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为何1.618034如此重要

Why is 1.618034 So Important?

试想是否有这样一个完美的数字
Imagine if there was a perfect number,
一个如此无瑕的数字
a single number so flawless,
其构成了所有艺术与音乐的基础
it formed the basis for all art and music.
一个重要到能够使用在
A number so important that it could be used
数学和物理法则的数字
across the disciplines of mathematics and physics.
一个有深刻目的的数字
And a number so profoundly purposeful
以至于自然世界和宇宙都屈服于它的奇想
that the natural world and the universe would bend to its whims.
这一数字 即是1.618034
That number, is 1.618034.
让我们一同探究为何它如此重要
So let’s find out why it’s so important.
[音乐]
[music]
第五 一些说明
At number five, an explanation.
[音乐]
[music]
斐波那契数列是一串
The Fibonacci sequence is a string of numbers
以0和1开始的数字
that begins with 0 and 1,
通过相邻两个数字相加
which can be extended infinitely
来得到数列中的下一个数字
by adding up any two consecutive numbers
斐波那契数列可以扩展至无穷
to find the next in the sequence.
当我们把0和1相加 将得到1
When we add 0 and 1, we get, 1,
即第三个斐波那契数
which is the third Fibonacci number.
接着把1和1加到一起 得到第四个斐波那契数 即2
Then we add 1 and 1 to obtain our fourth Fibonacci number which is 2.
如果我们继续进行这一基本动作 将得到
And if we continue with elementary exercise in addition, we get numbers
3 5 8 13 21 34 55 89等等
3 5 8 13 21 34 55 89, et cetera,
这一模式可以一直延续到无穷大
in a pattern that can be extended all the way to infinity.
比萨的莱昂纳多 也就是斐波那契
This sequence was introduced to the West in 1202
在1202年将这一数列引进到西方
by Leonardo of Pisa, also known as Fibonacci,
尽管这一数列已在此一千多年前
although it had already been identified by Indian mathematicians
由印度的数学家们所证实
over a thousand years beforehand.
但是来自比萨的这家伙率先宣布了这一数列
But this guy from Pisa shouted it first.
因此得以用他的名字来命名此数列
So he gets to name it after himself,
这就是事情经过
that’s just how things work.
随着世界对于数学的理解进一步发展
As the world began to develop its understanding of mathematics,
人们很快意识到这一串数字至关重要
we soon realised this string of digits was of fundamental importance.
如今人们已通过各种实际方式应用了这一知识
And today we apply this knowledge in all manner of practical ways.
搜索算法 股票交易 赌博赔率
Search algorithms, stock trading, gambling odds,
都利用了斐波那契数列
all make use of the Fibonacci sequence.
而你最可能遇到斐波那契数列的方式
But the way in which you have most likely encountered it
就是通过神秘的黄金比例了
is via the mysterious golden ratio.
它可能出现在比味精和杰西·海曼组合更随机的东西中
Which appears in more random stuff than MSG in Jesse Heiman combined.
[音乐]
[music]
第四 黄金比例
At four, the golden ratio.
黄金比例是用于描述
The golden ratio is a mathematical term
两个数字之间关系的数学术语
used to describe the relationship of two figures,
其中的数字似乎存在某种互补的比例
whereby the numbers seem to be in some form of complementary ratio.
如果有一个数字a和一个比a小的数字b
If you have a number a and a lower number b,
并且 a/b 与 (a+b)/a 相等
Then they two are in the golden ratio if the ratio between a versus b
那么a和b就是成黄金比例的
is similar to the ratio between the sum of a+b versus a.
这一比例的希腊字母是Φ
The Greek letter ascribed to this ratio is Φ.
其数值缩短为1.618034
And its value is contracted to 1.618034.
基本上 任何有着接近这一比例的东西
Basically, anything which comes close to this value
都被认为是成完美比例的
in terms of its ratio is said to be perfectly proportioned.
例如
For example,
一个长12.94厘米 宽8厘米的矩形
a rectangle that measures 12.94 by 8 centimeters
是成黄金比例的
is in the golden ratio.
因为12.94除以8是1.6175
Because 12.94 divided by 8 is 1.6175.
如果我们把矩形的长和宽相加
And if we add the width and length of the rectangle together
得到20.94
to get 20.94.
其与长度为12.94的较长边的比值
The ratio between this and the longer side, 12.94,
是1.6182
is 1.6182.
黄金比例可以用于计算完美螺旋
The golden ratio can be used to calculate perfect spirals,
