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	<title>Geek Drivel &#187; Mathematics</title>
	<atom:link href="http://geekblog.oakcircle.com/category/interests/technology/mathematics/feed/" rel="self" type="application/rss+xml" />
	<link>http://geekblog.oakcircle.com</link>
	<description>Miscellaneous ramblings on miscellaneous topics</description>
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		<title>&#8220;Researchers propose simple fix to thwart e-voting attack&#8221;</title>
		<link>http://geekblog.oakcircle.com/2011/11/13/politics-the-ultimate-dirty-joke/</link>
		<comments>http://geekblog.oakcircle.com/2011/11/13/politics-the-ultimate-dirty-joke/#comments</comments>
		<pubDate>Sun, 13 Nov 2011 14:29:32 +0000</pubDate>
		<dc:creator>Head Geek</dc:creator>
				<category><![CDATA[Law]]></category>
		<category><![CDATA[Mathematics]]></category>
		<category><![CDATA[Politics]]></category>
		<category><![CDATA[Robotics and/or Computing Hardware]]></category>
		<category><![CDATA[Science and Technology]]></category>
		<category><![CDATA[Science Fiction and Fantasy]]></category>
		<category><![CDATA[Security (Digital And Otherwise)]]></category>
		<category><![CDATA[Software and Software Development]]></category>

		<guid isPermaLink="false">http://geekblog.oakcircle.com/?p=4173</guid>
		<description><![CDATA[This had better become required by law, and soon, if the government wants people to trust electronic voting machines. Every security expert who&#8217;s even glanced at them has been appalled at how easily they can be manipulated. Related and possibly-interesting note: a significant part of one of the Stainless Steel Rat books &#8212; written long [...]]]></description>
			<content:encoded><![CDATA[<p><a href="http://www.theregister.co.uk/2011/11/01/electronic_voting_fraud_mitigation/">This</a> had better become required by law, and soon, if the government wants people to trust electronic voting machines. Every security expert who&#8217;s even glanced at them has been appalled at how easily they can be manipulated.</p>

<p>Related and possibly-interesting note: a significant part of one of the <em>Stainless Steel Rat</em> books &#8212; written long before the first electronic voting machines made their debut &#8212; revolved around a rigged electronic voting system. The main character <em>knew</em> that the electronic system would be rigged, and was counting on it, because he&#8217;d found a clause in the constitution of the planet in question that allowed him to force a <em>manually-counted</em> election if the electronic one was shown to be grossly in error. The manual one was even more rigged than the electronic one, but since it <em>was</em> manual, the current <strike>dictator</strike> <em>President</em> found it much harder to cheat &#8212; and the good guys found it much <em>easier.</em> The end result was very, VERY close, but I&#8217;m sure you can guess the outcome. <img src='http://geekblog.oakcircle.com/wp-includes/images/smilies/icon_smile.gif' alt=':-)' class='wp-smiley' /> </p>
]]></content:encoded>
			<wfw:commentRss>http://geekblog.oakcircle.com/2011/11/13/politics-the-ultimate-dirty-joke/feed/</wfw:commentRss>
		<slash:comments>4</slash:comments>
		</item>
		<item>
		<title>&#8220;How Big is Your Haystack?&#8221;</title>
		<link>http://geekblog.oakcircle.com/2011/11/12/mine-is-enormous-oh-you-were-talking-about-passwords-sorry/</link>
		<comments>http://geekblog.oakcircle.com/2011/11/12/mine-is-enormous-oh-you-were-talking-about-passwords-sorry/#comments</comments>
		<pubDate>Sat, 12 Nov 2011 15:03:59 +0000</pubDate>
		<dc:creator>Head Geek</dc:creator>
				<category><![CDATA[Internet]]></category>
		<category><![CDATA[Mathematics]]></category>
		<category><![CDATA[Memory]]></category>
		<category><![CDATA[Security (Digital And Otherwise)]]></category>
		<category><![CDATA[Software and Software Development]]></category>

