Da Vinci's Vitruvian Man of math - James Earle

達文西的《维特鲁威人》數學 - 詹姆士．厄爾

譯者: Nathalie Cheng 審譯者: Kuanju Chou

This image of the Vitruvian Man, taken from Leonardo's sketches,

這個维特鲁威人人的圖像，

是取自達文西的素描，

has become one of the most recognizable symbols of the Renaissance.

它已經成為文藝復興時期

最為人所知的代表之一。

But why?

但是為什麼呢？

這只是簡單的筆墨畫，不是嗎？

It's a simple pen and ink drawing, right?

錯了！

Wrong!

Let's start to answer this question with a math problem.

讓我們從一道數學題

來回答這個問題。

我知道怎麼計算一個圓的面積。

I know how to calculate the area of a circle.

我用圓周率的值，

I take the value for pi and multiply it by the radius squared.

再乘以半徑的平方。

I also know how to take the area of a square.

我也知道怎麼計算正方形的面積，

I multiply the base by itself.

我用底的邊長再乘上它自己。

But how can I take the area of a circle and create a square with an equal area?

但是我要怎麼用圓的面積

來做出一個等面積的正方形？

This is a problem often called "squaring a circle"

這個問題常被稱為「化圓為方」

在遠古時期就被提出來過。

that was first proposed in the ancient world.

And like many ideas of the ancient world,

就像許多在遠古時期就有的想法，

它在文藝復興時期被賦予新的生命。

it was given new life during the Renaissance.

結果我們發現，

As it turns out, this problem is impossible to solve

因為圓周率本身的特性，

這個問題無解，

because of the nature of pi,

but that's another story.

但這又是另一個故事了。

Leonardo's sketch,

里奧納多的素描，

把人放在一個圓和一個正方形

which is influenced by the writings of the Roman architect, Vitruvius,

的中心點，

其實是受到羅馬時期的建築師

places a man firmly at the center of a circle and a square.

维特鲁威許多著作的影響。

Vitruvius claimed the navel is the center of the human body

维特鲁威人主張

肚臍是人體的中心點

and that if one takes a compass and places the fixed point on the navel,

如果一個人拿圓規

把定點定在肚臍上，

a circle can be drawn perfectly around the body.

可以圍繞著人體畫一個完美的圓。

Additionally, Vitruvius recognized that arm span and height

另外，维特鲁威也發現

人手臂伸長的長度

have a nearly perfect correspondence in the human body,

和人的身高近乎一致，

thus placing the body perfectly inside a square as well.

所以也可以把一個人 完美的放進正方形裡頭。

Leonardo used the ideas of Vitruvius

里奧納多利用魯特威的這些想法

to solve the problem of squaring a circle metaphorically

以比喻的方式將人體 當做兩個不同圖形的面積，

using mankind as the area for both shapes.

來解決這個化圓為方的問題。

不過里奧納多並不是只有想到魯特威而已。

Leonardo wasn't just thinking about Vitruvius, though.

There was an intellectual movement in Italy at the time called Neoplatonism.

義大利在當時

有個知識份子的運動，

稱作新柏拉圖主義。

This movement took an old concept from the 4th century

這個運動把西元四世紀時

柏拉圖和亞理斯多德 所提出的一個古老觀念，

developed by Plato and Aristotle,

called "The Great Chain of Being."

被稱作「存在巨鏈」。

This belief holds that the universe has a hierarchy resembling a chain,

這個觀念認為宇宙是個像鎖鏈一般的

階級制度，

and that chain starts at the top with God,

關係鏈的頂端是上帝，

沿著下來有天使，

then travels down through the angels, planets, stars, and all lifeforms

星球，

星星，

和所有的生命體，

再來尾端是惡魔和魔鬼。

before ending with demons and devils.

Early in this philosophic movement,

在這個哲學運動的早期，

人類被認為是被擺在

it was thought that mankind's place in this chain was exactly in the center.

這個關係鏈的正中間。

Because humans have a mortal body accompanied by an immortal soul,

因為人類擁有會腐壞的軀殼，

又有著不死的靈魂，

we divide the universe nicely in half.

我們漂亮的把宇宙一分為二。

Around the time Leonardo sketched the Vitruvian Man, however,

但在里奧納多繪製

维特鲁威人的時期，

a Neoplatonist named Pico Della Mirandola had a different idea.

一個名為皮科·德拉·米蘭多拉 的新柏拉圖主義者

有不同的想法。

He pried mankind off the chain

他把人類由關係鏈中移出來，

並主張人類有一個獨特的能力

and claimed that humans have a unique ability

可以任意選擇他們所要的位置。

to take any position they want.

Pico claimed that God desired a being capable of comprehending

皮科主張上帝希望

人類有能力可以理解

the beautiful and complicated universe he had created.

祂所創造的這個美麗又複雜的宇宙。

This led to the creation of mankind,

所以當他創造人類，

which he placed at the center of the universe

這個祂擺在宇宙中心的生命，

with the ability to take whatever form he pleases.

有能力來選擇自己所想要的方式。

Mankind, according to Pico,

人類，依照皮科的主張，

could crawl down the chain and behave like an animal

可以爬下關係鏈並行為像動物一般，

or crawl up the chain and behave like a god,

或這爬上關係鏈表現的像上帝一樣，

這是我們的選擇。

it's our choice.

Looking back at the sketch,

回到這個素描，

we can see that by changing the position of the man,

我們可以看到當我們改變人的姿勢，

他可以填滿一個圓形和一個正方形

he can fill the irreconcilable areas of a circle and a square.

這兩個無法相容的面積。

If geometry is the language the universe is written in,

如果幾何學是創造宇宙的語言，

then this sketch seems to say we can exist within all its elements.

那這個素描像是在說，

我們可以存在於它所有的元素中。

人類可以填滿任何的圖形，

Mankind can fill whatever shape he pleases geometrically

他欣賞幾何學原理，

and philosophically as well.

同時也欣賞哲學原理。

In this one sketch, Leonardo was able to combine

在這一個素描裡面，

里奧納多可以包含

the mathematics, religion, philosophy, architecture,

數學，

信仰，

哲學，

建築，

and artistic skill of his age.

和他當時代的藝術技巧。

No wonder it has become such an icon for the entire time period.

難怪它成為一個可以成為

整個時期的代表。