<rss xmlns:itunes="http://www.itunes.com/dtds/podcast-1.0.dtd" version="2.0">
  <channel>
    <title>MaplePrimes - Maple Posts and Questions</title>
    <link>http://www.mapleprimes.com/tags/Maple</link>
    <language>en-us</language>
    <copyright>2026 Maplesoft, A Division of Waterloo Maple Inc.</copyright>
    <generator>Maplesoft Document System</generator>
    <lastBuildDate>Sun, 23 Aug 2026 16:51:08 GMT</lastBuildDate>
    <pubDate>Sun, 23 Aug 2026 16:51:08 GMT</pubDate>
    <itunes:subtitle />
    <itunes:summary />
    <description>Maple Questions and Posts on MaplePrimes</description>
    <image>
      <url>http://www.mapleprimes.com/images/mapleprimeswhite.jpg</url>
      <title>MaplePrimes - Maple Posts and Questions</title>
      <link>http://www.mapleprimes.com/tags/Maple</link>
    </image>
    <item>
      <title>How can this ode error message be avoided?</title>
      <link>http://www.mapleprimes.com/questions/243741-How-Can-This-Ode-Error-Message-Be-Avoided?ref=Feed:MaplePrimes:Tagged With Maple</link>
      <itunes:summary>&lt;p&gt;The uploaded worksheet contains a second order ode with initial conditions which elicits an error message.&lt;br&gt;
How can this error be avoided?&lt;/p&gt;

&lt;p&gt;&lt;a href="/view.aspx?sf=243741_question/Bobs_sliding.mw"&gt;Bobs_sliding.mw&lt;/a&gt;&lt;/p&gt;
</itunes:summary>
      <description>&lt;p&gt;The uploaded worksheet contains a second order ode with initial conditions which elicits an error message.&lt;br&gt;
How can this error be avoided?&lt;/p&gt;

&lt;p&gt;&lt;a href="/view.aspx?sf=243741_question/Bobs_sliding.mw"&gt;Bobs_sliding.mw&lt;/a&gt;&lt;/p&gt;
</description>
      <guid>243741</guid>
      <pubDate>Sun, 23 Aug 2026 14:08:48 Z</pubDate>
      <itunes:author>Earl</itunes:author>
      <author>Earl</author>
    </item>
    <item>
      <title>AI Assistant with Anthropic Claude Max and other providers</title>
      <link>http://www.mapleprimes.com/questions/243737-AI-Assistant-With-Anthropic-Claude-Max?ref=Feed:MaplePrimes:Tagged With Maple</link>
      <itunes:summary>&lt;p&gt;Can the AI Assistant in the Maple 2026 GUI be configured to use Anthropic&amp;#39;s Claude Max plans, local AIs (e.g., via LM Studio), or other providers?&lt;/p&gt;
</itunes:summary>
      <description>&lt;p&gt;Can the AI Assistant in the Maple 2026 GUI be configured to use Anthropic&amp;#39;s Claude Max plans, local AIs (e.g., via LM Studio), or other providers?&lt;/p&gt;
</description>
      <guid>243737</guid>
      <pubDate>Sun, 16 Aug 2026 18:14:35 Z</pubDate>
      <itunes:author>OptimusMaplePrime</itunes:author>
      <author>OptimusMaplePrime</author>
    </item>
    <item>
      <title>Interupting Maple not working</title>
      <link>http://www.mapleprimes.com/questions/243736-Interupting-Maple-Not-Working?ref=Feed:MaplePrimes:Tagged With Maple</link>
      <itunes:summary>&lt;p&gt;I am only occasionally using Maple versions with the new ribon user interface and noticed about 2 weeks ago that I cannot&amp;nbsp;interrupt for loops under these interfaces. For example this one&lt;/p&gt;

&lt;pre class="prettyprint"&gt;
for i to 1000 do
    i^i;
end do&lt;/pre&gt;

&lt;p&gt;I re-run the code today (after installing windows updates) and could interrupt before the screen was filled with output but not after executing the code a second time (without restart).&lt;/p&gt;

&lt;p&gt;Is that reproducible on other installations?&lt;/p&gt;

&lt;p&gt;Are there other commands that cannot be interrupted?&amp;nbsp;&lt;br&gt;
If that is known, are there workarounds?&lt;/p&gt;

&lt;p&gt;Update:&lt;br&gt;
I have restarted Maple and have two worksheets open with the same code. I can repeatedly interrupt in one worksheet but not in other&lt;/p&gt;
</itunes:summary>
      <description>&lt;p&gt;I am only occasionally using Maple versions with the new ribon user interface and noticed about 2 weeks ago that I cannot&amp;nbsp;interrupt for loops under these interfaces. For example this one&lt;/p&gt;

&lt;pre class="prettyprint"&gt;
for i to 1000 do
    i^i;
end do&lt;/pre&gt;

&lt;p&gt;I re-run the code today (after installing windows updates) and could interrupt before the screen was filled with output but not after executing the code a second time (without restart).&lt;/p&gt;

&lt;p&gt;Is that reproducible on other installations?&lt;/p&gt;

&lt;p&gt;Are there other commands that cannot be interrupted?&amp;nbsp;&lt;br /&gt;
If that is known, are there workarounds?&lt;/p&gt;

&lt;p&gt;Update:&lt;br /&gt;
I have restarted Maple and have two worksheets open with the same code. I can repeatedly interrupt in one worksheet but not in other&lt;/p&gt;
</description>
      <guid>243736</guid>
      <pubDate>Sun, 16 Aug 2026 17:18:37 Z</pubDate>
      <itunes:author>C_R</itunes:author>
      <author>C_R</author>
    </item>
    <item>
      <title>What type of matrix normalisation is this</title>
      <link>http://www.mapleprimes.com/questions/243735-What-Type-Of-Matrix-Normalisation-Is-This?ref=Feed:MaplePrimes:Tagged With Maple</link>
      <itunes:summary>&lt;p&gt;Could anyone tell me what type of matrix normalisation this is and it it built into Maple? I found this in a paper and Google AI said this is the process of normailsation being used.&lt;/p&gt;

&lt;form name="worksheet_form"&gt;&lt;input name="md.ref" type="hidden" value="CDEFC0EE840B9A7FD98DC65B73D79678"&gt;
&lt;table align="center" width="768"&gt;
	&lt;tbody&gt;
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						&lt;td&gt;&lt;span style="color:#78000e;font-size: 100%;font-family: monospace,monospace;font-weight:bold;font-style:normal;"&gt;&amp;gt;&amp;nbsp;&lt;/span&gt;&lt;/td&gt;
						&lt;td&gt;
						&lt;p align="left" style="margin:0 0 0 0; padding-top:3px; padding-bottom:3px"&gt;&lt;span style="color:#78000e;font-size: 100%;font-family: monospace,monospace;font-weight:bold;font-style:normal;"&gt;restart&lt;/span&gt;&lt;/p&gt;
						&lt;/td&gt;
					&lt;/tr&gt;
				&lt;/tbody&gt;
			&lt;/table&gt;

			&lt;table style="margin-left:0px;margin-right:0px"&gt;
				&lt;tbody&gt;
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						&lt;td&gt;&lt;span style="color:#78000e;font-size: 100%;font-family: monospace,monospace;font-weight:bold;font-style:normal;"&gt;&amp;gt;&amp;nbsp;&lt;/span&gt;&lt;/td&gt;
						&lt;td&gt;
						&lt;p align="left" style="margin:0 0 0 0; padding-top:3px; padding-bottom:3px"&gt;&lt;span style="color:#78000e;font-size: 100%;font-family: monospace,monospace;font-weight:bold;font-style:normal;"&gt;with(LinearAlgebra):&lt;/span&gt;&lt;/p&gt;
						&lt;/td&gt;
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				&lt;/tbody&gt;
			&lt;/table&gt;

