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	<title>Comments on: 2006 Year in Review</title>
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		<title>By: Walt</title>
		<link>http://www.arsmathematica.net/2007/01/01/2006-year-in-review/#comment-1528</link>
		<dc:creator><![CDATA[Walt]]></dc:creator>
		<pubDate>Thu, 04 Jan 2007 20:14:05 +0000</pubDate>
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		<description><![CDATA[People must have been familiar with the idea of computation using pen and paper for a long time.  They must have had an intuitive sense of what it meant that long division, for example, would finish in a certain amount of steps as a function of the input.  What probably compelled Hermann to write down a definition is that the algorithms she discovered were sufficiently complicated that it wasn&#039;t obvious you would ever stop.]]></description>
		<content:encoded><![CDATA[<p>People must have been familiar with the idea of computation using pen and paper for a long time.  They must have had an intuitive sense of what it meant that long division, for example, would finish in a certain amount of steps as a function of the input.  What probably compelled Hermann to write down a definition is that the algorithms she discovered were sufficiently complicated that it wasn&#8217;t obvious you would ever stop.</p>
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		<title>By: PeterMcB</title>
		<link>http://www.arsmathematica.net/2007/01/01/2006-year-in-review/#comment-1525</link>
		<dc:creator><![CDATA[PeterMcB]]></dc:creator>
		<pubDate>Wed, 03 Jan 2007 19:07:49 +0000</pubDate>
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		<description><![CDATA[On your Grete Hermann post, Walt, you said: &lt;i&gt;&quot;Hermann did this before the  invention of the computer, or even before the notion of an effective  procedure had been formalized.&quot;&lt;/i&gt;

I wonder if anyone knows when exactly our modern notions of computation first arose and were named.   After all, Babbage and, before him, Leibniz, had built machines capable of executing computations long before Hermann.   And, we should not forget manufacturing industry. 

In 1984, I saw in operation in a factory in Harare, Zimbabwe, a machine used to make wooden floor-brushes  which used a ribbon with holes in it to guide the movements and placement of a drill which made holes in the wooden base for the brush bristles.  By changing the ribbon, different patterns of bristle holes could be produced for different shaped brushes, all on the same machine.  This machine had been made in Sheffield, England, in 1870.  I believe there were similar machines in operation much earlier than this in the textile industry. 

No doubt the engineers of Sheffield who designed this machine did not call the ribbon a program, nor perhaps even distinguish between what we would call &quot;hardware&quot; and &quot;software&quot;.  But the concepts were clearly present, even if named differently or even not named.]]></description>
		<content:encoded><![CDATA[<p>On your Grete Hermann post, Walt, you said: <i>&#8220;Hermann did this before the  invention of the computer, or even before the notion of an effective  procedure had been formalized.&#8221;</i></p>
<p>I wonder if anyone knows when exactly our modern notions of computation first arose and were named.   After all, Babbage and, before him, Leibniz, had built machines capable of executing computations long before Hermann.   And, we should not forget manufacturing industry. </p>
<p>In 1984, I saw in operation in a factory in Harare, Zimbabwe, a machine used to make wooden floor-brushes  which used a ribbon with holes in it to guide the movements and placement of a drill which made holes in the wooden base for the brush bristles.  By changing the ribbon, different patterns of bristle holes could be produced for different shaped brushes, all on the same machine.  This machine had been made in Sheffield, England, in 1870.  I believe there were similar machines in operation much earlier than this in the textile industry. </p>
<p>No doubt the engineers of Sheffield who designed this machine did not call the ribbon a program, nor perhaps even distinguish between what we would call &#8220;hardware&#8221; and &#8220;software&#8221;.  But the concepts were clearly present, even if named differently or even not named.</p>
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		<title>By: Ars Mathematica &#187; Blog Archive &#187; Perelman-Tian-Yau Star On Wikipedia</title>
		<link>http://www.arsmathematica.net/2007/01/01/2006-year-in-review/#comment-1523</link>
		<dc:creator><![CDATA[Ars Mathematica &#187; Blog Archive &#187; Perelman-Tian-Yau Star On Wikipedia]]></dc:creator>
		<pubDate>Wed, 03 Jan 2007 05:19:05 +0000</pubDate>
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		<description><![CDATA[[...] Ars Mathematica Dedicated to the mathematical arts.      &#171; 2006 Year in Review [...]]]></description>
		<content:encoded><![CDATA[<p>[&#8230;] Ars Mathematica Dedicated to the mathematical arts.      &laquo; 2006 Year in Review [&#8230;]</p>
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