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

"星夜"背後的秘密：梵谷與紊流 - Natalya St.Clair

譯者: yi lee 審譯者: 韻庭 顏

One of the most remarkable aspects of the human brain

人類大腦有一個驚人的特性

is its ability to recognize patterns and describe them.

能認出事物運作的模式並描述它

Among the hardest patterns we've tried to understand

其中讓我們最難了解的

is the concept of turbulent flow in fluid dynamics.

是流體力學中紊流的概念

The German physicist Werner Heisenberg said,

德國物理學家維爾納·海森堡曾說

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

「當我見到上帝時，我要問祂兩個問題：

why relativity and why turbulence?

相對論與紊流為什麼存在？

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

我相信祂可以回答前者」

As difficult as turbulence is to understand mathematically,

用數理方法理解紊流相當困難

we can use art to depict the way it looks.

但是我們可以把它畫出來

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

1889年六月，梵谷畫了日出前

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

從聖雷米療養院窗戶望出去的景色

in Saint-Rémy-de-Provence,

where he'd admitted himself after mutilating his own ear

他將自己耳朵割除後

in a psychotic episode.

住在那個精神病院

In "The Starry Night," his circular brushstrokes

在畫作《星空》裡，他用漩渦狀的筆觸

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

畫出充滿卷雲和渦狀星星的夜空

Van Gogh and other Impressionists represented light in a different way

梵谷和後期印象派畫家 以另一種形式呈現光影

than their predecessors,

而前期畫家則是著重於刻畫動作

seeming to capture its motion, for instance,

across sun-dappled waters,

例如：陽光斑駁的水面

or here in star light that twinkles and melts

在湛藍夜空中 加上乳白色波浪線條

through milky waves of blue night sky.

畫出搖曳的星光

The effect is caused by luminance,

這個效果是光的亮度

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

也就是油畫中色彩強度造成的

The more primitive part of our visual cortex,

我們視覺皮質裡比較原生的部分

which sees light contrast and motion, but not color,

判斷光線對比和物體運動 而非辨識色彩

will blend two differently colored areas together

也就是將兩種不同顏色

但同樣亮度的區域混在一起

if they have the same luminance.

But our brains' primate subdivision

但視覺皮質中演化的分支

will see the contrasting colors without blending.

會區辨顏色對比而不會將他們混合

With these two interpretations happening at once,

當兩種視覺處理方式同時發生時

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

印象派畫中的光線變得非常突出

That's how this and other Impressionist works

這就是為什麼印象派的作品

use quickly executed prominent brushstrokes

傾向用大膽的筆觸來捕捉

to capture something strikingly real about how light moves.

細微的光影流動

Sixty years later, Russian mathematician Andrey Kolmogorov

六十年後俄羅斯數學家 安德雷·柯爾莫哥洛夫

開拓了數理上對紊流的理解

furthered our mathematical understanding of turbulence

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

他提出在一個長度R的紊水流中

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

能量會與R的5/3次方成正比

Experimental measurements show Kolmogorov

實驗數據證實柯爾莫哥洛夫的模型

was remarkably close to the way turbulent flow works,

非常接近紊流的流動方式

although a complete description of turbulence

雖然紊流完整的解釋

remains one of the unsolved problems in physics.

仍是物理學中一項待解的難題

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

有能量梯度的紊流型態都相類似

換句話說 大渦流傳遞能量給小渦流

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

which do likewise at other scales.

這在其他規模也適用

Examples of this include Jupiter's Great Red Spot,

舉例來說，木星上的紅斑

cloud formations and interstellar dust particles.

雲、星際塵埃都包含在內

In 2004, using the Hubble Space Telescope,

2004年 科學家用哈伯天文望遠鏡

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

觀測到星星周圍 有漩渦狀的星塵和氣體

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

因此想起了梵谷的「星空」

This motivated scientists from Mexico, Spain and England

促使墨西哥、西班牙 和英國的科學家

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

開始研究梵谷畫作裡的顏色亮度

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

他們發現梵谷畫中有紊流結構

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

類似柯爾莫哥洛夫的模型

The researchers digitized the paintings,

研究者將這些畫作數位化

and measured how brightness varies between any two pixels.

並測量兩點像素間的亮度

From the curves measured for pixel separations,

以及像素間的曲率

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

他們認為梵谷精神病期間的作品

behave remarkably similar to fluid turbulence.

精準畫出紊流的型態

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

而平穩期間叼著菸斗的自畫像

則不符合紊流的結構

showed no sign of this correspondence.

And neither did other artists' work

其他畫家所作類似紊流的畫

that seemed equally turbulent at first glance,

like Munch's "The Scream."

如孟克的「吶喊」，也不符合

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

雖然我們可以說是梵谷的天賦

enabled him to depict turbulence,

讓他描繪出紊流的結構

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

人們很難在承受痛苦時

that in a period of intense suffering,

精準表達如此困難的概念

Van Gogh was somehow able to perceive and represent

梵谷竟然能夠理解並呈現

one of the most supremely difficult concepts

世界上最深奧複雜的概念

nature has ever brought before mankind,

甚至早於人類出現的概念

and to unite his unique mind's eye

他用獨特的慧眼

with the deepest mysteries of movement, fluid and light.

看透移動、水流和光影的奧秘