{"id":1668,"date":"2020-08-26T00:04:37","date_gmt":"2020-08-26T00:04:37","guid":{"rendered":"http:\/\/region12.herbzinser07.com\/dir\/science08\/?p=1668"},"modified":"2020-08-26T00:04:37","modified_gmt":"2020-08-26T00:04:37","slug":"boston-marathon-b100dy-math-war-explained-by-isaac-asimov","status":"publish","type":"post","link":"http:\/\/region12.herbzinser07.com\/dir\/science08-ucsystem\/2020\/08\/26\/boston-marathon-b100dy-math-war-explained-by-isaac-asimov\/","title":{"rendered":"Boston Marathon b100dy math war explained by Isaac Asimov"},"content":{"rendered":"<p class=\"c1\"><span class=\"c9 c10\">Rd-blog-number-3203 by Herb Zinser<\/span><\/p>\n<h1 id=\"h.1xm9csr1nfnv\" class=\"c13\"><span class=\"c25\">Boston Marathon b100<\/span><span class=\"c21\">dy math<\/span><span class=\"c9 c25\">\u00a0war explained by Isaac Asimov<\/span><\/h1>\n<p class=\"c1\"><span class=\"c9 c10\">This blog post \u2026.. \u00a0a \u00a0 year 2013 \u00a0Psychohistory WAR battle \u00a0analysis \u00a0report.<\/span><\/p>\n<p class=\"c1\"><span class=\"c9 c0\">The bio-mathematics expression of B100D are well-known. Using the Herbert Spencer model of INTERNAL and EXTERNAL correspondence &#8230; we see \u00a0the INTERNAL b100d SYMBOL MACHINE conflicts express themselves in EXTERNAL \u00a0display format using human activities with the identifier signs \u00a0&#8230;&#8230; a b100dy, tragic \u00a0event.<\/span><\/p>\n<h3 id=\"h.4by5gk4snu6o\" class=\"c8\"><span class=\"c11\"><a class=\"c2\" href=\"https:\/\/www.google.com\/url?q=http:\/\/oll.libertyfund.org\/title\/1394\/101633&amp;sa=D&amp;ust=1598403532907000&amp;usg=AOvVaw0gVLf7i80z2SU3zWARsfRw\">Chapter IV.: The\u00a0<\/a><\/span><span class=\"c11 c12\"><a class=\"c2\" href=\"https:\/\/www.google.com\/url?q=http:\/\/oll.libertyfund.org\/title\/1394\/101633&amp;sa=D&amp;ust=1598403532908000&amp;usg=AOvVaw1L1pzuKPAqJQDbFmWln2Ue\">Correspondence<\/a><\/span><span class=\"c11\"><a class=\"c2\" href=\"https:\/\/www.google.com\/url?q=http:\/\/oll.libertyfund.org\/title\/1394\/101633&amp;sa=D&amp;ust=1598403532908000&amp;usg=AOvVaw1L1pzuKPAqJQDbFmWln2Ue\">\u00a0Between Life and Its Circumstances.<\/a><\/span><\/h3>\n<p class=\"c1\"><span class=\"c9 c10\">oll.libertyfund.org\/title\/1394\/101633\u200e<\/span><\/p>\n<p class=\"c1\"><span class=\"c10 c12\">Herbert Spencer<\/span><span class=\"c10\">, The Principles of Psychology [<\/span><span class=\"c10 c12\">1855<\/span><span class=\"c10\">]\u00a0<\/span><span class=\"c0\">&#8230;<\/span><span class=\"c10\">\u00a0Author:\u00a0<\/span><span class=\"c10 c12\">Herbert Spencer<\/span><span class=\"c10\">\u00a0<\/span><span class=\"c0\">&#8230;.<\/span><span class=\"c10\">\u00a0form links in the\u00a0<\/span><span class=\"c10 c12\">correspondence<\/span><span class=\"c10\">\u00a0between\u00a0<\/span><span class=\"c10 c12\">internal<\/span><span class=\"c10\">\u00a0and\u00a0<\/span><span class=\"c10 c12\">external<\/span><span class=\"c9 c10\">\u00a0changes.<\/span><\/p>\n<h3 id=\"h.1hlomfqpdy23\" class=\"c8\"><span class=\"c11 c12\"><a class=\"c2\" href=\"https:\/\/www.google.com\/url?q=http:\/\/www.ncbi.nlm.nih.gov\/pmc\/articles\/PMC1592350\/&amp;sa=D&amp;ust=1598403532910000&amp;usg=AOvVaw36oIrVe_jCkFguItslSbZT\">Herbert Spencer&#8217;s<\/a><\/span><span class=\"c11\"><a class=\"c2\" href=\"https:\/\/www.google.com\/url?q=http:\/\/www.ncbi.nlm.nih.gov\/pmc\/articles\/PMC1592350\/&amp;sa=D&amp;ust=1598403532910000&amp;usg=AOvVaw36oIrVe_jCkFguItslSbZT\">\u00a0Contributions to Behavior Analysis: A &#8230;<\/a><\/span><\/h3>\n<p class=\"c1\"><span class=\"c10\">www.ncbi.nlm.nih.gov \u203a &#8230; \u203a<\/span><span class=\"c10\"><a class=\"c2\" href=\"https:\/\/www.google.com\/url?q=http:\/\/www.ncbi.nlm.nih.gov\/pmc\/journals\/299\/&amp;sa=D&amp;ust=1598403532911000&amp;usg=AOvVaw3aCDPPldcJQ_NYp7bUuLFH\">\u00a0<\/a><\/span><span class=\"c4\"><a class=\"c2\" href=\"https:\/\/www.google.com\/url?q=http:\/\/www.ncbi.nlm.nih.gov\/pmc\/journals\/299\/&amp;sa=D&amp;ust=1598403532911000&amp;usg=AOvVaw3aCDPPldcJQ_NYp7bUuLFH\">J Exp Anal Behav<\/a><\/span><span class=\"c10\">\u00a0\u203a<\/span><span class=\"c10\"><a class=\"c2\" href=\"https:\/\/www.google.com\/url?q=http:\/\/www.ncbi.nlm.nih.gov\/pmc\/issues\/135567\/&amp;sa=D&amp;ust=1598403532911000&amp;usg=AOvVaw13bcGzLFp1Hw_j0Mp1xlvZ\">\u00a0<\/a><\/span><span class=\"c4\"><a class=\"c2\" href=\"https:\/\/www.google.com\/url?q=http:\/\/www.ncbi.nlm.nih.gov\/pmc\/issues\/135567\/&amp;sa=D&amp;ust=1598403532912000&amp;usg=AOvVaw31P21z-HEp4MO_FGUMEGjb\">v.86(1); Jul 2006<\/a><\/span><span class=\"c9 c10\">\u200e<\/span><\/p>\n<p class=\"c1\"><span class=\"c10\">by JC Leslie &#8211; \u200e2006 &#8211; \u200e<\/span><span class=\"c4\"><a class=\"c2\" href=\"https:\/\/www.google.com\/url?q=https:\/\/scholar.google.com\/scholar?rlz%26um%3D1%26ie%3DUTF-8%26lr%26cites%3D11610144832918322238&amp;sa=D&amp;ust=1598403532912000&amp;usg=AOvVaw1jLhLoD0gnHI0m04WEt7fp\">Cited by 4<\/a><\/span><span class=\"c10\">\u00a0&#8211; \u200e<\/span><span class=\"c4\"><a class=\"c2\" href=\"https:\/\/www.google.com\/url?q=https:\/\/scholar.google.com\/scholar?rlz%26um%3D1%26ie%3DUTF-8%26lr%26q%3Drelated:PvzuXDaFH6H4hM:scholar.google.com\/&amp;sa=D&amp;ust=1598403532913000&amp;usg=AOvVaw06lepJU5r7sp9pITbIxk9X\">Related articles<\/a><\/span><\/p>\n<p class=\"c1\"><span class=\"c10 c12\">Correspondence<\/span><span class=\"c10\">\u00a0should be sent to J.C Leslie, School of Psychology,\u00a0<\/span><span class=\"c0\">&#8230;<\/span><span class=\"c10\">\u00a0<\/span><span class=\"c10 c12\">Herbert Spencer&#8217;s<\/span><span class=\"c10\">\u00a0Principles of Psychology (<\/span><span class=\"c10 c12\">1855<\/span><span class=\"c10\">, first edition) was regarded by his\u00a0<\/span><span class=\"c0\">&#8230;..<\/span><span class=\"c10\">\u00a0We have to identify the physical process by which an\u00a0<\/span><span class=\"c10 c12\">external<\/span><span class=\"c10\">\u00a0relation that habitually affects an organism, produces in the organism an adjusted\u00a0<\/span><span class=\"c10 c12\">internal<\/span><span class=\"c9 c10\">\u00a0relation\u201d (p.<\/span><\/p>\n<h3 id=\"h.k1aky2by4mdl\" class=\"c8\"><span class=\"c11\"><a class=\"c2\" href=\"https:\/\/www.google.com\/url?q=http:\/\/fair-use.org\/herbert-spencer\/the-data-of-ethics\/s.17&amp;sa=D&amp;ust=1598403532915000&amp;usg=AOvVaw0beprw3XcEIUPEK7SpE5GC\">\u00a717: THE DATA OF ETHICS (1879) by\u00a0<\/a><\/span><span class=\"c11 c12\"><a class=\"c2\" href=\"https:\/\/www.google.com\/url?q=http:\/\/fair-use.org\/herbert-spencer\/the-data-of-ethics\/s.17&amp;sa=D&amp;ust=1598403532915000&amp;usg=AOvVaw0beprw3XcEIUPEK7SpE5GC\">Herbert Spencer<\/a><\/span><\/h3>\n<p class=\"c1\"><span class=\"c10\">fair-use.org\/<\/span><span class=\"c0\">herbert<\/span><span class=\"c10\">&#8211;<\/span><span class=\"c0\">spencer<\/span><span class=\"c9 c10\">\/the-data-of-ethics\/s.17\u200e<\/span><\/p>\n<p class=\"c1\"><span class=\"c10\">Again, even the simplest notion of\u00a0<\/span><span class=\"c10 c12\">cause<\/span><span class=\"c10\">, as we understand it, can be reached\u00a0<\/span><span class=\"c0\">&#8230;<\/span><span class=\"c10\">\u00a0ideas of uniformity of sequence and of\u00a0<\/span><span class=\"c10 c12\">co<\/span><span class=\"c10\">&#8211;<\/span><span class=\"c10 c12\">existence<\/span><span class=\"c10\">\u2014the idea of natural law.\u00a0<\/span><span class=\"c0\">&#8230;<\/span><span class=\"c10\">\u00a0by him: the necessary relations among\u00a0<\/span><span class=\"c10 c12\">causes<\/span><span class=\"c10\">\u00a0and\u00a0<\/span><span class=\"c10 c12\">effects<\/span><span class=\"c10\">\u00a0are tacitly ignored by\u00a0<\/span><span class=\"c9 c0\">&#8230;<\/span><\/p>\n<p class=\"c1\"><span class=\"c9 c0\">In addition we have Boston University professor Isaac Asimov predictions about math expressions.<\/span><\/p>\n<p class=\"c1\"><img decoding=\"async\" title=\"\" src=\"http:\/\/region12.herbzinser07.com\/dir\/science08-ucsystem\/wp-content\/uploads\/sites\/15\/2020\/08\/img_5f45a7157e793.jpg\" alt=\"\" \/><\/p>\n<h3 id=\"h.5vwoez68gax7\" class=\"c8\"><span class=\"c11\"><a class=\"c2\" href=\"https:\/\/www.google.com\/url?q=http:\/\/www.depauw.edu\/sfs\/backissues\/8\/elkins8art.htm&amp;sa=D&amp;ust=1598403532918000&amp;usg=AOvVaw1oynFlRtyNyFf73oMnnPb-\">Charles Elkins-\u00a0<\/a><\/span><span class=\"c11 c12\"><a class=\"c2\" href=\"https:\/\/www.google.com\/url?q=http:\/\/www.depauw.edu\/sfs\/backissues\/8\/elkins8art.htm&amp;sa=D&amp;ust=1598403532919000&amp;usg=AOvVaw3XOcecCmkpaJWUMp4Oo_-B\">Isaac Asimov&#8217;s<\/a><\/span><span class=\"c11\"><a class=\"c2\" href=\"https:\/\/www.google.com\/url?q=http:\/\/www.depauw.edu\/sfs\/backissues\/8\/elkins8art.htm&amp;sa=D&amp;ust=1598403532919000&amp;usg=AOvVaw3XOcecCmkpaJWUMp4Oo_-B\">\u00a0FOUNDATION Novels: Historical &#8230;<\/a><\/span><\/h3>\n<p class=\"c1\"><span class=\"c9 c10\">www.depauw.edu\/sfs\/backissues\/8\/elkins8art.htm\u200e<\/span><\/p>\n<p class=\"c1\"><span class=\"c10 c12\">Isaac Asimov&#8217;s<\/span><span class=\"c10\">\u00a0FOUNDATION Novels: Historical Materialism Distorted into Cyclical\u00a0<\/span><span class=\"c0\">&#8230;.<\/span><span class=\"c10\">\u00a0Instead of\u00a0<\/span><span class=\"c10 c12\">events<\/span><span class=\"c10\">\u00a0growing out of the inner logic and premises of the narrative\u00a0<\/span><span class=\"c0\">&#8230;<\/span><span class=\"c10\">\u00a0it [Seldon&#8217;s Plan] formulated definite laws capable of\u00a0<\/span><span class=\"c10 c12\">mathematical<\/span><span class=\"c10\">\u00a0analysis and\u00a0<\/span><span class=\"c0\">&#8230;.