			&lt;table style="margin-left:0px;margin-right:0px"&gt;
				&lt;tbody&gt;
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						&lt;td&gt;&lt;span style="color:#78000e;font-size: 100%;font-family: monospace,monospace;font-weight:bold;font-style:normal;"&gt;&amp;gt;&amp;nbsp;&lt;/span&gt;&lt;/td&gt;
						&lt;td&gt;
						&lt;p align="left" style="margin:0 0 0 0; padding-top:3px; padding-bottom:3px"&gt;&lt;span style="color:#78000e;font-size: 100%;font-family: monospace,monospace;font-weight:bold;font-style:normal;"&gt;J:=Matrix([[ 1 , 0 , 0 ],&lt;/span&gt;&lt;br&gt;
						&lt;span style="color:#78000e;font-size: 100%;font-family: monospace,monospace;font-weight:bold;font-style:normal;"&gt;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;[ 0 , 1 , 0 ],&lt;/span&gt;&lt;br&gt;
						&lt;span style="color:#78000e;font-size: 100%;font-family: monospace,monospace;font-weight:bold;font-style:normal;"&gt;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;[ 0 , 0 , -1 ]]);&lt;/span&gt;&lt;/p&gt;
						&lt;/td&gt;
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			&lt;table&gt;
				&lt;tbody&gt;
					&lt;tr valign="baseline"&gt;
						&lt;td&gt;
						&lt;p align="center" style="margin:0 0 0 0; padding-top:0px; padding-bottom:0px"&gt;&lt;img alt="Matrix(3, 3, {(1, 1) = 1, (1, 2) = 0, (1, 3) = 0, (2, 1) = 0, (2, 2) = 1, (2, 3) = 0, (3, 1) = 0, (3, 2) = 0, (3, 3) = -1})" height="23" src="/view.aspx?sf=243735_question/6a2765bbe392ed370c47348b261f164e.gif" style="vertical-align:-6px" width="58"&gt;&lt;/p&gt;
						&lt;/td&gt;
						&lt;td align="right" style="color:#000000; font-family:Times, serif; font-weight:bold; font-style:normal;"&gt;(1)&lt;/td&gt;
					&lt;/tr&gt;
				&lt;/tbody&gt;
			&lt;/table&gt;

			&lt;p align="left" style="margin:0 0 0 0; padding-top:3px; padding-bottom:3px"&gt;&lt;span style="color:#000000;font-size: 91%;font-family: DejaVu Sans;font-weight:normal;font-style:normal;"&gt;Matrix N has already been scaled, so the rows are of equal magnitude &amp;nbsp;x^2 + y^2 - z^2= k&lt;/span&gt;&lt;/p&gt;

			&lt;table style="margin-left:0px;margin-right:0px"&gt;
				&lt;tbody&gt;
					&lt;tr valign="baseline"&gt;
						&lt;td&gt;&lt;span style="color:#78000e;font-size: 100%;font-family: monospace,monospace;font-weight:bold;font-style:normal;"&gt;&amp;gt;&amp;nbsp;&lt;/span&gt;&lt;/td&gt;
						&lt;td&gt;
						&lt;p align="left" style="margin:0 0 0 0; padding-top:3px; padding-bottom:3px"&gt;&lt;span style="color:#78000e;font-size: 100%;font-family: monospace,monospace;font-weight:bold;font-style:normal;"&gt;N:=Matrix(3, 3, [[4, -3, 2], [-1/2*sqrt(70), -3/10*sqrt(70), 1/5*sqrt(70)], [1/11*sqrt(77), 6/11*sqrt(77), 2/11*sqrt(77)]])&lt;/span&gt;&lt;/p&gt;
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			&lt;table&gt;
				&lt;tbody&gt;
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						&lt;p align="center" style="margin:0 0 0 0; padding-top:0px; padding-bottom:0px"&gt;&lt;img alt="Matrix(3, 3, {(1, 1) = 4, (1, 2) = -3, (1, 3) = 2, (2, 1) = -(1/2)*sqrt(70), (2, 2) = -(3/10)*sqrt(70), (2, 3) = (1/5)*sqrt(70), (3, 1) = (1/11)*sqrt(77), (3, 2) = (6/11)*sqrt(77), (3, 3) = (2/11)*sqrt(77)})" height="23" src="/view.aspx?sf=243735_question/d8ba50222cfc56b9be370717c4dbd948.gif" style="vertical-align:-6px" width="62"&gt;&lt;/p&gt;
						&lt;/td&gt;
						&lt;td align="right" style="color:#000000; font-family:Times, serif; font-weight:bold; font-style:normal;"&gt;(2)&lt;/td&gt;
					&lt;/tr&gt;
				&lt;/tbody&gt;
			&lt;/table&gt;

			&lt;p align="left" style="margin:0 0 0 0; padding-top:3px; padding-bottom:3px"&gt;&lt;span style="color:#000000;font-size: 91%;font-family: DejaVu Sans;font-weight:normal;font-style:normal;"&gt;&amp;nbsp; &lt;/span&gt;&lt;/p&gt;

			&lt;table style="margin-left:0px;margin-right:0px"&gt;
				&lt;tbody&gt;
					&lt;tr valign="baseline"&gt;
						&lt;td&gt;&lt;span style="color:#78000e;font-size: 100%;font-family: monospace,monospace;font-weight:bold;font-style:normal;"&gt;&amp;gt;&amp;nbsp;&lt;/span&gt;&lt;/td&gt;
						&lt;td&gt;
						&lt;p align="left" style="margin:0 0 0 0; padding-top:3px; padding-bottom:3px"&gt;&lt;span style="color:#78000e;font-size: 100%;font-family: monospace,monospace;font-weight:bold;font-style:normal;"&gt;for i to 3 do&lt;/span&gt;&lt;br&gt;
						&lt;span style="color:#78000e;font-size: 100%;font-family: monospace,monospace;font-weight:bold;font-style:normal;"&gt;add(N[i,j]^2,j=1..2)-N[i,3]^2;&lt;/span&gt;&lt;br&gt;
						&lt;span style="color:#78000e;font-size: 100%;font-family: monospace,monospace;font-weight:bold;font-style:normal;"&gt;end do&lt;/span&gt;&lt;/p&gt;
						&lt;/td&gt;
					&lt;/tr&gt;
				&lt;/tbody&gt;
			&lt;/table&gt;

			&lt;table&gt;
				&lt;tbody&gt;
					&lt;tr valign="baseline"&gt;
						&lt;td&gt;
						&lt;p align="center" style="margin:0 0 0 0; padding-top:0px; padding-bottom:0px"&gt;&lt;img alt="21" height="23" src="/view.aspx?sf=243735_question/6909a36186573d74cca7d3880b5d7ba3.gif" style="vertical-align:-6px" width="21"&gt;&lt;/p&gt;
						&lt;/td&gt;
						&lt;td align="right" style="color:#000000; font-family:Times, serif; font-weight:bold; font-style:normal;"&gt;&amp;nbsp;&lt;/td&gt;
					&lt;/tr&gt;
				&lt;/tbody&gt;
			&lt;/table&gt;

