{"id":81772,"date":"2022-04-11T13:52:40","date_gmt":"2022-04-11T17:52:40","guid":{"rendered":"https:\/\/newsroom.carleton.ca\/?post_type=cu_story&#038;p=81772"},"modified":"2025-08-19T09:37:10","modified_gmt":"2025-08-19T13:37:10","slug":"universe-without-mathematics","status":"publish","type":"cu_story","link":"https:\/\/carleton.ca\/news\/story\/universe-without-mathematics\/","title":{"rendered":"A universe without mathematics is beyond the scope of our imagination"},"content":{"rendered":"\n<section class=\"w-screen px-6 cu-section cu-section--white ml-offset-center md:px-8 lg:px-14\">\n    <div class=\"space-y-6 cu-max-w-child-max  md:space-y-10 cu-prose-first-last\">\n\n        \n                    \n                    \n            \n    <div class=\"cu-wideimage relative flex items-center justify-center mx-auto px-8 overflow-hidden md:px-16 rounded-xl not-prose  my-6 md:my-12 first:mt-0 bg-opacity-50 bg-cover bg-cu-black-50 pt-24 pb-32 md:pt-28 md:pb-44 lg:pt-36 lg:pb-60 xl:pt-48 xl:pb-72\" style=\"background-image: url(https:\/\/carleton.ca\/news\/wp-content\/uploads\/sites\/162\/conversation-galaxy-math-1200w-1.jpg); background-position: 50% 50%;\">\n\n                    <div class=\"absolute top-0 w-full h-screen\" style=\"background-color:rgba(0,0,0,0.600);\"><\/div>\n        \n        <div class=\"relative z-[2] max-w-4xl w-full flex flex-col items-center gap-2 cu-wideimage-image cu-zero-first-last\">\n            <header class=\"mx-auto mb-6 text-center text-white cu-pageheader cu-component-updated cu-pageheader--center md:mb-12\">\n\n                                    <h1 class=\"cu-prose-first-last font-semibold mb-2 text-3xl md:text-4xl lg:text-5xl lg:leading-[3.5rem] cu-pageheader--center text-center mx-auto after:left-px\">\n                        A universe without mathematics is beyond the scope of our imagination\n                    <\/h1>\n                \n                            <\/header>\n        <\/div>\n\n                    <svg xmlns=\"http:\/\/www.w3.org\/2000\/svg\" class=\"absolute bottom-0 w-full z-[1]\" fill=\"none\" viewbox=\"0 0 1280 312\">\n                <path fill=\"#fff\" d=\"M26.412 315.608c-.602-.268-6.655-2.412-13.524-4.769a1943.84 1943.84 0 0 1-14.682-5.144l-2.276-.858v-5.358c0-4.876.086-5.358.773-5.09 1.674.643 21.38 5.84 34.646 9.109 14.682 3.59 28.935 6.858 45.936 10.449l9.874 2.089H57.322c-16.4 0-30.31-.16-30.91-.428ZM460.019 315.233c42.974-10.074 75.602-19.88 132.443-39.867 76.16-26.791 152.063-57.709 222.385-90.663 16.7-7.823 21.336-10.074 44.262-21.273 85.004-41.688 134.719-64.193 195.291-88.413 66.55-26.577 145.2-53.584 194.27-66.765C1258.5 5.626 1281.34 0 1282.24 0c.17 0 .34 27.596.34 61.3v61.299l-2.23.375c-84.7 13.718-165.93 35.955-310.736 84.931-46.494 15.753-65.427 22.076-96.166 32.15-9.102 3-24.814 8.198-34.989 11.574-107.543 35.954-153.008 50.422-196.626 62.639l-6.74 1.876-89.126-.054c-78.135-.054-88.782-.161-85.948-.857ZM729.628 312.875c33.229-10.985 69.248-23.523 127.506-44.207 118.705-42.223 164.596-57.709 217.446-73.302 2.62-.75 8.29-2.465 12.67-3.751 56.19-16.772 126.94-33.597 184.17-43.671 5.07-.91 9.66-1.768 10.22-1.875l.94-.161v170.236l-281.28-.054H719.968l9.66-3.215ZM246.864 313.411c-65.041-2.251-143.047-12.11-208.432-26.256-18.375-3.965-41.73-9.538-42.202-10.074-.171-.214-.257-21.38-.214-47.046l.129-46.618 6.654 3.697c57.313 32.043 118.491 56.531 197.699 79.143 40.313 11.521 83.459 18.058 138.669 21.059 15.584.857 65.685.857 81.14 0 33.744-1.876 61.306-4.93 88.396-9.806 6.396-1.126 11.634-1.983 11.722-1.929.255.375-20.48 7.769-30.999 11.038-28.592 8.948-59.288 15.646-91.873 20.147-26.36 3.59-50.015 5.627-78.35 6.698-15.584.59-55.209.59-72.339-.053Z\"><\/path>\n                <path fill=\"#fff\" d=\"M-3.066 295.067 32.06 304.1v9.033H-3.066v-18.066Z\"><\/path>\n            <\/svg>\n            <\/div>\n\n    \n\n    <\/div>\n<\/section>\n\n<p>This article is <a href=\"https:\/\/theconversation.com\/a-universe-without-mathematics-is-beyond-the-scope-of-our-imagination-175813\" rel=\"noopener noreferrer\" target=\"_blank\">republished<\/a> from The Conversation under a Creative Commons licence. All photos provided by <a href=\"https:\/\/theconversation.com\" rel=\"noopener noreferrer\" target=\"_blank\">The Conversation<\/a> from various sources.