<\/span><span class=\"c10\">\u00a0&#8220;<\/span><span class=\"c10 c12\">Psycho-history<\/span><span class=\"c9 c10\">\u00a0is,&#8221;<\/span><\/p>\n<h3 id=\"h.14q40ufeb7ec\" class=\"c8\"><span class=\"c11 c12\"><a class=\"c2\" href=\"https:\/\/www.google.com\/url?q=http:\/\/en.wikipedia.org\/wiki\/Psychohistory_%2528fictional%2529&amp;sa=D&amp;ust=1598403532921000&amp;usg=AOvVaw14EnMpixoygHFPi87EB8PI\">Psychohistory<\/a><\/span><span class=\"c11\"><a class=\"c2\" href=\"https:\/\/www.google.com\/url?q=http:\/\/en.wikipedia.org\/wiki\/Psychohistory_%2528fictional%2529&amp;sa=D&amp;ust=1598403532922000&amp;usg=AOvVaw2s3-lEomljitcErPulvflP\">\u00a0 &#8211; Wikipedia cryptic SYMBOL code, the \u00a0free (abbreviation for frequency ) \u00a0 en +cycle+ open + dia<\/a><\/span><\/h3>\n<p class=\"c1\"><span class=\"c10\">en.wikipedia.org\/wiki\/<\/span><span class=\"c0\">Psychohistory<\/span><span class=\"c9 c10\">_(fictional)\u200e<\/span><\/p>\n<p class=\"c1\"><span class=\"c10\">For the study of the psychological motivation of historical and current\u00a0<\/span><span class=\"c10 c12\">events<\/span><span class=\"c10\">, see\u00a0<\/span><span class=\"c0\">&#8230;<\/span><span class=\"c10\">\u00a0<\/span><span class=\"c10 c12\">Psychohistory<\/span><span class=\"c10\">\u00a0is a new \u00a0science theory described \u00a0 in\u00a0<\/span><span class=\"c10 c12\">Isaac Asimov<\/span><span class=\"c10\">&#8216;s Foundation universe\u00a0<\/span><span class=\"c0\">&#8230;<\/span><span class=\"c10\">\u00a0etc., and\u00a0<\/span><span class=\"c10 c12\">mathematical<\/span><span class=\"c10\">\u00a0statistics to make general predictions about the future\u00a0<\/span><span class=\"c9 c0\">&#8230;<\/span><\/p>\n<h3 id=\"h.di5eqfj0zkzy\" class=\"c8\"><span class=\"c11\"><a class=\"c2\" href=\"https:\/\/www.google.com\/url?q=http:\/\/www3.imperial.ac.uk\/portal\/page\/portallive\/D094BCEA2ED0A88EE040C69B47396491&amp;sa=D&amp;ust=1598403532924000&amp;usg=AOvVaw2DsBxpCs0YgU1H6SeLB6Y1\">A mathematician&#8217;s view on\u00a0<\/a><\/span><span class=\"c11 c12\"><a class=\"c2\" href=\"https:\/\/www.google.com\/url?q=http:\/\/www3.imperial.ac.uk\/portal\/page\/portallive\/D094BCEA2ED0A88EE040C69B47396491&amp;sa=D&amp;ust=1598403532925000&amp;usg=AOvVaw2c3EserZVdK-OXu3DiJhhP\">Asimov&#8217;s psychohistory<\/a><\/span><\/h3>\n<p class=\"c1\"><span class=\"c9 c10\">www3.imperial.ac.uk\/&#8230;\/D094BCEA2ED0A88EE040C69B47396491\u200e<\/span><\/p>\n<p class=\"c1\"><span class=\"c10\">Jan 23, 2013 &#8211; Professor Dan Crisan takes a look at legendary science writer Isaac\u00a0<\/span><span class=\"c0\">&#8230;<\/span><span class=\"c10\">\u00a0<\/span><span class=\"c10 c12\">Event<\/span><span class=\"c10\">\u00a0type: Lecture, Seminar\u00a0<\/span><span class=\"c0\">&#8230;<\/span><span class=\"c10\">\u00a0Based on current research, it would appear that a\u00a0<\/span><span class=\"c10 c12\">mathematical<\/span><span class=\"c10\">\u00a0model for predicting the future behaviour of very large groups, akin to the fictional science\u00a0<\/span><span class=\"c10 c12\">psychohistory<\/span><span class=\"c10\">\u00a0in\u00a0<\/span><span class=\"c10 c12\">Isaac Asimov&#8217;s<\/span><span class=\"c9 c10\">\u00a0book<\/span><\/p>\n<h3 id=\"h.lvm279ddksy3\" class=\"c8\"><span class=\"c11\"><a class=\"c2\" href=\"https:\/\/www.google.com\/url?q=http:\/\/www.dailykos.com\/story\/2013\/06\/09\/1214813\/-Is-Metadata-Psychohistory&amp;sa=D&amp;ust=1598403532927000&amp;usg=AOvVaw1tOHcFAjdlOLoAcE9BFsUE\">Daily Kos: Is Metadata\u00a0<\/a><\/span><span class=\"c11 c12\"><a class=\"c2\" href=\"https:\/\/www.google.com\/url?q=http:\/\/www.dailykos.com\/story\/2013\/06\/09\/1214813\/-Is-Metadata-Psychohistory&amp;sa=D&amp;ust=1598403532927000&amp;usg=AOvVaw1tOHcFAjdlOLoAcE9BFsUE\">Psychohistory<\/a><\/span><span class=\"c11\"><a class=\"c2\" href=\"https:\/\/www.google.com\/url?q=http:\/\/www.dailykos.com\/story\/2013\/06\/09\/1214813\/-Is-Metadata-Psychohistory&amp;sa=D&amp;ust=1598403532927000&amp;usg=AOvVaw1tOHcFAjdlOLoAcE9BFsUE\">?<\/a><\/span><\/h3>\n<p class=\"c1\"><span class=\"c10\">www.dailykos.com\/story\/2013\/06\/09\/&#8230;\/-Is-Metadata-<\/span><span class=\"c0\">Psychohistory<\/span><span class=\"c9 c10\">\u200e<\/span><\/p>\n<p class=\"c1\"><span class=\"c10\">Jun 9, 2013 &#8211;\u00a0<\/span><span class=\"c10 c12\">Psychohistory<\/span><span class=\"c10\">\u00a0is a concept in\u00a0<\/span><span class=\"c10 c12\">Isaac Asimov&#8217;s<\/span><span class=\"c10\">\u00a0science fiction novels which\u00a0<\/span><span class=\"c0\">&#8230;<\/span><span class=\"c10\">\u00a0a branch of\u00a0<\/span><span class=\"c10 c12\">mathematics<\/span><span class=\"c10\">\u00a0known as\u00a0<\/span><span class=\"c10 c12\">psychohistory<\/span><span class=\"c10\">, a concept of\u00a0<\/span><span class=\"c10 c12\">mathematical<\/span><span class=\"c10\">\u00a0<\/span><span class=\"c0\">&#8230;<\/span><span class=\"c10\">\u00a0a scientific model to predict future\u00a0<\/span><span class=\"c10 c12\">events<\/span><span class=\"c9 c10\">\u00a0just like weather forecasting.<\/span><\/p>\n<p class=\"c1\"><img decoding=\"async\" title=\"\" src=\"http:\/\/region12.herbzinser07.com\/dir\/science08-ucsystem\/wp-content\/uploads\/sites\/15\/2020\/08\/img_5f45a715c24fc.jpg\" alt=\"http:\/\/img.gawkerassets.com\/img\/18lrayn2vyogtjpg\/ku-medium.jpg\" \/><\/p>\n<p class=\"c1\"><img decoding=\"async\" title=\"\" src=\"http:\/\/region12.herbzinser07.com\/dir\/science08-ucsystem\/wp-content\/uploads\/sites\/15\/2020\/08\/img_5f45a7160ee08.png\" alt=\"\" \/><\/p>\n<p class=\"c1\"><img decoding=\"async\" title=\"\" src=\"http:\/\/region12.herbzinser07.com\/dir\/science08-ucsystem\/wp-content\/uploads\/sites\/15\/2020\/08\/img_5f45a7164db13.png\" alt=\"\" \/><\/p>\n<p class=\"c1\"><span class=\"c9 c0\">Let&#8217;s look at the bloody math tragedy in Boston in year 2013.<\/span><\/p>\n<p class=\"c1\"><span class=\"c9 c0\">The math EVENT involved a continuous function and its line\/curve represented on the geography surface of EARTH by the \u00a0Boston Marathon race route.<\/span><\/p>\n<p class=\"c1\"><span class=\"c9 c0\">Below, is the mathematical-geophysics continuous line &#8230;.. with calculus 1st derivatives that became involved \u00a0in the Boston financial derivatives LINK to calculus derivatives &#8230;.. the conflict &#8230;.. \u00a0the math calculations and math accounting systems war.<\/span><\/p>\n<h3 id=\"h.2x99j6v7sbmd\" class=\"c8\"><span class=\"c11 c12\"><a class=\"c2\" href=\"https:\/\/www.google.com\/url?q=http:\/\/www.themathpage.com\/acalc\/continuous-function.htm&amp;sa=D&amp;ust=1598403532931000&amp;usg=AOvVaw0LGYjN_vn9au27JQoa8o6F\">Continuous functions<\/a><\/span><span class=\"c11\"><a class=\"c2\" href=\"https:\/\/www.google.com\/url?q=http:\/\/www.themathpage.com\/acalc\/continuous-function.htm&amp;sa=D&amp;ust=1598403532932000&amp;usg=AOvVaw1acAPG0rt_e3CzkIDRBHZS\">\u00a0&#8211; An approach to\u00a0<\/a><\/span><span class=\"c11 c12\"><a class=\"c2\" href=\"https:\/\/www.google.com\/url?q=http:\/\/www.themathpage.com\/acalc\/continuous-function.htm&amp;sa=D&amp;ust=1598403532932000&amp;usg=AOvVaw1acAPG0rt_e3CzkIDRBHZS\">calculus<\/a><\/span><span class=\"c11\"><a class=\"c2\" href=\"https:\/\/www.google.com\/url?q=http:\/\/www.themathpage.com\/acalc\/continuous-function.htm&amp;sa=D&amp;ust=1598403532932000&amp;usg=AOvVaw1acAPG0rt_e3CzkIDRBHZS\">\u00a0&#8211; The Math Page (with applied math life \u00a0in Boston)<\/a><\/span><span class=\"c9 c37\">\u00a0<\/span><\/h3>\n<p class=\"c1\"><span class=\"c10\">www.themathpage.com\/acalc\/<\/span><span class=\"c0\">continuous<\/span><span class=\"c10\">&#8211;<\/span><span class=\"c0\">function<\/span><span class=\"c9 c10\">.htm\u200e<\/span><\/p>\n<p class=\"c1\"><span class=\"c10\">Therefore, consider the\u00a0<\/span><span class=\"c10 c12\">graph<\/span><span class=\"c10\">\u00a0of a function f(x) &#8230;&#8230;&#8230;t. The\u00a0<\/span><span class=\"c10 c12\">graph<\/span><span class=\"c10\">\u00a0is a continuous, unbroken line. Therefore we want to say that f(x) is a\u00a0<\/span><span class=\"c10 c12\">continuous function<\/span><span class=\"c9 c10\">.<\/span><\/p>\n<h3 id=\"h.b7bpf81nacyc\" class=\"c8\"><span class=\"c11\"><a class=\"c2\" href=\"https:\/\/www.google.com\/url?q=https:\/\/www.google.com\/search?q%3Dcalculus%2Bcontinuous%2Bfunction%2Bcurve%26tbm%3Disch%26tbo%3Du%26source%3Duniv%26sa%3DX%26ei%3DY3MjUqrYJtXPsASG-oCwDg%26ved%3D0CEcQsAQ&amp;sa=D&amp;ust=1598403532934000&amp;usg=AOvVaw3nj30n2hMHvzPBiasej83C\">Images for\u00a0<\/a><\/span><span class=\"c11 c12\"><a class=\"c2\" href=\"https:\/\/www.google.com\/url?q=https:\/\/www.google.com\/search?q%3Dcalculus%2Bcontinuous%2Bfunction%2Bcurve%26tbm%3Disch%26tbo%3Du%26source%3Duniv%26sa%3DX%26ei%3DY3MjUqrYJtXPsASG-oCwDg%26ved%3D0CEcQsAQ&amp;sa=D&amp;ust=1598403532934000&amp;usg=AOvVaw3nj30n2hMHvzPBiasej83C\">calculus continuous function curve<\/a><\/span><\/h3>\n<p class=\"c1\"><span class=\"c9 c0\">\u00a0<\/span><\/p>\n<p class=\"c1\"><img decoding=\"async\" title=\"\" src=\"http:\/\/region12.herbzinser07.com\/dir\/science08-ucsystem\/wp-content\/uploads\/sites\/15\/2020\/08\/img_5f45a71695477.jpg\" alt=\"http:\/\/media.cmgdigital.com\/shared\/lt\/lt_cache\/thumbnail\/610\/img\/photos\/2013\/04\/15\/a7\/9f\/041714BostonMarathonRouteCO.jpg\" \/><\/p>\n<h3 id=\"h.uzg01573zwuq\" class=\"c8\"><span class=\"c11 c12\"><a class=\"c2\" href=\"https:\/\/www.google.com\/url?q=http:\/\/en.wikipedia.org\/wiki\/Continuous_function&amp;sa=D&amp;ust=1598403532935000&amp;usg=AOvVaw1-35jVdr3hen3CKcgDuiqi\">Continuous function<\/a><\/span><span class=\"c11\"><a class=\"c2\" href=\"https:\/\/www.google.com\/url?q=http:\/\/en.wikipedia.org\/wiki\/Continuous_function&amp;sa=D&amp;ust=1598403532935000&amp;usg=AOvVaw1-35jVdr3hen3CKcgDuiqi\">\u00a0&#8211; Wikipedia, the free encyclopedia<\/a><\/span><\/h3>\n<p class=\"c1\"><span class=\"c10\">en.wikipedia.org\/wiki\/<\/span><span class=\"c0\">Continuous<\/span><span class=\"c10\">_<\/span><span class=\"c0\">function<\/span><span class=\"c9 c10\">\u200e<\/span><\/p>\n<p class=\"c1\"><span class=\"c10\">Differential\u00a0<\/span><span class=\"c10 c12\">calculus<\/span><span class=\"c10\">\u00a0<\/span><span class=\"c0\">&#8230;<\/span><span class=\"c10\">\u00a0In mathematics, a\u00a0<\/span><span class=\"c10 c12\">continuous function<\/span><span class=\"c10\">\u00a0is a function for which, intuitively, &#8220;small&#8221; changes in the\u00a0<\/span><span class=\"c0\">&#8230;<\/span><span class=\"c10\">\u00a0plane; such a function is continuous if, roughly speaking, the\u00a0<\/span><span class=\"c10 c12\">graph<\/span><span class=\"c10\">\u00a0is a single unbroken\u00a0<\/span><span class=\"c10 c12\">curve<\/span><span class=\"c9 c10\">\u00a0with no &#8220;holes&#8221; or &#8220;jumps&#8221;.