<?xml version="1.0" encoding="UTF-8"?><rss xmlns:dc="http://purl.org/dc/elements/1.1/" xmlns:content="http://purl.org/rss/1.0/modules/content/" xmlns:atom="http://www.w3.org/2005/Atom" version="2.0"><channel><title><![CDATA[RSS Feed]]></title><description><![CDATA[RSS Feed]]></description><link>http://direct.ecency.com</link><image><url>http://direct.ecency.com/logo512.png</url><title>RSS Feed</title><link>http://direct.ecency.com</link></image><generator>RSS for Node</generator><lastBuildDate>Tue, 21 Apr 2026 18:43:42 GMT</lastBuildDate><atom:link href="http://direct.ecency.com/created/sophism/rss.xml" rel="self" type="application/rss+xml"/><item><title><![CDATA[Sophism #20: The Braess's Paradox]]></title><description><![CDATA[Sophisms are closely related to paradoxes. Both assume the form of a statement that contradicts your intuition. In case of a sophism, your intuition is right in telling you that the statement is wrong]]></description><link>http://direct.ecency.com/economics/@konstantint/sophism-20-the-braess-s-paradox</link><guid isPermaLink="true">http://direct.ecency.com/economics/@konstantint/sophism-20-the-braess-s-paradox</guid><category><![CDATA[economics]]></category><dc:creator><![CDATA[konstantint]]></dc:creator><pubDate>Wed, 11 Oct 2017 21:01:15 GMT</pubDate><enclosure url="https://images.ecency.com/p/Zskj9C56UondJxcjVaienfhVaNb7LJVWG6e787gZr3h7frkYisNsUdysGH6DyVUMVDfhNRxX8CJkj5kvagfDzeqxh86XZhtNGdb5UupanQtEMh9ShS5k?format=match&amp;mode=fit" length="0" type="false"/></item><item><title><![CDATA[Sophism #19: Rectangle vs Parallelogram]]></title><description><![CDATA[Consider a rectangle ABCD and a parallelogram EFGH with the same base length and height. Let us cut the rectangle ABCD into infinitely many infinitely thin strips: lines, which fill the whole area of the]]></description><link>http://direct.ecency.com/math/@konstantint/sophism-19-rectangle-vs-parallelogram</link><guid isPermaLink="true">http://direct.ecency.com/math/@konstantint/sophism-19-rectangle-vs-parallelogram</guid><category><![CDATA[math]]></category><dc:creator><![CDATA[konstantint]]></dc:creator><pubDate>Mon, 04 Sep 2017 17:26:33 GMT</pubDate><enclosure url="https://images.ecency.com/p/2gsjgna1uruvUuS7ndh9YqVwYGPLVszbFLwwpAYXYc19Gf4MLoyg6bfHZcZXEuJXQMtBFZtYFgM2ZGZeatywbBtyB4zyXHgk3ZHWgnzRJ2cvq5PAfQ?format=match&amp;mode=fit" length="0" type="false"/></item><item><title><![CDATA[Sophism #18: Derivatives]]></title><description><![CDATA[Taking derivatives from both sides of a valid equation we obtain Dividing both sides by x, we must conclude that 2 = 1. For other sophisms check out my other posts.]]></description><link>http://direct.ecency.com/math/@konstantint/sophism-18-derivatives</link><guid isPermaLink="true">http://direct.ecency.com/math/@konstantint/sophism-18-derivatives</guid><category><![CDATA[math]]></category><dc:creator><![CDATA[konstantint]]></dc:creator><pubDate>Thu, 31 Aug 2017 08:30:00 GMT</pubDate><enclosure url="https://images.ecency.com/p/2gsjgna1uruvUuS7ndh9YqVwYGPLVszbFLwwpAYXYqwdyZDkP4mafQs63J1yJbBpauVXrv8Lu5TbyLCtZphAFbHdtzLaJPsuEr2gCE2B7HBrw8gxzz?format=match&amp;mode=fit" length="0" type="false"/></item><item><title><![CDATA[Sophism #17: The Paradox of Life]]></title><description><![CDATA[Time is infinite. Your life is finite. Consequently, the probability of you being alive at this particular moment is zero. ... and yet you are alive! For other sophisms see my other posts.]]></description><link>http://direct.ecency.com/sophism/@konstantint/sophism-17-the-paradox-of-life</link><guid isPermaLink="true">http://direct.ecency.com/sophism/@konstantint/sophism-17-the-paradox-of-life</guid><category><![CDATA[sophism]]></category><dc:creator><![CDATA[konstantint]]></dc:creator><pubDate>Mon, 28 Aug 2017 12:02:33 GMT</pubDate><enclosure url="https://images.ecency.com/p/PB8ro82ZpZP5xqHVTtgzxr9jRnPYTxeDK7ZMexdNwC1tfTZr7gQNP2zp3zurAEftjVKqijJrrVc94hw8u4ARFiUetSbQwUKBzJ6qxa2vVoTecHMQ?format=match&amp;mode=fit" length="0" type="false"/></item><item><title><![CDATA[Sophism #16: The More You Know - The Less You Earn]]></title><description><![CDATA[As we know from physics, the amount of work done is proportional to power applied and the time spent: Work = Power × Time Substituting into this formula the well-known equations Knowledge = Power, Time]]></description><link>http://direct.ecency.com/funny/@konstantint/sophism-16-the-more-you-know-the-less-you-earn</link><guid isPermaLink="true">http://direct.ecency.com/funny/@konstantint/sophism-16-the-more-you-know-the-less-you-earn</guid><category><![CDATA[funny]]></category><dc:creator><![CDATA[konstantint]]></dc:creator><pubDate>Wed, 16 Aug 2017 10:38:09 GMT</pubDate><enclosure url="https://images.ecency.com/p/2gsjgna1uruvUuS7ndh9YqVwYGPLVszbFLwwpAYXYcd1SPb6CkRLYHMBrCQZs5xdhkkSMPLFHauysVK4E2ijwqeENHGyZdALCeR1C1ESPnfA3ydDAE?format=match&amp;mode=fit" length="0" type="false"/></item><item><title><![CDATA[Sophism #15: All Triangles are Isosceles]]></title><description><![CDATA[Consider an arbitrary triangle ABC. Let G be the midpoint of AB and let D be the intersection of the midpoint perpendicular of AB with the bisector of ∠C. Drop perpendiculars DE and DF to the sides AC]]></description><link>http://direct.ecency.com/math/@konstantint/sophism-15-all-triangles-are-isosceles</link><guid isPermaLink="true">http://direct.ecency.com/math/@konstantint/sophism-15-all-triangles-are-isosceles</guid><category><![CDATA[math]]></category><dc:creator><![CDATA[konstantint]]></dc:creator><pubDate>Mon, 14 Aug 2017 11:09:42 GMT</pubDate><enclosure url="https://images.ecency.com/p/3W72119s5BjWPGGUiZ9pqnZoj8JHYxCCp9dtn2QVeomN4zAbmyhPJ1tgrj6iw1pfohJAaAfr9qUbYayVEZqH2M6Tm78FQqLBnHsQNtZTAFyQwV5B5sQ7Sn?format=match&amp;mode=fit" length="0" type="false"/></item><item><title><![CDATA[Sophism #14: Square Root of -1]]></title><description><![CDATA[For other sophisms check out my other posts.]]></description><link>http://direct.ecency.com/math/@konstantint/sophism-14-square-root-of-1</link><guid isPermaLink="true">http://direct.ecency.com/math/@konstantint/sophism-14-square-root-of-1</guid><category><![CDATA[math]]></category><dc:creator><![CDATA[konstantint]]></dc:creator><pubDate>Sat, 12 Aug 2017 08:02:51 GMT</pubDate><enclosure url="https://images.ecency.com/p/qjrE4yyfw5pQYiuVvgYiUBP16WHGGN7UNn1BCdGdZT1YrG2n2iPxujPBwhpjAgwf2gBuuDqX3qii2Rp62ZMvgTAi2cPab9g2p1CBjnP7ifaPQymgPKGQAYwQ?format=match&amp;mode=fit" length="0" type="false"/></item><item><title><![CDATA[Sophism #13: The Missing Dollar]]></title><description><![CDATA[Bart's Cookie Store is selling two types of cookies - vanilla and chocolate. Vanilla cookies sell at $1 per three