			&lt;table&gt;
				&lt;tbody&gt;
					&lt;tr valign="baseline"&gt;
						&lt;td&gt;
						&lt;p align="center" style="margin:0 0 0 0; padding-top:0px; padding-bottom:0px"&gt;&lt;img alt="21" height="23" src="/view.aspx?sf=243735_question/ffe2a15af9750c646c7427bfb3a8668b.gif" style="vertical-align:-6px" width="21"&gt;&lt;/p&gt;
						&lt;/td&gt;
						&lt;td align="right" style="color:#000000; font-family:Times, serif; font-weight:bold; font-style:normal;"&gt;&amp;nbsp;&lt;/td&gt;
					&lt;/tr&gt;
				&lt;/tbody&gt;
			&lt;/table&gt;

			&lt;table&gt;
				&lt;tbody&gt;
					&lt;tr valign="baseline"&gt;
						&lt;td&gt;
						&lt;p align="center" style="margin:0 0 0 0; padding-top:0px; padding-bottom:0px"&gt;&lt;img alt="21" height="23" src="/view.aspx?sf=243735_question/283fc73e5ffdc146a7619e22f89c78fb.gif" style="vertical-align:-6px" width="21"&gt;&lt;/p&gt;
						&lt;/td&gt;
						&lt;td align="right" style="color:#000000; font-family:Times, serif; font-weight:bold; font-style:normal;"&gt;(3)&lt;/td&gt;
					&lt;/tr&gt;
				&lt;/tbody&gt;
			&lt;/table&gt;

			&lt;p align="left" style="margin:0 0 0 0; padding-top:3px; padding-bottom:3px"&gt;&lt;span style="color:#000000;font-size: 91%;font-family: DejaVu Sans;font-weight:normal;font-style:normal;"&gt;Normalisation process to produce C&lt;/span&gt;&lt;/p&gt;

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					&lt;tr valign="baseline"&gt;
						&lt;td&gt;&lt;span style="color:#78000e;font-size: 100%;font-family: monospace,monospace;font-weight:bold;font-style:normal;"&gt;&amp;gt;&amp;nbsp;&lt;/span&gt;&lt;/td&gt;
						&lt;td&gt;
						&lt;p align="left" style="margin:0 0 0 0; padding-top:3px; padding-bottom:3px"&gt;&lt;span style="color:#78000e;font-size: 100%;font-family: monospace,monospace;font-weight:bold;font-style:normal;"&gt;A:=N.J.N^%T&lt;/span&gt;&lt;/p&gt;
						&lt;/td&gt;
					&lt;/tr&gt;
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			&lt;/table&gt;

			&lt;table&gt;
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						&lt;td&gt;
						&lt;p align="center" style="margin:0 0 0 0; padding-top:0px; padding-bottom:0px"&gt;&lt;img alt="Matrix(3, 3, {(1, 1) = 21, (1, 2) = -(3/2)*sqrt(70), (1, 3) = -(18/11)*sqrt(77), (2, 1) = -(3/2)*sqrt(70), (2, 2) = 21, (2, 3) = -(27/110)*sqrt(70)*sqrt(77), (3, 1) = -(18/11)*sqrt(77), (3, 2) = -(27/110)*sqrt(70)*sqrt(77), (3, 3) = 21})" height="23" src="/view.aspx?sf=243735_question/c736d9b31b7c2dbf52e1113653214077.gif" style="vertical-align:-6px" width="61"&gt;&lt;/p&gt;
						&lt;/td&gt;
						&lt;td align="right" style="color:#000000; font-family:Times, serif; font-weight:bold; font-style:normal;"&gt;(4)&lt;/td&gt;
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			&lt;table style="margin-left:0px;margin-right:0px"&gt;
				&lt;tbody&gt;
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						&lt;td&gt;&lt;span style="color:#78000e;font-size: 100%;font-family: monospace,monospace;font-weight:bold;font-style:normal;"&gt;&amp;gt;&amp;nbsp;&lt;/span&gt;&lt;/td&gt;
						&lt;td&gt;
						&lt;p align="left" style="margin:0 0 0 0; padding-top:3px; padding-bottom:3px"&gt;&lt;span style="color:#78000e;font-size: 100%;font-family: monospace,monospace;font-weight:bold;font-style:normal;"&gt;dA:=DiagonalMatrix(1/~(sqrt~(abs(Diagonal((A))))));&lt;/span&gt;&lt;/p&gt;
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			&lt;table&gt;
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						&lt;td&gt;
						&lt;p align="center" style="margin:0 0 0 0; padding-top:0px; padding-bottom:0px"&gt;&lt;img alt="Matrix(3, 3, {(1, 1) = (1/21)*sqrt(21), (1, 2) = 0, (1, 3) = 0, (2, 1) = 0, (2, 2) = (1/21)*sqrt(21), (2, 3) = 0, (3, 1) = 0, (3, 2) = 0, (3, 3) = (1/21)*sqrt(21)})" height="23" src="/view.aspx?sf=243735_question/8b5ce197cce43f96bf9581e7bf740875.gif" style="vertical-align:-6px" width="68"&gt;&lt;/p&gt;
						&lt;/td&gt;
						&lt;td align="right" style="color:#000000; font-family:Times, serif; font-weight:bold; font-style:normal;"&gt;(5)&lt;/td&gt;
					&lt;/tr&gt;
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			&lt;/table&gt;

			&lt;table style="margin-left:0px;margin-right:0px"&gt;
				&lt;tbody&gt;
					&lt;tr valign="baseline"&gt;
						&lt;td&gt;&lt;span style="color:#78000e;font-size: 100%;font-family: monospace,monospace;font-weight:bold;font-style:normal;"&gt;&amp;gt;&amp;nbsp;&lt;/span&gt;&lt;/td&gt;
						&lt;td&gt;
						&lt;p align="left" style="margin:0 0 0 0; padding-top:3px; padding-bottom:3px"&gt;&lt;span style="color:#78000e;font-size: 100%;font-family: monospace,monospace;font-weight:bold;font-style:normal;"&gt;C:=(dA.A.dA);&lt;/span&gt;&lt;/p&gt;
						&lt;/td&gt;
					&lt;/tr&gt;
				&lt;/tbody&gt;
			&lt;/table&gt;