<\/span><\/p>\n<p class=\"c1\"><img decoding=\"async\" title=\"\" src=\"http:\/\/region12.herbzinser07.com\/dir\/science08-ucsystem\/wp-content\/uploads\/sites\/15\/2020\/08\/img_5f45a716ca626.jpg\" alt=\"\" \/><\/p>\n<h3 id=\"h.31zbypsvwvua\" class=\"c8\"><span class=\"c11\"><a class=\"c2\" href=\"https:\/\/www.google.com\/url?q=http:\/\/www.wyzant.com\/help\/math\/calculus\/limits\/continuity&amp;sa=D&amp;ust=1598403532938000&amp;usg=AOvVaw0DFbXro-wIXXvfPqkyZdCE\">Help with Continuity and Limits &#8211;\u00a0<\/a><\/span><span class=\"c11 c12\"><a class=\"c2\" href=\"https:\/\/www.google.com\/url?q=http:\/\/www.wyzant.com\/help\/math\/calculus\/limits\/continuity&amp;sa=D&amp;ust=1598403532938000&amp;usg=AOvVaw0DFbXro-wIXXvfPqkyZdCE\">Calculus<\/a><\/span><span class=\"c11\"><a class=\"c2\" href=\"https:\/\/www.google.com\/url?q=http:\/\/www.wyzant.com\/help\/math\/calculus\/limits\/continuity&amp;sa=D&amp;ust=1598403532939000&amp;usg=AOvVaw3HtCF9Ula2TQzpT1R-PMnt\">\u00a0Help | WyzAnt Tutoring<\/a><\/span><\/h3>\n<p class=\"c1\"><span class=\"c10\">www.wyzant.com\/help\/math\/<\/span><span class=\"c0\">calculus<\/span><span class=\"c9 c10\">\/limits\/continuity\u200e<\/span><\/p>\n<p class=\"c1\"><span class=\"c10\">Many theorems in\u00a0<\/span><span class=\"c10 c12\">calculus<\/span><span class=\"c10\">\u00a0require that\u00a0<\/span><span class=\"c10 c12\">functions<\/span><span class=\"c10\">\u00a0be\u00a0<\/span><span class=\"c10 c12\">continuous<\/span><span class=\"c10\">\u00a0on intervals of real\u00a0<\/span><span class=\"c0\">&#8230;<\/span><span class=\"c10\">\u00a0Even though it is\u00a0<\/span><span class=\"c10 c12\">continuous<\/span><span class=\"c10\">\u00a0and we can draw the\u00a0<\/span><span class=\"c10 c12\">graph<\/span><span class=\"c10\">\u00a0without lifting our\u00a0<\/span><span class=\"c9 c0\">&#8230;<\/span><\/p>\n<h3 id=\"h.tlqv9fd5rnoa\" class=\"c8\"><span class=\"c11\"><a class=\"c2\" href=\"https:\/\/www.google.com\/url?q=https:\/\/www.google.com\/search?q%3Dcalculus%2Bcontinuous%2Bfunction%2Bcurve%26tbm%3Disch%26tbo%3Du%26source%3Duniv%26sa%3DX%26ei%3DY3MjUqrYJtXPsASG-oCwDg%26ved%3D0CEcQsAQ&amp;sa=D&amp;ust=1598403532941000&amp;usg=AOvVaw1jr4pRylgLBJ6JSrRQgsPg\">Images for\u00a0<\/a><\/span><span class=\"c11 c12\"><a class=\"c2\" href=\"https:\/\/www.google.com\/url?q=https:\/\/www.google.com\/search?q%3Dcalculus%2Bcontinuous%2Bfunction%2Bcurve%26tbm%3Disch%26tbo%3Du%26source%3Duniv%26sa%3DX%26ei%3DY3MjUqrYJtXPsASG-oCwDg%26ved%3D0CEcQsAQ&amp;sa=D&amp;ust=1598403532942000&amp;usg=AOvVaw3NMX0u4qEIW-t0iBscKO-Y\">calculus continuous function curve<\/a><\/span><\/h3>\n<h3 id=\"h.8o6nhhmwvhmu\" class=\"c7\"><img decoding=\"async\" title=\"\" src=\"http:\/\/region12.herbzinser07.com\/dir\/science08-ucsystem\/wp-content\/uploads\/sites\/15\/2020\/08\/img_5f45a71701d24.jpg\" alt=\"\" \/><\/h3>\n<h3 id=\"h.6ddqs1cw0l0e\" class=\"c8\"><span class=\"c11\"><a class=\"c2\" href=\"https:\/\/www.google.com\/url?q=https:\/\/www.google.com\/search?q%3Dcalculus%2Bcontinuous%2Bfunction%2Bcurve%26tbm%3Disch%26tbo%3Du%26source%3Duniv%26sa%3DX%26ei%3DY3MjUqrYJtXPsASG-oCwDg%26ved%3D0CEcQsAQ&amp;sa=D&amp;ust=1598403532943000&amp;usg=AOvVaw1D_ut8P7dfEEyEjNKh8gig\">Images for\u00a0<\/a><\/span><span class=\"c11 c12\"><a class=\"c2\" href=\"https:\/\/www.google.com\/url?q=https:\/\/www.google.com\/search?q%3Dcalculus%2Bcontinuous%2Bfunction%2Bcurve%26tbm%3Disch%26tbo%3Du%26source%3Duniv%26sa%3DX%26ei%3DY3MjUqrYJtXPsASG-oCwDg%26ved%3D0CEcQsAQ&amp;sa=D&amp;ust=1598403532944000&amp;usg=AOvVaw2x-Ek45NV-MdP4wywMffkL\">calculus continuous function curve<\/a><\/span><\/h3>\n<h3 id=\"h.3hqxhi32kz5k\" class=\"c8 c24\"><\/h3>\n<h3 id=\"h.d4leyuk2as2x\" class=\"c8 c24\"><\/h3>\n<p class=\"c1\"><img decoding=\"async\" title=\"\" src=\"http:\/\/region12.herbzinser07.com\/dir\/science08-ucsystem\/wp-content\/uploads\/sites\/15\/2020\/08\/img_5f45a7173c793.png\" alt=\"\" \/><\/p>\n<h3 id=\"h.ybost0fzxg85\" class=\"c8\"><span class=\"c11\"><a class=\"c2\" href=\"https:\/\/www.google.com\/url?q=https:\/\/www.google.com\/search?q%3Dcalculus%2Bcontinuous%2Bfunction%2Bcurve%26tbm%3Disch%26tbo%3Du%26source%3Duniv%26sa%3DX%26ei%3DY3MjUqrYJtXPsASG-oCwDg%26ved%3D0CEcQsAQ&amp;sa=D&amp;ust=1598403532945000&amp;usg=AOvVaw2WpB2eFE2N7gqWqYdNOJjR\">Images for\u00a0<\/a><\/span><span class=\"c11 c12\"><a class=\"c2\" href=\"https:\/\/www.google.com\/url?q=https:\/\/www.google.com\/search?q%3Dcalculus%2Bcontinuous%2Bfunction%2Bcurve%26tbm%3Disch%26tbo%3Du%26source%3Duniv%26sa%3DX%26ei%3DY3MjUqrYJtXPsASG-oCwDg%26ved%3D0CEcQsAQ&amp;sa=D&amp;ust=1598403532946000&amp;usg=AOvVaw08Xsqdg4pl_s0brG_M5W3M\">calculus continuous function curve<\/a><\/span><\/h3>\n<p class=\"c1\"><img decoding=\"async\" title=\"\" src=\"http:\/\/region12.herbzinser07.com\/dir\/science08-ucsystem\/wp-content\/uploads\/sites\/15\/2020\/08\/img_5f45a717873ca.gif\" alt=\"\" \/><\/p>\n<h3 id=\"h.fucd624two8w\" class=\"c8 c24\"><\/h3>\n<h3 id=\"h.xu8kgxyqjgxx\" class=\"c8\"><span class=\"c11\"><a class=\"c2\" href=\"https:\/\/www.google.com\/url?q=https:\/\/www.google.com\/search?q%3Dcalculus%2Bcontinuous%2Bfunction%2Bcurve%26tbm%3Disch%26tbo%3Du%26source%3Duniv%26sa%3DX%26ei%3DY3MjUqrYJtXPsASG-oCwDg%26ved%3D0CEcQsAQ&amp;sa=D&amp;ust=1598403532947000&amp;usg=AOvVaw04t46ljZjA1PMH47TQfABh\">Images for\u00a0<\/a><\/span><span class=\"c11 c12\"><a class=\"c2\" href=\"https:\/\/www.google.com\/url?q=https:\/\/www.google.com\/search?q%3Dcalculus%2Bcontinuous%2Bfunction%2Bcurve%26tbm%3Disch%26tbo%3Du%26source%3Duniv%26sa%3DX%26ei%3DY3MjUqrYJtXPsASG-oCwDg%26ved%3D0CEcQsAQ&amp;sa=D&amp;ust=1598403532948000&amp;usg=AOvVaw1NZ24dUzGYfFlM5YbtgMDw\">calculus continuous function curve<\/a><\/span><\/h3>\n<h3 id=\"h.tx22lvtqpcbz\" class=\"c8\"><span class=\"c11\"><a class=\"c2\" href=\"https:\/\/www.google.com\/url?q=http:\/\/www.zweigmedia.com\/RealWorld\/calctopic1\/contanddiffb.html&amp;sa=D&amp;ust=1598403532949000&amp;usg=AOvVaw2fVK4bPnX4zIirVaq9W8Nr\">Continuity and Differentiability<\/a><\/span><\/h3>\n<p class=\"c1\"><span class=\"c9 c10\">www.zweigmedia.com\/RealWorld\/calctopic1\/contanddiffb.html\u200e<\/span><\/p>\n<p class=\"c1\"><span class=\"c10 c12\">Calculus<\/span><span class=\"c10\">\u00a0Applied to the Real World\u00a0<\/span><span class=\"c0\">&#8230;<\/span><span class=\"c9 c10\">\u00a0To begin, we recall the definition of the derivative of a function, and what it<\/span><\/p>\n<p class=\"c1\"><span class=\"c10\">Are all\u00a0<\/span><span class=\"c10 c12\">continuous functions<\/span><span class=\"c9 c10\">\u00a0differentiable?<\/span><\/p>\n<h3 id=\"h.3u5y2y1pmjsz\" class=\"c8\"><span class=\"c20 c35\"><a class=\"c2\" href=\"https:\/\/www.google.com\/url?q=https:\/\/www.math.ucdavis.edu\/~kouba\/CalcOneDIRECTORY\/graphingdirectory\/&amp;sa=D&amp;ust=1598403532951000&amp;usg=AOvVaw23wpu87OS6XSBosd-8grVA\">\u00a0<\/a><\/span><span class=\"c12 c15\"><a class=\"c2\" href=\"https:\/\/www.google.com\/url?q=https:\/\/www.math.ucdavis.edu\/~kouba\/CalcOneDIRECTORY\/graphingdirectory\/&amp;sa=D&amp;ust=1598403532952000&amp;usg=AOvVaw1N4MoRpb8AC1QZeuGm71Ts\">First<\/a><\/span><span class=\"c15\"><a class=\"c2\" href=\"https:\/\/www.google.com\/url?q=https:\/\/www.math.ucdavis.edu\/~kouba\/CalcOneDIRECTORY\/graphingdirectory\/&amp;sa=D&amp;ust=1598403532952000&amp;usg=AOvVaw1N4MoRpb8AC1QZeuGm71Ts\">\u00a0\u00a0<\/a><\/span><span class=\"c15 c12\"><a class=\"c2\" href=\"https:\/\/www.google.com\/url?q=https:\/\/www.math.ucdavis.edu\/~kouba\/CalcOneDIRECTORY\/graphingdirectory\/&amp;sa=D&amp;ust=1598403532953000&amp;usg=AOvVaw39EoEt_MlnBg1ZwM_jHGOb\">Derivatives<\/a><\/span><\/h3>\n<h3 id=\"h.f8pc4q8hcu3f\" class=\"c8\"><span class=\"c11 c12\"><a class=\"c2\" href=\"https:\/\/www.google.com\/url?q=http:\/\/en.wikipedia.org\/wiki\/Derivative&amp;sa=D&amp;ust=1598403532954000&amp;usg=AOvVaw1rUFzN9wq6xDhBKe9IZdq7\">Derivative<\/a><\/span><span class=\"c11\"><a class=\"c2\" href=\"https:\/\/www.google.com\/url?q=http:\/\/en.wikipedia.org\/wiki\/Derivative&amp;sa=D&amp;ust=1598403532954000&amp;usg=AOvVaw1rUFzN9wq6xDhBKe9IZdq7\">\u00a0&#8211; Wikipedia, the free encyclopedia<\/a><\/span><\/h3>\n<p class=\"c1\"><span class=\"c10\">en.wikipedia.org\/wiki\/<\/span><span class=\"c0\">Derivative<\/span><span class=\"c9 c10\">\u200e<\/span><\/p>\n<p class=\"c1\"><span class=\"c10\">If f is a\u00a0<\/span><span class=\"c10 c12\">continuous function<\/span><span class=\"c10\">, meaning that its graph is an unbroken\u00a0<\/span><span class=\"c10 c12\">curve<\/span><span class=\"c10\">\u00a0with\u00a0<\/span><span class=\"c0\">&#8230;..<\/span><span class=\"c10\">\u00a0to a function f to give the\u00a0<\/span><span class=\"c10 c12\">first derivative<\/span><span class=\"c9 c10\">\u00a0Df.<\/span><\/p>\n<h3 id=\"h.cuor18ci1s1j\" class=\"c8\"><span class=\"c11\"><a class=\"c2\" href=\"https:\/\/www.google.com\/url?q=https:\/\/www.math.ucdavis.edu\/~kouba\/CalcOneDIRECTORY\/graphingdirectory\/&amp;sa=D&amp;ust=1598403532956000&amp;usg=AOvVaw3KS2xXo6-QkCMIdE9j90L4\">Graphing Using\u00a0<\/a><\/span><span class=\"c11 c12\"><a class=\"c2\" href=\"https:\/\/www.google.com\/url?q=https:\/\/www.math.ucdavis.edu\/~kouba\/CalcOneDIRECTORY\/graphingdirectory\/&amp;sa=D&amp;ust=1598403532957000&amp;usg=AOvVaw2-UrQa79_Nah7_rc1mmVhW\">First<\/a><\/span><span class=\"c11\"><a class=\"c2\" href=\"https:\/\/www.google.com\/url?q=https:\/\/www.math.ucdavis.edu\/~kouba\/CalcOneDIRECTORY\/graphingdirectory\/&amp;sa=D&amp;ust=1598403532957000&amp;usg=AOvVaw2-UrQa79_Nah7_rc1mmVhW\">\u00a0and Second\u00a0<\/a><\/span><span class=\"c11 c12\"><a class=\"c2\" href=\"https:\/\/www.google.com\/url?q=https:\/\/www.math.ucdavis.edu\/~kouba\/CalcOneDIRECTORY\/graphingdirectory\/&amp;sa=D&amp;ust=1598403532958000&amp;usg=AOvVaw3YXFEusJks9KiV845bNGgA\">Derivatives<\/a><\/span><\/h3>\n<p class=\"c1\"><span class=\"c9 c10\">https:\/\/www.math.ucdavis.edu\/~kouba\/&#8230;\/graphingdirectory\/\u200e<\/span><\/p>\n<p class=\"c1\"><span class=\"c10\">GRAPHING OF FUNCTIONS USING\u00a0<\/span><span class=\"c10 c12\">FIRST<\/span><span class=\"c10\">\u00a0AND SECOND\u00a0<\/span><span class=\"c10 c12\">DERIVATIVES<\/span><span class=\"c9 c10\">. The following problems illustrate detailed graphing of functions of one variable using<\/span><\/p>\n<h3 id=\"h.9rt1zjh8ts5\" class=\"c8\"><span class=\"c11 c12\"><a class=\"c2\" href=\"https:\/\/www.google.com\/url?q=http:\/\/en.wikipedia.org\/wiki\/Derivative&amp;sa=D&amp;ust=1598403532959000&amp;usg=AOvVaw2vRnazK0kIGc1dRHcGRMKW\">Derivative<\/a><\/span><span class=\"c11\"><a class=\"c2\" href=\"https:\/\/www.google.com\/url?q=http:\/\/en.wikipedia.org\/wiki\/Derivative&amp;sa=D&amp;ust=1598403532960000&amp;usg=AOvVaw0oiy8YxRTu_5h2ppiRTO_Q\">\u00a0&#8211; Wikipedia, the free encyclopedia<\/a><\/span><\/h3>\n<p class=\"c1\"><span class=\"c10\">en.wikipedia.org\/wiki\/<\/span><span class=\"c0\">Derivative<\/span><span class=\"c9 c10\">\u200e<\/span><\/p>\n<p class=\"c1\"><span class=\"c10\">The\u00a0<\/span><span class=\"c10 c12\">slope<\/span><span class=\"c10\">\u00a0of the tangent line is equal to the\u00a0<\/span><span class=\"c10 c12\">derivative<\/span><span class=\"c10\">\u00a0of the function at the marked\u00a0<\/span><span class=\"c0\">&#8230;<\/span><span class=\"c10\">\u00a0In Leibniz&#8217;s notation, such an infinitesimal change in x is denoted by\u00a0<\/span><span class=\"c10 c12\">dx<\/span><span class=\"c10\">, and the\u00a0<\/span><span class=\"c0\">&#8230;.