The unexpected math behind Van Gogh's "Starry Night" - Natalya St. Clair

梵高《星夜》背后的数学秘密

翻译人员: Sunny Wang 校对人员: Qingqing Mao

One of the most remarkable aspects of the human brain

人脑最神奇的功能之一

is its ability to recognize patterns and describe them.

就是识别出模式并把其描述出来的能力。

Among the hardest patterns we've tried to understand

流体动力学里湍流的概念

is the concept of turbulent flow in fluid dynamics.

就是我们探求过的最艰深的模式之一。

The German physicist Werner Heisenberg said,

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：

"When I meet God, I'm going to ask him two questions:

why relativity and why turbulence?

为什么创造相对论？为什么创造湍流？

I really believe he will have an answer for the first."

我相信他会对前者有个解释。”

As difficult as turbulence is to understand mathematically,

因为用数学去理解湍流太困难，

we can use art to depict the way it looks.

我们可以用艺术来描绘它的样子。

In June 1889, Vincent van Gogh painted the view just before sunrise

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，

from the window of his room at the Saint-Paul-de-Mausole asylum

透过窗户画下了日出前的景象。

in Saint-Rémy-de-Provence,

where he'd admitted himself after mutilating his own ear

在一次精神病发作中，他自残耳朵，

in a psychotic episode.

之后便自愿进入疗养院。

In "The Starry Night," his circular brushstrokes

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。

create a night sky filled with swirling clouds and eddies of stars.

Van Gogh and other Impressionists represented light in a different way

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。

than their predecessors,

seeming to capture its motion, for instance,

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，

across sun-dappled waters,

or here in star light that twinkles and melts

又如在《星夜》里用深蓝夜空中乳白色的波动

through milky waves of blue night sky.

来表现星星的闪烁。

The effect is caused by luminance,

这种效果源于亮度的不同，

the intensity of the light in the colors on the canvas.

即画布上不同颜色反光强度的不同。

The more primitive part of our visual cortex,

我们视觉皮层中较初级的部分

which sees light contrast and motion, but not color,

能区分光强以及感知光的运动但不能感知颜色，

will blend two differently colored areas together

所以如果两个不同颜色的色块有相同的亮度，

if they have the same luminance.

就会被混在一起。

But our brains' primate subdivision

可是我们大脑中的灵长类部分

will see the contrasting colors without blending.

能把不同颜色区分开来。

With these two interpretations happening at once,

当这两种功能同时发生，

the light in many Impressionist works seems to pulse, flicker and radiate oddly.

印象派的画作便流光溢彩地闪烁、跳跃了起来。

That's how this and other Impressionist works

梵高等印象派画家就是这样用犀利的笔触

use quickly executed prominent brushstrokes

捕捉了光的动感，

to capture something strikingly real about how light moves.

使得画作栩栩如生。

Sixty years later, Russian mathematician Andrey Kolmogorov

六十年后，俄国数学家安德雷·柯尔莫哥洛夫

furthered our mathematical understanding of turbulence

推进了我们对湍流的数学理解。

when he proposed that energy in a turbulent fluid at length R

他提出：长度为R的湍流的能量

varies in proportion to the 5/3rds power of R.

与R的三分之五次幂成正比。

Experimental measurements show Kolmogorov

实验测量显示柯尔莫哥洛夫的结果

was remarkably close to the way turbulent flow works,

与湍流的实际运动规律极其近似。

although a complete description of turbulence

然而，物理学界至今也未能

remains one of the unsolved problems in physics.

完全地描述湍流。

A turbulent flow is self-similar if there is an energy cascade.

湍流是在不同能级上是自相似的，

In other words, big eddies transfer their energy to smaller eddies,

也就是说，大的涡流会把能量传给小的涡流，

which do likewise at other scales.

后者只是前者的缩小版。

Examples of this include Jupiter's Great Red Spot,

这样的例子包括：木星的大红斑、

cloud formations and interstellar dust particles.

云的形成以及星际尘埃。

In 2004, using the Hubble Space Telescope,

2004年，通过哈勃太空望远镜

scientists saw the eddies of a distant cloud of dust and gas around a star,

科学家观测到一颗遥远恒星周围的气体和尘埃云。

and it reminded them of Van Gogh's "Starry Night."

这让他们想到了梵高的《星夜》。

This motivated scientists from Mexico, Spain and England

受到启发的墨西哥、西班牙和英国科学家们

to study the luminance in Van Gogh's paintings in detail.

决定详细地研究梵高画作中的亮度。

They discovered that there is a distinct pattern of turbulent fluid structures

他们发现：梵高的许多画作中都隐藏着

close to Kolmogorov's equation hidden in many of Van Gogh's paintings.

显著的与柯氏方程相近的湍流结构的模式。

The researchers digitized the paintings,

研究者们把画作数字化，

and measured how brightness varies between any two pixels.

然后测量不同像素间的亮度差异。

From the curves measured for pixel separations,

从反应像素分离的曲线中

they concluded that paintings from Van Gogh's period of psychotic agitation

他们得出结论：梵高精神焦虑时期的画作中

behave remarkably similar to fluid turbulence.

表现出了与湍流极其相似的特性。

His self-portrait with a pipe, from a calmer period in Van Gogh's life,

他病情较稳定时期的那副拿着烟斗的自画像

showed no sign of this correspondence.

则并未出现类似现象。

And neither did other artists' work

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，

that seemed equally turbulent at first glance,

like Munch's "The Scream."

比如蒙克的《尖叫》。

While it's too easy to say Van Gogh's turbulent genius

虽然我们不能就这样说

enabled him to depict turbulence,

梵高具有描绘湍流的天赋。

it's also far too difficult to accurately express the rousing beauty of the fact

但是有一个美丽的事实同样难以解释清楚：

that in a period of intense suffering,

在极度的痛苦中，

Van Gogh was somehow able to perceive and represent

梵高不可思议地认识并表现出

one of the most supremely difficult concepts

一种在人类之前就已出现的

nature has ever brought before mankind,

极其深奥的概念，

and to unite his unique mind's eye

并用他独特的想象力

with the deepest mysteries of movement, fluid and light.

去感受流光动影的终极秘密。