			&lt;table&gt;
				&lt;tbody&gt;
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						&lt;td&gt;
						&lt;p align="center" style="margin:0 0 0 0; padding-top:0px; padding-bottom:0px"&gt;&lt;img alt="Matrix(3, 3, {(1, 1) = 1, (1, 2) = -(1/14)*sqrt(70), (1, 3) = -(6/77)*sqrt(77), (2, 1) = -(1/14)*sqrt(70), (2, 2) = 1, (2, 3) = -(9/770)*sqrt(70)*sqrt(77), (3, 1) = -(6/77)*sqrt(77), (3, 2) = -(9/770)*sqrt(70)*sqrt(77), (3, 3) = 1})" height="23" src="/view.aspx?sf=243735_question/316bbc50908db91632604426b957ecbc.gif" style="vertical-align:-6px" width="62"&gt;&lt;/p&gt;
						&lt;/td&gt;
						&lt;td align="right" style="color:#000000; font-family:Times, serif; font-weight:bold; font-style:normal;"&gt;(6)&lt;/td&gt;
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			&lt;table style="margin-left:0px;margin-right:0px"&gt;
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					&lt;tr valign="baseline"&gt;
						&lt;td&gt;&lt;span style="color:#78000e;font-size: 100%;font-family: monospace,monospace;font-weight:bold;font-style:normal;"&gt;&amp;gt;&amp;nbsp;&lt;/span&gt;&lt;/td&gt;
						&lt;td&gt;
						&lt;p align="left" style="margin:0 0 0 0; padding-top:3px; padding-bottom:3px"&gt;&lt;span style="color:#78000e;font-size: 100%;font-family: monospace,monospace;font-weight:bold;font-style:normal;"&gt;evalf(C)&lt;/span&gt;&lt;/p&gt;
						&lt;/td&gt;
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			&lt;table&gt;
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						&lt;td&gt;
						&lt;p align="center" style="margin:0 0 0 0; padding-top:0px; padding-bottom:0px"&gt;&lt;img alt="Matrix(3, 3, {(1, 1) = 1., (1, 2) = -.5976143047, (1, 3) = -.6837634587, (2, 1) = -.5976143047, (2, 2) = 1., (2, 3) = -.8581163304, (3, 1) = -.6837634587, (3, 2) = -.8581163304, (3, 3) = 1.})" height="23" src="/view.aspx?sf=243735_question/4530853d6d8a38cd668a41f2420b761b.gif" style="vertical-align:-6px" width="26"&gt;&lt;/p&gt;
						&lt;/td&gt;
						&lt;td align="right" style="color:#000000; font-family:Times, serif; font-weight:bold; font-style:normal;"&gt;(7)&lt;/td&gt;
					&lt;/tr&gt;
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			&lt;table style="margin-left:0px;margin-right:0px"&gt;
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&lt;p&gt;&lt;a href="/view.aspx?sf=243735_question/2026-08-14_Q_What_Type_of_Matrix_Normalisation.mw"&gt;Download 2026-08-14_Q_What_Type_of_Matrix_Normalisation.mw&lt;/a&gt;&lt;/p&gt;
</itunes:summary>
      <description>&lt;p&gt;Could anyone tell me what type of matrix normalisation this is and it it built into Maple? I found this in a paper and Google AI said this is the process of normailsation being used.&lt;/p&gt;

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						&lt;p align="left" style="margin:0 0 0 0; padding-top:3px; padding-bottom:3px"&gt;&lt;span style="color:#78000e;font-size: 100%;font-family: monospace,monospace;font-weight:bold;font-style:normal;"&gt;with(LinearAlgebra):&lt;/span&gt;&lt;/p&gt;
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						&lt;p align="left" style="margin:0 0 0 0; padding-top:3px; padding-bottom:3px"&gt;&lt;span style="color:#78000e;font-size: 100%;font-family: monospace,monospace;font-weight:bold;font-style:normal;"&gt;J:=Matrix([[ 1 , 0 , 0 ],&lt;/span&gt;&lt;br&gt;
						&lt;span style="color:#78000e;font-size: 100%;font-family: monospace,monospace;font-weight:bold;font-style:normal;"&gt;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;[ 0 , 1 , 0 ],&lt;/span&gt;&lt;br&gt;
						&lt;span style="color:#78000e;font-size: 100%;font-family: monospace,monospace;font-weight:bold;font-style:normal;"&gt;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;[ 0 , 0 , -1 ]]);&lt;/span&gt;&lt;/p&gt;
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						&lt;p align="center" style="margin:0 0 0 0; padding-top:0px; padding-bottom:0px"&gt;&lt;img alt="Matrix(3, 3, {(1, 1) = 1, (1, 2) = 0, (1, 3) = 0, (2, 1) = 0, (2, 2) = 1, (2, 3) = 0, (3, 1) = 0, (3, 2) = 0, (3, 3) = -1})" height="23" src="/view.aspx?sf=243735_question/6a2765bbe392ed370c47348b261f164e.gif" style="vertical-align:-6px" width="58"&gt;&lt;/p&gt;
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						&lt;td align="right" style="color:#000000; font-family:Times, serif; font-weight:bold; font-style:normal;"&gt;(1)&lt;/td&gt;
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			&lt;p align="left" style="margin:0 0 0 0; padding-top:3px; padding-bottom:3px"&gt;&lt;span style="color:#000000;font-size: 91%;font-family: DejaVu Sans;font-weight:normal;font-style:normal;"&gt;Matrix N has already been scaled, so the rows are of equal magnitude &amp;nbsp;x^2 + y^2 - z^2= k&lt;/span&gt;&lt;/p&gt;

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						&lt;p align="left" style="margin:0 0 0 0; padding-top:3px; padding-bottom:3px"&gt;&lt;span style="color:#78000e;font-size: 100%;font-family: monospace,monospace;font-weight:bold;font-style:normal;"&gt;N:=Matrix(3, 3, [[4, -3, 2], [-1/2*sqrt(70), -3/10*sqrt(70), 1/5*sqrt(70)], [1/11*sqrt(77), 6/11*sqrt(77), 2/11*sqrt(77)]])&lt;/span&gt;&lt;/p&gt;
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						&lt;p align="center" style="margin:0 0 0 0; padding-top:0px; padding-bottom:0px"&gt;&lt;img alt="Matrix(3, 3, {(1, 1) = 4, (1, 2) = -3, (1, 3) = 2, (2, 1) = -(1/2)*sqrt(70), (2, 2) = -(3/10)*sqrt(70), (2, 3) = (1/5)*sqrt(70), (3, 1) = (1/11)*sqrt(77), (3, 2) = (6/11)*sqrt(77), (3, 3) = (2/11)*sqrt(77)})" height="23" src="/view.aspx?sf=243735_question/d8ba50222cfc56b9be370717c4dbd948.gif" style="vertical-align:-6px" width="62"&gt;&lt;/p&gt;
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						&lt;td align="right" style="color:#000000; font-family:Times, serif; font-weight:bold; font-style:normal;"&gt;(2)&lt;/td&gt;
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						&lt;p align="left" style="margin:0 0 0 0; padding-top:3px; padding-bottom:3px"&gt;&lt;span style="color:#78000e;font-size: 100%;font-family: monospace,monospace;font-weight:bold;font-style:normal;"&gt;for i to 3 do&lt;/span&gt;&lt;br&gt;
						&lt;span style="color:#78000e;font-size: 100%;font-family: monospace,monospace;font-weight:bold;font-style:normal;"&gt;add(N[i,j]^2,j=1..2)-N[i,3]^2;&lt;/span&gt;&lt;br&gt;
						&lt;span style="color:#78000e;font-size: 100%;font-family: monospace,monospace;font-weight:bold;font-style:normal;"&gt;end do&lt;/span&gt;&lt;/p&gt;
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						&lt;td align="right" style="color:#000000; font-family:Times, serif; font-weight:bold; font-style:normal;"&gt;(3)&lt;/td&gt;
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			&lt;p align="left" style="margin:0 0 0 0; padding-top:3px; padding-bottom:3px"&gt;&lt;span style="color:#000000;font-size: 91%;font-family: DejaVu Sans;font-weight:normal;font-style:normal;"&gt;Normalisation process to produce C&lt;/span&gt;&lt;/p&gt;