pieces, while chocolate ones sell at $1 per two. At the beginning of the day Bart had 30]]></description><link>http://direct.ecency.com/math/@konstantint/sophism-13-the-missing-dollar</link><guid isPermaLink="true">http://direct.ecency.com/math/@konstantint/sophism-13-the-missing-dollar</guid><category><![CDATA[math]]></category><dc:creator><![CDATA[konstantint]]></dc:creator><pubDate>Thu, 10 Aug 2017 16:40:51 GMT</pubDate><enclosure url="https://images.ecency.com/p/2gsjgna1uruvUuS7ndh9YqVwYGPLVszbFLwwpAYXYmQm5BunhytfCx1EchCdWZoPzSqEvfiMsRVdRSD7oSWgD5xNL1oPctc6dCPMhLtuKzymHbYgJR?format=match&amp;mode=fit" length="0" type="false"/></item><item><title><![CDATA[Sophism #12: The Earth is Flat]]></title><description><![CDATA[Consider the following statement: This whole statement is true if and only if the Earth is flat Let us denote the whole statement by A. Note that we can then rewrite it a bit more formally as the following]]></description><link>http://direct.ecency.com/math/@konstantint/sophism-12-the-earth-is-flat</link><guid isPermaLink="true">http://direct.ecency.com/math/@konstantint/sophism-12-the-earth-is-flat</guid><category><![CDATA[math]]></category><dc:creator><![CDATA[konstantint]]></dc:creator><pubDate>Fri, 28 Jul 2017 17:07:21 GMT</pubDate><enclosure url="https://images.ecency.com/p/RGgukq5E6HBSiAzSkyhEAkSC3YAWs8PUjMWejNbjKbQb9PZS5brXRqDNGTySuWxZMztXLTBeW3k1jJATctMxSBsnz4b37GF1HefaY9e5Cu9w7hEyPtDeUa1CGujiCYE?format=match&amp;mode=fit" length="0" type="false"/></item><item><title><![CDATA[Sophism #11: The Liar's Paradox]]></title><description><![CDATA[The Liar's Paradox is perhaps the shortest sophism there is. In its most common form it fits in just four words: This sentence is false. Think about it: if the sentence is indeed false, then we should]]></description><link>http://direct.ecency.com/math/@konstantint/sophism-11-the-liar-s-paradox</link><guid isPermaLink="true">http://direct.ecency.com/math/@konstantint/sophism-11-the-liar-s-paradox</guid><category><![CDATA[math]]></category><dc:creator><![CDATA[konstantint]]></dc:creator><pubDate>Mon, 24 Jul 2017 11:29:48 GMT</pubDate><enclosure url="https://images.ecency.com/p/4i88GgaV8qiGEw1xifwYz2xp7RJEnNpBZq7dn2K6326ztQW36mCMLW9m4UibedK41SsjjfEvfvEeYEjHfzTTYjxhZwNfXqhgzHZQQwk5QmagykHvgLKrjFrgyt?format=match&amp;mode=fit" length="0" type="false"/></item><item><title><![CDATA[Sophisms #1-#10: Discussion and Spoilers]]></title><description><![CDATA[Edit: Originally this post was named "Sophisms: Table of Contents" and was intended to be a single, regularly updated, table of contents for all the sophisms I'm posting here because I've just]]></description><link>http://direct.ecency.com/math/@konstantint/sophisms-table-of-contents</link><guid isPermaLink="true">http://direct.ecency.com/math/@konstantint/sophisms-table-of-contents</guid><category><![CDATA[math]]></category><dc:creator><![CDATA[konstantint]]></dc:creator><pubDate>Thu, 20 Jul 2017 13:08:36 GMT</pubDate></item><item><title><![CDATA[Sophism #10: Continued Fractions]]></title><description><![CDATA[Number one may be represented as an infinite continued fraction as follows: Number two may also be represented in exactly the same way: Consequently, we should conclude that 1 = 2. Please, avoid posting]]></description><link>http://direct.ecency.com/math/@konstantint/sophism-10-continued-fractions</link><guid