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<p><\/p>\n\n\n\n<p>Almost 400 years ago, in <em>The Assayer<\/em>, Galileo wrote: \u201c<a href=\"https:\/\/web.stanford.edu\/%7Ejsabol\/certainty\/readings\/Galileo-Assayer.pdf\" target=\"_blank\" rel=\"noopener noreferrer\">Philosophy is written in this grand book, the universe \u2026 [But the book] is written in the language of mathematics<\/a>.\u201d He was much more than an astronomer, and this can almost be thought of as the first writing on the scientific method.<\/p>\n\n\n\n<p>We do not know who first started applying mathematics to scientific study, but it is plausible that it was the <a href=\"https:\/\/www.wiley.com\/en-ca\/A+History+of+Mathematics%2C+3rd+Edition-p-9780470630563\" target=\"_blank\" rel=\"noopener noreferrer\">Babylonians, who used it to discover the pattern underlying eclipses<\/a>, nearly 3,000 years ago. But it took 2,500 years and the invention of calculus and <a href=\"https:\/\/plato.stanford.edu\/entries\/newton-principia\/\" target=\"_blank\" rel=\"noopener noreferrer\">Newtonian physics<\/a> to explain the patterns.<\/p>\n\n\n\n<figure class=\"wp-block-embed\"><div class=\"wp-block-embed__wrapper\">\n<iframe loading=\"lazy\" title=\"Math whizzes of ancient Babylon figured out forerunner of calculus\" width=\"500\" height=\"281\" src=\"https:\/\/www.youtube.com\/embed\/Rx-5dCXx1SI?feature=oembed\" frameborder=\"0\" allow=\"accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture; web-share\" referrerpolicy=\"strict-origin-when-cross-origin\" allowfullscreen><\/iframe>\n<\/div><\/figure>\n\n\n\n<p>Since then, probably every single major scientific discovery has used mathematics in some form, simply because it is far more powerful than any other human language. It is not surprising that this has led many people to claim that <a href=\"https:\/\/www.maths.ed.ac.uk\/%7Ev1ranick\/papers\/wigner.pdf\" target=\"_blank\" rel=\"noopener noreferrer\">mathematics is much more<\/a>: that the universe is <a href=\"https:\/\/www.scientificamerican.com\/article\/is-the-universe-made-of-math-excerpt\/\" target=\"_blank\" rel=\"noopener noreferrer\">created by a mathematician<\/a>. <\/p>\n\n\n\n<p>So could we imagine a universe in which mathematics does not work?<\/p>\n\n\n\n<h2 id=\"the-language-of-mathematics\" class=\"wp-block-heading\">The language of mathematics<\/h2>\n\n\n\n<p>The <a href=\"https:\/\/www.sciencedirect.com\/topics\/psychology\/sapir-whorf-hypothesis\" target=\"_blank\" rel=\"noopener noreferrer\">Sapir-Whorf hypothesis<\/a> asserts that you cannot discuss a concept unless you have the language to describe it.<\/p>\n\n\n\n<p>In any science, and physics in particular, we need to describe concepts that do not map well on to any human language. One can describe an electron, but the moment we start asking questions like \u201cWhat colour is it?\u201d we start to realize the inadequacies of English. <\/p>\n\n\n\n<p>The colour of an object depends on the wavelengths of light reflected by it, so an electron has no colour, or more accurately, all colours. The question itself is meaningless. But ask \u201cHow does an electron behave?