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						&lt;p align="center" style="margin:0 0 0 0; padding-top:0px; padding-bottom:0px"&gt;&lt;img alt="Matrix(3, 3, {(1, 1) = 21, (1, 2) = -(3/2)*sqrt(70), (1, 3) = -(18/11)*sqrt(77), (2, 1) = -(3/2)*sqrt(70), (2, 2) = 21, (2, 3) = -(27/110)*sqrt(70)*sqrt(77), (3, 1) = -(18/11)*sqrt(77), (3, 2) = -(27/110)*sqrt(70)*sqrt(77), (3, 3) = 21})" height="23" src="/view.aspx?sf=243735_question/c736d9b31b7c2dbf52e1113653214077.gif" style="vertical-align:-6px" width="61"&gt;&lt;/p&gt;
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						&lt;p align="left" style="margin:0 0 0 0; padding-top:3px; padding-bottom:3px"&gt;&lt;span style="color:#78000e;font-size: 100%;font-family: monospace,monospace;font-weight:bold;font-style:normal;"&gt;dA:=DiagonalMatrix(1/~(sqrt~(abs(Diagonal((A))))));&lt;/span&gt;&lt;/p&gt;
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						&lt;p align="center" style="margin:0 0 0 0; padding-top:0px; padding-bottom:0px"&gt;&lt;img alt="Matrix(3, 3, {(1, 1) = (1/21)*sqrt(21), (1, 2) = 0, (1, 3) = 0, (2, 1) = 0, (2, 2) = (1/21)*sqrt(21), (2, 3) = 0, (3, 1) = 0, (3, 2) = 0, (3, 3) = (1/21)*sqrt(21)})" height="23" src="/view.aspx?sf=243735_question/8b5ce197cce43f96bf9581e7bf740875.gif" style="vertical-align:-6px" width="68"&gt;&lt;/p&gt;
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						&lt;p align="center" style="margin:0 0 0 0; padding-top:0px; padding-bottom:0px"&gt;&lt;img alt="Matrix(3, 3, {(1, 1) = 1, (1, 2) = -(1/14)*sqrt(70), (1, 3) = -(6/77)*sqrt(77), (2, 1) = -(1/14)*sqrt(70), (2, 2) = 1, (2, 3) = -(9/770)*sqrt(70)*sqrt(77), (3, 1) = -(6/77)*sqrt(77), (3, 2) = -(9/770)*sqrt(70)*sqrt(77), (3, 3) = 1})" height="23" src="/view.aspx?sf=243735_question/316bbc50908db91632604426b957ecbc.gif" style="vertical-align:-6px" width="62"&gt;&lt;/p&gt;
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						&lt;p align="center" style="margin:0 0 0 0; padding-top:0px; padding-bottom:0px"&gt;&lt;img alt="Matrix(3, 3, {(1, 1) = 1., (1, 2) = -.5976143047, (1, 3) = -.6837634587, (2, 1) = -.5976143047, (2, 2) = 1., (2, 3) = -.8581163304, (3, 1) = -.6837634587, (3, 2) = -.8581163304, (3, 3) = 1.})" height="23" src="/view.aspx?sf=243735_question/4530853d6d8a38cd668a41f2420b761b.gif" style="vertical-align:-6px" width="26"&gt;&lt;/p&gt;
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&lt;p&gt;&lt;a href="/view.aspx?sf=243735_question/2026-08-14_Q_What_Type_of_Matrix_Normalisation.mw"&gt;Download 2026-08-14_Q_What_Type_of_Matrix_Normalisation.mw&lt;/a&gt;&lt;/p&gt;
</description>
      <guid>243735</guid>
      <pubDate>Fri, 14 Aug 2026 05:22:23 Z</pubDate>
      <itunes:author>Ronan</itunes:author>
      <author>Ronan</author>
    </item>
    <item>
      <title>Maple transactions new issue?</title>
      <link>http://www.mapleprimes.com/questions/243734-Maple-Transactions-New-Issue?ref=Feed:MaplePrimes:Tagged With Maple</link>
      <itunes:summary>&lt;p&gt;I notice that Maple transactions journal does not publish any new issue ever since March this year. Based on the previous recording it is supposed to publish issue each season. When is it going to promote a new issue? My research is supposed to publish there and I believe I have made some interesting progress and it is of interest to the community.&lt;/p&gt;
</itunes:summary>
      <description>&lt;p&gt;I notice that Maple transactions journal does not publish any new issue ever since March this year. Based on the previous recording it is supposed to publish issue each season. When is it going to promote a new issue? My research is supposed to publish there and I believe I have made some interesting progress and it is of interest to the community.&lt;/p&gt;
</description>
      <guid>243734</guid>
      <pubDate>Thu, 13 Aug 2026 18:25:08 Z</pubDate>
      <itunes:author>Steven_Huang</itunes:author>
      <author>Steven_Huang</author>
    </item>
    <item>
      <title>Poisoned Wine Bottle </title>
      <link>http://www.mapleprimes.com/posts/235447-Poisoned-Wine-Bottle-?ref=Feed:MaplePrimes:Tagged With Maple</link>
      <itunes:summary>&lt;p style="margin-bottom:11px"&gt;&lt;span style="font-size:12pt"&gt;&lt;span style="line-height:115%"&gt;You are hosting a big party tonight and prepared 1000 bottles of wine. A spiteful neighbor sneaks in and poisons exactly one bottle. The poison is colorless, tasteless, and takes about an hour to take effect and kill. Your party also starts in an hour, and you don&amp;rsquo;t want to throw all the wine away.&lt;/span&gt;&lt;/span&gt;&lt;/p&gt;

&lt;p style="margin-bottom:11px"&gt;&lt;span style="font-size:12pt"&gt;&lt;span style="line-height:115%"&gt;You have 10 mice and time for only one round of tasting. In that round, a mouse can taste from any number of bottles. How can you identify that single poisoned bottle among 1000?&lt;/span&gt;&lt;/span&gt;&lt;/p&gt;

&lt;p style="margin-bottom:11px"&gt;&lt;span style="font-size:12pt"&gt;&lt;span style="line-height:115%"&gt;Pause here and try to solve the problem yourself!&lt;/span&gt;&lt;/span&gt;&lt;/p&gt;

&lt;p style="margin-bottom:11px"&gt;&lt;img src="/view.aspx?sf=235447_post/Poisoned_Bottle_Diagram_1.png"&gt;&lt;/p&gt;

&lt;p style="margin-bottom:11px"&gt;&lt;span style="font-size:12pt"&gt;&lt;span style="line-height:115%"&gt;An obvious solution might be to group the wine into 10 batches of 100 bottles and have each mouse drink from one batch. But if a mouse dies, you have only narrowed it down to 100 bottles, and there is no time for a second round. Whatever test you run, you only get one shot.&lt;/span&gt;&lt;/span&gt;&lt;/p&gt;

&lt;div style="border-bottom:solid windowtext 1.0pt; padding:0in 0in 1.0pt 0in"&gt;
&lt;p style="border:none; padding:0in; margin-bottom:11px"&gt;&lt;span style="font-size:12pt"&gt;&lt;span style="line-height:115%"&gt;Ten mice. A thousand bottles. The problem sounds impossible &amp;ndash; until you realize each mouse isn&amp;rsquo;t just a taster. &lt;/span&gt;&lt;/span&gt;&lt;/p&gt;

&lt;p style="border:none; padding:0in; margin-bottom:11px"&gt;&lt;span style="font-size:12pt"&gt;&lt;span style="line-height:115%"&gt;The exact idea that powers com&lt;/span&gt;&lt;/span&gt;&lt;span style="font-size:12pt"&gt;&lt;span style="line-height:115%"&gt;puters is also what solves our wine puzzle.&lt;/span&gt;&lt;/span&gt;&lt;/p&gt;
&lt;/div&gt;

&lt;p style="margin-bottom:11px"&gt;&lt;span style="font-size:12pt"&gt;&lt;span style="line-height:115%"&gt;&lt;b&gt;&lt;span style="font-size:16.0pt"&gt;&lt;span style="line-height:115%"&gt;A 300-Year-Old Idea&lt;/span&gt;&lt;/span&gt;&lt;/b&gt;&lt;/span&gt;&lt;/span&gt;&lt;/p&gt;