isPermaLink="true">http://direct.ecency.com/math/@konstantint/sophism-10-continued-fractions</guid><category><![CDATA[math]]></category><dc:creator><![CDATA[konstantint]]></dc:creator><pubDate>Thu, 20 Jul 2017 10:59:09 GMT</pubDate><enclosure url="https://images.ecency.com/p/Zskj9C56UondJxcjVaienfhVaNb7LJVWG6e787gZxJcwLH9gmEz97XwQA5wivmWbUFPMEVmJwKccLYWCDWX4cMLbXSnvsCH6XtGtRVaR3vYgjmWKkK9Q?format=match&amp;mode=fit" length="0" type="false"/></item><item><title><![CDATA[Sophism #9: 3=2]]></title><description><![CDATA[Consider again three arbitrary numbers a, b, c, such that a+b = c Then: (3a-2a)+(3b-2b) = (3c-2c) Reorganize and simplify: 3a+3b-3c = 2a+2b-2c 3(a+b-c) = 2(a+b-c) 3 = 2 QED. Note that you may use the same]]></description><link>http://direct.ecency.com/math/@konstantint/sophism-9-3-2</link><guid isPermaLink="true">http://direct.ecency.com/math/@konstantint/sophism-9-3-2</guid><category><![CDATA[math]]></category><dc:creator><![CDATA[konstantint]]></dc:creator><pubDate>Mon, 17 Jul 2017 21:54:03 GMT</pubDate></item><item><title><![CDATA[Sophism #8: Cryptocurrency Trading is Evil]]></title><description><![CDATA[Sophisms come in various shapes and sizes. Some are simple mathematical "find-the-mistake" puzzles. Others are subtle observations, requiring whole theories to resolve them. Some are deeply]]></description><link>http://direct.ecency.com/funny/@konstantint/sophism-8-cryptocurrency-trading-is-evil</link><guid isPermaLink="true">http://direct.ecency.com/funny/@konstantint/sophism-8-cryptocurrency-trading-is-evil</guid><category><![CDATA[funny]]></category><dc:creator><![CDATA[konstantint]]></dc:creator><pubDate>Sun, 16 Jul 2017 11:27:06 GMT</pubDate><enclosure url="https://images.ecency.com/p/C3TZR1g81UNchGPKLQuxAL7oEwDJ42cT977qXjChUS31VBsE8pAgumkEEaqa5JEWJmXey7YjU8sXfFetFnAy7dnyjv6WiVNUK7DBXVBHsUh9vHT6CLxqT42?format=match&amp;mode=fit" length="0" type="false"/></item><item><title><![CDATA[Sophism #7: The Arrow Paradox]]></title><description><![CDATA[Homer threw a baseball to Bart. Like that: Notice that at the moment in time depicted on the image, the ball is located at a certain fixed position in space. While it is being in that fixed position, it]]></description><link>http://direct.ecency.com/math/@konstantint/sophism-7-the-arrow-paradox</link><guid isPermaLink="true">http://direct.ecency.com/math/@konstantint/sophism-7-the-arrow-paradox</guid><category><![CDATA[math]]></category><dc:creator><![CDATA[konstantint]]></dc:creator><pubDate>Fri, 14 Jul 2017 13:09:15 GMT</pubDate><enclosure url="https://images.ecency.com/p/HNWT6DgoBc18GVREvvsnAjfLwLF5qHHFduNHKinq4TG2taUScpz1Hp1CrRFPxWg3PXyV4D1iWYuEPENQTpcM7gU8daJDjTf9vvXjNm5vMmrZtuGV2tkkvoJfhB4?format=match&amp;mode=fit" length="0" type="false"/></item><item><title><![CDATA[Sophism #6: The Dichotomy Paradox]]></title><description><![CDATA[One sunny Monday morning Homer decided to go to his favourite bar to get a can of beer. Right before leaving the house, he paused to think for a moment: "The bar is located 1km away. If I start walking]]></description><link>http://direct.ecency.com/math/@konstantint/sophism-6-the-dichotomy-paradox</link><guid isPermaLink="true">http://direct.ecency.com/math/@konstantint/sophism-6-the-dichotomy-paradox</guid><category><![CDATA[math]]></category><dc:creator><![CDATA[konstantint]]></dc:creator><pubDate>Thu, 