\u201d and the answer is, in principle, simple. In 1928, Paul A.M. Dirac wrote down <a href=\"https:\/\/www.sciencedirect.com\/topics\/physics-and-astronomy\/dirac-equation\" target=\"_blank\" rel=\"noopener noreferrer\">an equation<\/a> that describes the behaviour of an electron almost perfectly under all circumstances. This does not mean it is simple when we look at the details. <\/p>\n\n\n\n<p>For example, an electron behaves as a tiny magnet. The magnitude can be calculated, but the <a href=\"https:\/\/arxiv.org\/pdf\/1704.06996.pdf\" target=\"_blank\" rel=\"noopener noreferrer\">calculation is horrendously complicated<\/a>. Explaining an aurora, for example, requires us to understand orbital mechanics, magnetic fields and atomic physics, but at heart, these are just more mathematics. <\/p>\n\n\n\n<p>But it is when we think of the individual that we realize that a human commitment to logical, mathematical thinking goes much deeper. The decision to overtake a slow-moving car does not involve the explicit integration of the equations of motion, but we certainly do it implicitly. A Tesla on autopilot will actually solve them explicitly.<\/p>\n\n\n\n<figure class=\"wp-block-image align-center zoomable\"><a href=\"https:\/\/images.theconversation.com\/files\/456989\/original\/file-20220407-22-misq8y.jpg?ixlib=rb-1.1.0&amp;q=45&amp;auto=format&amp;w=1000&amp;fit=clip\" target=\"_blank\" rel=\"noopener noreferrer\"><img decoding=\"async\" src=\"https:\/\/images.theconversation.com\/files\/456989\/original\/file-20220407-22-misq8y.jpg?ixlib=rb-1.1.0&amp;q=45&amp;auto=format&amp;w=754&amp;fit=clip\" alt=\"view from the cockpit of a tesla with another car ahead and the driver working on their devices\"\/><\/a><figcaption class=\"wp-element-caption\">\n              <span class=\"caption\">When overtaking a car, a Tesla will explicitly calculate what a human driver processes implicitly.<\/span><br>\n              <span class=\"attribution\"><span class=\"source\">(Shutterstock)<\/span><\/span><br>\n            <\/figcaption><\/figure>\n\n\n\n<h2 id=\"predicting-chaos\" class=\"wp-block-heading\">Predicting chaos<\/h2>\n\n\n\n<p>So we really should not be surprised that mathematics is not just a language for describing the external world, but in many ways the only one. But just because something can be described mathematically does not mean it can be predicted. <\/p>\n\n\n\n<p>One of the more remarkable discoveries of the last 50 years has been the discovery of \u201c<a href=\"https:\/\/www.stsci.edu\/%7Elbradley\/seminar\/chaos.html\" target=\"_blank\" rel=\"noopener noreferrer\">chaotic systems<\/a>.\u201d These can be apparently simple mathematical systems that cannot be solved precisely. It turns out that many systems are chaotic in this sense. Hurricane tracks in the Caribbean are superficially similar to eclipse tracks, but we cannot predict them precisely with all the power of modern computers. <\/p>\n\n\n\n<p>However, we understand why: the equations that describe weather are intrinsically chaotic, so we can make accurate predictions in the short term, (about 24 hours), but these become increasingly unreliable over days. Similarly, quantum mechanics provides a theory where we know precisely what predictions cannot be made precisely. One can calculate the properties of an electron very accurately, but we cannot predict what an <a href=\"https:\/\/doi.org\/10.1038\/d41586-018-05892-6\" target=\"_blank\" rel=\"noopener noreferrer\">individual one will do<\/a>.<\/p>\n\n\n\n<p>Hurricanes are obviously intermittent events, and we cannot predict when one will happen in advance. But the mere fact that we cannot predict an event precisely does not mean we cannot describe it when it happens. We can even handle one-off events: it is generally accepted that the universe was created in the Big Bang and we have a remarkably <a href=\"https:\/\/www.nationalgeographic.com\/science\/article\/origins-of-the-universe\" target=\"_blank\" rel=\"noopener noreferrer\">precise theory of that<\/a>.