黄金三角 以及其他的形状和图案
golden triangles, and other shapes and patterns too.
而这与斐波那契数列有什么关系呢
But what does this have to do with the Fibonacci sequence?
[音乐]
[music]
第三 联系
At three, the link.
为了将斐波那契数列和黄金比例联系起来
To link the Fibonacci sequence and the golden ratio,
必须考虑两个连续的斐波那契数之间的比
we must look at the ratio between two consecutive Fibonacci numbers,
同时观察这个比例的模式
and observe the pattern in this ratio takes as you go on.
因为结果表明 沿着斐波那契数列越向后
Because it turns out that the further along the Fibonacci sequence you go,
两个相邻数字的比例
the closer the ratio between any two numbers
越接近黄金比例
is to the golden ratio.
3和2的比值是1.5
The ratio between 3 and 2 is 1.5.
5和3的比值是1.66
The ratio between 5 and 3 is 1.66.
如果跳过一些数字 去计算
And if we skip along a few to see the ratio
第12个和第13个斐波那契数的比值
between the 12th and 13th Fibonacci numbers,
我们会发现它们的比值是1.6179
we’ll see that their ratio is 1.6179.
而144与233的比值是1.6180
The ratio between 144 and 233 is 1.6180.
等等等等
And so on and so forth.
正如我们之前提到的
As we mentioned earlier,
黄金比例是1.618034
the golden ratio is 1.618034.
因此 黄金比例和斐波那契数列之间
So, clearly, the golden ratio and the Fibonacci sequence
显然存在某些我们仍不清楚的关系
have some sort of link which we haven’t worked out yet.
这也是为什么诸多聪明人
And that is why so many smart folks
完全沉迷于黄金比例
have become absolutely obsessed with it.
[音乐]
[music]
第二 用途
At number two, the uses.
自从黄金比例几千年前被发现以来
The golden ratio has fascinated the world’s most knowledgeable people
世上最有学识的人都一直为之着迷
for millennia since its discovery.
我们已在人类创造的顶尖作品中
And we have seen its influence in some of the finest works
见证了它的影响力
mankind has ever produced.
柏拉图对黄金比例的研究
Plato’s study into the golden ratio
被用于帕台农神庙的设计
was used in the designs of the Parthenon.
埃及人在金字塔的策划和建造中展现了黄金比例
The Egyptians displayed it in the planning and construction of the Pyramids.
而诸如泰姬陵 巴黎圣母院
And the likes of the Taj Mahal, Notre Dame,
以及凯鲁万大清真寺
and the Great Mosque of Kairouan,
都依照这一重要的数学法则建造
were also built according to this important mathematical law.
从达芬奇到达利等艺术家
Artists from Da Vinci to Dali
也将黄金比例融入到他们绘画的设计中
also incorporated the golden ratio in the layout of their paintings.
黄金比例也出现在德彪西
And the ratio can also be detected in the music of Debussy,
巴赫 莫扎特 肖邦 贝多芬的音乐中
Bach, Mozart, Chopin, and Beethoven.
就连在圣经中也提到以黄金比例建造的物体
Even the Bible mentions things being constructed in the golden ratio
诺亚方舟和约柜
with Noah’s Ark and the Ark of the Covenant
都是按照上帝所定下的比例建造的
both built in accordance with the ratio-driven commandments laid down by God.
然而 有一点是我们不能完全确定的
However, the one thing we’re not entirely sure about is
那就是 这些或者这一切都是故意的吗?
whether any or all of this was deliberate.
现代艺术家和建筑师了解黄金比例
Modern artists and architects know about the golden ratio,
并懂得有目的地应用于他们的作品中
and are known to apply it purposefully to their works.
我们知道 至少一些历史建筑和艺术品
And we know that at least some historical buildings and artworks
是由了解黄金比例和其价值的人创造的
were created by people who knew of the golden ratio and its value.
而这一令人费解又令人愉悦的比例
But this inexplicably pleasing proportion has been used
也被忽视其存在的人所用
by people ignorant of its existence, too.
所以说黄金比例只是
So is the golden ratio merely something
令所有人着迷的东西吗?
which all human beings are attracted to?
它是不是本来就会令人满足呢?
Is it something that we find inherently satisfying?
而对于1.618034这一数字的热爱
And is this love of the number 1.618034
仅仅限于人类吗?
limited only to humans?
[音乐]
[music]
第一 自然的设计
And at number one, nature’s design.
黄金比例是自然界普遍适用的法则吗?
Is the golden ratio a universal law applied by nature?
证据表明似乎如此
