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Have you ever noticed that some rounded stones are almost spherical, while others are kind
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of flat like a bar of soap?
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The spherical stones form that way because they never have the chance to settle into
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a preferred orientation: they're either sloshing around in pot holes, or rolling along the
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bottom of a river, or if they're small enough, getting blown around by the wind.
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Since they have no preferred orientation, these stones get weathered the same amount
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on all sides, and they'll end up looking the same from all sides as well.
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That's spherical symmetry!
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But for flat stones, even if they're a smooth disk perfect for skipping, there's obviously
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a preferred, or special, orientation - the direction perpendicular to, or 'away from'
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the flat sides.
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Where did this preference come from?
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And how do flat stones get flat?
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Gravity.
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It's kind of like the difference between dumplings and biscuits.
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A dumpling is a lump of dough dropped in a pot of water, and gravity doesn't really affect
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its orientation very much when it's rolling and bobbing about.
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A biscuit, on the other hand, is a lump of dough pulled down by gravity onto a baking
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sheet, so it tends to be flat and has a clear top and bottom.
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And while the details are ultimately more complicated, when sedimentary rock forms,
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it forms layers, or when stones too heavy to roll are worn down by abrasion at the bottom
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of a river or lake, they tend to be worn a bit flat.
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In both cases the preferred direction is dictated by gravity.
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And gravity is also why we build buildings in layers, with a basement, floors and a roof
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– if we were in outer space without a preferred direction from gravity, we'd probably just
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live in blobs.