&lt;p style="margin-bottom:11px"&gt;&lt;span style="font-size:12pt"&gt;&lt;span style="line-height:115%"&gt;Some background information before we solve the problem.&lt;/span&gt;&lt;/span&gt;&lt;/p&gt;

&lt;p style="margin-bottom:11px"&gt;&lt;span style="font-size:12pt"&gt;&lt;span style="line-height:115%"&gt;In 1703, Gottfried Leibniz published a paper describing how every number can be written using only two symbols: 0 and 1. To him, the concept felt almost divine &amp;ndash; an entire universe created out of nothingness and unity. But for over two centuries, binary remained an idea trapped on paper.&lt;/span&gt;&lt;/span&gt;&lt;/p&gt;

&lt;p style="margin-bottom:11px"&gt;&lt;span style="font-size:12pt"&gt;&lt;span style="line-height:115%"&gt;Everything changed when a young engineer named Claude Shannon realized that 0 and 1 map perfectly onto the physical states of an electrical switch: off and on. That single insight laid the groundwork for digital circuits, eventually powering every smartphone, laptop, and text message on the planet.&lt;/span&gt;&lt;/span&gt;&lt;/p&gt;

&lt;p style="margin-bottom:11px"&gt;&lt;span style="font-size:12pt"&gt;&lt;span style="line-height:115%"&gt;Yet binary is more than just how machines store information. It is a way of extracting information. &lt;/span&gt;&lt;/span&gt;&lt;/p&gt;

&lt;p style="margin-bottom:11px"&gt;&lt;span style="font-size:12pt"&gt;&lt;span style="line-height:115%"&gt;0 and 1 not only reflect the underlying logic of switches, but they also correspond to every yes/no question you ask: &amp;ldquo;did this mouse die, or not?&amp;rdquo;. And 10 binary digits can cover 2&amp;sup1;⁰ = 1024 different possibilities.&lt;/span&gt;&lt;/span&gt;&lt;/p&gt;

&lt;div style="border-bottom:solid windowtext 1.0pt; padding:0in 0in 1.0pt 0in"&gt;
&lt;p style="border:none; padding:0in; margin-bottom:11px"&gt;&lt;span style="font-size:12pt"&gt;&lt;span style="line-height:115%"&gt;1024 is more than 1000.&lt;/span&gt;&lt;/span&gt;&lt;/p&gt;
&lt;/div&gt;

&lt;p style="margin-bottom:11px"&gt;&lt;span style="font-size:12pt"&gt;&lt;span style="line-height:115%"&gt;&lt;b&gt;&lt;span style="font-size:16.0pt"&gt;&lt;span style="line-height:115%"&gt;The Solution&amp;nbsp;&amp;nbsp; &lt;/span&gt;&lt;/span&gt;&lt;/b&gt;&lt;/span&gt;&lt;/span&gt;&lt;/p&gt;

&lt;p style="margin-bottom:11px"&gt;&lt;span style="font-size:12pt"&gt;&lt;span style="line-height:115%"&gt;&lt;b&gt;Step 1: Relabel the bottles in binary&lt;/b&gt;&lt;/span&gt;&lt;/span&gt;&lt;/p&gt;

&lt;p style="margin-bottom:11px"&gt;&lt;span style="font-size:12pt"&gt;&lt;span style="line-height:115%"&gt;Write each bottle&amp;rsquo;s number, 1 through 1000, as a 10-digit binary number, padding the front with 0s. For example, bottle 17 is 10001 in binary, so its label becomes 0000010001. Every bottle now carries a unique 10-digit barcode of 0s and 1s.&lt;/span&gt;&lt;/span&gt;&lt;/p&gt;

&lt;p style="margin-bottom:11px"&gt;&lt;img src="/view.aspx?sf=235447_post/Poisoned_Bottle_Diagram_2.png"&gt;&lt;/p&gt;

&lt;p style="margin-bottom:11px"&gt;&lt;span style="font-size:12pt"&gt;&lt;span style="line-height:115%"&gt;&lt;b&gt;Step 2: Assign each mouse a digit&lt;/b&gt;&lt;/span&gt;&lt;/span&gt;&lt;/p&gt;

&lt;p style="margin-bottom:11px"&gt;&lt;span style="font-size:12pt"&gt;&lt;span style="line-height:115%"&gt;Line up the mice and assign each one a digit: mouse #1 owns the leftmost digit, mouse #10 the rightmost. Then, run the tasting by the simple rule of a mouse drinks from a bottle if and only if its digit in that bottle&amp;rsquo;s label is a 1.&lt;/span&gt;&lt;/span&gt;&lt;/p&gt;

&lt;p style="margin-bottom:11px"&gt;&lt;span style="font-size:12pt"&gt;&lt;span style="line-height:115%"&gt;For bottle 17, only mouse #6 and mouse #10 take a sip. No two bottles are sampled by the same combination of mice; each bottle&amp;rsquo;s binary label is its unique drinking pattern.&lt;/span&gt;&lt;/span&gt;&lt;/p&gt;

&lt;p style="margin-bottom:11px"&gt;&lt;img src="/view.aspx?sf=235447_post/Poisoned_Bottle_Animation.gif"&gt;&lt;/p&gt;

&lt;p style="margin-bottom:11px"&gt;&lt;span style="font-size:12pt"&gt;&lt;span style="line-height:115%"&gt;&lt;b&gt;Step 3: Read the answer off the casualties&lt;/b&gt;&lt;/span&gt;&lt;/span&gt;&lt;/p&gt;

&lt;div style="border-bottom:solid windowtext 1.0pt; padding:0in 0in 1.0pt 0in"&gt;
&lt;p style="border:none; padding:0in; margin-bottom:11px"&gt;&lt;span style="font-size:12pt"&gt;&lt;span style="line-height:115%"&gt;Wait an hour. Then, write a 1 in every position with a dead mouse and a 0 otherwise. The string you end up with is the binary label of the poisoned bottle.&lt;/span&gt;&lt;/span&gt;&lt;/p&gt;
&lt;/div&gt;

&lt;p style="margin-bottom:11px"&gt;&lt;span style="font-size:12pt"&gt;&lt;span style="line-height:115%"&gt;&lt;b&gt;&lt;span style="font-size:16.0pt"&gt;&lt;span style="line-height:115%"&gt;One More Sip&lt;/span&gt;&lt;/span&gt;&lt;/b&gt;&lt;/span&gt;&lt;/span&gt;&lt;/p&gt;

&lt;p style="margin-bottom:11px"&gt;&lt;span style="font-size:12pt"&gt;&lt;span style="line-height:115%"&gt;Before you pop the corks, one last question: was the binary system essential here, or could we have used a different method?&lt;/span&gt;&lt;/span&gt;&lt;/p&gt;

&lt;p style="margin-bottom:11px"&gt;&lt;span style="font-size:12pt"&gt;&lt;span style="line-height:115%"&gt;Here&amp;rsquo;s a food for thought: suppose your neighbor used a cheaper poison that kicks in 30 minutes instead of an hour, now there is time for a second round of tasting.&lt;/span&gt;&lt;/span&gt;&lt;/p&gt;

&lt;p style="margin-bottom:11px"&gt;&lt;span style="font-size:12pt"&gt;&lt;span style="line-height:115%"&gt;Now each mouse has three possible outcomes instead of two: dies in round 1, dies in round 2, or survives. Binary is the wrong language here; you want base 3.&lt;/span&gt;&lt;/span&gt;&lt;/p&gt;