<\/span><span class=\"c10\">\u00a0However, in 1872 Weierstrass found the\u00a0<\/span><span class=\"c10 c12\">first<\/span><span class=\"c10\">\u00a0example of a function that is\u00a0<\/span><span class=\"c9 c0\">..<\/span><\/p>\n<p class=\"c1\"><span class=\"c10\">\u00a0In Leibniz&#8217;s notation, such an infinitesimal change in x is denoted by\u00a0<\/span><span class=\"c3\">dx<\/span><\/p>\n<p class=\"c1\"><span class=\"c10\">\u00a0In Leibniz&#8217;s notation, such an infinitesimal change in x is denoted by\u00a0<\/span><span class=\"c3\">dx<\/span><\/p>\n<p class=\"c1\"><span class=\"c10\">\u00a0In Leibniz&#8217;s notation, such an infinitesimal change in x is denoted by\u00a0<\/span><span class=\"c3\">dx<\/span><\/p>\n<h1 id=\"h.ebagjef4b7a2\" class=\"c13\"><span class=\"c9 c25\">Tangent to a curve<\/span><\/h1>\n<p class=\"c1\"><img decoding=\"async\" title=\"File:Tangent to a curve.svg ... Shift+R improves the quality of this image. Shift+A improves the quality of all images on this page.\" src=\"http:\/\/region12.herbzinser07.com\/dir\/science08-ucsystem\/wp-content\/uploads\/sites\/15\/2020\/08\/img_5f45a717b92f1.png\" alt=\"\" \/><\/p>\n<p class=\"c1\"><span class=\"c10\">The<\/span><span class=\"c10\"><a class=\"c2\" href=\"https:\/\/www.google.com\/url?q=http:\/\/en.wikipedia.org\/wiki\/Graph_of_a_function&amp;sa=D&amp;ust=1598403532964000&amp;usg=AOvVaw3jEbE1PPU_iveSGYgxyh1r\">\u00a0<\/a><\/span><span class=\"c4\"><a class=\"c2\" href=\"https:\/\/www.google.com\/url?q=http:\/\/en.wikipedia.org\/wiki\/Graph_of_a_function&amp;sa=D&amp;ust=1598403532965000&amp;usg=AOvVaw2Y1Y7HLscmGUyEFzuzyIhW\">graph of a function<\/a><\/span><span class=\"c10\">, drawn in black, and a<\/span><span class=\"c10\"><a class=\"c2\" href=\"https:\/\/www.google.com\/url?q=http:\/\/en.wikipedia.org\/wiki\/Tangent_line&amp;sa=D&amp;ust=1598403532965000&amp;usg=AOvVaw272yGAETWmZmfL3UXiEaRz\">\u00a0<\/a><\/span><span class=\"c4\"><a class=\"c2\" href=\"https:\/\/www.google.com\/url?q=http:\/\/en.wikipedia.org\/wiki\/Tangent_line&amp;sa=D&amp;ust=1598403532965000&amp;usg=AOvVaw272yGAETWmZmfL3UXiEaRz\">tangent line<\/a><\/span><span class=\"c10\">\u00a0to that function, drawn in red. The<\/span><span class=\"c10\"><a class=\"c2\" href=\"https:\/\/www.google.com\/url?q=http:\/\/en.wikipedia.org\/wiki\/Slope&amp;sa=D&amp;ust=1598403532966000&amp;usg=AOvVaw1QSeACkKrUnv3mJEfn-keg\">\u00a0<\/a><\/span><span class=\"c4\"><a class=\"c2\" href=\"https:\/\/www.google.com\/url?q=http:\/\/en.wikipedia.org\/wiki\/Slope&amp;sa=D&amp;ust=1598403532966000&amp;usg=AOvVaw1QSeACkKrUnv3mJEfn-keg\">slope<\/a><\/span><span class=\"c9 c10\">\u00a0of the tangent line is equal to the derivative of the function at the marked point.<\/span><\/p>\n<p class=\"c16\"><span class=\"c10\">This gives an exact value for the slope of a straight line. If the function\u00a0<\/span><span class=\"c10 c12\">f<\/span><span class=\"c10\">\u00a0is not linear (i.e. its graph is not a straight line), however, then the change in\u00a0<\/span><span class=\"c10 c12\">y<\/span><span class=\"c10\">\u00a0divided by the change in\u00a0<\/span><span class=\"c10 c12\">x<\/span><span class=\"c10\">\u00a0varies: differentiation is a method to find an exact value for this rate of change at any given value of\u00a0<\/span><span class=\"c10 c12\">x<\/span><span class=\"c9 c10\">.<\/span><\/p>\n<p class=\"c44\"><span class=\"c9 c0\">Rate of change as a limiting value<\/span><\/p>\n<p class=\"c31\"><img decoding=\"async\" title=\"\" src=\"http:\/\/region12.herbzinser07.com\/dir\/science08-ucsystem\/wp-content\/uploads\/sites\/15\/2020\/08\/img_5f45a717ec996.png\" alt=\"http:\/\/upload.wikimedia.org\/wikipedia\/commons\/thumb\/d\/d2\/Tangent-calculus.svg\/640px-Tangent-calculus.svg.png\" \/><\/p>\n<p class=\"c31\"><span class=\"c0\">Figure 1<\/span><span class=\"c10\">. The<\/span><span class=\"c10\"><a class=\"c2\" href=\"https:\/\/www.google.com\/url?q=http:\/\/en.wikipedia.org\/wiki\/Tangent&amp;sa=D&amp;ust=1598403532969000&amp;usg=AOvVaw2hYUg40W7jNxf0oSLYzTui\">\u00a0<\/a><\/span><span class=\"c4\"><a class=\"c2\" href=\"https:\/\/www.google.com\/url?q=http:\/\/en.wikipedia.org\/wiki\/Tangent&amp;sa=D&amp;ust=1598403532969000&amp;usg=AOvVaw2hYUg40W7jNxf0oSLYzTui\">tangent<\/a><\/span><span class=\"c10\">\u00a0line at (<\/span><span class=\"c10 c12\">x<\/span><span class=\"c10\">,\u00a0<\/span><span class=\"c10 c12\">f<\/span><span class=\"c10\">(<\/span><span class=\"c10 c12\">x<\/span><span class=\"c9 c10\">))<\/span><\/p>\n<p class=\"c16\"><span class=\"c10\">The idea, illustrated by Figures 1 to 3, is to compute the rate of change as the<\/span><span class=\"c10\"><a class=\"c2\" href=\"https:\/\/www.google.com\/url?q=http:\/\/en.wikipedia.org\/wiki\/Limit_of_a_function&amp;sa=D&amp;ust=1598403532970000&amp;usg=AOvVaw2Ap47cptFdO1dxuHrHJpSX\">\u00a0<\/a><\/span><span class=\"c4\"><a class=\"c2\" href=\"https:\/\/www.google.com\/url?q=http:\/\/en.wikipedia.org\/wiki\/Limit_of_a_function&amp;sa=D&amp;ust=1598403532971000&amp;usg=AOvVaw1PF0M2pKq8DflNybmMTF96\">limiting value<\/a><\/span><span class=\"c10\">\u00a0of the<\/span><span class=\"c10\"><a class=\"c2\" href=\"https:\/\/www.google.com\/url?q=http:\/\/en.wikipedia.org\/wiki\/Difference_quotient&amp;sa=D&amp;ust=1598403532971000&amp;usg=AOvVaw0Gr9EEQ0xyn_Wq5e9FtE9t\">\u00a0<\/a><\/span><span class=\"c4\"><a class=\"c2\" href=\"https:\/\/www.google.com\/url?q=http:\/\/en.wikipedia.org\/wiki\/Difference_quotient&amp;sa=D&amp;ust=1598403532971000&amp;usg=AOvVaw0Gr9EEQ0xyn_Wq5e9FtE9t\">ratio of the differences<\/a><\/span><span class=\"c10\">\u00a0\u0394<\/span><span class=\"c10 c12\">y<\/span><span class=\"c10\">\u00a0\/ \u0394<\/span><span class=\"c10 c12\">x<\/span><span class=\"c10\">\u00a0as \u0394<\/span><span class=\"c10 c12\">x<\/span><span class=\"c9 c10\">\u00a0becomes infinitely small.<\/span><\/p>\n<p class=\"c16\"><span class=\"c10\">In<\/span><span class=\"c10\"><a class=\"c2\" href=\"https:\/\/www.google.com\/url?q=http:\/\/en.wikipedia.org\/wiki\/Leibniz%2527s_notation&amp;sa=D&amp;ust=1598403532973000&amp;usg=AOvVaw3gCG_5WGMvde97OLfhyRoM\">\u00a0<\/a><\/span><span class=\"c4\"><a class=\"c2\" href=\"https:\/\/www.google.com\/url?q=http:\/\/en.wikipedia.org\/wiki\/Leibniz%2527s_notation&amp;sa=D&amp;ust=1598403532973000&amp;usg=AOvVaw3gCG_5WGMvde97OLfhyRoM\">Leibniz&#8217;s notation<\/a><\/span><span class=\"c10\">, such an<\/span><span class=\"c10\"><a class=\"c2\" href=\"https:\/\/www.google.com\/url?q=http:\/\/en.wikipedia.org\/wiki\/Infinitesimal&amp;sa=D&amp;ust=1598403532973000&amp;usg=AOvVaw2wnjisdR-wpL9GjbAiS1-i\">\u00a0<\/a><\/span><span class=\"c4\"><a class=\"c2\" href=\"https:\/\/www.google.com\/url?q=http:\/\/en.wikipedia.org\/wiki\/Infinitesimal&amp;sa=D&amp;ust=1598403532973000&amp;usg=AOvVaw2wnjisdR-wpL9GjbAiS1-i\">infinitesimal<\/a><\/span><span class=\"c10\">\u00a0change in\u00a0<\/span><span class=\"c10 c12\">x<\/span><span class=\"c10\">\u00a0is denoted by\u00a0<\/span><span class=\"c10 c12\">dx<\/span><span class=\"c10\">, and the derivative of\u00a0<\/span><span class=\"c10 c12\">y<\/span><span class=\"c10\">\u00a0with respect to\u00a0<\/span><span class=\"c10 c12\">x<\/span><span class=\"c9 c10\">\u00a0is written<\/span><\/p>\n<p class=\"c1\"><img decoding=\"async\" title=\"\" src=\"http:\/\/region12.herbzinser07.com\/dir\/science08-ucsystem\/wp-content\/uploads\/sites\/15\/2020\/08\/img_5f45a71844f16.png\" alt=\" \\frac{dy}{dx} \\,\\!\" \/><\/p>\n<p class=\"c1\"><span class=\"c9 c0\">Using super-symmetry physics we have the dynamic parallel MODEL \u00a0to the Boston Marathon human bio-math runners \u00a0running along the mathematics geography curve.<\/span><\/p>\n<h1 id=\"h.7ecdaadwc3y9\" class=\"c13\"><span class=\"c9 c25\">Graph of sliding first derivative line \u00a0dx<\/span><\/h1>\n<p class=\"c1\"><img decoding=\"async\" title=\"File:Graph of sliding derivative line.gif ... Shift+R improves the quality of this image. Shift+A improves the quality of all images on this page.\" src=\"http:\/\/region12.herbzinser07.com\/dir\/science08-ucsystem\/wp-content\/uploads\/sites\/15\/2020\/08\/img_5f45a71961b28.gif\" alt=\"\" \/><\/p>\n<p class=\"c1\"><span class=\"c10\">At each point, the derivative of\u00a0<\/span><img decoding=\"async\" title=\"\" src=\"http:\/\/region12.herbzinser07.com\/dir\/science08-ucsystem\/wp-content\/uploads\/sites\/15\/2020\/08\/img_5f45a7199bfbd.png\" alt=\"f(x)=x\\cdot\\sin(x^2) + 1\" \/><span class=\"c10\">\u00a0is the<\/span><span class=\"c10\"><a class=\"c2\" href=\"https:\/\/www.google.com\/url?q=http:\/\/en.wikipedia.org\/wiki\/Slope&amp;sa=D&amp;ust=1598403532976000&amp;usg=AOvVaw0hVyP4cKANN9etdvHdeYk6\">\u00a0<\/a><\/span><span class=\"c4\"><a class=\"c2\" href=\"https:\/\/www.google.com\/url?q=http:\/\/en.wikipedia.org\/wiki\/Slope&amp;sa=D&amp;ust=1598403532977000&amp;usg=AOvVaw3Miml90229yf9FleozOXG6\">slope<\/a><\/span><span class=\"c10\">\u00a0of a<\/span><span class=\"c10\"><a class=\"c2\" href=\"https:\/\/www.google.com\/url?q=http:\/\/en.wikipedia.org\/wiki\/Line_%2528geometry%2529&amp;sa=D&amp;ust=1598403532977000&amp;usg=AOvVaw0no_wDtujtZ6dTmQHhrKQB\">\u00a0<\/a><\/span><span class=\"c4\"><a class=\"c2\" href=\"https:\/\/www.google.com\/url?q=http:\/\/en.wikipedia.org\/wiki\/Line_%2528geometry%2529&amp;sa=D&amp;ust=1598403532977000&amp;usg=AOvVaw0no_wDtujtZ6dTmQHhrKQB\">line<\/a><\/span><span class=\"c10\">\u00a0that is<\/span><span class=\"c10\"><a class=\"c2\" href=\"https:\/\/www.google.com\/url?q=http:\/\/en.wikipedia.org\/wiki\/Tangent&amp;sa=D&amp;ust=1598403532978000&amp;usg=AOvVaw17284kAut1hwgSOP4S4Ep5\">\u00a0<\/a><\/span><span class=\"c4\"><a class=\"c2\" href=\"https:\/\/www.google.com\/url?q=http:\/\/en.wikipedia.org\/wiki\/Tangent&amp;sa=D&amp;ust=1598403532978000&amp;usg=AOvVaw17284kAut1hwgSOP4S4Ep5\">tangent<\/a><\/span><span class=\"c10\">\u00a0to the<\/span><span class=\"c10\"><a class=\"c2\" href=\"https:\/\/www.google.com\/url?q=http:\/\/en.wikipedia.org\/wiki\/Curve&amp;sa=D&amp;ust=1598403532978000&amp;usg=AOvVaw3SL-0P48u0YyQhW8mQgGvK\">\u00a0<\/a><\/span><span class=\"c4\"><a class=\"c2\" href=\"https:\/\/www.google.com\/url?q=http:\/\/en.wikipedia.org\/wiki\/Curve&amp;sa=D&amp;ust=1598403532979000&amp;usg=AOvVaw2lh4Mcf0iV2GqI0wKBQrd7\">curve<\/a><\/span><span class=\"c10\">. The line is always tangent to the blue curve; its slope is the derivative. Note derivative is<\/span><span class=\"c10\"><a class=\"c2\" href=\"https:\/\/www.google.com\/url?q=http:\/\/en.wikipedia.org\/wiki\/Positive_number&amp;sa=D&amp;ust=1598403532979000&amp;usg=AOvVaw1_jBOarWP9Ys3fdtstc9tE\">\u00a0<\/a><\/span><span class=\"c4\"><a class=\"c2\" href=\"https:\/\/www.google.com\/url?q=http:\/\/en.wikipedia.org\/wiki\/Positive_number&amp;sa=D&amp;ust=1598403532980000&amp;usg=AOvVaw1pUH8v3y_LbpLEZ8ydHALA\">positive<\/a><\/span><span class=\"c10\">\u00a0where a green line appears,<\/span><span class=\"c10\"><a class=\"c2\" href=\"https:\/\/www.google.com\/url?q=http:\/\/en.wikipedia.org\/wiki\/Negative_number&amp;sa=D&amp;ust=1598403532980000&amp;usg=AOvVaw0AAhm3m_-v1-irSk6RXrde\">\u00a0<\/a><\/span><span class=\"c4\"><a class=\"c2\" href=\"https:\/\/www.google.com\/url?q=http:\/\/en.wikipedia.org\/wiki\/Negative_number&amp;sa=D&amp;ust=1598403532980000&amp;usg=AOvVaw0AAhm3m_-v1-irSk6RXrde\">negative<\/a><\/span><span class=\"c10\">\u00a0where a red line appears, and<\/span><span class=\"c10\"><a class=\"c2\" href=\"https:\/\/www.google.com\/url?q=http:\/\/en.wikipedia.org\/wiki\/Zero_%2528number%2529&amp;sa=D&amp;ust=1598403532981000&amp;usg=AOvVaw1wBixz472fkse2h_L1c6-m\">\u00a0<\/a><\/span><span class=\"c4\"><a class=\"c2\" href=\"https:\/\/www.google.com\/url?q=http:\/\/en.wikipedia.org\/wiki\/Zero_%2528number%2529&amp;sa=D&amp;ust=1598403532981000&amp;usg=AOvVaw1wBixz472fkse2h_L1c6-m\">zero<\/a><\/span><span class=\"c9 c10\">\u00a0where a black line appears.