Barber's Paradox
http://plus.maths.org/content/taxonomy/term/1270
enVisual curiosities and mathematical paradoxes
http://plus.maths.org/content/visual-curiosities-and-mathematical-paradoxes
<div class="field field-type-text field-field-author">
<div class="field-items">
<div class="field-item odd">
Linda Becerra and Ron Barnes </div>
</div>
</div>
<div class="field field-type-filefield field-field-abs-img">
<div class="field-items">
<div class="field-item odd">
<img class="imagefield imagefield-field_abs_img" width="100" height="100" alt="" src="http://plus.maths.org/content/sites/plus.maths.org/files/abstractpics/5/21%20Oct%202010%20-%2016%3A38/icon.jpg?1287675519" /> </div>
</div>
</div>
<div class="field field-type-text field-field-abs-txt">
<div class="field-items">
<div class="field-item odd">
<p>When your eyes see a picture they send an image to your brain, which your brain then has to make sense of. But sometimes your brain gets it wrong. The result is an optical illusion. Similarly in logic, statements or figures can lead to contradictory conclusions, which we call paradoxes. This article looks at examples of geometric optical illusions and paradoxes and gives explanations of what's really going on.</p>
</div>
</div>
</div>
<p>When your eyes see a picture they send an image to your brain, which your brain then has to make sense of. But sometimes your brain gets it wrong. The result is an optical illusion. Similarly in logic, statements or figures can lead to contradictory conclusions; appear to be true but in actual fact are self-contradictory; or appear contradictory, even absurd, but in fact may be true. Here again it is up to your brain to make sense of these situations. Again, your brain may get it wrong. These situations are referred to as paradoxes.<p><a href="http://plus.maths.org/content/visual-curiosities-and-mathematical-paradoxes" target="_blank">read more</a></p>http://plus.maths.org/content/visual-curiosities-and-mathematical-paradoxes#commentsarchitectureBanach-Tarski paradoxBarber's Paradoxeschergeometryimpossible objectoptical illusionparadoxPenrose staircasePenrose triangleperspectiveRussell's ParadoxWed, 17 Nov 2010 14:06:13 +0000mf3445337 at http://plus.maths.org/contentMathematical mysteries: The Barber's Paradox
http://plus.maths.org/content/mathematical-mysteries-barbers-paradox
<div class="field field-type-text field-field-author">
<div class="field-items">
<div class="field-item odd">
Helen Joyce </div>
</div>
</div>
<div class="field field-type-filefield field-field-abs-img">
<div class="field-items">
<div class="field-item odd">
<img class="imagefield imagefield-field_abs_img" width="100" height="100" alt="" src="http://plus.maths.org/content/sites/plus.maths.org/files/abstractpics/5/30%20Jun%202010%20-%2014%3A58/icon-2.jpg?1277906288" /> </div>
</div>
</div>
<div class="field field-type-text field-field-abs-txt">
<div class="field-items">
<div class="field-item odd">
<p>Suppose you walk past a barber's shop one day, and see a sign that says</p>
<p>"Do you shave yourself? If not, come in and I'll shave you! I shave anyone who does not shave himself, and noone else."<br />
This seems fair enough, and fairly simple, until, a little later, the following question occurs to you - does the barber shave himself?</p>
</div>
</div>
</div>
<div class="pub_date">May 2002</div>
<!-- plusimport -->
<h2>A close shave for set theory</h2>
<p><!-- FILE: include/leftfig.html --></p>
<div class="leftimage" style="width: 280px;"><img src="/issue20/xfile/barber.jpg" alt="" width="280" height="280" /></div>
<!-- END OF FILE: include/leftfig.html -->
<!-- drawn and copyright Charles Trevelyan -->
<p>Suppose you walk past a barber's shop one day, and see a sign that says</p><p><a href="http://plus.maths.org/content/mathematical-mysteries-barbers-paradox" target="_blank">read more</a></p>http://plus.maths.org/content/mathematical-mysteries-barbers-paradox#comments20Barber's ParadoxlogicMathematical mysteriesphilosophy of mathematicsRussell's Paradoxset theoryTheory of Typeswhat is impossibleZermelo-Fraenkel axiomatisation of set theoryTue, 30 Apr 2002 23:00:00 +0000plusadmin4757 at http://plus.maths.org/content