a-disaster-for-society/</link>
		<comments>http://whyfiles.org/2005/failure-at-math-is-a-disaster-for-society/#comments</comments>
		<pubDate>Thu, 10 Nov 2005 21:21:22 +0000</pubDate>
		<dc:creator>schulte</dc:creator>
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		<guid isPermaLink="false">http://whyfiles.org/?p=855</guid>
		<description><![CDATA[For some reason, 2005 has been the year of living dangerously. Or maybe for no reason at all. Maybe it&#8217;s just bad luck, with random earthquakes and hurricanes just striking with more power and ferocity than usual. Bad things happen.]]></description>
			<content:encoded><![CDATA[<p>For some reason, 2005 has been the year of living dangerously. Or maybe for no reason at all. Maybe it&#8217;s just bad luck, with random earthquakes and hurricanes just striking with more power and ferocity than usual. Bad things happen.<span id="more-855"></span></p>
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		<title>Storytelling: What Relationship to Math Skills?</title>
		<link>http://whyfiles.org/2004/storytelling/</link>
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		<pubDate>Thu, 05 Aug 2004 19:22:37 +0000</pubDate>
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		<description><![CDATA[Three specific storytelling skills are related to certain math skills, but not to math skills in general. If you can adopt a character's perspective in a story, does that mean you are likely to be a math whiz?]]></description>
			<content:encoded><![CDATA[<p>Language. Math. To many of us, these fields of thought are as different as, well, letters and numbers. Some people are good at one, some at the other, a lucky few at both. But scientists have found little evidence that kids with excellent language ability are also masters of math.<span id="more-779"></span></p>
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		<title>Movies Show Scientists: What Do We Learn?</title>
		<link>http://whyfiles.org/2002/movies-show-science/</link>
		<comments>http://whyfiles.org/2002/movies-show-science/#comments</comments>
		<pubDate>Fri, 11 Jan 2002 19:59:54 +0000</pubDate>
		<dc:creator>schulte</dc:creator>
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		<guid isPermaLink="false">http://whyfiles.org/?p=764</guid>
		<description><![CDATA[A Beautiful Mind raises the issue: How are mathematicians and scientists portrayed in movies and film? We dig white coats on silver screens.]]></description>
			<content:encoded><![CDATA[<p>A Beautiful Mind shows how mathematicians and scientists are portrayed in movies and film. We dig deeper into white coats on the silver screen.<span id="more-764"></span></p>
]]></content:encoded>
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		<title>Pray for Prey</title>
		<link>http://whyfiles.org/2000/pray-for-prey/</link>
		<comments>http://whyfiles.org/2000/pray-for-prey/#comments</comments>
		<pubDate>Thu, 30 Nov 2000 15:14:58 +0000</pubDate>
		<dc:creator>schulte</dc:creator>
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		<guid isPermaLink="false">http://whyfiles.org/?p=556</guid>
		<description><![CDATA[If predators devour prey, how do predators survive once the prey are dead? Ecology benefits when the locations of prey and predators are taken into account, a study shows.]]></description>
			<content:encoded><![CDATA[If predators devour prey, how do predators survive once the prey are dead? Ecology benefits when the locations of prey and predators are taken into account, a study shows.]]></content:encoded>
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		<title>Letter from Archimedes: Math-Man Speaks!</title>
		<link>http://whyfiles.org/2000/a-letter-from-archimedes/</link>
		<comments>http://whyfiles.org/2000/a-letter-from-archimedes/#comments</comments>
		<pubDate>Mon, 24 Jul 2000 19:18:32 +0000</pubDate>
		<dc:creator>schulte</dc:creator>
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		<guid isPermaLink="false">http://whyfiles.org/?p=821</guid>
		<description><![CDATA[Ancient mathematician's writing found, restored, after 22 centuries!]]></description>
			<content:encoded><![CDATA[<p>Ancient mathematician&#8217;s writing found, restored, after 22 centuries.<span id="more-821"></span></p>
]]></content:encoded>
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