<\/span><\/p>\n<p class=\"c1\"><span class=\"c9 c10\">The Isaac Asimov mathematical \u00a0social influence DEMO signaling EVENT ..<\/span><\/p>\n<h1 id=\"h.84i95d4uwm32\" class=\"c13\"><span class=\"c9 c25\">Boston Marathon bombings and the FOUNDATION Science WARS<\/span><\/h1>\n<h3 id=\"h.kpaezgfb26xg\" class=\"c8\"><span class=\"c11 c12\"><a class=\"c2\" href=\"https:\/\/www.google.com\/url?q=http:\/\/www.physicstoday.org\/daily_edition\/science_and_the_media\/1.2880923&amp;sa=D&amp;ust=1598403532983000&amp;usg=AOvVaw3_19KOa7VQnF59NlQf6kqv\">New York Times<\/a><\/span><span class=\"c11\"><a class=\"c2\" href=\"https:\/\/www.google.com\/url?q=http:\/\/www.physicstoday.org\/daily_edition\/science_and_the_media\/1.2880923&amp;sa=D&amp;ust=1598403532983000&amp;usg=AOvVaw3_19KOa7VQnF59NlQf6kqv\">\u00a0columnist Paul Krugman tries to &#8230; &#8211;\u00a0<\/a><\/span><span class=\"c11 c12\"><a class=\"c2\" href=\"https:\/\/www.google.com\/url?q=http:\/\/www.physicstoday.org\/daily_edition\/science_and_the_media\/1.2880923&amp;sa=D&amp;ust=1598403532983000&amp;usg=AOvVaw3_19KOa7VQnF59NlQf6kqv\">Physics<\/a><\/span><span class=\"c11\"><a class=\"c2\" href=\"https:\/\/www.google.com\/url?q=http:\/\/www.physicstoday.org\/daily_edition\/science_and_the_media\/1.2880923&amp;sa=D&amp;ust=1598403532984000&amp;usg=AOvVaw2mbh8D-c7-Jw4OlZnDtVCw\">\u00a0Today<\/a><\/span><\/h3>\n<p class=\"c1\"><span class=\"c10\">www.<\/span><span class=\"c0\">physics<\/span><span class=\"c10\">today.org\/daily_edition\/<\/span><span class=\"c0\">science<\/span><span class=\"c9 c10\">_and_the&#8230;\/1.2880923\u200e<\/span><\/p>\n<p class=\"c1\"><span class=\"c10\">Nov 26, 2012 &#8211; Rubio&#8217;s answer caused conservative\u00a0<\/span><span class=\"c10 c12\">New York Times<\/span><span class=\"c10\">\u00a0columnist Ross\u00a0<\/span><span class=\"c0\">&#8230;.<\/span><span class=\"c10\">\u00a0In fact, why did\u00a0<\/span><span class=\"c10 c12\">Physics<\/span><span class=\"c10\">\u00a0Today refer to this as the &#8220;<\/span><span class=\"c10 c12\">Science Wars<\/span><span class=\"c10\">&#8220;,\u00a0<\/span><span class=\"c9 c0\">..<\/span><\/p>\n<h3 id=\"h.tbs0zcf4zgeo\" class=\"c8\"><span class=\"c11\"><a class=\"c2\" href=\"https:\/\/www.google.com\/url?q=http:\/\/www.economist.com\/node\/109188&amp;sa=D&amp;ust=1598403532985000&amp;usg=AOvVaw1BB1dvFjpso9RFzApwWN84\">You can&#8217;t follow the\u00a0<\/a><\/span><span class=\"c11 c12\"><a class=\"c2\" href=\"https:\/\/www.google.com\/url?q=http:\/\/www.economist.com\/node\/109188&amp;sa=D&amp;ust=1598403532985000&amp;usg=AOvVaw1BB1dvFjpso9RFzApwWN84\">science wars<\/a><\/span><span class=\"c11\"><a class=\"c2\" href=\"https:\/\/www.google.com\/url?q=http:\/\/www.economist.com\/node\/109188&amp;sa=D&amp;ust=1598403532986000&amp;usg=AOvVaw0aZQL_KqQQbOTvZg43zFOL\">\u00a0without a battle map &#8211; The Economist<\/a><\/span><\/h3>\n<p class=\"c1\"><span class=\"c9 c10\">www.economist.com\/node\/109188\u200e<\/span><\/p>\n<p class=\"c1\"><span class=\"c10\">As the name suggests, the &#8220;<\/span><span class=\"c10 c12\">science wars<\/span><span class=\"c10\">\u201d belong mostly to the second sort.\u00a0<\/span><span class=\"c0\">&#8230;<\/span><span class=\"c10\">\u00a0the publication in May 1996 of an article by Alan Sokal, a\u00a0<\/span><span class=\"c10 c12\">physicist<\/span><span class=\"c10\">\u00a0at\u00a0<\/span><span class=\"c10 c12\">New York<\/span><span class=\"c10\">\u00a0University,\u00a0<\/span><span class=\"c0\">&#8230;<\/span><span class=\"c10\">\u00a0Listening to Messrs Sokal and Bricmont, you hear at\u00a0<\/span><span class=\"c10 c12\">times<\/span><span class=\"c10\">\u00a0the sound of\u00a0<\/span><span class=\"c9 c0\">&#8230;<\/span><\/p>\n<h3 id=\"h.kcwpuvwevfo\" class=\"c8 c24\"><\/h3>\n<h1 id=\"h.dxp5pcmg0qzg\" class=\"c13\"><span class=\"c9 c25\">Boston Marathon<\/span><\/h1>\n<h1 id=\"h.b0zfbusgpzlo\" class=\"c13\"><span class=\"c9 c25\">Boston Ma&#8230;th<\/span><\/h1>\n<h1 id=\"h.div12r8oonw2\" class=\"c13\"><span class=\"c9 c25\">Boston Math \u00a0with Isaac Asimov &#8211;&gt; living mathematics expressions in society<\/span><\/h1>\n<p class=\"c1\"><span class=\"c10\">During the<\/span><span class=\"c10\"><a class=\"c2\" href=\"https:\/\/www.google.com\/url?q=http:\/\/en.wikipedia.org\/wiki\/2013_Boston_Marathon&amp;sa=D&amp;ust=1598403532990000&amp;usg=AOvVaw1FjQYO4NBMbDAP9jEO1vUv\">\u00a0<\/a><\/span><span class=\"c4\"><a class=\"c2\" href=\"https:\/\/www.google.com\/url?q=http:\/\/en.wikipedia.org\/wiki\/2013_Boston_Marathon&amp;sa=D&amp;ust=1598403532990000&amp;usg=AOvVaw1FjQYO4NBMbDAP9jEO1vUv\">Boston Marathon<\/a><\/span><span class=\"c10\">\u00a0on April 15, 2013, two<\/span><span class=\"c10\"><a class=\"c2\" href=\"https:\/\/www.google.com\/url?q=http:\/\/en.wikipedia.org\/wiki\/Pressure_cooker_bombs&amp;sa=D&amp;ust=1598403532991000&amp;usg=AOvVaw2gdRFA8sMKIxeSdrhoMFNl\">\u00a0<\/a><\/span><span class=\"c4\"><a class=\"c2\" href=\"https:\/\/www.google.com\/url?q=http:\/\/en.wikipedia.org\/wiki\/Pressure_cooker_bombs&amp;sa=D&amp;ust=1598403532991000&amp;usg=AOvVaw2gdRFA8sMKIxeSdrhoMFNl\">pressure cooker bombs<\/a><\/span><span class=\"c10\">\u00a0exploded at 2:49 pm<\/span><span class=\"c10\"><a class=\"c2\" href=\"https:\/\/www.google.com\/url?q=http:\/\/en.wikipedia.org\/wiki\/Eastern_Time_Zone&amp;sa=D&amp;ust=1598403532992000&amp;usg=AOvVaw1Us1rExLPALK7k6z4ScC53\">\u00a0<\/a><\/span><span class=\"c4\"><a class=\"c2\" href=\"https:\/\/www.google.com\/url?q=http:\/\/en.wikipedia.org\/wiki\/Eastern_Time_Zone&amp;sa=D&amp;ust=1598403532992000&amp;usg=AOvVaw1Us1rExLPALK7k6z4ScC53\">EDT<\/a><\/span><span class=\"c10\">\u00a0(18:49<\/span><span class=\"c10\"><a class=\"c2\" href=\"https:\/\/www.google.com\/url?q=http:\/\/en.wikipedia.org\/wiki\/Coordinated_Universal_Time&amp;sa=D&amp;ust=1598403532993000&amp;usg=AOvVaw3DGFohl0i0gzNtZLUVHwqU\">\u00a0<\/a><\/span><span class=\"c4\"><a class=\"c2\" href=\"https:\/\/www.google.com\/url?q=http:\/\/en.wikipedia.org\/wiki\/Coordinated_Universal_Time&amp;sa=D&amp;ust=1598403532993000&amp;usg=AOvVaw3DGFohl0i0gzNtZLUVHwqU\">UTC<\/a><\/span><span class=\"c10\">), killing 3 people and injuring an estimated 264 others.<\/span><span class=\"c4 c26\"><a class=\"c2\" href=\"https:\/\/www.google.com\/url?q=http:\/\/en.wikipedia.org\/wiki\/Boston_Marathon_bombings%23cite_note-globe-number-injured-3&amp;sa=D&amp;ust=1598403532994000&amp;usg=AOvVaw3dyCgpYh3L0VoFV-66yMrK\">[3]<\/a><\/span><span class=\"c10\">\u00a0The bombs exploded about 13 seconds and 210 yards (190 m) apart, near the finish line on<\/span><span class=\"c10\"><a class=\"c2\" href=\"https:\/\/www.google.com\/url?q=http:\/\/en.wikipedia.org\/wiki\/Boylston_Street&amp;sa=D&amp;ust=1598403532994000&amp;usg=AOvVaw2FrLz8K_lnyadZT8Rk2G_a\">\u00a0<\/a><\/span><span class=\"c4\"><a class=\"c2\" href=\"https:\/\/www.google.com\/url?q=http:\/\/en.wikipedia.org\/wiki\/Boylston_Street&amp;sa=D&amp;ust=1598403532994000&amp;usg=AOvVaw2FrLz8K_lnyadZT8Rk2G_a\">Boylston Street<\/a><\/span><span class=\"c10\">.<\/span><span class=\"c4 c26\"><a class=\"c2\" href=\"https:\/\/www.google.com\/url?q=http:\/\/en.wikipedia.org\/wiki\/Boston_Marathon_bombings%23cite_note-NYDN-5.2F15-2&amp;sa=D&amp;ust=1598403532995000&amp;usg=AOvVaw2ruWX9ELvSsFvLGZb2AkFO\">[2]<\/a><\/span><span class=\"c4 c26\"><a class=\"c2\" href=\"https:\/\/www.google.com\/url?q=http:\/\/en.wikipedia.org\/wiki\/Boston_Marathon_bombings%23cite_note-cnn-what-we-know-8&amp;sa=D&amp;ust=1598403532995000&amp;usg=AOvVaw16lsMkvzr7M5vf0IiqiqGy\">[8]<\/a><\/span><span class=\"c10\">\u00a0The<\/span><span class=\"c10\"><a class=\"c2\" href=\"https:\/\/www.google.com\/url?q=http:\/\/en.wikipedia.org\/wiki\/Federal_Bureau_of_Investigation&amp;sa=D&amp;ust=1598403532996000&amp;usg=AOvVaw2Tf7a74NvuM5Sh23aUjyFe\">\u00a0<\/a><\/span><span class=\"c4\"><a class=\"c2\" href=\"https:\/\/www.google.com\/url?q=http:\/\/en.wikipedia.org\/wiki\/Federal_Bureau_of_Investigation&amp;sa=D&amp;ust=1598403532996000&amp;usg=AOvVaw2Tf7a74NvuM5Sh23aUjyFe\">Federal Bureau of Investigation<\/a><\/span><span class=\"c10\">\u00a0(FBI) took over the investigation, and on April 18, released photographs and surveillance video of two suspects.<\/span><span class=\"c4 c26\"><a class=\"c2\" href=\"https:\/\/www.google.com\/url?q=http:\/\/en.wikipedia.org\/wiki\/Boston_Marathon_bombings%23cite_note-Clark_Estes-9&amp;sa=D&amp;ust=1598403532997000&amp;usg=AOvVaw1xR42kdBQAWmO2hY1gHeZ6\">[9]<\/a><\/span><span class=\"c4 c26\"><a class=\"c2\" href=\"https:\/\/www.google.com\/url?q=http:\/\/en.wikipedia.org\/wiki\/Boston_Marathon_bombings%23cite_note-AutoLC-4-10&amp;sa=D&amp;ust=1598403532997000&amp;usg=AOvVaw2mjDKQ3T4QrCeGDF5Ro8-s\">[10]<\/a><\/span><span class=\"c4 c26\"><a class=\"c2\" href=\"https:\/\/www.google.com\/url?q=http:\/\/en.wikipedia.org\/wiki\/Boston_Marathon_bombings%23cite_note-AutoLC-5-11&amp;sa=D&amp;ust=1598403532997000&amp;usg=AOvVaw30s7eesSwCZ4bbK5ugZAdy\">[11]<\/a><\/span><span class=\"c10\">\u00a0The suspects were identified later that day as<\/span><span class=\"c10\"><a class=\"c2\" href=\"https:\/\/www.google.com\/url?q=http:\/\/en.wikipedia.org\/wiki\/Dzhokhar_and_Tamerlan_Tsarnaev&amp;sa=D&amp;ust=1598403532998000&amp;usg=AOvVaw3UsGyTSveJnLlLH3uIjsF4\">\u00a0<\/a><\/span><span class=\"c4\"><a class=\"c2\" href=\"https:\/\/www.google.com\/url?q=http:\/\/en.wikipedia.org\/wiki\/Dzhokhar_and_Tamerlan_Tsarnaev&amp;sa=D&amp;ust=1598403532998000&amp;usg=AOvVaw3UsGyTSveJnLlLH3uIjsF4\">Dzhokhar and Tamerlan Tsarnaev<\/a><\/span><span class=\"c9 c10\">.<\/span><\/p>\n<p class=\"c1\"><span class=\"c9 c10\">Now geography city of Boston has 3-dimensional \u00a0office building \u00a0that exist in EARTHLY mathematical-physics space &#8230;.. known to high school algebra and plane geometry students as the \u00a0math SYMBOL \/ graph coordinates X, Y, Z.<\/span><\/p>\n<p class=\"c1\"><span class=\"c9 c10\">On a \u00a02-dimensional sheet of cellulose paper in high school class &#8230;we see &#8230;<\/span><\/p>\n<p class=\"c1\"><img decoding=\"async\" title=\"\" src=\"http:\/\/region12.herbzinser07.com\/dir\/science08-ucsystem\/wp-content\/uploads\/sites\/15\/2020\/08\/img_5f45a719bdc70.png\" alt=\"http:\/\/1.bp.blogspot.com\/-b7otHbFkv0E\/Tz1CLxwAq6I\/AAAAAAAAAOw\/d0CltwWFdnY\/s1600\/250px-Cartesian-coordinate-system.svg.png\" \/><\/p>\n<p class=\"c1\"><span class=\"c9 c10\">In high school physics and basic college science courses we become more acquainted with &#8230;. the 3-dimensions of \u00a0office buildings and the 3-D surface REALITY on geography EARTH.<\/span><\/p>\n<p class=\"c1\"><span class=\"c9 c10\">Below, is an image of the \u00a0contents that are required to be \u00a0inside your adult brain SYMBOL maps \u00a0&#8230; as stated by S.I. Hayakawa in &#8221; Language in Thought and Action&#8221;.<\/span><\/p>\n<p class=\"c1\"><img decoding=\"async\" title=\"\" src=\"http:\/\/region12.herbzinser07.com\/dir\/science08-ucsystem\/wp-content\/uploads\/sites\/15\/2020\/08\/img_5f45a71a0f44a.gif\" alt=\"http:\/\/www.shodor.org\/chemviz\/zmatrices\/students\/formald3.gif\" \/><\/p>\n<p class=\"c16\"><span class=\"c9 c10\">The Proposal for \u00a0Boston designed by \u00a0mathematical-physics VIA \u00a0 human expression devices.<\/span><\/p>\n<p class=\"c16\"><img decoding=\"async\" title=\"\" src=\"http:\/\/region12.herbzinser07.com\/dir\/science08-ucsystem\/wp-content\/uploads\/sites\/15\/2020\/08\/img_5f45a71a470d5.gif\" alt=\"\" \/><\/p>\n<p class=\"c16\"><span class=\"c9 c10\">Let look at the \u00a0BOSTON math event \u00a0&#8230; in concept terms &#8230;.. in \u00a0 the Boston region comprised \u00a0of \u00a0the multi-faceted dimensions and formats within \u00a0Sartre existentialism.<\/span><\/p>\n<p class=\"c16\"><span class=\"c9 c10\">We are interested in the 1st derivatives of continuous math space (and \u00a0math economic \u00a0 transaction activities with that math space &#8230;such as financial derivatives and their citizen\/government \u00a0approved ERROR violations of Nature&#8217;s math accounting \u00a0space)<\/span><\/p>\n<p class=\"c16\"><span class=\"c9 c28 c36\">The 1st derivatives of continuous math space<\/span><\/p>\n<p class=\"c16\"><span class=\"c9 c28 c36\">or<\/span><\/p>\n<p class=\"c16\"><span class=\"c9 c28 c36\">\u00a0the related concept of triple \u00a0integral<\/span><\/p>\n<p class=\"c16\"><span class=\"c9 c47 c39 c46\">\u00a0using \u00a0dx,dy,dz<\/span><\/p>\n<p class=\"c16\"><span class=\"c9 c10\">\u00a0<\/span><\/p>\n<h3 id=\"h.ovqy0rlvd6gg\" class=\"c8\"><span class=\"c11 c12\"><a class=\"c2\" href=\"https:\/\/www.google.com\/url?q=http:\/\/www.merriam-webster.com\/dictionary\/symbolism&amp;sa=D&amp;ust=1598403533005000&amp;usg=AOvVaw1hUS-qqVxLvCaplHFQsfZU\">Symbolism<\/a><\/span><span class=\"c11\"><a class=\"c2\" href=\"https:\/\/www.google.com\/url?q=http:\/\/www.merriam-webster.com\/dictionary\/symbolism&amp;sa=D&amp;ust=1598403533006000&amp;usg=AOvVaw2f09tWIjrkVNt4aE1_53l6\">\u00a0&#8211; Merriam-Webster Online<\/a><\/span><\/h3>\n<p class=\"c1\"><span class=\"c10\">www.merriam-webster.com\/dictionary\/<\/span><span class=\"c0\">symbolism<\/span><span class=\"c9 c10\">\u200e<\/span><\/p>\n<p class=\"c1\"><span class=\"c0\">the art or practice of using symbols especially by investing things with a\u00a0<\/span><span class=\"c0 c12\">symbolic<\/span><span class=\"c9 c0\">\u00a0meaning or<\/span><\/p>\n<p class=\"c1\"><span class=\"c9 c0\">by expressing the invisible or intangible by means of visible<\/span><\/p>\n<p class=\"c16\"><span class=\"c9 c10\">Math concepts for dx,dy,dz \u00a0&#8230; in one of the concept formats \u00a0.. derivative or integral<\/span><\/p>\n<h3 id=\"h.kosnzftan61g\" class=\"c8\"><span class=\"c11\"><a class=\"c2\" href=\"https:\/\/www.google.com\/url?q=http:\/\/www.math.byu.edu\/~math302\/content\/learningmod\/coordinates\/rectangular\/rectzyxexample.html&amp;sa=D&amp;ust=1598403533008000&amp;usg=AOvVaw3-TJo9UFdLNttGw9AzaJwv\">Setting up an\u00a0<\/a><\/span><span class=\"c11 c12\"><a class=\"c2\" href=\"https:\/\/www.google.com\/url?q=http:\/\/www.math.byu.edu\/~math302\/content\/learningmod\/coordinates\/rectangular\/rectzyxexample.html&amp;sa=D&amp;ust=1598403533008000&amp;usg=AOvVaw3-TJo9UFdLNttGw9AzaJwv\">Integral<\/a><\/span><span class=\"c11\"><a class=\"c2\" href=\"https:\/\/www.google.com\/url?q=http:\/\/www.math.byu.edu\/~math302\/content\/learningmod\/coordinates\/rectangular\/rectzyxexample.html&amp;sa=D&amp;ust=1598403533009000&amp;usg=AOvVaw2DUbAcCbsojTElMGEoKaBl\">\u00a0Over a Solid with Order of Integration\u00a0<\/a><\/span><span class=\"c11 c12\"><a class=\"c2\" href=\"https:\/\/www.google.com\/url?q=http:\/\/www.math.byu.edu\/~math302\/content\/learningmod\/coordinates\/rectangular\/rectzyxexample.html&amp;sa=D&amp;ust=1598403533009000&amp;usg=AOvVaw2DUbAcCbsojTElMGEoKaBl\">dz dy dx<\/a><\/span><\/h3>\n<p class=\"c1\"><span class=\"c9 c10\">www.math.byu.edu\/~math302\/content\/&#8230;\/rectzyxexample.html\u200e<\/span><\/p>\n<p class=\"c1\"><span class=\"c10\">Setting up an Integral Over a Solid with Order of Integration\u00a0<\/span><span class=\"c10 c12\">dz dy dx<\/span><span class=\"c10\">. Example. Let T be the solid\u00a0<\/span><span class=\"c0\">&#8230;<\/span><span class=\"c10\">\u00a0These will be the limits of integration on the\u00a0<\/span><span class=\"c10 c12\">first integral<\/span><span class=\"c9 c10\">\u00a0sign<\/span><\/p>\n<h3 id=\"h.qq1xzq5k0n8t\" class=\"c8\"><span class=\"c11\"><a class=\"c2\" href=\"https:\/\/www.google.com\/url?q=http:\/\/www2.econ.iastate.edu\/classes\/econ301\/qiao\/math%2520review%2520%2528II%2529.pdf&amp;sa=D&amp;ust=1598403533012000&amp;usg=AOvVaw15qpQdu1wbpgovRGe0XDc2\">\u00a0dy\u00a0<\/a><\/span><span class=\"c11 c12\"><a class=\"c2\" href=\"https:\/\/www.google.com\/url?q=http:\/\/www2.econ.iastate.edu\/classes\/econ301\/qiao\/math%2520review%2520%2528II%2529.pdf&amp;sa=D&amp;ust=1598403533012000&amp;usg=AOvVaw15qpQdu1wbpgovRGe0XDc2\">dy dz dx<\/a><\/span><span class=\"c11\"><a class=\"c2\" href=\"https:\/\/www.google.com\/url?q=http:\/\/www2.econ.iastate.edu\/classes\/econ301\/qiao\/math%2520review%2520%2528II%2529.pdf&amp;sa=D&amp;ust=1598403533013000&amp;usg=AOvVaw3k873QwH51eeCM2pg4rA9I\">\u00a0dz\u00a0<\/a><\/span><span class=\"c11 c12\"><a class=\"c2\" href=\"https:\/\/www.google.com\/url?q=http:\/\/www2.econ.iastate.edu\/classes\/econ301\/qiao\/math%2520review%2520%2528II%2529.pdf&amp;sa=D&amp;ust=1598403533013000&amp;usg=AOvVaw3k873QwH51eeCM2pg4rA9I\">dx<\/a><\/span><\/h3>\n<p class=\"c1\"><span class=\"c9 c10\">www2.econ.iastate.edu\/classes\/econ301\/qiao\/math%20review%20(II).pdf\u200e<\/span><\/p>\n<p class=\"c1\"><span class=\"c10\">function of only one variable x, the partial\u00a0<\/span><span class=\"c10 c12\">derivative<\/span><span class=\"c10\">\u00a0and the total\u00a0<\/span><span class=\"c10 c12\">derivative<\/span><span class=\"c10\">\u00a0(i.e.\u00a0<\/span><span class=\"c10 c12\">dy<\/span><span class=\"c10\">\/<\/span><span class=\"c10 c12\">dx<\/span><span class=\"c9 c10\">) are the same. A few common examples follow : FUNCTION (y).<\/span><\/p>\n<p class=\"c16\"><span class=\"c9 c10\">Let&#8217;s then look at the Boston tragedy for the math components oft eh EVENT covered by the Theory of Everything in physics, \u00a0bio-physics and geo-physics.<\/span><\/p>\n<p class=\"c16\"><span class=\"c6\">1)<\/span><span class=\"c9 c10\">\u00a0Let the SYMBOL MACHINE function F(x) and the derivative dx .. \u00a0be represented the continuous street route \u00a0of the race<\/span><\/p>\n<p class=\"c16\"><img decoding=\"async\" title=\"\" src=\"http:\/\/region12.herbzinser07.com\/dir\/science08-ucsystem\/wp-content\/uploads\/sites\/15\/2020\/08\/img_5f45a71a8b4d5.jpg\" alt=\"http:\/\/media.cmgdigital.com\/shared\/lt\/lt_cache\/thumbnail\/610\/img\/photos\/2013\/04\/15\/a7\/9f\/041714BostonMarathonRouteCO.jpg\" \/><\/p>\n<p class=\"c16\"><span class=\"c47 c46\">2)<\/span><span class=\"c10\">\u00a0 the bombing tragedy produced the 2nd math SYMBOL MACHINE signal\u00a0<\/span><span class=\"c9 c23 c38\">&#8211;&gt; dy<\/span><\/p>\n<h3 id=\"h.hn2og0fzmclv\" class=\"c8\"><span class=\"c20\"><a class=\"c2\" href=\"https:\/\/www.google.com\/url?q=https:\/\/www.google.com\/search?q%3Dboston%2Bmarathon%2Bbloody%2Bbombing%26biw%3D1920%26bih%3D977%26source%3Duniv%26tbm%3Dnws%26tbo%3Du%26sa%3DX%26ei%3DoZwjUr2OEOqP2gWm6YGwCg%26ved%3D0CCkQqAI&amp;sa=D&amp;ust=1598403533017000&amp;usg=AOvVaw13TtJOyke1KFsX6iB0LsP1\">News for\u00a0<\/a><\/span><span class=\"c20 c12\"><a class=\"c2\" href=\"https:\/\/www.google.com\/url?q=https:\/\/www.google.com\/search?q%3Dboston%2Bmarathon%2Bbloody%2Bbombing%26biw%3D1920%26bih%3D977%26source%3Duniv%26tbm%3Dnws%26tbo%3Du%26sa%3DX%26ei%3DoZwjUr2OEOqP2gWm6YGwCg%26ved%3D0CCkQqAI&amp;sa=D&amp;ust=1598403533018000&amp;usg=AOvVaw0M-IxcKlC4BFatogRtSTLX\">boston marathon bloody bombing<\/a><\/span><\/h3>\n<p class=\"c16\"><span class=\"c9 c10\">\u00a0<\/span><\/p>\n<h3 id=\"h.jtwimqw56tv6\" class=\"c8\"><span class=\"c20 c12\"><a class=\"c2\" href=\"https:\/\/www.google.com\/url?q=https:\/\/www.google.com\/search?q%3Dboston%2Bmarathon%2Bbloody%2Bbombing%26biw%3D1920%26bih%3D977%26source%3Duniv%26tbm%3Dnws%26tbo%3Du%26sa%3DX%26ei%3DoZwjUr2OEOqP2gWm6YGwCg%26ved%3D0CCkQqAI&amp;sa=D&amp;ust=1598403533019000&amp;usg=AOvVaw3aEi8X-YT1BtqLJTGma9TU\">bloody<\/a><\/span><\/h3>\n<h3 id=\"h.ndvvo1450anv\" class=\"c8\"><span class=\"c20 c12\"><a