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What are you arguing for exactly? That there may in theory exist some abstract spherical volume of perfect water in vacuum that freezes entirely in an instant that none of us will ever encounter in our lives? But that it is exactly what we should imagine when we think of how ice forms-- humanity's mental image should be of water instantly transforming into ice? Please clarify:)

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Clear water freezes exactly at 0 degrees. I guess the graduality depends on if you think about this as interpolating the water temperature, or interpolating the energy given/taken from a body of water.

> Clear water freezes exactly at 0 degrees.

Water never arrives at 0 degrees all at once, so for practical purposes no. Even if it did, you cannot measure the temperature of every water molecule simultaneously to prove it.

In a way - yes. Ice in nature forms usually by water cooling heterogeneously, but not by water being below 0 all the time and everywhere and the ice forming slowly in some areas then.

Not just in nature, your glass of water in the freezer also has uneven temperature throughout the volume and becomes ice gradually (though faster than a lake)

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