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I'm convinced that the huge running-shoe collections of world-famous hip-hop artists and basketballers owe their existence primarily to one fundamental drawback of sneakers: it's really difficult to keep them clean. Expensive leather shoes can be polished. Canvas and polyester mesh, on the other hand, stain from the slightest brush with grass or subway grime, and they rip easily. You wear a pair of sneakers three times – even if only to rap awards ceremonies – and they look as if you've been been playing British Bulldog in gravel for a week.

Which is not good if your sneakers are meant to be evidence of your high spending power and fashionability. Hence all those walk-in closets shown on MTV Cribs, with racks and racks of proudly untouched Adidas and Nikes – they cannot be worn more than once or they will be wrecked, so new pairs must be bought weekly to maintain a perfect image. Large sneaker collections are evidence of the fundamental unwearability of this kind of fashion.

This is a paradox, for sneakers are meant, in theory, to be the most practical of footwear, designed to enhance athletic performance. The history of rubber-soled practical footwear, in fact, is documented in the strangely fascinating exhibition currently at the Bata Shoe Museum in Toronto, called Out of the Box: The Rise of Sneaker Culture. The show consists of a collection of more than 100 pairs of significant rubber-soled shoes, including some of the earliest rubber overshoes (hard, crusty things from the early 1800s) and uncomfortable-looking leather sprinting shoes, with medieval torture spikes, from the 1860s.

The show, curated by Elizabeth Semmelhack, contrasts the humble origins of the athletic footwear first called plimsolls in the 19th century (after the invention of flexible, vulcanized rubber in 1839) with the extravagant and absurdly expensive designs of Prada, McQueen and Jeremy Scott in the 21st. The word sneaker first came into use in the late-1800s because of the silent treading that could be effected with a rubber sole.

The first American sneakers were all produced by rubber companies – in the early 1900s, Goodyear, U.S. Rubber and Converse began selling iconic canvas designs that have hardly changed since. Keds, created by U.S. Rubber, were the first to use the word "sneakers" in marketing, in 1929. Bata itself made a fortune with its Czech version, called trampki.

A paradox emerged early: Although sneakers were inexpensive and casual shoes, the ability to participate in leisure activities was restricted to the upper classes. So in the beginning, sneakers actually signified privilege.

Now, design houses such as Lanvin and Jeremy Scott create limited, special-edition Nikes and Adidas for dandies and collectors. Some ludicrously elaborate ones are on display here. The bright green Prada "Kiltie Wingtips" from 2013 look like 1970s' golf shoes on acid; the 2012 Louboutins are covered in prickly gold spikes. Industrial designer Karim Rashid, who created the look of this whole display, contributed one of the most bizarre pairs, black Fessura boots with gold accents, a sultan's shoes from a dark fairy tale. These shoes have no relation to sport of any kind.

At the very end of the show you'll find the most rarefied result of the fixation with sneaker as art form: A 2009 design by postmodernist sculptor Tom Sachs for Nike is "unconstructed" – that is, it was meant to be sold unfinished, held together with pieces of tape and the logo scrawled on it with a Sharpie. The idea was to "engage the fetishization of branding." A purchaser would be acquiring not just an art work but a whole grad-school language.

The idea of the perfect sneaker put me in mind of Spike Lee's character Buggin Out from Do The Right Thing (1989), who wears a pristine pair of white Air Jordans and takes any scuff as a racist affront. The impossibility of maintaining the unblemished whiteness on his shoes leads to an inevitable confrontation.

This isn't just a black thing, though. My very white friend Alex used to buy white tennis shoes two pairs at a time – one to wear, the other to keep in a box, forever untouched. For him, knowing that one pair was clean, no matter what muddy environment he was forced to work in, constituted a kind of talismanic protection against the indignities of the world, a sense of perfection somewhere. This is, I think, partly why we put running shoes in museums: They will stay pristine forever, ideal footwear for a dream world.

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