{"id":188521,"date":"2012-10-10T00:00:00","date_gmt":"2012-10-11T10:44:15","guid":{"rendered":"https:\/\/www.microsoft.com\/en-us\/research\/msr-research-item\/real-applications-of-non-real-numbers\/"},"modified":"2016-08-22T11:27:11","modified_gmt":"2016-08-22T18:27:11","slug":"real-applications-of-non-real-numbers","status":"publish","type":"msr-video","link":"https:\/\/www.microsoft.com\/en-us\/research\/video\/real-applications-of-non-real-numbers\/","title":{"rendered":"Real Applications of Non-Real Numbers"},"content":{"rendered":"<div class=\"asset-content\">\n<p>The system of real numbers are defined mathematically as a &#8220;completion&#8217; of the rational numbers. But this is not the only way to do it! In fact there are infinitely many others completions- the so called &#8220;p-adic numbers&#8221;. These numbers were defined for pure mathematical reasons and have been a  subject of research for a century. But in the last 3 decades they have found &#8216;real world&#8217; applications in computer science, construction of networks, algorithms etc. We will try to tell the story in a way which hopefully will make sense also to non-mathematicians.<\/p>\n<\/div>\n<p><!-- .asset-content --><\/p>\n","protected":false},"excerpt":{"rendered":"<p>The system of real numbers are defined mathematically as a &#8220;completion&#8217; of the rational numbers. But this is not the only way to do it! In fact there are infinitely many others completions- the so called &#8220;p-adic numbers&#8221;. These numbers were defined for pure mathematical reasons and have been a subject of research for a [&hellip;]<\/p>\n","protected":false},"featured_media":197209,"template":"","meta":{"msr-url-field":"","msr-podcast-episode":"","msrModifiedDate":"","msrModifiedDateEnabled":false,"ep_exclude_from_search":false,"footnotes":""},"research-area":[],"msr-video-type":[],"msr-locale":[268875],"msr-impact-theme":[],"msr-pillar":[],"class_list":["post-188521","msr-video","type-msr-video","status-publish","has-post-thumbnail","hentry","msr-locale-en_us"],"msr_download_urls":"","msr_external_url":"https:\/\/youtu.be\/_Nw-IYDHAA8","msr_secondary_video_url":"","msr_video_file":"","_links":{"self":[{"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-video\/188521"}],"collection":[{"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-video"}],"about":[{"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/types\/msr-video"}],"version-history":[{"count":0,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-video\/188521\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/media\/197209"}],"wp:attachment":[{"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/media?parent=188521"}],"wp:term":[{"taxonomy":"msr-research-area","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/research-area?post=188521"},{"taxonomy":"msr-video-type","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-video-type?post=188521"},{"taxonomy":"msr-locale","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-locale?post=188521"},{"taxonomy":"msr-impact-theme","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-impact-theme?post=188521"},{"taxonomy":"msr-pillar","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-pillar?post=188521"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}