&lt;p style="margin-bottom:11px"&gt;&lt;span style="font-size:12pt"&gt;&lt;span style="line-height:115%"&gt;The scheme goes as follows. Label the bottles in base 3, give each mouse a digit position, and follow one rule: if digit 1, drink in round 1; if digit 2, drink in round 2; if digit 0, sit out. Each mouse&amp;rsquo;s fate is its digit on the poisoned bottle&amp;rsquo;s label.&lt;/span&gt;&lt;/span&gt;&lt;/p&gt;

&lt;p style="margin-bottom:11px"&gt;&lt;img src="/view.aspx?sf=235447_post/Poisoned_Bottle_Diagram_3.png"&gt;&lt;/p&gt;

&lt;div style="border-bottom:solid windowtext 1.0pt; padding:0in 0in 1.0pt 0in"&gt;
&lt;p style="border:none; padding:0in; margin-bottom:11px"&gt;&lt;span style="font-size:12pt"&gt;&lt;span style="line-height:115%"&gt;The ternary system&amp;rsquo;s power grows exponentially. Ten mice can now handle 3&amp;sup1;⁰ = 59049 bottles &amp;ndash; our 1000 can be covered by seven mice (3⁷ = 2187). Generalized, with r rounds, the whole construction runs in base r+1. &lt;/span&gt;&lt;/span&gt;&lt;/p&gt;
&lt;/div&gt;

&lt;p style="margin-bottom:11px"&gt;&lt;span style="font-size:12pt"&gt;&lt;span style="line-height:115%"&gt;That is the lesson hidden in the wine cellar. The binary system is more than the foundation of our telecom network, it is also a way of thinking &amp;ndash; a reminder that any question, no matter how large, can be answered by a patient sequence of yes and no. You walked into an impossible evening with ten mice and walked out with 999 bottles of perfectly good wine. &lt;/span&gt;&lt;/span&gt;&lt;/p&gt;

&lt;p style="margin-bottom:11px"&gt;&lt;span style="font-size:12pt"&gt;&lt;span style="line-height:115%"&gt;Enjoy the party.&lt;/span&gt;&lt;/span&gt;&lt;/p&gt;
</itunes:summary>
      <description>&lt;p style="margin-bottom:11px"&gt;&lt;span style="font-size:12pt"&gt;&lt;span style="line-height:115%"&gt;You are hosting a big party tonight and prepared 1000 bottles of wine. A spiteful neighbor sneaks in and poisons exactly one bottle. The poison is colorless, tasteless, and takes about an hour to take effect and kill. Your party also starts in an hour, and you don&amp;rsquo;t want to throw all the wine away.&lt;/span&gt;&lt;/span&gt;&lt;/p&gt;

&lt;p style="margin-bottom:11px"&gt;&lt;span style="font-size:12pt"&gt;&lt;span style="line-height:115%"&gt;You have 10 mice and time for only one round of tasting. In that round, a mouse can taste from any number of bottles. How can you identify that single poisoned bottle among 1000?&lt;/span&gt;&lt;/span&gt;&lt;/p&gt;

&lt;p style="margin-bottom:11px"&gt;&lt;span style="font-size:12pt"&gt;&lt;span style="line-height:115%"&gt;Pause here and try to solve the problem yourself!&lt;/span&gt;&lt;/span&gt;&lt;/p&gt;

&lt;p style="margin-bottom:11px"&gt;&lt;img src="/view.aspx?sf=235447_post/Poisoned_Bottle_Diagram_1.png"&gt;&lt;/p&gt;

&lt;p style="margin-bottom:11px"&gt;&lt;span style="font-size:12pt"&gt;&lt;span style="line-height:115%"&gt;An obvious solution might be to group the wine into 10 batches of 100 bottles and have each mouse drink from one batch. But if a mouse dies, you have only narrowed it down to 100 bottles, and there is no time for a second round. Whatever test you run, you only get one shot.&lt;/span&gt;&lt;/span&gt;&lt;/p&gt;

&lt;div style="border-bottom:solid windowtext 1.0pt; padding:0in 0in 1.0pt 0in"&gt;
&lt;p style="border:none; padding:0in; margin-bottom:11px"&gt;&lt;span style="font-size:12pt"&gt;&lt;span style="line-height:115%"&gt;Ten mice. A thousand bottles. The problem sounds impossible &amp;ndash; until you realize each mouse isn&amp;rsquo;t just a taster. &lt;/span&gt;&lt;/span&gt;&lt;/p&gt;

&lt;p style="border:none; padding:0in; margin-bottom:11px"&gt;&lt;span style="font-size:12pt"&gt;&lt;span style="line-height:115%"&gt;The exact idea that powers com&lt;/span&gt;&lt;/span&gt;&lt;span style="font-size:12pt"&gt;&lt;span style="line-height:115%"&gt;puters is also what solves our wine puzzle.&lt;/span&gt;&lt;/span&gt;&lt;/p&gt;
&lt;/div&gt;

&lt;p style="margin-bottom:11px"&gt;&lt;span style="font-size:12pt"&gt;&lt;span style="line-height:115%"&gt;&lt;b&gt;&lt;span lang="EN-US" style="font-size:16.0pt"&gt;&lt;span style="line-height:115%"&gt;A 300-Year-Old Idea&lt;/span&gt;&lt;/span&gt;&lt;/b&gt;&lt;/span&gt;&lt;/span&gt;&lt;/p&gt;

&lt;p style="margin-bottom:11px"&gt;&lt;span style="font-size:12pt"&gt;&lt;span style="line-height:115%"&gt;Some background information before we solve the problem.&lt;/span&gt;&lt;/span&gt;&lt;/p&gt;

&lt;p style="margin-bottom:11px"&gt;&lt;span style="font-size:12pt"&gt;&lt;span style="line-height:115%"&gt;In 1703, Gottfried Leibniz published a paper describing how every number can be written using only two symbols: 0 and 1. To him, the concept felt almost divine &amp;ndash; an entire universe created out of nothingness and unity. But for over two centuries, binary remained an idea trapped on paper.&lt;/span&gt;&lt;/span&gt;&lt;/p&gt;

&lt;p style="margin-bottom:11px"&gt;&lt;span style="font-size:12pt"&gt;&lt;span style="line-height:115%"&gt;Everything changed when a young engineer named Claude Shannon realized that 0 and 1 map perfectly onto the physical states of an electrical switch: off and on. That single insight laid the groundwork for digital circuits, eventually powering every smartphone, laptop, and text message on the planet.&lt;/span&gt;&lt;/span&gt;&lt;/p&gt;

&lt;p style="margin-bottom:11px"&gt;&lt;span style="font-size:12pt"&gt;&lt;span style="line-height:115%"&gt;Yet binary is more than just how machines store information. It is a way of extracting information. &lt;/span&gt;&lt;/span&gt;&lt;/p&gt;

&lt;p style="margin-bottom:11px"&gt;&lt;span style="font-size:12pt"&gt;&lt;span style="line-height:115%"&gt;0 and 1 not only reflect the underlying logic of switches, but they also correspond to every yes/no question you ask: &amp;ldquo;did this mouse die, or not?&amp;rdquo;. And 10 binary digits can cover 2&amp;sup1;⁰ = 1024 different possibilities.&lt;/span&gt;&lt;/span&gt;&lt;/p&gt;

&lt;div style="border-bottom:solid windowtext 1.0pt; padding:0in 0in 1.0pt 0in"&gt;
&lt;p style="border:none; padding:0in; margin-bottom:11px"&gt;&lt;span style="font-size:12pt"&gt;&lt;span style="line-height:115%"&gt;1024 is more than 1000.&lt;/span&gt;&lt;/span&gt;&lt;/p&gt;
&lt;/div&gt;

