{"id":6858,"date":"2021-04-01T17:10:55","date_gmt":"2021-04-01T21:10:55","guid":{"rendered":"https:\/\/blogs.mathworks.com\/cleve\/?p=6858"},"modified":"2021-04-01T17:10:55","modified_gmt":"2021-04-01T21:10:55","slug":"odd-rock-on-mars-exhibits-almost-magic-square","status":"publish","type":"post","link":"https:\/\/blogs.mathworks.com\/cleve\/2021\/04\/01\/odd-rock-on-mars-exhibits-almost-magic-square\/","title":{"rendered":"&#8220;Odd Rock&#8221; on Mars Exhibits (Almost) Magic Square"},"content":{"rendered":"<div class=\"content\"><!--introduction--><p>A news story released yesterday, March 31,by c|net <a href=\"https:\/\/www.cnet.com\/news\/nasa-perseverance-mars-rover-investigates-odd-rock-zaps-it\/\">has the headline<\/a><\/p><pre>  NASA Perseverance Mars rover investigates 'odd' rock<\/pre><!--\/introduction--><p>Markings etched into the rock attempt to describe a magic square.  The discovery is a reminder of the Chinese legend of the <a href=\"https:\/\/en.wikipedia.org\/wiki\/Lo_Shu_Square\">Lo Shu square<\/a> on the back of a turtle three thousand years ago.<\/p><p><img decoding=\"async\" vspace=\"5\" hspace=\"5\" src=\"http:\/\/blogs.mathworks.com\/cleve\/files\/rock.png\" alt=\"\"> <\/p><p>The ancient Chinese Lo Shu is 3-by-3 and is generated in MATLAB by<\/p><pre class=\"codeinput\">   LoShu =  magic(3)\r\n<\/pre><pre class=\"codeoutput\">\r\nLoShu =\r\n\r\n     8     1     6\r\n     3     5     7\r\n     4     9     2\r\n\r\n<\/pre><p>All the row sums, column sum and diagonal sums are 15.<\/p><p>However, the number grid on the Martian rock is only 2-by-2. For <tt>n = 2<\/tt>, MATLAB produces a similar array.<\/p><pre class=\"codeinput\">   Mars = magic(2)\r\n<\/pre><pre class=\"codeoutput\">\r\nMars =\r\n\r\n     1     3\r\n     4     2\r\n\r\n<\/pre><p>The column sums are both 5, but the row  sums and the diagonal sums do not cooperate.<\/p><p>Magic squares of order 2 do not exist, at least under our terrestrial rules of arithmetic.<\/p><p>Is it possible that under some arithmetic system, this array has magic properties?  If so, then we certainly have evidence that intelligent life once existed on Mars or wherever this fragment originated.<\/p><script language=\"JavaScript\"> <!-- \r\n    function grabCode_cdfe6128305a4d5a95856d3be3628d6a() {\r\n        \/\/ Remember the title so we can use it in the new page\r\n        title = document.title;\r\n\r\n        \/\/ Break up these strings so that their presence\r\n        \/\/ in the Javascript doesn't mess up the search for\r\n        \/\/ the MATLAB code.\r\n        t1='cdfe6128305a4d5a95856d3be3628d6a ' + '##### ' + 'SOURCE BEGIN' + ' #####';\r\n        t2='##### ' + 'SOURCE END' + ' #####' + ' cdfe6128305a4d5a95856d3be3628d6a';\r\n    \r\n        b=document.getElementsByTagName('body')[0];\r\n        i1=b.innerHTML.indexOf(t1)+t1.length;\r\n        i2=b.innerHTML.indexOf(t2);\r\n \r\n        code_string = b.innerHTML.substring(i1, i2);\r\n        code_string = code_string.replace(\/REPLACE_WITH_DASH_DASH\/g,'--');\r\n\r\n        \/\/ Use \/x3C\/g instead of the less-than character to avoid errors \r\n        \/\/ in the XML parser.\r\n        \/\/ Use '\\x26#60;' instead of '<' so that the XML parser\r\n        \/\/ doesn't go ahead and substitute the less-than character. \r\n        code_string = code_string.replace(\/\\x3C\/g, '\\x26#60;');\r\n\r\n        copyright = 'Copyright 2021 The MathWorks, Inc.';\r\n\r\n        w = window.open();\r\n        d = w.document;\r\n        d.write('<pre>\\n');\r\n        d.write(code_string);\r\n\r\n        \/\/ Add copyright line at the bottom if specified.