The unexpected math behind Van Gogh's "Starry Night”
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The unexpected math behind Van Gogh's "Starry Night"
One of the most remarkable aspects of the human brain is its ability to recognize patterns and describe them. Among the hardest patterns we've tried to understand is the concept of turbulent flow in fluid dynamics. The German physicist Werner Heisenberg said, "When I meet God, I'm going to ask him two questions: why relativity and why turbulence? I really believe he will have an answer for the first."
人脑最神奇的功能之一 就是识别出模式并把其描述出来的能力。 流体动力学里湍流的概念 就是我们探求过的最艰深的模式之一。 德国物理学家维尔纳·海森伯格曾说, “如果我碰到上帝,我会问他两个问题: 为什么创造相对论?为什么创造湍流? 我相信他会对前者有个解释。”
As difficult as turbulence is to understand mathematically, we can use art to depict the way it looks. In June 1889, Vincent van Gogh painted the view just before sunrise from the window of his room at the Saint-Paul-de-Mausole asylum in Saint-Rémy-de-Provence, where he'd admitted himself after mutilating his own ear in a psychotic episode. In "The Starry Night," his circular brushstrokes create a night sky filled with swirling clouds and eddies of stars. Van Gogh and other Impressionists represented light in a different way than their predecessors, seeming to capture its motion, for instance, across sun-dappled waters, or here in star light that twinkles and melts through milky waves of blue night sky. The effect is caused by luminance, the intensity of the light in the colors on the canvas. The more primitive part of our visual cortex, which sees light contrast and motion, but not color, will blend two differently colored areas together if they have the same luminance. But our brains' primate subdivision will see the contrasting colors without blending. With these two interpretations happening at once, the light in many Impressionist works seems to pulse, flicker and radiate oddly. That's how this and other Impressionist works use quickly executed prominent brushstrokes to capture something strikingly real about how light moves.
因为用数学去理解湍流太困难, 我们可以用艺术来描绘它的样子。 1899年6月,文森特·梵高 在他位于普罗旺斯圣雷米的圣保罗疗养院的房间里, 透过窗户画下了日出前的景象。 在一次精神病发作中,他自残耳朵, 之后便自愿进入疗养院。 在《星夜》中,他旋转的画笔 创造了一个满是旋转的星云的夜空。 梵高和其他印象派画家对光线的表达 采用了不同于前辈们的方法。 他们好似能捕捉光线的动感, 比如通过波光粼粼的水面表现光的跃动, 又如在《星夜》里用深蓝夜空中乳白色的波动 来表现星星的闪烁。 这种效果源于亮度的不同, 即画布上不同颜色反光强度的不同。 我们视觉皮层中较初级的部分 能区分光强以及感知光的运动但不能感知颜色, 所以如果两个不同颜色的色块有相同的亮度, 就会被混在一起。 可是我们大脑中的灵长类部分 能把不同颜色区分开来。 当这两种功能同时发生, 印象派的画作便流光溢彩地闪烁、跳跃了起来。 梵高等印象派画家就是这样用犀利的笔触 捕捉了光的动感, 使得画作栩栩如生。
Sixty years later, Russian mathematician Andrey Kolmogorov furthered our mathematical understanding of turbulence when he proposed that energy in a turbulent fluid at length R varies in proportion to the 5/3rds power of R. Experimental measurements show Kolmogorov was remarkably close to the way turbulent flow works, although a complete description of turbulence remains one of the unsolved problems in physics. A turbulent flow is self-similar if there is an energy cascade. In other words, big eddies transfer their energy to smaller eddies, which do likewise at other scales. Examples of this include Jupiter's Great Red Spot, cloud formations and interstellar dust particles.
六十年后,俄国数学家安德雷·柯尔莫哥洛夫 推进了我们对湍流的数学理解。 他提出:长度为R的湍流的能量 与R的三分之五次幂成正比。 实验测量显示柯尔莫哥洛夫的结果 与湍流的实际运动规律极其近似。 然而,物理学界至今也未能 完全地描述湍流。 湍流是在不同能级上是自相似的, 也就是说,大的涡流会把能量传给小的涡流, 后者只是前者的缩小版。 这样的例子包括:木星的大红斑、 云的形成以及星际尘埃。
In 2004, using the Hubble Space Telescope, scientists saw the eddies of a distant cloud of dust and gas around a star, and it reminded them of Van Gogh's "Starry Night." This motivated scientists from Mexico, Spain and England to study the luminance in Van Gogh's paintings in detail. They discovered that there is a distinct pattern of turbulent fluid structures close to Kolmogorov's equation hidden in many of Van Gogh's paintings.
2004年,通过哈勃太空望远镜 科学家观测到一颗遥远恒星周围的气体和尘埃云。 这让他们想到了梵高的《星夜》。 受到启发的墨西哥、西班牙和英国科学家们 决定详细地研究梵高画作中的亮度。 他们发现:梵高的许多画作中都隐藏着 显著的与柯氏方程相近的湍流结构的模式。
The researchers digitized the paintings, and measured how brightness varies between any two pixels. From the curves measured for pixel separations, they concluded that paintings from Van Gogh's period of psychotic agitation behave remarkably similar to fluid turbulence. His self-portrait with a pipe, from a calmer period in Van Gogh's life, showed no sign of this correspondence. And neither did other artists' work that seemed equally turbulent at first glance, like Munch's "The Scream."
研究者们把画作数字化, 然后测量不同像素间的亮度差异。 从反应像素分离的曲线中 他们得出结论:梵高精神焦虑时期的画作中 表现出了与湍流极其相似的特性。 他病情较稳定时期的那副拿着烟斗的自画像 则并未出现类似现象。 其他艺术家那些第一眼看起来 像是有湍流的作品亦是如此, 比如蒙克的《尖叫》。
While it's too easy to say Van Gogh's turbulent genius enabled him to depict turbulence, it's also far too difficult to accurately express the rousing beauty of the fact that in a period of intense suffering, Van Gogh was somehow able to perceive and represent one of the most supremely difficult concepts nature has ever brought before mankind, and to unite his unique mind's eye with the deepest mysteries of movement, fluid and light.
虽然我们不能就这样说 梵高具有描绘湍流的天赋。 但是有一个美丽的事实同样难以解释清楚: 在极度的痛苦中, 梵高不可思议地认识并表现出 一种在人类之前就已出现的 极其深奥的概念, 并用他独特的想象力 去感受流光动影的终极秘密。