Simply creating AI that can navigate a three-dimensional world without getting stuck has been the undoing of many a game.

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And just as Matisse's paeans to the tension between the three-dimensional world and the flat canvas have been dismissed as "decorative" because of their glorious color and patterning, Veronese's lush figure groups have been similarly labeled, for similar reasons.

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Kay wants to take computing forward with his next great invention, an operating system that puts the user in a three-dimensional graphic world with scores of other users, all computing collaboratively and communicating through audio and visual messaging.

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His conjecture, made in 1904, was that in this four-dimensional world, all closed three-dimensional surfaces that are simply connected could be transformed to look like a three-dimensional sphere.

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Our spatial world is three-dimensional.

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But so is verifying anyone's identity in a world where even three-dimensional objects like Stradivarius violins can easily be "printed", let alone copied en masse.

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The world at the molecular level is a three-dimensional one with its own busy, complex environment.

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