Mathematicians Prove Melting Ice Stays Smooth (quantamagazine.org) 22
After decades of effort, mathematicians now have a complete understanding of the complicated equations that model the motion of free boundaries, like the one between ice and water.
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Relax, its a (bad?) joke. I'm not even a Donald fan.
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when you lose an election you don't get to dictate terms.
We do get to demand that the other asshole follows the rules and discharges his duties faithfully. Not every conservative is a Trumper.
I missed out on a Nobel prize (Score:5, Funny)
I found out not only that melting ice is smooth, but also that I could do the splits, in New England decades ago. Unfortunately, I didn't publish on it .. in fact, I didn't tell anyone in order to keep my ego intact.
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I also have done the splits. But they were too large to fit in this margin.
(Look up "Fermat's Last Theorem" for the reference)
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And water is still wet.
It could be worse. (Score:2)
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Or how "Grizzly bear poop has little bells in it and smells like pepper
spray."
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Or how "Grizzly bear poop has little bells in it and smells like pepper
spray."
...or how as often as not, also has a pair of runners in it.
(I told that bastard playing dead works better. Turns out bears like a good chase.)
Mathematicians may have a model (Score:2)
of melting ice that is smooth but it doesn't "prove" anything. Mathematics doesn't "prove" the natural world it only attempts to model it.
How smooth are we talking? (Score:2)
Proof (Score:2)
Bartender! Another scotch on the rocks.
Mathematicians don't "prove" anything. (Score:2)
Their own axioms haven't been proven yet. And never will. [wikipedia.org]
Because in reality, there is no such thing as "proof". There is only statistical reliability.
And if that is ignored, it literally isn't science. Which sadly, is very often the case in mathematics (and in philosophy).
And yes, that XKCD comic you're now thinking of is very bad because of that missing clue, and a great example of the one-eyed leading the blind.
Re:Mathematicians don't "prove" anything. (Score:5, Interesting)
Because in reality, there is no such thing as "proof". There is only statistical reliability.
That may well apply to empirical knowledge, or to the kind of proof required in a court of law, but I don't think mathematical proofs work like that. For example, there is a proof that the square root of two cannot be expressed as the ratio of two integers. Are you suggesting that there might be some rare circumstances under which this is found to be false?
In this particular case, the mathematics is being applied to model the physical world. I presume the mathematics can be proved to be correct, but whether it accurately models the real world is a different problem. The puzzle here is that observations tell us that the surface of melting ice is always smooth, but flawed mathematical models suggested the possibility of singularities (sharp bits). The discovery described here is a refined mathematical model demonstrating that such singularities would rapidly dissipate, leaving a smooth surface.
Re:Mathematicians don't "prove" anything. (Score:4, Interesting)
Their own axioms haven't been proven yet.
You don't prove axioms. Axioms are things you assume, and then you derive various theorems, based on the axioms. Mathematicians have at various times tried to derive what were previously treated as axioms as theorems, derivable from more fundamental axioms. This was eventually shown to be impossible. Alan Turing's Halting Problem is an example of a mathematical system in which certain propositions can be neither proved nor disproved.
None of this actually stops mathematics being a valid system of reasoning. If you accept the truth of some axioms, then what logically follows from those axioms is also true, and if some proposition is inconsistent with the axioms, it is false. This seems perfectly reasonable to me, but then I am just an engineer, doing applied maths.
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This just means that you haven't personally accepted the axioms. I mean, on one hand, you've accepted that the natural numbers exist; that's a consequence of believing Goedel's Incompleteness, which is a statement about the natural numbers. On the other hand, you seem to deny that any progress has been made because of proof statements, but that seems like a foolish choice for somebody typing on a computer to make.
What are you trying to demonstrate here? This is Mt. Stupid (SMBC, not xkcd https://www.smbc-co [smbc-comics.com]
Well no shit (Score:3)
The news here isn't that melting ice remains smooth, it's that a better model for ice has been created.
Of course it remains smooth, any parts that stick out have more surface area to volume ratio and that increases the melt rate
Fascinating article (Score:2)
Fascinating article. Though I understood the image of a razor thin sheet of ice existing for a moment before flashing away, I had trouble visualizing the super-rare "branching singularity" but my understanding is that basically all the singularities are rare and end up being at the bottom of a cone or some fractal conical thing (not sure what "a cone as you zoom into it") meant. Really interesting and would like to see if anyone can take this information and create CG rendered videos. As I read the article