class=\"c2\" href=\"https:\/\/www.google.com\/url?q=https:\/\/www.google.com\/search?q%3Dboston%2Bmarathon%2Bbloody%2Bbombing%26biw%3D1920%26bih%3D977%26source%3Duniv%26tbm%3Dnws%26tbo%3Du%26sa%3DX%26ei%3DoZwjUr2OEOqP2gWm6YGwCg%26ved%3D0CCkQqAI&amp;sa=D&amp;ust=1598403533020000&amp;usg=AOvVaw02_3hZEuLK3vigoL4q31iI\">bloody<\/a><\/span><\/h3>\n<h3 id=\"h.zgcd5mhia3p2\" class=\"c8\"><span class=\"c20 c12\"><a class=\"c2\" href=\"https:\/\/www.google.com\/url?q=https:\/\/www.google.com\/search?q%3Dboston%2Bmarathon%2Bbloody%2Bbombing%26biw%3D1920%26bih%3D977%26source%3Duniv%26tbm%3Dnws%26tbo%3Du%26sa%3DX%26ei%3DoZwjUr2OEOqP2gWm6YGwCg%26ved%3D0CCkQqAI&amp;sa=D&amp;ust=1598403533020000&amp;usg=AOvVaw02_3hZEuLK3vigoL4q31iI\">bloo<\/a><\/span><span class=\"c20 c12 c32\"><a class=\"c2\" href=\"https:\/\/www.google.com\/url?q=https:\/\/www.google.com\/search?q%3Dboston%2Bmarathon%2Bbloody%2Bbombing%26biw%3D1920%26bih%3D977%26source%3Duniv%26tbm%3Dnws%26tbo%3Du%26sa%3DX%26ei%3DoZwjUr2OEOqP2gWm6YGwCg%26ved%3D0CCkQqAI&amp;sa=D&amp;ust=1598403533021000&amp;usg=AOvVaw3P1MOFbf8CiAQBW9qrFNCa\">dy<\/a><\/span><\/h3>\n<h3 id=\"h.7jc4tjmn1xkw\" class=\"c8 c24\"><\/h3>\n<h3 id=\"h.5c4qxvrpp90u\" class=\"c8\"><span class=\"c20 c12\"><a class=\"c2\" href=\"https:\/\/www.google.com\/url?q=http:\/\/www.huffingtonpost.com\/2013\/04\/21\/boston-marathon-bombing-nurses_n_3128617.html&amp;sa=D&amp;ust=1598403533022000&amp;usg=AOvVaw3IFGiOhswGSGjUVECP4kNu\">Boston Marathon Bombing<\/a><\/span><span class=\"c20\"><a class=\"c2\" href=\"https:\/\/www.google.com\/url?q=http:\/\/www.huffingtonpost.com\/2013\/04\/21\/boston-marathon-bombing-nurses_n_3128617.html&amp;sa=D&amp;ust=1598403533022000&amp;usg=AOvVaw3IFGiOhswGSGjUVECP4kNu\">: Nurses Tell Of\u00a0<\/a><\/span><span class=\"c12 c20\"><a class=\"c2\" href=\"https:\/\/www.google.com\/url?q=http:\/\/www.huffingtonpost.com\/2013\/04\/21\/boston-marathon-bombing-nurses_n_3128617.html&amp;sa=D&amp;ust=1598403533022000&amp;usg=AOvVaw3IFGiOhswGSGjUVECP4kNu\">Bloody<\/a><\/span><span class=\"c20\"><a class=\"c2\" href=\"https:\/\/www.google.com\/url?q=http:\/\/www.huffingtonpost.com\/2013\/04\/21\/boston-marathon-bombing-nurses_n_3128617.html&amp;sa=D&amp;ust=1598403533023000&amp;usg=AOvVaw1_aQkSjaMa2x220p05LvLg\">\u00a0Aftermath<\/a><\/span><\/h3>\n<p class=\"c1\"><span class=\"c10\">www.huffingtonpost.com\/&#8230;\/<\/span><span class=\"c0\">boston<\/span><span class=\"c10\">&#8211;<\/span><span class=\"c0\">marathon<\/span><span class=\"c10\">&#8211;<\/span><span class=\"c0\">bombing<\/span><span class=\"c9 c10\">-nurses_n_3128&#8230;\u200e<\/span><\/p>\n<p class=\"c1\"><span class=\"c10\">Apr 21, 2013 &#8211;\u00a0<\/span><span class=\"c10 c12\">BOSTON<\/span><span class=\"c10\">\u00a0\u2014 The screams and cries of\u00a0<\/span><span class=\"c10 c12\">bloody marathon bombing<\/span><span class=\"c10\">\u00a0victims still haunt the nurses who treated them one week ago. They did their\u00a0<\/span><span class=\"c9 c0\">.<\/span><\/p>\n<h3 id=\"h.af4tiykq8n8s\" class=\"c8\"><span class=\"c11\"><a class=\"c2\" href=\"https:\/\/www.google.com\/url?q=http:\/\/www.huffingtonpost.com\/2013\/04\/21\/boston-marathon-bombing-nurses_n_3128617.html&amp;sa=D&amp;ust=1598403533025000&amp;usg=AOvVaw2xQrp6v2O9No8FxuEJeERl\">\u00a0<\/a><\/span><span class=\"c11 c12\"><a class=\"c2\" href=\"https:\/\/www.google.com\/url?q=http:\/\/www.huffingtonpost.com\/2013\/04\/21\/boston-marathon-bombing-nurses_n_3128617.html&amp;sa=D&amp;ust=1598403533026000&amp;usg=AOvVaw1RXlJhISZCmRd909WejaAT\">Bloody<\/a><\/span><span class=\"c11\"><a class=\"c2\" href=\"https:\/\/www.google.com\/url?q=http:\/\/www.huffingtonpost.com\/2013\/04\/21\/boston-marathon-bombing-nurses_n_3128617.html&amp;sa=D&amp;ust=1598403533027000&amp;usg=AOvVaw2QQP5IMze7Eyw-ZTSTFPGr\">\u00a0Aftermath<\/a><\/span><\/h3>\n<h3 id=\"h.r883wqc8kxq6\" class=\"c8\"><span class=\"c11\"><a class=\"c2\" href=\"https:\/\/www.google.com\/url?q=http:\/\/www.huffingtonpost.com\/2013\/04\/21\/boston-marathon-bombing-nurses_n_3128617.html&amp;sa=D&amp;ust=1598403533027000&amp;usg=AOvVaw2QQP5IMze7Eyw-ZTSTFPGr\">\u00a0<\/a><\/span><span class=\"c11 c12\"><a class=\"c2\" href=\"https:\/\/www.google.com\/url?q=http:\/\/www.huffingtonpost.com\/2013\/04\/21\/boston-marathon-bombing-nurses_n_3128617.html&amp;sa=D&amp;ust=1598403533028000&amp;usg=AOvVaw2EW1bu6p_9Ny_HUIPyiyVe\">Bloody<\/a><\/span><span class=\"c11\"><a class=\"c2\" href=\"https:\/\/www.google.com\/url?q=http:\/\/www.huffingtonpost.com\/2013\/04\/21\/boston-marathon-bombing-nurses_n_3128617.html&amp;sa=D&amp;ust=1598403533028000&amp;usg=AOvVaw2EW1bu6p_9Ny_HUIPyiyVe\">\u00a0Aftermath<\/a><\/span><\/h3>\n<h3 id=\"h.tnswihwvak7u\" class=\"c8\"><span class=\"c11\"><a class=\"c2\" href=\"https:\/\/www.google.com\/url?q=http:\/\/www.huffingtonpost.com\/2013\/04\/21\/boston-marathon-bombing-nurses_n_3128617.html&amp;sa=D&amp;ust=1598403533029000&amp;usg=AOvVaw3Q6-acDCO_-6Y9DMgTo7PV\">\u00a0<\/a><\/span><span class=\"c11 c12\"><a class=\"c2\" href=\"https:\/\/www.google.com\/url?q=http:\/\/www.huffingtonpost.com\/2013\/04\/21\/boston-marathon-bombing-nurses_n_3128617.html&amp;sa=D&amp;ust=1598403533030000&amp;usg=AOvVaw1YcY2KW2Ng7f4fLMdwBwoS\">Bloo<\/a><\/span><span class=\"c20 c12 c32\"><a class=\"c2\" href=\"https:\/\/www.google.com\/url?q=http:\/\/www.huffingtonpost.com\/2013\/04\/21\/boston-marathon-bombing-nurses_n_3128617.html&amp;sa=D&amp;ust=1598403533030000&amp;usg=AOvVaw1YcY2KW2Ng7f4fLMdwBwoS\">dy<\/a><\/span><span class=\"c11\"><a class=\"c2\" href=\"https:\/\/www.google.com\/url?q=http:\/\/www.huffingtonpost.com\/2013\/04\/21\/boston-marathon-bombing-nurses_n_3128617.html&amp;sa=D&amp;ust=1598403533030000&amp;usg=AOvVaw1YcY2KW2Ng7f4fLMdwBwoS\">\u00a0After<\/a><\/span><span class=\"c20 c32\"><a class=\"c2\" href=\"https:\/\/www.google.com\/url?q=http:\/\/www.huffingtonpost.com\/2013\/04\/21\/boston-marathon-bombing-nurses_n_3128617.html&amp;sa=D&amp;ust=1598403533031000&amp;usg=AOvVaw2gOggsjazkLoio24Y-Opud\">math<\/a><\/span><\/h3>\n<p class=\"c1\"><img decoding=\"async\" title=\"\" src=\"http:\/\/region12.herbzinser07.com\/dir\/science08-ucsystem\/wp-content\/uploads\/sites\/15\/2020\/08\/img_5f45a71ac250c.png\" alt=\"\" \/><\/p>\n<p class=\"c1\"><span class=\"c6\">San<\/span><span class=\"c6 c40\">dy<\/span><span class=\"c9 c6\">\u00a0Hook school math battle<\/span><\/p>\n<p class=\"c1\"><img decoding=\"async\" title=\"\" src=\"http:\/\/region12.herbzinser07.com\/dir\/science08-ucsystem\/wp-content\/uploads\/sites\/15\/2020\/08\/img_5f45a71b091e4.png\" alt=\"\" \/><\/p>\n<p class=\"c1\"><span class=\"c6\">3)<\/span><span class=\"c9 c10\">\u00a0the 3rd math sign &#8230;&#8230;. of a bio-math expression structure and his bio-math proper noun<\/span><\/p>\n<p class=\"c16\"><span class=\"c10\">The suspects were identified later that day as\u00a0<\/span><span class=\"c4\"><a class=\"c2\" href=\"https:\/\/www.google.com\/url?q=http:\/\/en.wikipedia.org\/wiki\/Dzhokhar_and_Tamerlan_Tsarnaev&amp;sa=D&amp;ust=1598403533035000&amp;usg=AOvVaw1kORU9TbybrNKfjrxfUKnG\">Dzhokhar and Tamerlan Tsarnaev<\/a><\/span><span class=\"c9 c10\">.<\/span><\/p>\n<p class=\"c1\"><span class=\"c10\">The suspects were identified later that day as\u00a0<\/span><span class=\"c4\"><a class=\"c2\" href=\"https:\/\/www.google.com\/url?q=http:\/\/en.wikipedia.org\/wiki\/Dzhokhar_and_Tamerlan_Tsarnaev&amp;sa=D&amp;ust=1598403533035000&amp;usg=AOvVaw1kORU9TbybrNKfjrxfUKnG\">Dzhokhar<\/a><\/span><span class=\"c9 c10\">.<\/span><\/p>\n<p class=\"c1\"><span class=\"c0\">The suspects were identified later that day as<\/span><span class=\"c47\">\u00a0<\/span><span class=\"c20 c35\"><a class=\"c2\" href=\"https:\/\/www.google.com\/url?q=http:\/\/en.wikipedia.org\/wiki\/Dzhokhar_and_Tamerlan_Tsarnaev&amp;sa=D&amp;ust=1598403533036000&amp;usg=AOvVaw1sjEJ0VzhcHfWMo_7pRYdP\">Dz<\/a><\/span><span class=\"c9 c6\">.<\/span><\/p>\n<p class=\"c1\"><img decoding=\"async\" title=\"\" src=\"http:\/\/region12.herbzinser07.com\/dir\/science08-ucsystem\/wp-content\/uploads\/sites\/15\/2020\/08\/img_5f45a71b500f2.png\" alt=\"\" \/><\/p>\n<p class=\"c1\"><img decoding=\"async\" title=\"\" src=\"http:\/\/region12.herbzinser07.com\/dir\/science08-ucsystem\/wp-content\/uploads\/sites\/15\/2020\/08\/img_5f45a71b95ac1.png\" alt=\"\" \/><\/p>\n<h3 id=\"h.iwvojq1jv6c\" class=\"c8\"><span class=\"c20 c17 c32\"><a class=\"c2\" href=\"https:\/\/www.google.com\/url?q=http:\/\/www.schoolsafetypartners.org\/resources\/vt\/12%2520CHAPTER%2520VIII%2520MASS%2520MURDER%2520AT%2520NORRIS%2520HALL.pdf&amp;sa=D&amp;ust=1598403533038000&amp;usg=AOvVaw3_6dY31-P9hYT7mHTaay6O\">Chapter VIII<br \/>\nMathematics CHAIN RULE battle<br \/>\nAT NORRIS HALL &#8211; School &#8230;<\/a><\/span><\/h3>\n<p class=\"c1\"><span class=\"c19 c14 c29\"><a class=\"c2\" href=\"https:\/\/www.google.com\/url?q=http:\/\/www.schoolsafetypartners.org\/resources\/vt\/12%2520CHAPTER%2520VIII%2520MASS%2520MURDER%2520AT%2520NORRIS%2520HALL.pdf&amp;sa=D&amp;ust=1598403533039000&amp;usg=AOvVaw0sA_BxN-tQRULWuh0vS4io\">www.schoolsafetypartners.org \u203a resources \u203a 12 CHAPT&#8230;<\/a><\/span><\/p>\n<p class=\"c1\"><span class=\"c10 c12\">shooting<\/span><span class=\"c10\">\u00a0started. In\u00a0<\/span><span class=\"c10 c12\">Norris Hall<\/span><span class=\"c10\">, Cho\u00a0<\/span><span class=\"c12 c30\">chained<\/span><span class=\"c10\">\u00a0shut the pair of\u00a0<\/span><span class=\"c10 c12\">doors<\/span><span class=\"c9 c10\">\u00a0at each of the three main entrances used by students. Figure 7 shows one such entrance.<\/span><\/p>\n<p class=\"c1\"><img decoding=\"async\" title=\"\" src=\"http:\/\/region12.herbzinser07.com\/dir\/science08-ucsystem\/wp-content\/uploads\/sites\/15\/2020\/08\/img_5f45a71be2915.png\" alt=\"\" \/><\/p>\n<p class=\"c1\"><span class=\"c9 c10\">Thus we see the 3 math derivatives as subset components of this math message EVENT.<\/span><\/p>\n<p class=\"c1\"><span class=\"c9 c10\">In addition, we known that the intermediate value theorem has something to do with middle \/ approximation \/ crossing a line\/ mid \u00a0&#8212;&gt;<\/span><\/p>\n<p class=\"c1\"><span class=\"c9 c10\">thus a possible LINK to the continuous math function life of a BLOOD vessel \u00a0and blood plasmid.<\/span><\/p>\n<p class=\"c1\"><span class=\"c9 c10\">plasmid &#8211;&gt; mid &#8212;&gt; middle &#8230;.. some bio-math ideas &#8230;..