Pyramids, cathedrals, and rockets exist not because of geometry or thermodynamics, but because they were first a picture in the minds of those who built them.

金字塔、大教堂和火箭的存在并不是因为几何形状或热力学，而是因为它们首先是建造它们的人的脑海中的图画。

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By tweaking the universe's geometry and the nature of its dark energy, the researchers corrected the picture until the galactic couples were indeed pointed in all directions, as would be expected.

通过调整宇宙的几何形状以及暗能量的性质，研究者们将宇宙图像校正成双星对都确实是指向所有的方向，正如所预期的那样。

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Ok, now I wanna draw a picture that represents what's this, this is algebra, what the geometry, what's the picture that goes with it?

好的，现在我要画一张图代表什么是…这是代数，什么是几何，这张图代表了什么？

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The two-dimensional equivalent is known as Penrose tiling (see picture above), after Sir Roger Penrose, the mathematician who put this form of geometry on a formal footing.

ECONOMIST: The 2011 Nobel prizes