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You, me, and even the most calming manatee are nothing but impurities in an otherwise beautifully simple universe.

Your existence wasn’t just predicated on amorousness and luck of your ancestors, but on an almost absurdly finely tuned universe. Had the universe opted to turn up the strength of the electromagnetic force by even a small factor, poof

if the universe were only minutely denser than the one we inhabit, it would have collapsed before it began.

Albert Einstein called her the most “significant” and “creative” female mathematician of all time, and others of her contemporaries were inclined to drop the modification by sex. She invented a theorem that united with magisterial concision two conceptual pillars of physics: symmetry in nature and the universal laws of conservation. Some consider Noether’s theorem, as it is now called, as important as Einstein’s theory of relativity; it undergirds much of today’s vanguard research in physics

At Göttingen, she pursued her passion for mathematical invariance, the study of numbers that can be manipulated in various ways and still remain constant. In the relationship between a star and its planet, for example, the shape and radius of the planetary orbit may change, but the gravitational attraction conjoining one to the other remains the same — and there’s your invariance.

Noether’s theorem, an expression of the deep tie between the underlying geometry of the universe and the behavior of the mass and energy that call the universe home. What the revolutionary theorem says, in cartoon essence, is the following: Wherever you find some sort of symmetry in nature, some predictability or homogeneity of parts, you’ll find lurking in the background a corresponding conservation — of momentum, electric charge, energy or the like. If a bicycle wheel is radially symmetric, if you can spin it on its axis and it still looks the same in all directions, well, then, that symmetric translation must yield a corresponding conservation.

The public middle school, which is part of a larger complex that includes Corona del Mar High School, now is attracting more students who would normally have gone to private school in this affluent Orange County district, said Principal Rebecca Gogel. “There has been a significant change in student behavior,” she said.

But what has gone into the design of this school goes much deeper than sheer aesthetics. Architects are now applying neuroscience to design schools, hospitals, community centers and even single-family homes.

meshing of architecture and brain science is starting to gain traction. Architects are studying the way the brain reacts to various environments through brain scanners and applying the findings to their designs.

after a decade of failed attempts, David Smith, a self-described shape hobbyist of Bridlington in East Yorkshire, England, suspected that he might have finally solved an open problem in the mathematics of tiling: That is, he thought he might have discovered an “einstein.”

In less poetic terms, an einstein is an “aperiodic monotile,” a shape that tiles a plane, or an infinite two-dimensional flat surface, but only in a nonrepeating pattern. (The term “einstein” comes from the German “ein stein,” or “one stone” — more loosely, “one tile” or “one shape.”)

Your typical wallpaper or tiled floor is part of an infinite pattern that repeats periodically; when shifted, or “translated,” the pattern can be exactly superimposed on itself