<\/p>\n\n\n\n<h2 id=\"designing-social-systems\" class=\"wp-block-heading\">Designing social systems<\/h2>\n\n\n\n<p>A whole host of social phenomena, from the <a href=\"https:\/\/www.science.org\/content\/article\/stock-market-using-mathematics-finance\" target=\"_blank\" rel=\"noopener noreferrer\">stock market<\/a> to <a href=\"https:\/\/uwspace.uwaterloo.ca\/handle\/10012\/10627\" target=\"_blank\" rel=\"noopener noreferrer\">revolutions<\/a>, lack good predictive mathematics, but we can describe what has happened and to some extent construct model systems. <\/p>\n\n\n\n<p>So how about personal relationships? Love may be blind, but relationships are certainly predictable. The vast majority of us choose partners inside our social class and linguistic group, so there is absolutely no doubt that is true in the statistical sense. But it is also true in the local sense. A host of dating sites make their money by algorithms that at least make some pretence at matching you to your ideal mate. <\/p>\n\n\n\n<figure class=\"wp-block-embed\"><div class=\"wp-block-embed__wrapper\">\n<iframe loading=\"lazy\" title=\"How I hacked online dating | Amy Webb\" width=\"500\" height=\"281\" src=\"https:\/\/www.youtube.com\/embed\/d6wG_sAdP0U?feature=oembed\" frameborder=\"0\" allow=\"accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture; web-share\" referrerpolicy=\"strict-origin-when-cross-origin\" allowfullscreen><\/iframe>\n<\/div><\/figure>\n\n\n\n<p>A universe that could not be described mathematically would need to be fundamentally irrational and not merely unpredictable. Just because a theory is implausible does not mean we could not describe it mathematically. <\/p>\n\n\n\n<p>But I do not think we live in that universe, and I suspect we cannot imagine a non-mathematical universe.<\/p>\n\n\n\n<p>&#8212;<br>\n<a href=\"https:\/\/newsroom.carleton.ca\/\" target=\"_blank\" rel=\"noopener noreferrer\">Carleton Newsroom<\/a><\/p>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/counter.theconversation.com\/content\/175813\/count.gif?distributor=republish-lightbox-basic\" alt=\"The Conversation\"\/><\/figure>\n\n\n\n<p><\/p>\n","protected":false},"excerpt":{"rendered":"<p>This article is republished from The Conversation under a Creative Commons licence. All photos provided by The Conversation from various sources. Almost 400 years ago, in The Assayer, Galileo wrote: \u201cPhilosophy is written in this grand book, the universe \u2026 [But the book] is written in the language of mathematics.\u201d He was much more than [&hellip;]<\/p>\n","protected":false},"author":410,"featured_media":81774,"template":"","meta":{"_acf_changed":false,"footnotes":"","_links_to":"","_links_to_target":""},"cu_story_type":[1623],"cu_story_tag":[],"class_list":["post-81772","cu_story","type-cu_story","status-publish","has-post-thumbnail","hentry","cu_story_type-expert-perspectives"],"acf":{"cu_post_thumbnail":"blueprint"},"_links":{"self":[{"href":"https:\/\/carleton.ca\/news\/wp-json\/wp\/v2\/cu_story\/81772","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/carleton.ca\/news\/wp-json\/wp\/v2\/cu_story"}],"about":[{"href":"https:\/\/carleton.ca\/news\/wp-json\/wp\/v2\/types\/cu_story"}],"author":[{"embeddable":true,"href":"https:\/\/carleton.ca\/news\/wp-json\/wp\/v2\/users\/410"}],"version-history":[{"count":3,"href":"https:\/\/carleton.ca\/news\/wp-json\/wp\/v2\/cu_story\/81772\/revisions"}],"predecessor-version":[{"id":81781,"href":"https:\/\/carleton.ca\/news\/wp-json\/wp\/v2\/cu_story\/81772\/revisions\/81781"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/carleton.ca\/news\/wp-json\/wp\/v2\/media\/81774"}],"wp:attachment":[{"href":"https:\/\/carleton.ca\/news\/wp-json\/wp\/v2\/media?parent=81772"}],"wp:term":[{"taxonomy":"cu_story_type","embeddable":true,"href":"https:\/\/carleton.ca\/news\/wp-json\/wp\/v2\/cu_story_type?post=81772"},{"taxonomy":"cu_story_tag","embeddable":true,"href":"https:\/\/carleton.ca\/news\/wp-json\/wp\/v2\/cu_story_tag?post=81772"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}