tag:blogger.com,1999:blog-6405662664343410797.post-15647218763060040072007-12-05T16:13:00.000-08:002007-12-05T18:01:31.696-08:00A while back, I came across a study that was done that came to a reasonable conclusion that a <a href="http://www.newscientist.com/article/dn9198-pigeonbrained-birds-can-think-in-logarithms.html">pigeon's brain worked on a logarithmic scale</a>. ( <a href="http://en.wikipedia.org/wiki/Logarithmic_scale">Logarithmic scale Wiki page</a> )<br /><br /><blockquote>In the experiment, pigeons were trained to tap one lever when a light flash was "short", perhaps 1 second long, and another lever when the flash was "long", say 16 seconds. When the birds then saw flashes of intermediate length, you would expect them to distinguish long from short around the mid-point of 8 or 9 seconds. But instead they switched at 4 seconds.</blockquote>I thought this was rather interesting, though didn't really think anything of it at the time. I mean really, what do I care about the numerical inner workings of a flying pest's brain who's droppings <a href="http://www.physorg.com/news107020653.html">take out bridges</a>?<br /><br />Today I read another study. This one about children, and how they first learn about numbers.<br /><a href="http://scienceblogs.com/cognitivedaily/2007/12/one_of_our_readers_emailed.php">From the article</a>:<br /><blockquote>... There's a pattern to the second-graders' responses. Nearly all the kids (93 were tested) understood that 750 was a larger number than 366; they just squeezed too many large numbers on the far-right side of the number line. In fact, their results show more of a logarithmic pattern than the proper linear pattern.</blockquote><div style="text-align: center;">This chart shows the average places the two grades placed the various numbers:<br /></div><a onblur="try {parent.deselectBloggerImageGracefully();} catch(e) {}" href="http://3.bp.blogspot.com/_Jm4QOrN9hPo/R1dPmfqsa4I/AAAAAAAAAIc/mMVMtunbFJo/s1600-h/2vs4.png"><img style="margin: 0px auto 10px; display: block; text-align: center; cursor: pointer;" src="http://3.bp.blogspot.com/_Jm4QOrN9hPo/R1dPmfqsa4I/AAAAAAAAAIc/mMVMtunbFJo/s400/2vs4.png" alt="" id="BLOGGER_PHOTO_ID_5140665022420904834" border="0" /></a><br /><div style="text-align: center;">When these results are plotted on a graph we get the following:<a onblur="try {parent.deselectBloggerImageGracefully();} catch(e) {}" href="http://4.bp.blogspot.com/_Jm4QOrN9hPo/R1dOlvqsa3I/AAAAAAAAAIU/WVMkKNHbryo/s1600-h/opfer2.gif"><img style="margin: 0px auto 10px; display: block; text-align: center; cursor: pointer;" src="http://4.bp.blogspot.com/_Jm4QOrN9hPo/R1dOlvqsa3I/AAAAAAAAAIU/WVMkKNHbryo/s400/opfer2.gif" alt="" id="BLOGGER_PHOTO_ID_5140663910024375154" border="0" /></a></div><br />So, it seems that before children are taught the "proper" linear way numbers work, they instead think of them in a logarithmic way... just like the pigeons. I would imagine that if we were to train any other animal, or even a baby, the way they trained the bird, they would see the same results; They would all think of things in a logarithmic scale, rather than a linear one.<br /><br />Now, why is it that we enforce this linear thinking of numbers upon our children, when our brains clearly work on a logarithmic scale? Perhaps we should instead let them continue with their proper way of thinking, rather than forcing them into a new one.<br /><br />After all, children are able to simply <a href="http://news.bbc.co.uk/2/hi/science/nature/3662928.stm">invent an entirely new language,</a> without any adult helping them out, so it's clear to me that there's alot more to a young mind than we think.<br /><br />I'll leave you with that to think about.<div class="blogger-post-footer"><img width='1' height='1' src='https://blogger.googleusercontent.com/tracker/6405662664343410797-1564721876306004007?l=felekar.blogspot.com'/></div>Felekarhttp://www.blogger.com/profile/17678091882454447185noreply@blogger.com0