tag:blogger.com,1999:blog-25232848588906315392024-02-19T10:49:07.800-05:00An Eternal BraidA team blog for readers of Godel, Escher, Bach: An Eternal Golden BraidAndreehttp://www.blogger.com/profile/08159511912645034019noreply@blogger.comBlogger1125tag:blogger.com,1999:blog-2523284858890631539.post-48025117252677328252008-03-07T06:34:00.004-05:002008-12-10T04:44:34.522-05:00Welcome! How This Blog Came To Be<a onblur="try {parent.deselectBloggerImageGracefully();} catch(e) {}" href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjEzWkgJ5dtefNxUoCRb2Q5foPuf4RQe7LEpuWXMtAL3S-i640mDX9zCM818E_eSJu_vJyb1K3uXtFKYXARYJNm0OBh7pskD3gW03WobBBXUbbldwNlksuvazo4iLWy8DVhJbW1YPlQkRk/s1600-h/800px-CollatzFractal.png" target="new"><img style="margin: 0px auto 10px; display: block; text-align: center; cursor: pointer;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjEzWkgJ5dtefNxUoCRb2Q5foPuf4RQe7LEpuWXMtAL3S-i640mDX9zCM818E_eSJu_vJyb1K3uXtFKYXARYJNm0OBh7pskD3gW03WobBBXUbbldwNlksuvazo4iLWy8DVhJbW1YPlQkRk/s400/800px-CollatzFractal.png" alt="" id="BLOGGER_PHOTO_ID_5174824096274403906" border="0" /></a>I ran across an interesting post yesterday from <a href="http://secondeffort.blogspot.com/" target="new">Second Effort</a> blog:<br /><br /><a href="http://secondeffort.blogspot.com/2008/03/heads-or-tails-28-7-things.html" target="new">Second Effort: Heads or Tails #28 -- 7 things</a><br /><blockquote>OK -- seven numbers: 1, 7, 10, 13, 19, 23, and 28.<br /><br />These, it turns out, are the first seven "<a href="http://en.wikipedia.org/wiki/Happy_number" target="new">happy numbers</a>"— something I'd never heard of either before undertaking today's assignment.<br /><br />Here's how they work:<br />7^2 = 49<br />4^2 + 9^2 = 97<br />9^2 + 7^2 = 130<br />1^2 + 3^2 + 0^2 = 10<br />1^2 + 0^2 = 1<br /><br />Did you get that? Take a number and square it. Break the resulting number into individual digits. Square each digit and add them up. Repeat for the resulting sum... and do so as necessary until (quoting now from the Wikipedia entry) "the number equals 1 (where it will stay), or it loops endlessly in a cycle which does not include 1. Those numbers for which this process ends in 1 are happy numbers, while those that do not end in 1 are unhappy numbers.</blockquote>I had never heard of Happy Numbers, either. The post reminded me of the Collatz Conjecture. I first heard of this conjecture in <span style="font-style: italic;"><a href="http://www.amazon.com/Godel-Escher-Bach-Eternal-Golden/dp/0465026567/ref=pd_bbs_sr_1?ie=UTF8&s=books&qid=1204857129&sr=8-1" target="new">Godel, Escher, Bach</a></span> by <a href="http://en.wikipedia.org/wiki/Douglas_Hofstadter" target="new">Douglas Hofstadter</a>. Hofstadter calls these numbers Wondrous Numbers.<br /><br />Take any whole number and apply one of these two rules to it: if the number is even, cut it in half, but if odd, multiply it by 3 and add 1. Whatever number results from this, apply one of the two rules to it. Do this again and again and you will notice something odd happening to the numbers that you get.<br /><br /><a href="http://www.cut-the-knot.org/" target="new">Cut The Knot</a> has a <a href="http://www.cut-the-knot.org/Curriculum/Arithmetic/Collatz.shtml" target="new">fun applet</a> to help you explore these numbers.<br /><br />Want to join? <a href="mailto:meeyauw@gmail.com?subject=Godel-Escher-Bach">Drop me an e-mail with the subject: Godel-Escher-Bach</a> (click that link and an e-mail message addressed to me with this subject will open in your e-mail client).<br /><br />Thank you.<br /><br /><span class="technoratitag">Technorati Tags: <a href="http://www.technorati.com/tag/Collatz+Conjecture%2C" target="_top" rel="tag" title="Technorati tag: Collatz Conjecture,">Collatz Conjecture,</a> <a href="http://www.technorati.com/tag/Happy+Numbers%2C" target="_top" rel="tag" title="Technorati tag: Happy Numbers,">Happy Numbers,</a> <a href="http://www.technorati.com/tag/Godel+Escher+Bach%2C" target="_top" rel="tag" title="Technorati tag: Godel Escher Bach,">Godel Escher Bach,</a> <a href="http://www.technorati.com/tag/Douglas+Hofstadter%2C" target="_top" rel="tag" title="Technorati tag: Douglas Hofstadter,">Douglas Hofstadter,</a> <a href="http://www.technorati.com/tag/Paul+Erdos%2C" target="_top" rel="tag" title="Technorati tag: Paul Erdos,">Paul Erdos,</a> <a href="http://www.technorati.com/tag/John+Allen+Paulos%2C" target="_top" rel="tag" title="Technorati tag: John Allen Paulos,">John Allen Paulos,</a> <a href="http://www.technorati.com/tag/fractal+art%2C" target="_top" rel="tag" title="Technorati tag: fractal art,">fractal art,</a> <a href="http://www.technorati.com/tag/Clay+Institute%2C" target="_top" rel="tag" title="Technorati tag: Clay Institute,">Clay Institute,</a> <a href="http://www.technorati.com/tag/Millenium+Problems" target="_top" rel="tag" title="Technorati tag: Millenium Problems">Millenium Problems</a> </span><br />_/\_/\_Andreehttp://www.blogger.com/profile/08159511912645034019noreply@blogger.com4