\r\n        if (copyright.length > 0) {\r\n            d.writeln('');\r\n            d.writeln('%%');\r\n            if (copyright.length > 0) {\r\n                d.writeln('% _' + copyright + '_');\r\n            }\r\n        }\r\n\r\n        d.write('<\/pre>\\n');\r\n\r\n        d.title = title + ' (MATLAB code)';\r\n        d.close();\r\n    }   \r\n     --> <\/script><p style=\"text-align: right; font-size: xx-small; font-weight:lighter;   font-style: italic; color: gray\"><br><a href=\"javascript:grabCode_cdfe6128305a4d5a95856d3be3628d6a()\"><span style=\"font-size: x-small;        font-style: italic;\">Get \r\n      the MATLAB code <noscript>(requires JavaScript)<\/noscript><\/span><\/a><br><br>\r\n      Published with MATLAB&reg; R2021a<br><\/p><\/div><!--\r\ncdfe6128305a4d5a95856d3be3628d6a ##### SOURCE BEGIN #####\r\n%% \"Odd Rock\" on Mars Exhibits (Almost) Magic Square\r\n% A news story released yesterday, March 31,by c|net\r\n% <https:\/\/www.cnet.com\/news\/nasa-perseverance-mars-rover-investigates-odd-rock-zaps-it\/\r\n% has the headline>\r\n%\r\n%    NASA Perseverance Mars rover investigates 'odd' rock\r\n\r\n%%\r\n%\r\n% Markings etched into the rock attempt to describe\r\n% a magic square.  The discovery is a reminder of the Chinese\r\n% legend of the\r\n% <https:\/\/en.wikipedia.org\/wiki\/Lo_Shu_Square Lo Shu square>\r\n% on the back of a turtle three thousand years ago.\r\n%\r\n% <<rock.png>>\r\n\r\n%% \r\n% The ancient Chinese Lo Shu is 3-by-3 and is generated in MATLAB by\r\n\r\n   LoShu =  magic(3)\r\n   \r\n%%\r\n% All the row sums, column sum and diagonal sums are 15.\r\n\r\n%%\r\n% However, the number grid on the Martian rock is only 2-by-2.\r\n% For |n = 2|, MATLAB produces a similar array.\r\n\r\n   Mars = magic(2)\r\n   \r\n%%\r\n% The column sums are both 5, but the row  sums and the diagonal sums\r\n% do not cooperate.\r\n\r\n%%\r\n% Magic squares of order 2 do not exist, at least under our terrestrial\r\n% rules of arithmetic.\r\n\r\n%%\r\n% Is it possible that under some arithmetic system, this array has\r\n% magic properties?  If so, then we certainly have evidence\r\n% that intelligent life once existed on Mars or wherever this\r\n% fragment originated.\r\n\r\n\r\n##### SOURCE END ##### cdfe6128305a4d5a95856d3be3628d6a\r\n-->","protected":false},"excerpt":{"rendered":"<div class=\"overview-image\"><img decoding=\"async\"  class=\"img-responsive\" src=\"http:\/\/blogs.mathworks.com\/cleve\/files\/rock.png\" onError=\"this.style.display ='none';\" \/><\/div><!--introduction--><p>A news story released yesterday, March 31,by c|net <a href=\"https:\/\/www.cnet.com\/news\/nasa-perseverance-mars-rover-investigates-odd-rock-zaps-it\/\">has the headline<\/a>... <a class=\"read-more\" href=\"https:\/\/blogs.mathworks.com\/cleve\/2021\/04\/01\/odd-rock-on-mars-exhibits-almost-magic-square\/\">read more >><\/a><\/p>","protected":false},"author":78,"featured_media":0,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":[],"categories":[5,4,9,10],"tags":[],"_links":{"self":[{"href":"https:\/\/blogs.mathworks.com\/cleve\/wp-json\/wp\/v2\/posts\/6858"}],"collection":[{"href":"https:\/\/blogs.mathworks.com\/cleve\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/blogs.mathworks.com\/cleve\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/blogs.mathworks.com\/cleve\/wp-json\/wp\/v2\/users\/78"}],"replies":[{"embeddable":true,"href":"https:\/\/blogs.mathworks.com\/cleve\/wp-json\/wp\/v2\/comments?post=6858"}],"version-history":[{"count":1,"href":"https:\/\/blogs.mathworks.com\/cleve\/wp-json\/wp\/v2\/posts\/6858\/revisions"}],"predecessor-version":[{"id":6864,"href":"https:\/\/blogs.mathworks.com\/cleve\/wp-json\/wp\/v2\/posts\/6858\/revisions\/6864"}],"wp:attachment":[{"href":"https:\/\/blogs.mathworks.com\/cleve\/wp-json\/wp\/v2\/media?parent=6858"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/blogs.mathworks.com\/cleve\/wp-json\/wp\/v2\/categories?post=6858"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/blogs.mathworks.com\/cleve\/wp-json\/wp\/v2\/tags?post=6858"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}