		<guid isPermaLink="false">http://geekblog.oakcircle.com/?p=4166</guid>
		<description><![CDATA[There are three interesting things on this page: An &#8220;interactive brute force search space calculator&#8221; for passwords, which you can play with to get a good idea how easily a brute-force attack would find YOUR passwords. Some comments further down the page on mathematical entropy, and how it doesn&#8217;t affect password strength (despite common wisdom [...]]]></description>
			<content:encoded><![CDATA[<p>There are three interesting things on <a href="https://www.grc.com/haystack.htm">this page</a>:</p>

<ul>
<li><p>An &#8220;interactive brute force search space calculator&#8221; for passwords, which you can play with to get a good idea how easily a brute-force attack would find YOUR passwords.</p></li>
<li><p>Some comments further down the page on mathematical entropy, and how it <em>doesn&#8217;t</em> affect password strength (despite common wisdom on the subject) nearly as much as pure password length.</p></li>
<li><p>A description of a &#8220;password padding&#8221; system that looks like it would generate strong and remember-able passwords.</p></li>
</ul>

<p>I have reason to know the math for this kind of thing myself, and it all looks pretty accurate. Of course, a &#8220;<a href="http://geekblog.oakcircle.com/2011/05/17/password-handling-made-simple/">password safe</a>&#8221; with truly random passwords (and a really good backup system) is the best way to go these days, hands down, but there will always be a few passwords that you&#8217;ll need to keep in your <a href="https://secure.wikimedia.org/wikipedia/en/wiki/Wetware_%28brain%29#Origin">wetware</a>.</p>
]]></content:encoded>
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		<slash:comments>0</slash:comments>
		</item>
		<item>
		<title>&#8220;Virtual cloud monkeys go bananas writing Shakespeare&#8221;</title>
		<link>http://geekblog.oakcircle.com/2011/09/28/i-dont-have-an-amusing-url-for-this-one-so-pss-on-it/</link>
		<comments>http://geekblog.oakcircle.com/2011/09/28/i-dont-have-an-amusing-url-for-this-one-so-pss-on-it/#comments</comments>
		<pubDate>Wed, 28 Sep 2011 12:51:53 +0000</pubDate>
		<dc:creator>Head Geek</dc:creator>
				<category><![CDATA[Amusing/Interesting/Appalling]]></category>
		<category><![CDATA[Mathematics]]></category>

		<guid isPermaLink="false">http://geekblog.oakcircle.com/?p=4005</guid>
		<description><![CDATA[I&#8217;m sure this experiment saved on banana costs &#8212; and machine repair and replacement costs, apparently &#8212; but a little statistical math could have told him the same thing a lot faster. (The comment about the interview with Fox News amuses me, as even more evidence that regular Fox News viewers are on the low [...]]]></description>
			<content:encoded><![CDATA[<p>I&#8217;m sure <a href="http://www.theregister.co.uk/2011/09/26/cloud_monkeys_bananas_producing_shakespeare/">this experiment</a> saved on banana costs &#8212; and machine repair and replacement costs, apparently &#8212; but a little statistical math could have told him the same thing a lot faster.</p>

<p>(The comment about the interview with Fox News amuses me, as even more evidence that regular Fox News viewers are on the low end of the intelligence spectrum. Not that more evidence was really necessary.)</p>
]]></content:encoded>
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		<slash:comments>0</slash:comments>
		</item>
		<item>
		<title>&#8220;Why Multi-word Phrases Make for More Secure Passwords Than Incomprehensible Gibberish&#8221;</title>
		<link>http://geekblog.oakcircle.com/2011/08/04/this-title-is-a-secure-password-believe-it-or-not/</link>
		<comments>http://geekblog.oakcircle.com/2011/08/04/this-title-is-a-secure-password-believe-it-or-not/#comments</comments>
		<pubDate>Thu, 04 Aug 2011 14:06:12 +0000</pubDate>
		<dc:creator>Head Geek</dc:creator>
				<category><![CDATA[Mathematics]]></category>
		<category><![CDATA[Security (Digital And Otherwise)]]></category>
		<category><![CDATA[Systems]]></category>