13 Jul 2017 22:32:00 GMT</pubDate><enclosure url="https://images.ecency.com/p/C3TZR1g81UNchGPKLQuxAL7oEwDJ42cT977qXjCha6cxKW3BKTSAxFudanU4CvDHAbr53hYucK4RtfBAnBLT5hrpmBefgqAhCfNqj63czwwufpG64rhtT2n?format=match&amp;mode=fit" length="0" type="false"/></item><item><title><![CDATA[Sophism #5: Achilles and the Tortoise]]></title><description><![CDATA[Zeno's paradoxes are among the most ancient and famous sophisms known to date. They are thought to be proposed (or collected) by the ancient greek philosopher Zeno in the V century BC. At least nine known]]></description><link>http://direct.ecency.com/math/@konstantint/sophism-5-achilles-and-the-tortoise</link><guid isPermaLink="true">http://direct.ecency.com/math/@konstantint/sophism-5-achilles-and-the-tortoise</guid><category><![CDATA[math]]></category><dc:creator><![CDATA[konstantint]]></dc:creator><pubDate>Thu, 13 Jul 2017 09:53:48 GMT</pubDate><enclosure url="https://images.ecency.com/p/S5Eokt4BcQdk7EHeT1aYjzebg2hC7hkthT45eP8xxVEbqRCMzUawJMEgMmXq3sz28End2R4?format=match&amp;mode=fit" length="0" type="false"/></item><item><title><![CDATA[Sophism #4: Any Two Numbers are Equal]]></title><description><![CDATA[Consider two arbitrary numbers a and b. Let a + b = 2c Rearrange this in two ways to get two new valid equations: a - 2c = -b a = -b + 2c Multiply the corresponding sides of the two equations: a2 - 2ac]]></description><link>http://direct.ecency.com/math/@konstantint/sophism-4-any-two-numbers-are-equal</link><guid isPermaLink="true">http://direct.ecency.com/math/@konstantint/sophism-4-any-two-numbers-are-equal</guid><category><![CDATA[math]]></category><dc:creator><![CDATA[konstantint]]></dc:creator><pubDate>Wed, 12 Jul 2017 12:03:51 GMT</pubDate></item><item><title><![CDATA[Sophism #3: Every Number Can Sometimes Be Equal to Zero]]></title><description><![CDATA[Let a, b, and c be arbitrary numbers, such that a = b + c Multiply both sides of the equation by (a-b) and open the brackets: a(a-b) = (b+c)(a-b) a2 - ab = ab + ac - b2 - bc Move ac to the left and extract:]]></description><link>http://direct.ecency.com/sophism/@konstantint/sophism-3-every-number-can-sometimes-be-equal-to-zero</link><guid isPermaLink="true">http://direct.ecency.com/sophism/@konstantint/sophism-3-every-number-can-sometimes-be-equal-to-zero</guid><category><![CDATA[sophism]]></category><dc:creator><![CDATA[konstantint]]></dc:creator><pubDate>Tue, 11 Jul 2017 23:31:33 GMT</pubDate></item><item><title><![CDATA[Sophism #2: Free Beer]]></title><description><![CDATA[Homer entered a bar. -- What beers do you serve here? -- Guinness at $3 a can, and Duff at $5, - answered the barman. Homer feverishly searched his pocket, scraping together $3 in small coins. He passed]]></description><link>http://direct.ecency.com/math/@konstantint/sophism-2-free-beer</link><guid isPermaLink="true">http://direct.ecency.com/math/@konstantint/sophism-2-free-beer</guid><category><![CDATA[math]]></category><dc:creator><![CDATA[konstantint]]></dc:creator><pubDate>Tue, 11 Jul 2017 09:43:57 GMT</pubDate><enclosure url="https://images.ecency.com/p/PB8ro82ZpZP5xqHVTtgzxr9jRnPYTxeDK7ZMexdNd7zGuVYMPWpAYTj2DFK6DYMZMcyfzT4jKLGMUGWwrsScB7cPCp3GAVYoTi7EnjQzedhcjGA2?format=match&amp;mode=fit" length="0" type="false"/></item></channel></rss>