Ok, i dunno if you guys are perplexed about this for real, so i will just post.
this is the effect similar to "can you boil water in a single piece of paper", and the answer is yes....
First and foremost, it's not hot water, i think the best results are achieved through the use of warm water (70 degree-ish vs 30 degrees or room temp). Then it's fairly simple thermodynamics, warm water will loose more heat, faster then cold water, loosing heat (that you can see as steam), will cool the warm water a lot faster then cold water, thus bringing down the temperature dramatically faster, and thus freezing it faster then the water that was initially at room temperature.
Vapor is the goal here, it takes lots of energy to convert water to its gas form, so then you have much energy released, colder water forms a convection current, exposing more hot water to the surface, which releases more steam, which uses up a lot of energy, and you have this process going on, the water will cool at an astonishingly faster rate, just not quite as uniformly as the room temperature water. end result is reaching a lower temperature over a fairly short period of time, and thus freezing faster
i know it's not a very scientific explanation, but that is as close as i can describe it, with my knowledge and without further investigation, but i hope it does well enough. linear math here would not work either, i would imagine that in order to describe this, you would need a fairly complex math model, water is one of those weird liquids, and liquids are hard to describe in math anyways... then it gets complicated by convection flows, vapor, change in density and the fact that below 4 degrees C, water will have a cold crust on top, which complicates everything, oh and did i mention supercooling?
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