		<guid isPermaLink="false">http://geekblog.oakcircle.com/?p=3794</guid>
		<description><![CDATA[I was rather surprised at this assertion, at first. Then I thought about it&#8230; there are only about 95 printable characters in the basic seven-bit ASCII character set. A very conservative estimate puts the number of distinct English words at well over 65,000, most of which are many letters long. If you knew that someone&#8217;s [...]]]></description>
			<content:encoded><![CDATA[<p>I was rather surprised at <a href="http://lifehacker.com/?_escaped_fragment_=5796816/why-multiword-phrases-make-more-secure-passwords-than-incomprehensible-gibberish">this</a> assertion, at first. Then I thought about it&#8230; there are only about 95 printable characters in the basic seven-bit ASCII character set. A <em>very</em> conservative estimate puts the number of distinct English words at well over 65,000, most of which are many letters long.</p>

<p>If you <em>knew</em> that someone&#8217;s password was several properly-spelled English words separated by single spaces, you&#8217;d still have 65,000-to-the-power-of-X combinations to go through for X words. That&#8217;s over four billion combinations to try for a two-word phrase, and about 275 trillion combinations for a three-word phrase &#8212; four billion is easy enough for a computer to handle, but 275 trillion is more secure than a seven-random-character password. And if you <em>didn&#8217;t</em> know that the password followed that pattern, or there was even one deliberately misspelled word or different bit of punctuation, the numbers skyrocket.</p>

<p>That said, I&#8217;m not about to abandon <a href="http://geekblog.oakcircle.com/2007/10/06/dont-forget-to/">my current password scheme</a>, but for some passwords, this might be useful.</p>
]]></content:encoded>
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		<slash:comments>10</slash:comments>
		</item>
		<item>
		<title>&#8220;Möbius Gear: a one-sided, toothed gear&#8221;</title>
		<link>http://geekblog.oakcircle.com/2011/04/19/you-cant-do-that-in-reality-or-can-you/</link>
		<comments>http://geekblog.oakcircle.com/2011/04/19/you-cant-do-that-in-reality-or-can-you/#comments</comments>
		<pubDate>Tue, 19 Apr 2011 13:28:59 +0000</pubDate>
		<dc:creator>Head Geek</dc:creator>
				<category><![CDATA[Amusing/Interesting/Appalling]]></category>
		<category><![CDATA[Mathematics]]></category>
		<category><![CDATA[Science and Technology]]></category>

		<guid isPermaLink="false">http://geekblog.oakcircle.com/?p=3424</guid>
		<description><![CDATA[If asked, I&#8217;d have said this wasn&#8217;t possible. Just goes to prove that I&#8217;m not omniscient. I wonder what use someone will find for it. The world is moving so fast these days that the man who says it can&#8217;t be done is generally interrupted by someone doing it. &#8212; Harry Emerson Fosdick]]></description>
			<content:encoded><![CDATA[<p>If asked, I&#8217;d have said <a href="http://www.boingboing.net/2011/04/06/mobius-gear-a-one-si.html">this</a> wasn&#8217;t possible. Just goes to prove that I&#8217;m not omniscient. <img src='http://geekblog.oakcircle.com/wp-includes/images/smilies/icon_wink.gif' alt=';-)' class='wp-smiley' />  I wonder what use someone will find for it.</p>

<blockquote>
  <p>The world is moving so fast these days that the man who says it can&#8217;t be done is generally interrupted by someone doing it.<br />
  &#8212; Harry Emerson Fosdick</p>
</blockquote>
]]></content:encoded>
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		<slash:comments>0</slash:comments>
		</item>
		<item>
		<title>And now, the news&#8230;</title>
		<link>http://geekblog.oakcircle.com/2011/04/17/and-now-the-news/</link>
		<comments>http://geekblog.oakcircle.com/2011/04/17/and-now-the-news/#comments</comments>
		<pubDate>Sun, 17 Apr 2011 12:21:19 +0000</pubDate>
		<dc:creator>Head Geek</dc:creator>
				<category><![CDATA[Life in General]]></category>
		<category><![CDATA[Mathematics]]></category>
		<category><![CDATA[Meta]]></category>