<\/span><\/p>\n<h3 id=\"h.i6inoqe4ej0m\" class=\"c8\"><span class=\"c20\"><a class=\"c2\" href=\"https:\/\/www.google.com\/url?q=http:\/\/www.ima.umn.edu\/~miller\/Newton-MVT.pdf&amp;sa=D&amp;ust=1598403533043000&amp;usg=AOvVaw2kKQZkZKpOlrJ7nHRylmok\">0.1 Newton&#8217;s method and the\u00a0<\/a><\/span><span class=\"c20 c12\"><a class=\"c2\" href=\"https:\/\/www.google.com\/url?q=http:\/\/www.ima.umn.edu\/~miller\/Newton-MVT.pdf&amp;sa=D&amp;ust=1598403533044000&amp;usg=AOvVaw0hVI-2sPc8Ou582dHoNIPn\">Mean Value Theorem<\/a><\/span><span class=\"c20\"><a class=\"c2\" href=\"https:\/\/www.google.com\/url?q=http:\/\/www.ima.umn.edu\/~miller\/Newton-MVT.pdf&amp;sa=D&amp;ust=1598403533044000&amp;usg=AOvVaw0hVI-2sPc8Ou582dHoNIPn\">\u00a0&#8211; IMA<\/a><\/span><\/h3>\n<p class=\"c1\"><span class=\"c9 c10\">www.ima.umn.edu\/~miller\/Newton-MVT.pdf\u200e<\/span><\/p>\n<p class=\"c1\"><span class=\"c10\">x \u2208 D, and set C = B\/A. By the\u00a0<\/span><span class=\"c10 c12\">Mean Value Theorem<\/span><span class=\"c10\">\u00a0there is a point. \u02dcxn \u2208 D\u00a0<\/span><span class=\"c0\">&#8230;<\/span><span class=\"c9 c10\">\u00a0Example 2<\/span><\/p>\n<p class=\"c1\"><span class=\"c10\">We approximate \u221a7 by using the\u00a0<\/span><span class=\"c10 c12\">midpoint<\/span><span class=\"c9 c10\">\u00a0method to find the positive<\/span><\/p>\n<p class=\"c1\"><span class=\"c10 c12\">midpoint<\/span><span class=\"c9 c10\">\u00a0method<\/span><\/p>\n<p class=\"c1\"><span class=\"c10 c12\">midpoint<\/span><span class=\"c9 c10\">\u00a0method<\/span><\/p>\n<p class=\"c1\"><span class=\"c10 c12\">midpoint<\/span><span class=\"c9 c10\">\u00a0method ???<\/span><\/p>\n<p class=\"c1\"><img decoding=\"async\" title=\"\" src=\"http:\/\/region12.herbzinser07.com\/dir\/science08-ucsystem\/wp-content\/uploads\/sites\/15\/2020\/08\/img_5f45a71c30292.png\" alt=\"\" \/><\/p>\n<p class=\"c1\"><span class=\"c9 c10\">Many questions about the Boston Math Marathon &#8230;&#8230;. and sadness that Boston University has no respect \u00a0for Isaac Asimov \u00a0and the INTELLECTUAL ideas and possibilities he gave the world.<\/span><\/p>\n<p class=\"c1\"><img decoding=\"async\" title=\"\" src=\"http:\/\/region12.herbzinser07.com\/dir\/science08-ucsystem\/wp-content\/uploads\/sites\/15\/2020\/08\/img_5f45a71c79e2d.png\" alt=\"\" \/><\/p>\n<h3 id=\"h.kueii6lwqh9f\" class=\"c8\"><span class=\"c20 c17 c23\"><a class=\"c2\" href=\"https:\/\/www.google.com\/url?q=https:\/\/en.wikipedia.org\/wiki\/Smolensk_air_disaster&amp;sa=D&amp;ust=1598403533049000&amp;usg=AOvVaw0iPue66PGZiDLNfsfN6RGX\">Smolensk air disaster &#8211; Wikipedia<\/a><\/span><\/h3>\n<p class=\"c1\"><span class=\"c4 c17\"><a class=\"c2\" href=\"https:\/\/www.google.com\/url?q=https:\/\/en.wikipedia.org\/wiki\/Smolensk_air_disaster&amp;sa=D&amp;ust=1598403533050000&amp;usg=AOvVaw3oxNyDbVxDDIPQHmo7RqlL\">en.wikipedia.org \u203a wiki \u203a Smolensk_air_disaster<\/a><\/span><\/p>\n<p class=\"c1\"><span class=\"c10\">The Smolensk air disaster occurred on 10 April 2010, when a Tupolev Tu-154\u00a0<\/span><span class=\"c10 c12\">aircraft<\/span><span class=\"c10\">\u00a0of the\u00a0<\/span><span class=\"c10 c12\">Polish<\/span><span class=\"c10\">\u00a0Air Force\u00a0<\/span><span class=\"c10 c12\">crashed<\/span><span class=\"c9 c10\">\u00a0near the Russian city of Smolensk, killing &#8230;<\/span><\/p>\n<p class=\"c1\"><span class=\"c10\">Missing:\u00a0<\/span><span class=\"c10 c17 c42\">s<\/span><\/p>\n<h3 id=\"h.lxnaaw7syei1\" class=\"c8\"><span class=\"c20 c32\"><a class=\"c2\" href=\"https:\/\/www.google.com\/url?q=https:\/\/www.oxfordscholarship.com\/view\/10.1093\/acprof:oso\/9780199556441.001.0001\/acprof-9780199556441-chapter-8&amp;sa=D&amp;ust=1598403533052000&amp;usg=AOvVaw0qxfanfo4Mm49Sc8fAOdhH\">SMOLUCHOWSKI EQUATION problems of Poland<\/a><\/span><span class=\"c20 c46\"><a class=\"c2\" href=\"https:\/\/www.google.com\/url?q=https:\/\/www.oxfordscholarship.com\/view\/10.1093\/acprof:oso\/9780199556441.001.0001\/acprof-9780199556441-chapter-8&amp;sa=D&amp;ust=1598403533052000&amp;usg=AOvVaw0qxfanfo4Mm49Sc8fAOdhH\">\u00a0<\/a><\/span><span class=\"c28\">and their lazy thinkers<\/span><\/h3>\n<h3 id=\"h.k0ce4mmp7ip\" class=\"c8\"><span class=\"c20 c17 c32\"><a class=\"c2\" href=\"https:\/\/www.google.com\/url?q=https:\/\/www.oxfordscholarship.com\/view\/10.1093\/acprof:oso\/9780199556441.001.0001\/acprof-9780199556441-chapter-8&amp;sa=D&amp;ust=1598403533053000&amp;usg=AOvVaw3ceteqGoq0ACezggMMq6RL\">&#8211; Oxford Scholarship<\/a><\/span><\/h3>\n<p class=\"c1\"><span class=\"c19 c14 c29\"><a class=\"c2\" href=\"https:\/\/www.google.com\/url?q=https:\/\/www.oxfordscholarship.com\/view\/10.1093\/acprof:oso\/9780199556441.001.0001\/acprof-9780199556441-chapter-8&amp;sa=D&amp;ust=1598403533054000&amp;usg=AOvVaw2nVOmbLgarWkaZQnBu_QMZ\">www.oxfordscholarship.com \u203a view \u203a acprof:oso \u203a acp&#8230;<\/a><\/span><\/p>\n<p class=\"c1\"><span class=\"c14\">This chapter discusses the\u00a0<\/span><span class=\"c14 c12\">Smoluchowski equation<\/span><span class=\"c14\">,<\/span><span class=\"c6 c45\">\u00a0a configuration space\u00a0<\/span><span class=\"c9 c14\">description of a Brownian particle in a field of force. It begins with the Kramers\u2013Klein &#8230;<\/span><\/p>\n<h3 id=\"h.tzswdqgf4jku\" class=\"c8\"><span class=\"c20\"><a class=\"c2\" href=\"https:\/\/www.google.com\/url?q=http:\/\/en.wikipedia.org\/wiki\/Isaac_Asimov&amp;sa=D&amp;ust=1598403533055000&amp;usg=AOvVaw1Yqdj0Z6yfFVXYkznyqTm2\">Isaac\u00a0<\/a><\/span><span class=\"c20 c12\"><a class=\"c2\" href=\"https:\/\/www.google.com\/url?q=http:\/\/en.wikipedia.org\/wiki\/Isaac_Asimov&amp;sa=D&amp;ust=1598403533055000&amp;usg=AOvVaw1Yqdj0Z6yfFVXYkznyqTm2\">Asimov<\/a><\/span><span class=\"c20\"><a class=\"c2\" href=\"https:\/\/www.google.com\/url?q=http:\/\/en.wikipedia.org\/wiki\/Isaac_Asimov&amp;sa=D&amp;ust=1598403533056000&amp;usg=AOvVaw0zZLgMTeSx_5hccL2pAn1Z\">\u00a0&#8211; Wikipedia, the free encyclopedia<\/a><\/span><\/h3>\n<p class=\"c1\"><span class=\"c10\">en.wikipedia.org\/wiki\/Isaac_<\/span><span class=\"c0\">Asimov<\/span><span class=\"c9 c10\">\u200e<\/span><\/p>\n<p class=\"c1\"><span class=\"c10\">After completing his doctorate,\u00a0<\/span><span class=\"c10 c12\">Asimov<\/span><span class=\"c10\">\u00a0joined the faculty of the\u00a0<\/span><span class=\"c10 c12\">Boston University<\/span><span class=\"c10\">\u00a0School of Medicine, with which he remained associated thereafter. From 1958\u00a0<\/span><span class=\"c9 c0\">&#8230;<\/span><\/p>\n<p class=\"c1\"><span class=\"c10\">\u200e<\/span><span class=\"c4\"><a class=\"c2\" href=\"https:\/\/www.google.com\/url?q=http:\/\/en.wikipedia.org\/wiki\/Foundation_series&amp;sa=D&amp;ust=1598403533057000&amp;usg=AOvVaw15jshaAuiwsZ4ym0OwozjV\">Foundation series<\/a><\/span><span class=\"c10\">\u00a0&#8211; \u200e<\/span><span class=\"c4\"><a class=\"c2\" href=\"https:\/\/www.google.com\/url?q=http:\/\/en.wikipedia.org\/wiki\/I,_Robot&amp;sa=D&amp;ust=1598403533058000&amp;usg=AOvVaw3jPJ5rJIj8XiXeL5TUmv0V\">I, Robot<\/a><\/span><span class=\"c10\">\u00a0&#8211; \u200e<\/span><span class=\"c4\"><a class=\"c2\" href=\"https:\/\/www.google.com\/url?q=http:\/\/en.wikipedia.org\/wiki\/Robot_series_%2528Asimov%2529&amp;sa=D&amp;ust=1598403533058000&amp;usg=AOvVaw3D6goGdnKgrgjOMy_PoTvi\">Robot series<\/a><\/span><span class=\"c10\">\u00a0&#8211; \u200e<\/span><span class=\"c4\"><a class=\"c2\" href=\"https:\/\/www.google.com\/url?q=http:\/\/en.wikipedia.org\/wiki\/Three_Laws_of_Robotics&amp;sa=D&amp;ust=1598403533059000&amp;usg=AOvVaw0r7PfvzU5nLHxDqJhPFLN2\">Three Laws of Robotics<\/a><\/span><\/p>\n<h3 id=\"h.wghxg73lh8x2\" class=\"c8\"><span class=\"c20\"><a class=\"c2\" href=\"https:\/\/www.google.com\/url?q=http:\/\/www.famousauthors.org\/isaac-asimov&amp;sa=D&amp;ust=1598403533060000&amp;usg=AOvVaw2JFaz21sD3FODApmRV7x2h\">Isaac\u00a0<\/a><\/span><span class=\"c20 c12\"><a class=\"c2\" href=\"https:\/\/www.google.com\/url?q=http:\/\/www.famousauthors.org\/isaac-asimov&amp;sa=D&amp;ust=1598403533060000&amp;usg=AOvVaw2JFaz21sD3FODApmRV7x2h\">Asimov<\/a><\/span><span class=\"c20\"><a class=\"c2\" href=\"https:\/\/www.google.com\/url?q=http:\/\/www.famousauthors.org\/isaac-asimov&amp;sa=D&amp;ust=1598403533061000&amp;usg=AOvVaw3aWaMFtMr2QQNIOKWD7Yhm\">\u00a0| Biography, Books and Facts &#8211; Famous Authors<\/a><\/span><\/h3>\n<p class=\"c1\"><span class=\"c10\">www.famousauthors.org\/isaac-<\/span><span class=\"c0\">asimov<\/span><span class=\"c9 c10\">\u200e<\/span><\/p>\n<p class=\"c1\"><span class=\"c10\">Also a professor of biochemistry at\u00a0<\/span><span class=\"c10 c12\">Boston University<\/span><span class=\"c10\">, Isaac\u00a0<\/span><span class=\"c10 c12\">Asimov<\/span><span class=\"c10\">\u00a0has over 500 published volumes in addition to 90,000 letters, postcards and other scientific\u00a0<\/span><span class=\"c9 c0\">&#8230;<\/span><\/p>\n<p class=\"c1\"><span class=\"c10\">Boston and East coast \u00a0universities are known for their social science, economics, and philosophy \u00a0marathon run-around.<\/span><span class=\"c9 c38 c43\">\u00a0 \u00a0<\/span><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Rd-blog-number-3203 by Herb Zinser Boston Marathon b100dy math\u00a0war explained by Isaac Asimov This blog post \u2026.. \u00a0a \u00a0 year 2013 [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[],"tags":[],"class_list":["post-1668","post","type-post","status-publish","format-standard","hentry"],"_links":{"self":[{"href":"http:\/\/region12.herbzinser07.com\/dir\/science08-ucsystem\/wp-json\/wp\/v2\/posts\/1668","targetHints":{"allow":["GET"]}}],"collection":[{"href":"http:\/\/region12.herbzinser07.com\/dir\/science08-ucsystem\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"http:\/\/region12.herbzinser07.com\/dir\/science08-ucsystem\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"http:\/\/region12.herbzinser07.com\/dir\/science08-ucsystem\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"http:\/\/region12.herbzinser07.com\/dir\/science08-ucsystem\/wp-json\/wp\/v2\/comments?post=1668"}],"version-history":[{"count":1,"href":"http:\/\/region12.herbzinser07.com\/dir\/science08-ucsystem\/wp-json\/wp\/v2\/posts\/1668\/revisions"}],"predecessor-version":[{"id":1694,"href":"http:\/\/region12.herbzinser07.com\/dir\/science08-ucsystem\/wp-json\/wp\/v2\/posts\/1668\/revisions\/1694"}],"wp:attachment":[{"href":"http:\/\/region12.herbzinser07.com\/dir\/science08-ucsystem\/wp-json\/wp\/v2\/media?parent=1668"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"http:\/\/region12.herbzinser07.com\/dir\/science08-ucsystem\/wp-json\/wp\/v2\/categories?post=1668"},{"taxonomy":"post_tag","embeddable":true,"href":"http:\/\/region12.herbzinser07.com\/dir\/science08-ucsystem\/wp-json\/wp\/v2\/tags?post=1668"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}