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The New York Times published an article in its magazine about one of the greatest mathematicians living today, Terry Tao. The first paragraph should whet one's appetite for the rest of the article:
This April, as undergraduates strolled along the street outside his modest office on the campus of the University of California, Los Angeles, the mathematician Terence Tao mused about the possibility that water could spontaneously explode. A widely used set of equations describes the behavior of fluids like water, but there seems to be nothing in those equations, he told me, that prevents a wayward eddy from suddenly turning in on itself, tightening into an angry gyre, until the density of the energy at its core becomes infinite: a catastrophic ‘‘singularity.’’ Someone tossing a penny into the fountain by the faculty center or skipping a stone at the Santa Monica beach could apparently set off a chain reaction that would take out Southern California.
There are some people who are just too smart, and this guy is one of them.
(Score: 5, Informative) by maxwell demon on Saturday July 25 2015, @10:55PM
Actually, physicists already know what's going on: It's the second law of thermodynamics. Certain things can happen in principle, but have an astronomically low probability to happen, and therefore won't actually happen. There's also nothing in the equations of notion that forbids the scattered pieces of a broken glass to suddenly jump from the floor, combine at some place on the floor to form the complete glass, and jump up onto the table. We know that can happen in principle because we know that the reverse process, the glass falling down and breaking into pieces that get scattered around, can happen, and the fundamental equations are symmetric under time reversal; therefore the self-forming glass is also a solution of those equations. But don't expect it to happen; it's so unlikely that even if there had been pieces of a broken glass lying around on every square meter of the surface of every planet in the known universe since the big bang, it would not have happened once.
Indeed, if you only go for what the equations allow without caring for the probability, you might also survive a nuclear bomb going off right above your head.
The Tao of math: The numbers you can count are not the real numbers.
(Score: 1, Funny) by Anonymous Coward on Sunday July 26 2015, @08:17AM
Entropy says the glass isn't putting the band back together. Hollywood isn't about to make a movie about it.
(Score: 2) by HiThere on Sunday July 26 2015, @06:07PM
Well, for that statement to work you need a few modifications to the experimental conditions. If friction is present, e.g., reassembling the glass isn't symmetric to shattering it...you need to totally eliminate friction and have a closed environment with totally elastic walls. (I think the elastic walls are needed because otherwise you get heat loss when the pieces of glass encounter the wall.)
Javascript is what you use to allow unknown third parties to run software you have no idea about on your computer.
(Score: 2) by maxwell demon on Sunday July 26 2015, @06:13PM
Microscopically, friction is also nothing else but ordinary motion. The non-reversibility of friction is again the second law in action. If you look at the fundamental equations, everything is indeed symmetrical. Including the interactions which macroscopically we see as friction.
The Tao of math: The numbers you can count are not the real numbers.