{"id":44233,"date":"2017-09-12T10:39:13","date_gmt":"2017-09-12T16:39:13","guid":{"rendered":"http:\/\/admin.patheos.com\/blogs\/danpeterson\/?p=44233"},"modified":"2017-09-12T10:39:13","modified_gmt":"2017-09-12T16:39:13","slug":"are-numbers-real","status":"publish","type":"post","link":"https:\/\/www.patheos.com\/blogs\/danpeterson\/2017\/09\/are-numbers-real.html","title":{"rendered":"“Are Numbers Real?”"},"content":{"rendered":"\n<\/head>

\u00a0<\/p>\n

\"Dr.<\/a>
A 1928 photograph of Eugene Paul Wigner (1902-1995), the Hungarian-American theoretical physicist, engineer, and mathematician who won the 1963 Nobel Prize in Physics. \u00a0(Wikimedia Commons)<\/figcaption><\/figure>\n

\u00a0<\/p>\n

I\u2019ve been reading a book by Brian Clegg titled Are Numbers Real? The Uncanny Relationship of Mathematics and the Physical World<\/em> (New York: St. Martin\u2019s Press, 2016). \u00a0It deals with a really interesting topic that, in my view, may point suggest the\u00a0falsehood of materialist\/reductionist views of the universe.<\/p>\n

\u00a0<\/p>\n

I\u2019ll share just a few passages from it:<\/p>\n

\u00a0<\/p>\n

\u201cWould numbers exist without people to think about them, or are they just valuable human inventions, the imaginary inhabitants of a useful fantasy world?\u201d \u00a0(1-2)<\/p>\n

\u00a0<\/p>\n

\u201cSimilarly, when mathematicians played around with an idea like the square root of a negative number, called an imaginary number, they were initially simply enjoying a new direction to take their mathematical game. \u00a0But, as it happened, because of the rules they decided to apply to this magical class of numbers, it became a hugely useful tool for physics and engineering.<\/p>\n

\u201cNo scientist or engineer ever said prior to the introduction of imaginary numbers, \u2018What we want is the square root of a negative number. \u00a0They would really help us with this problem we\u2019ve got.\u2019 \u00a0Similarly, no one in mathematics thought, \u2018How can we solve this particular problem that the physicists have?\u2019 before dreaming up imaginary numbers. \u00a0The mathematicians just played with the implications of their new concept and the set of rules attached to it. \u00a0The applications emerged later.\u201d \u00a0(7-8)<\/p>\n

\u00a0<\/p>\n

\u201cSome scientists, such as physicist Max Tegmark, go so far as to suggest that the universe is mathematical. \u00a0That numbers aren\u2019t just real, but are what make everything happen.\u201d \u00a0(10)<\/p>\n

\u00a0<\/p>\n

The Pythagoreans, whose motto, carved on the lintel of the door to their principal school, was \u201cAll is number\u201d: \u00a0\u201cThey were of the opinion that everything in the universe was structured on\u00a0numbers \u2014 that numbers were not merely a human creation, but provided the underlying architecture of reality.\u201d \u00a0(30)<\/p>\n

\u00a0<\/p>\n

\u201cYou could . . . say that mathematics is an agreed fiction, a shared mental world that mathematicians agree to collectively inhabit. \u00a0But their world isn\u2019t allowed the looseness of literary fiction, because here all the rules have to be pinned down and agreed. \u00a0As long as a piece of mathematics is consistent with those rules it is acceptable, whether or not it has any parallel with the physical universe. \u00a0Yet we keep coming back to the fact that a sizable subset of mathematics not only has parallels, but has an uncanny ability to mirror what the real world can offer. \u00a0It could just be because so much of the essential structure that mathematics is built on \u2014 like the nature of whole number arithmetic \u2014 started as a reflection of the real world.\u201d \u00a0(52)<\/p>\n

\u00a0<\/p>\n

Brian Clegg is looking at the same general issue as that raised by the Nobel-laureate physicist Eugene Wigner in his famous 1960 paper \u201cThe Unreasonable Effectiveness of Mathematics in the Natural Sciences.\u201d<\/a><\/p>\n

\u00a0<\/p>\n

The English physicist, astronomer, and mathematician Sir James Jeans (d. 1949) had perhaps been thinking along similar lines when he remarked, in his 1944 book The Mysterious Universe<\/em>, that \u201cThe stream of knowledge is heading towards a non-mechanical reality; the Universe begins to look more like a great thought than like a great machine. Mind no longer appears to be an accidental intruder into the realm of matter. . . . \u00a0we ought rather hail it as the creator and governor of the realm of matter.\u201d<\/p>\n

\u00a0<\/p>\n

\u00a0<\/p>\n<\/body><\/html>\n","protected":false},"excerpt":{"rendered":"

\u00a0 \u00a0 I\u2019ve been reading a book by Brian Clegg titled Are Numbers Real? The Uncanny Relationship of Mathematics and the Physical World (New York: St. Martin\u2019s Press, 2016). \u00a0It deals with a really interesting topic that, in my view, may point suggest the\u00a0falsehood of materialist\/reductionist views of the universe. \u00a0 I\u2019ll share just a […]<\/p>\n","protected":false},"author":1019,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1],"tags":[],"class_list":["post-44233","post","type-post","status-publish","format-standard","hentry","category-uncategorized"],"yoast_head":"\n"Are Numbers Real?"<\/title>\n<meta name=\"description\" content=\"    I've been reading a book by Brian Clegg titled Are Numbers Real? 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