		<guid isPermaLink="false">http://geekblog.oakcircle.com/?p=3413</guid>
		<description><![CDATA[I think the spammer registration problem may be dealt with, at least for the moment. Since I added the new layers of defenses, only one spammer account has gotten through the first layer of registration (which checks its information against multiple online databases of known spammers). It failed the e-mail confirmation step and was auto-deleted [...]]]></description>
			<content:encoded><![CDATA[<p>I think the spammer registration problem may be dealt with, at least for the moment. Since I <a href="http://geekblog.oakcircle.com/2011/04/02/spambot-purge/">added the new layers of defenses</a>, only one spammer account has gotten through the first layer of registration (which checks its information against multiple online databases of known spammers). It failed the e-mail confirmation step and was auto-deleted last night, a week after the confirmation e-mail was sent. I love it when technology works. <img src='http://geekblog.oakcircle.com/wp-includes/images/smilies/icon_smile.gif' alt=':-)' class='wp-smiley' /> </p>

<p><a href="http://geekblog.oakcircle.com/2010/10/29/its-a-date/">Project M</a> is nearing usability, at long last. A couple days ago I finished a very tricky bit of code involving caching pages of results from a database query on demand and tracking their offsets as the database is updated in the background. It was vital for handling large result sets; now Project M should be able to handle sets as large as any program of its type, very quickly, even when sorted on unindexed columns. <img src='http://geekblog.oakcircle.com/wp-includes/images/smilies/icon_biggrin.gif' alt=':-D' class='wp-smiley' /> </p>

<p>I&#8217;m also trying to implement a new form of public-key signature for <a href="http://geekblog.oakcircle.com/2008/07/19/ascii-unicode-and-windows/">Project Badger</a> (new to me anyway; it&#8217;s about ten years old). If done properly, it promises to be much faster than the signature system which we were forced to adopt a while back. It&#8217;s a fun project to work on, but I haven&#8217;t gotten it to work yet, so we&#8217;ll see how that goes.</p>

<p>Our personal taxes were actually done <em>early</em> this year, for a change&#8230; they&#8217;re usually done just in the nick of time, but I managed to force myself to do it several weeks before the deadline, even though it meant an entire day spent on nothing else. This being-responsible thing really sucks. <img src='http://geekblog.oakcircle.com/wp-includes/images/smilies/icon_wink.gif' alt=';-)' class='wp-smiley' /> </p>

<p>All in all, things are looking up, and in a couple months we may even be able to afford furniture for a room or two, as GoddessJ has wanted for the last seven months. We&#8217;ll see how that goes.</p>
]]></content:encoded>
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		<slash:comments>2</slash:comments>
		</item>
		<item>
		<title>Antikythera Mechanism Duplicated &#8212; in Lego!</title>
		<link>http://geekblog.oakcircle.com/2010/12/13/thats-damned-impressive/</link>
		<comments>http://geekblog.oakcircle.com/2010/12/13/thats-damned-impressive/#comments</comments>
		<pubDate>Mon, 13 Dec 2010 14:38:07 +0000</pubDate>
		<dc:creator>Head Geek</dc:creator>
				<category><![CDATA[Amusing/Interesting/Appalling]]></category>
		<category><![CDATA[Mathematics]]></category>
		<category><![CDATA[Robotics and/or Computing Hardware]]></category>
		<category><![CDATA[Science and Technology]]></category>

		<guid isPermaLink="false">http://geekblog.oakcircle.com/?p=3276</guid>
		<description><![CDATA[The odds are that you&#8217;ve heard about the Antikythera mechanism, an ancient (2000+ years old) mechanical device that was dredged up off of Greece more than a century ago. Four years ago, scientists finally figured out what it was for, calculating solar eclipses and other celestial events. It was really big news at the time, [...]]]></description>
			<content:encoded><![CDATA[<p>The odds are that you&#8217;ve heard about the Antikythera mechanism, an ancient (2000+ years old) mechanical device that was dredged up off of Greece more than a century ago. Four years ago, scientists finally figured out what it was for, calculating solar eclipses and other celestial events. It was really big news at the time, because we hadn&#8217;t realized that the ancient Greeks had the knowledge and skill to pull off that kind of feat.</p>

<p>Well, <a href="http://www.youtube.com/watch?v=RLPVCJjTNgk">these guys</a> have built a mechanical computer that duplicates its function &#8212; and they did it entirely out of Lego!</p>