&lt;p style="margin-bottom:11px"&gt;&lt;span style="font-size:12pt"&gt;&lt;span style="line-height:115%"&gt;&lt;b&gt;&lt;span lang="EN-US" style="font-size:16.0pt"&gt;&lt;span style="line-height:115%"&gt;The Solution&amp;nbsp;&amp;nbsp; &lt;/span&gt;&lt;/span&gt;&lt;/b&gt;&lt;/span&gt;&lt;/span&gt;&lt;/p&gt;

&lt;p style="margin-bottom:11px"&gt;&lt;span style="font-size:12pt"&gt;&lt;span style="line-height:115%"&gt;&lt;b&gt;Step 1: Relabel the bottles in binary&lt;/b&gt;&lt;/span&gt;&lt;/span&gt;&lt;/p&gt;

&lt;p style="margin-bottom:11px"&gt;&lt;span style="font-size:12pt"&gt;&lt;span style="line-height:115%"&gt;Write each bottle&amp;rsquo;s number, 1 through 1000, as a 10-digit binary number, padding the front with 0s. For example, bottle 17 is 10001 in binary, so its label becomes 0000010001. Every bottle now carries a unique 10-digit barcode of 0s and 1s.&lt;/span&gt;&lt;/span&gt;&lt;/p&gt;

&lt;p style="margin-bottom:11px"&gt;&lt;img src="/view.aspx?sf=235447_post/Poisoned_Bottle_Diagram_2.png"&gt;&lt;/p&gt;

&lt;p style="margin-bottom:11px"&gt;&lt;span style="font-size:12pt"&gt;&lt;span style="line-height:115%"&gt;&lt;b&gt;Step 2: Assign each mouse a digit&lt;/b&gt;&lt;/span&gt;&lt;/span&gt;&lt;/p&gt;

&lt;p style="margin-bottom:11px"&gt;&lt;span style="font-size:12pt"&gt;&lt;span style="line-height:115%"&gt;Line up the mice and assign each one a digit: mouse #1 owns the leftmost digit, mouse #10 the rightmost. Then, run the tasting by the simple rule of a mouse drinks from a bottle if and only if its digit in that bottle&amp;rsquo;s label is a 1.&lt;/span&gt;&lt;/span&gt;&lt;/p&gt;

&lt;p style="margin-bottom:11px"&gt;&lt;span style="font-size:12pt"&gt;&lt;span style="line-height:115%"&gt;For bottle 17, only mouse #6 and mouse #10 take a sip. No two bottles are sampled by the same combination of mice; each bottle&amp;rsquo;s binary label is its unique drinking pattern.&lt;/span&gt;&lt;/span&gt;&lt;/p&gt;

&lt;p style="margin-bottom:11px"&gt;&lt;img src="/view.aspx?sf=235447_post/Poisoned_Bottle_Animation.gif"&gt;&lt;/p&gt;

&lt;p style="margin-bottom:11px"&gt;&lt;span style="font-size:12pt"&gt;&lt;span style="line-height:115%"&gt;&lt;b&gt;Step 3: Read the answer off the casualties&lt;/b&gt;&lt;/span&gt;&lt;/span&gt;&lt;/p&gt;

&lt;div style="border-bottom:solid windowtext 1.0pt; padding:0in 0in 1.0pt 0in"&gt;
&lt;p style="border:none; padding:0in; margin-bottom:11px"&gt;&lt;span style="font-size:12pt"&gt;&lt;span style="line-height:115%"&gt;Wait an hour. Then, write a 1 in every position with a dead mouse and a 0 otherwise. The string you end up with is the binary label of the poisoned bottle.&lt;/span&gt;&lt;/span&gt;&lt;/p&gt;
&lt;/div&gt;

&lt;p style="margin-bottom:11px"&gt;&lt;span style="font-size:12pt"&gt;&lt;span style="line-height:115%"&gt;&lt;b&gt;&lt;span style="font-size:16.0pt"&gt;&lt;span style="line-height:115%"&gt;One More Sip&lt;/span&gt;&lt;/span&gt;&lt;/b&gt;&lt;/span&gt;&lt;/span&gt;&lt;/p&gt;

&lt;p style="margin-bottom:11px"&gt;&lt;span style="font-size:12pt"&gt;&lt;span style="line-height:115%"&gt;Before you pop the corks, one last question: was the binary system essential here, or could we have used a different method?&lt;/span&gt;&lt;/span&gt;&lt;/p&gt;

&lt;p style="margin-bottom:11px"&gt;&lt;span style="font-size:12pt"&gt;&lt;span style="line-height:115%"&gt;Here&amp;rsquo;s a food for thought: suppose your neighbor used a cheaper poison that kicks in 30 minutes instead of an hour, now there is time for a second round of tasting.&lt;/span&gt;&lt;/span&gt;&lt;/p&gt;

&lt;p style="margin-bottom:11px"&gt;&lt;span style="font-size:12pt"&gt;&lt;span style="line-height:115%"&gt;Now each mouse has three possible outcomes instead of two: dies in round 1, dies in round 2, or survives. Binary is the wrong language here; you want base 3.&lt;/span&gt;&lt;/span&gt;&lt;/p&gt;

&lt;p style="margin-bottom:11px"&gt;&lt;span style="font-size:12pt"&gt;&lt;span style="line-height:115%"&gt;The scheme goes as follows. Label the bottles in base 3, give each mouse a digit position, and follow one rule: if digit 1, drink in round 1; if digit 2, drink in round 2; if digit 0, sit out. Each mouse&amp;rsquo;s fate is its digit on the poisoned bottle&amp;rsquo;s label.&lt;/span&gt;&lt;/span&gt;&lt;/p&gt;

&lt;p style="margin-bottom:11px"&gt;&lt;img src="/view.aspx?sf=235447_post/Poisoned_Bottle_Diagram_3.png"&gt;&lt;/p&gt;

&lt;div style="border-bottom:solid windowtext 1.0pt; padding:0in 0in 1.0pt 0in"&gt;
&lt;p style="border:none; padding:0in; margin-bottom:11px"&gt;&lt;span style="font-size:12pt"&gt;&lt;span style="line-height:115%"&gt;The ternary system&amp;rsquo;s power grows exponentially. Ten mice can now handle 3&amp;sup1;⁰ = 59049 bottles &amp;ndash; our 1000 can be covered by seven mice (3⁷ = 2187). Generalized, with r rounds, the whole construction runs in base r+1. &lt;/span&gt;&lt;/span&gt;&lt;/p&gt;
&lt;/div&gt;

&lt;p style="margin-bottom:11px"&gt;&lt;span style="font-size:12pt"&gt;&lt;span style="line-height:115%"&gt;That is the lesson hidden in the wine cellar. The binary system is more than the foundation of our telecom network, it is also a way of thinking &amp;ndash; a reminder that any question, no matter how large, can be answered by a patient sequence of yes and no. You walked into an impossible evening with ten mice and walked out with 999 bottles of perfectly good wine. &lt;/span&gt;&lt;/span&gt;&lt;/p&gt;

&lt;p style="margin-bottom:11px"&gt;&lt;span style="font-size:12pt"&gt;&lt;span style="line-height:115%"&gt;Enjoy the party.&lt;/span&gt;&lt;/span&gt;&lt;/p&gt;
</description>
      <guid>235447</guid>
      <pubDate>Thu, 13 Aug 2026 16:59:30 Z</pubDate>
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