{"id":3308,"date":"2021-07-08T09:23:07","date_gmt":"2021-07-08T09:23:07","guid":{"rendered":"http:\/\/www.simonings.net\/?p=3308"},"modified":"2021-07-08T09:23:07","modified_gmt":"2021-07-08T09:23:07","slug":"how-many-holes-has-a-straw","status":"publish","type":"post","link":"http:\/\/www.simonings.net\/?p=3308","title":{"rendered":"How many holes has a straw?"},"content":{"rendered":"

\"\"<\/a><\/p>\n

Reading Jordan Ellenberg’s Shape for the Telegraph, 7 July 2021<\/a><\/p>\n

\u201cOne can\u2019t help feeling that, in those opening years of the 1900s, something was in the air,\u201d writes mathematician Jordan Ellenburg.<\/p>\n

It\u2019s page 90, and he\u2019s launching into the second act of his dramatic, complex history of geometry (think \u201cHistory of the World in 100 Shapes\u201d, some of them very screwy indeed).
\nFor page after reassuring page, we\u2019ve been introduced to symmetry, to topology, and to the kinds of notation that make sense of knotty-sounding questions like \u201chow many holes has a straw\u201d?<\/p>\n

Now, though, the gloves are off, as Ellenburg records the fin de siecle\u2019s \u201cpainful recognition of some unavoidable bubbling randomness at the very bottom of things.\u201d
\nNormally when sentiments of this sort are trotted out, they\u2019re there to introduce readers to the wild world of quantum mechanics (and, incidentally, we can expect a lot of that sort of thing in the next few years: there\u2019s a centenary looming). Quantum\u2019s got such a grip on our imagination, we tend to forget that it was the johnny-come-lately icing on an already fairly indigestible cake.<\/p>\n

A good twenty years before physical reality was shown to be unreliable at small scales, mathematicians were pretzeling our very ideas of space. They had no choice: at the Louisiana Purchase Exposition in 1904, Henri Poincarre, by then the world\u2019s most famous geometer, described how he was trying to keep reality stuck together in light of Maxwell\u2019s famous equations of electromagnetism (Maxwell\u2019s work absolutely refused to play nicely with space). In that talk, he came startlingly close to gazumping Einstein to a theory of relativity.
\nAlso at the same exposition was Sir Ronald Ross, who had discovered that malaria was carried by the bite of the anopheles mosquito. He baffled and disappointed many with his presentation of an entirely mathematical model of disease transmission — the one we use today to predict, well, just about everything, from pandemics to political elections.
\nIt\u2019s hard to imagine two mathematical talks less alike than those of Poincarre and Ross. And yet they had something vital in common: both shook their audiences out of mere three-dimensional thinking.<\/p>\n

And thank goodness for it: Ellenburg takes time to explain just how restrictive Euclidean thinking is. For Euclid, the first geometer, living in the 4th century BC, everything was geometry. When he multiplied two numbers, he thought of the result as the area of a rectangle. When he multiplied three numbers, he called the result a \u201csolid\u2019. Euclid\u2019s geometric imagination gave us number theory; but tying mathematical values to physical experience locked him out of more or less everything else. Multiplying four numbers? Now how are you supposed to imagine that in three-dimensional space?<\/p>\n

For the longest time, geometry seemed exhausted: a mental gym; sometimes a branch of rhetoric. (There\u2019s a reason Lincoln\u2019s Gettysburg Address characterises the United States as \u201cdedicated to the proposition that all men are created equal\u201d. A proposition is a Euclidean term, meaning a fact that follows logically from self-evident axioms.)<\/p>\n

The more dimensions you add, however, the more capable and surprising geometry becomes. And this, thanks to runaway advances in our calculating ability, is why geometry has become our go-to manner of explanation for, well, everything. For games, for example: and extrapolating from games, for the sorts of algorithmical processes we saddle with that profoundly unhelpful label \u201cartificial intelligence\u201d (\u201cartificial alternatives to intelligence\u201d would be better).<\/p>\n

All game-playing machines (from the chess player on my phone to DeepMind\u2019s AlphaGo) share the same ghost, the \u201cMarkov chain\u201d, formulated by Andrei Markov to map the probabilistic landscape generated by sequences of likely choices. An atheist before the Russian revolution, and treated with predictable shoddiness after it, Markov used his eponymous chain, rhetorically, to strangle religiose notions of free will in their cradle.<\/p>\n

From isosceles triangles to free will is quite a leap, and by now you will surely have gathered that Shape is anything but a straight story. That\u2019s the thing about mathematics: it does not advance; it proliferates. It\u2019s the intellectual equivalent of Stephen Leacock\u2019s Lord Ronald, who \u201cflung himself upon his horse and rode madly off in all directions\u201d.<\/p>\n

Containing multitudes as he must, Ellenberg\u2019s eyes grow wider and wider, his prose more and more energetic, as he moves from what geometry means to what geometry does in the modern world.<\/p>\n

I mean no complaint (quite the contrary, actually) when I say that, by about two-thirds the way in, Ellenberg comes to resemble his friend John Horton Conway. Of this game-playing, toy-building celebrity of the maths world, who died from COVID last year, Ellenburg writes, \u201cHe wasn\u2019t being wilfully difficult; it was just the way his mind worked, more associative than deductive. You asked him something and he told you what your question reminded him of.\u201d
\nThis is why Ellenberg took the trouble to draw out a mind map at the start of his book. This and the index offer the interested reader (and who could possibly be left indifferent?) a whole new way (\u201cmore associative than deductive\u201d) of re-reading the book. And believe me, you will want to. Writing with passion for a nonmathematical audience, Ellenberg is a popular educator at the top of his game.<\/p>\n","protected":false},"excerpt":{"rendered":"

Reading Jordan Ellenberg’s Shape for the Telegraph, 7 July 2021 \u201cOne can\u2019t help feeling that, in those opening years of the 1900s, something was in the air,\u201d writes mathematician Jordan Ellenburg. It\u2019s page 90, and he\u2019s launching into the second … Continue reading →<\/span><\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[617,78],"tags":[905,533,904,223,418,906,523,287],"class_list":["post-3308","post","type-post","status-publish","format-standard","hentry","category-books-reviews-and-opinion","category-reviews-and-opinion","tag-drunkards-walk","tag-geometry","tag-markov","tag-mathematics","tag-prediction","tag-randomness","tag-statistics","tag-telegraph"],"_links":{"self":[{"href":"http:\/\/www.simonings.net\/index.php?rest_route=\/wp\/v2\/posts\/3308","targetHints":{"allow":["GET"]}}],"collection":[{"href":"http:\/\/www.simonings.net\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"http:\/\/www.simonings.net\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"http:\/\/www.simonings.net\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"http:\/\/www.simonings.net\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=3308"}],"version-history":[{"count":1,"href":"http:\/\/www.simonings.net\/index.php?rest_route=\/wp\/v2\/posts\/3308\/revisions"}],"predecessor-version":[{"id":3310,"href":"http:\/\/www.simonings.net\/index.php?rest_route=\/wp\/v2\/posts\/3308\/revisions\/3310"}],"wp:attachment":[{"href":"http:\/\/www.simonings.net\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=3308"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"http:\/\/www.simonings.net\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=3308"},{"taxonomy":"post_tag","embeddable":true,"href":"http:\/\/www.simonings.net\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=3308"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}