<p>Now <em>that&#8217;s</em> freakin&#8217; awesome. <img src='http://geekblog.oakcircle.com/wp-includes/images/smilies/icon_smile.gif' alt=':-)' class='wp-smiley' /> </p>

<p>I&#8217;m sure you&#8217;ll be able to buy a Lego kit specifically for this, at some point, if there&#8217;s enough interest in it. I&#8217;m not sure I&#8217;d have the interest to buy it, but I know several people who might.</p>

<p>(Thanks for the heads-up, c-square!)</p>
]]></content:encoded>
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		<slash:comments>0</slash:comments>
		</item>
		<item>
		<title>&#8220;Street-Fighting Math: down and dirty guide to approximation and problem-solving&#8221;</title>
		<link>http://geekblog.oakcircle.com/2010/08/25/i-estimate-that-this-book-will-be-good/</link>
		<comments>http://geekblog.oakcircle.com/2010/08/25/i-estimate-that-this-book-will-be-good/#comments</comments>
		<pubDate>Wed, 25 Aug 2010 14:16:47 +0000</pubDate>
		<dc:creator>Head Geek</dc:creator>
				<category><![CDATA[Mathematics]]></category>
		<category><![CDATA[Thought and Learning]]></category>

		<guid isPermaLink="false">http://geekblog.oakcircle.com/?p=2971</guid>
		<description><![CDATA[A useful skill. I didn&#8217;t realize that anyone had written a book about it. It&#8217;s available as a free PDF file too, there&#8217;s a download link in the &#8220;related links&#8221; section. I&#8217;ve picked it up, and I plan to read it when I have a chance. (Via BoingBoing)]]></description>
			<content:encoded><![CDATA[<p>A <a href="http://mitpress.mit.edu/catalog/item/default.asp?ttype=2&amp;tid=12156">useful skill</a>. I didn&#8217;t realize that anyone had written a book about it. It&#8217;s available as a free PDF file too, there&#8217;s a download link in the &#8220;related links&#8221; section. I&#8217;ve picked it up, and I plan to read it when I have a chance.</p>

<p><em>(Via <a href="http://www.boingboing.net/2010/07/26/street-fighting-math.html">BoingBoing</a>)</em></p>
]]></content:encoded>
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		<slash:comments>0</slash:comments>
		</item>
		<item>
		<title>&#8220;Google, boffins crack Rubik&#8217;s Cube mystery&#8221;</title>
		<link>http://geekblog.oakcircle.com/2010/08/24/pwning-the-rubiks-cube/</link>
		<comments>http://geekblog.oakcircle.com/2010/08/24/pwning-the-rubiks-cube/#comments</comments>
		<pubDate>Tue, 24 Aug 2010 12:42:11 +0000</pubDate>
		<dc:creator>Head Geek</dc:creator>
				<category><![CDATA[Amusing/Interesting/Appalling]]></category>
		<category><![CDATA[Mathematics]]></category>
		<category><![CDATA[Science and Technology]]></category>

		<guid isPermaLink="false">http://geekblog.oakcircle.com/?p=2968</guid>
		<description><![CDATA[The Ultimate Answer to Life, The Universe, and Everything may be 42, but it seems that the ultimate answer to how many moves (at most) it would take for an omniscient being to solve the Rubik&#8217;s Cube is much lower. (No omniscient beings were harmed in the calculation of that answer.)]]></description>
			<content:encoded><![CDATA[<p>The Ultimate Answer to Life, The Universe, and Everything may be 42, but it seems that the ultimate answer to how many moves (at most) it would take for an omniscient being to <a href="http://www.theregister.co.uk/2010/08/12/google_rubik_solved/">solve the Rubik&#8217;s Cube</a> is much lower.</p>

