binary code
http://plus.maths.org/content/taxonomy/term/304
enOmega and why maths has no TOEs
http://plus.maths.org/content/omega-and-why-maths-has-no-toes
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Gregory Chaitin </div>
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<img class="imagefield imagefield-field_abs_img" width="100" height="100" alt="" src="http://plus.maths.org/content/sites/plus.maths.org/files/issue37/features/omega/icon.jpg?1133395200" /> </div>
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Kurt Gödel, who would have celebrated his 100th birthday next year, showed in 1931 that the power of maths to explain the world is limited: his famous incompleteness theorem proves mathematically that maths cannot prove everything. <b>Gregory Chaitin</b> explains why he thinks that Gödel's incompleteness theorem is only the tip of the iceberg, and why mathematics is far too complex ever to be
described by a single theory. </div>
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<div class="pub_date">December 2005</div>
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<p><i>Over the millennia, many mathematicians have hoped that mathematics would one day produce a Theory of Everything (TOE); a finite set of axioms and rules from which every mathematical truth could be derived. But in 1931 this hope received a serious blow: Kurt Gödel published his famous Incompleteness Theorem, which states that in every mathematical theory, no matter how extensive, there will
always be statements which can't be proven to be true or false.</i></p><p><a href="http://plus.maths.org/content/omega-and-why-maths-has-no-toes" target="_blank">read more</a></p>http://plus.maths.org/content/omega-and-why-maths-has-no-toes#comments37binary codeGödel's Incompleteness Theoremphilosophy of mathematicsproofThu, 01 Dec 2005 00:00:00 +0000plusadmin2278 at http://plus.maths.org/contentRIP Claude Shannon
http://plus.maths.org/content/rip-claude-shannon
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Rachel Thomas </div>
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Claude Shannon, who died on February 24, was the founder of Information Theory, which is the basis of modern telecommunications. <b>Rachel Thomas</b> looks at Shannon's life and works. </div>
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<div class="pub_date">May 2001</div>
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<p>What do the following all have in common: digital communications, juggling machines, mechanical maze-solving mice and motorized pogo sticks? The answer is that they were all invented by the mathematician Claude Shannon.</p><p><a href="http://plus.maths.org/content/rip-claude-shannon" target="_blank">read more</a></p>http://plus.maths.org/content/rip-claude-shannon#comments15binary codeboolean algebraMon, 30 Apr 2001 23:00:00 +0000plusadmin2186 at http://plus.maths.org/contentCodes, trees and the prefix property
http://plus.maths.org/content/codes-trees-and-prefix-property
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Kona Macphee </div>
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<img class="imagefield imagefield-field_abs_img" width="130" height="130" alt="" src="http://plus.maths.org/content/sites/plus.maths.org/files/issue10/features/infotheory/icon.jpg?946684800" /> </div>
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Underlying our vast global telecommunications networks are codes: formal schemes for representing information in machine-readable and transmissible formats. <strong>Kona Macphee</strong> examines the prefix property, one of the important features of a good code. </div>
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<div class="pub_date">January 2000</div>
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<h2>Introduction</h2>
<p>These days we take fast, reliable global telecommunications for granted. From our own homes we can ring up our friends all over the country, send facsimile reproductions of our documents to businesses overseas, and download files and web pages from all over the world.</p><p><a href="http://plus.maths.org/content/codes-trees-and-prefix-property" target="_blank">read more</a></p>http://plus.maths.org/content/codes-trees-and-prefix-property#comments10binary codecodenodepathprefix propertytreeSat, 01 Jan 2000 00:00:00 +0000plusadmin2161 at http://plus.maths.org/content