The evidence seems to suggest so,
而且之前提到的莱昂纳多·达芬奇
and the aforementioned Leonardo da Vinci
或许已在他的一些名作中暗示了这一点
may have alluded to this in some of his most famous works.
《Divina proportione》是一本在1498年
The ‘Divina proportione’ was a mathematical textbook
由达芬奇作插图的数学教科书
illustrated by Da Vinci in 1498.
在这本书以及他的画作《维特鲁威人》中
And in both this and his drawing of ‘The Vitruvian Man’,
他指出了人体内蕴含黄金比例的例子
he points out examples of the golden ratio found within the human body.
心理学家也指出 面部 身体以及骨骼
Psychologists have also noted that people whose facial,
符合黄金比例的人通常被认为
body and bone structures adhere to the golden ratio
比对应部位不成黄金比例的人更有吸引力
are often deemed to be more attractive than their non-proportional counterparts.
如果你想立刻暂停视频去测量自己的脸
And if you’d like to pause the video to go measure your face right now,
我们完全理解
we totally understand.
但你也许更愿意稍等一下
But you might want to hold on a second,
因为人类体内蕴含黄金比例
because the most shocking example of the golden ratio
的最震惊的例子更加有趣
within the human beings is far more interesting.
你知道吗 黄金比例也适用于我们的DNA
Did you know that the golden ratio even applies to our DNA?
这是真的 我们的双曲螺旋结构DNA
It’s true, as both our double helix spirals
以及单个DNA分子的组成
and the composition of a single DNA molecule
似乎都是按照神圣的黄金比例组建的
both seem to have been made in accordance with the divine proportion of the golden ratio.
而这不仅仅出现在人类身上
And it’s not just humans either.
正如我们看到的 黄金比例展现在蜗牛壳中
As we’ve seen, the ratio demontrated in the shells of snails,
一朵花的花瓣数量中
the number of petals in a flower,
种子头内单个种子的排列
and the arrangement of individual seeds within seed heads,
松果 树枝 以及根系
pine cones, tree branches, and root systems
都遵从黄金比例
also follow the golden ratio,
某些种类的藻类和某些动物的身体也是如此
as do some forms of algae and the bodies of certain animals.
有些生物甚至按照黄金比例生活
Some creatures even live according to the golden ratio,
据悉 蜂群将雄性和雌性的比例维持在
with honeybee colonies known to maintain the ratio of males to females
1到1.618之间
at 1 to 1.618.
那么 这一比例是否证明自然是以某种形式设计的?
So, is this ratio evidence that nature has been somehow designed?
地球上的一切都是上帝或先进的外星种族
Was everything on earth created by a god or advanced extraterrestrial race
依照一确定数字创造的吗?
to adhere to a certain number?
看起来确实有点可疑
It does look a little suspicious,
尤其是当你发现黄金比例
especially when you also find out that the golden ratio
也适用于飓风 螺旋星系
also applies to hurricanes, spiral galaxies,
以及量子级的物体
and objects at the quantum level, too.
我们将在额外的视频中讨论如下想法
We are going to explore this idea in our bonus video,
《黄金比例:智能设计的证明?》
“The Golden Ratio: Evidence of Intelligent Design?”,
你可以在我们的 Patreon 网站上观看网址是 patreon.com/strangemysteries
which you can watch on our Patreon page atpatreon.com/strangemysteries.
通过可以随时取消的
For a $2 a month pledge,
每月2美元的定期捐款
which you can cancel at any time,
你可以观看这个视频
you’ll get to watch this
实际上 你也能观赏到我们的额外内容
and indeed all of our bonus content
以更深入地探讨
which goes deeper and darker
YouTube 所允许的每一个课题
into every topic that YouTube allows.
如果你不想捐款也没关系 我们仍然爱你
If you don’t want to donate, then it’s cool, we still love you.
我们也会继续尽可能地提供
And we’ll continue to provide the best content we can
符合YouTube限制的最佳内容
under YouTube’s restrictions.
如果你看了我们近期的视频
As you’ll see, if you watch our recent video
《人类过去的缺失部分》 你就会看到
on missing pieces of humanity’s past.

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视频概述

1.618034被认为是完美的数字,自然界以及人类的设计中无不蕴含着这一数字,本视频带你一同探索为何1.618034如此重要。

听录译者

绛蓝

翻译译者

绛蓝

审核员

审核员B

视频来源

https://www.youtube.com/watch?v=keLN89CWZ-A

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