<p>(No omniscient beings were harmed in the calculation of that answer.) <img src='http://geekblog.oakcircle.com/wp-includes/images/smilies/icon_wink.gif' alt=';-)' class='wp-smiley' /> </p>
]]></content:encoded>
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		<slash:comments>0</slash:comments>
		</item>
		<item>
		<title>&#8220;Enhancing the Placebo&#8221;</title>
		<link>http://geekblog.oakcircle.com/2010/05/05/enhancing-the-placebo/</link>
		<comments>http://geekblog.oakcircle.com/2010/05/05/enhancing-the-placebo/#comments</comments>
		<pubDate>Wed, 05 May 2010 22:58:54 +0000</pubDate>
		<dc:creator>Head Geek</dc:creator>
				<category><![CDATA[Amusing/Interesting/Appalling]]></category>
		<category><![CDATA[Life in General]]></category>
		<category><![CDATA[Mathematics]]></category>
		<category><![CDATA[Religions]]></category>
		<category><![CDATA[Thought and Learning]]></category>

		<guid isPermaLink="false">http://geekblog.oakcircle.com/?p=2573</guid>
		<description><![CDATA[I find the placebo effect to be utterly fascinating. It&#8217;s almost certainly responsible for the successes of shamans, faith-based healers, and homeopathy. And, on the other side of the coin, the documented successful witch doctors&#8217; curses. But it&#8217;s literally all in your head. Which means that everyone who has ever been affected by any of [...]]]></description>
			<content:encoded><![CDATA[<p>I find <a href="http://opinionator.blogs.nytimes.com/2010/05/03/enhancing-the-placebo/">the placebo effect</a> to be utterly fascinating. It&#8217;s almost certainly responsible for the successes of shamans, faith-based healers, and homeopathy. And, on the other side of the coin, the documented successful witch doctors&#8217; curses. <em>But it&#8217;s literally all in your head.</em> Which means that everyone who has ever been affected by any of the above-mentioned things has always had the power to heal &#8212; or harm &#8212; themselves, without any outside assistance at all. And presumably, so does every other human on the planet.</p>

<p>There&#8217;s so much that this implies, from the evolutionary reasons for religion, to questions about whether we&#8217;re really as insignificant in the grand scheme of things as we seem to be, to metaphysical questions of all sorts that can never be scientifically answered. For instance, is this ability limited to our physical bodies, or might healing simply be one manifestation of something a lot more extensive, as many people have claimed through the centuries? <em>The Secret</em> was widely dismissed as mystical bunk when it was released a few years ago, but some people who heard its message found that it simply described what they&#8217;d already experienced. (I&#8217;ve had a few such experiences myself, things that my rational, scientific side find difficult to assign to chance alone, even with the help of my mathematical and statistical side.)</p>

<p>The more I learn about the world, and the more I experience, the more I have to admit that mere physical processes simply don&#8217;t explain it all. There&#8217;s a lot of circumstantial evidence to back up that view, if you&#8217;re willing to see it. Never enough to <em>prove</em> anything&#8230; which is itself suggestive&#8230; but enough to put doubts into any truly logical mind.</p>

<p>My take on it? The entire universe is fake. Some kind of simulation, a la The Matrix and many science fiction works before it. These little inconsistencies are clues that whoever is responsible for it have deliberately left in the program, presumably so that we would have some chance of noticing them. There&#8217;s never any conclusive proof because the program is deliberately designed to prevent that from ever happening. I can only speculate why, but think about it&#8230; if we could <em>prove</em> that it was all fake, that would change our collective behavior in myriad ways, many of which the majority of us probably wouldn&#8217;t want.</p>

<p>Who could be responsible for such a thing? Who would design and build a simulation like this, which presumably could be perfect, but leave so many clues that at least a few people in every generation are bound to notice and wonder about? It&#8217;s impossible to say, of course, but assuming that they aren&#8217;t simply mistakes on the part of the designers, think about this: if some person or group was responsible for designing a computer simulation that would have billions of inhabitants during its run, why would they deliberately leave any clues to its artificial nature at all? A malevolent force like the machines in The Matrix certainly wouldn&#8217;t, why give their captives any reason to believe they could ever escape? A benevolent force wouldn&#8217;t either, because it would be cruel to give the poor sods within any glimpse of something they could never have. And an indifferent force would see no reason to do so. But if that person or group was going to subject <em>themselves</em> to it&#8230;</p>

<p>&#8216;Nuf said.</p>
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