Just an old classic this week, for Sunday reflection:
"It ain't what you don't know that gets you into trouble. It's what you know for sure that just ain't so." -- Mark TwainIndeed!...
“Today’s press conference in Helsinki was one of the most disgraceful performances by an American president in memory. The damage inflicted by President Trump’s naiveté, egotism, false equivalence, and sympathy for autocrats is difficult to calculate. But it is clear that the summit in Helsinki was a tragic mistake."
"...a lot of effort was devoted to the three-body problem: the motion of a system consisting of three point masses (such as Sun, Earth, Moon) moving under Newtonian gravitation. It's easy enough to write down the appropriate equations of motion; but immensely harder to solve them... As an aside: it has been said that one can gauge the progress of science by the value of n for which the n-body problem cannot be solved. In Newtonian mechanics the 3-body problem appears to be insoluble. In Relativity, it is the 2-body problem that causes trouble. Quantum Theory gets hung up on the 1-body problem (a particle); and Relativistic Quantum Field Theory runs into trouble with the 0-body problem (the vacuum)!"
-- Ian Stewart
“One of the most painful aspects of teaching mathematics is seeing my students damaged by the cult of the genius. That cult tells students that it’s not worth doing math unless you’re the best at math — because those special few are the only ones whose contributions really count.”-- Jordan Ellenberg
"Give me your tired, your poor, your huddled masses, yearning to breathe free...." Indeed.
...But it’s good to also be reminded of the America I grew up with... good to be "flushed with nostalgia and gratitude" on this day, and think back to a time of station wagons with wooden panels. If you’re a teacher (…or an American, or a human, or a dreamer, or a vertebrate ;)) and haven’t already done so, you must read this post from Phương now. That’s an order (...or no fireworks for you)!:
(If light source is at point "A" then point "B," amazingly, is in the dark.)
There are other solutions (not all polygonal) to the problem, and the Wikipedia take on it is here: