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  • Would mathematics exist if people didn't?

    如果沒有人類,那麼數學還會存在嗎?

  • Since ancient times, mankind has hotly debated

    自從遠古時代,人類就開始激烈的辯論

  • whether mathematics was discovered or invented.

    是我們發現了數學還是我們發明了數學。

  • Did we create mathematical concepts to help us understand the universe around us,

    是我們創造了數學的概念 來幫助我們理解周圍的世界,

  • or is math the native language of the universe itself,

    還是數學本來就是宇宙的一種語言,

  • existing whether we find its truths or not?

    我們是否發現了它的真理?

  • Are numbers, polygons and equations truly real,

    數字,形狀和等式真實存在,

  • or merely ethereal representations of some theoretical ideal?

    還是它們僅僅是 理論上想法的縹緲的代表?

  • The independent reality of math has some ancient advocates.

    ‘數學獨立於現實’在古代有不少擁護者。

  • The Pythagoreans of 5th Century Greece believed numbers were both

    5世紀希臘的畢達哥拉斯相信

  • living entities and universal principles.

    數字既是存在的實體,也是宇宙的原理。

  • They called the number one, "the monad," the generator of all other numbers

    他們把數字“一”叫做單個體。 它是其他所有數字的創造者,

  • and source of all creation.

    也是所有創造的源泉。

  • Numbers were active agents in nature.

    數字是自然界活躍的特工。

  • Plato argued mathematical concepts were concrete

    比拉圖認為數學的概念應是具體的,

  • and as real as the universe itself, regardless of our knowledge of them.

    就像宇宙本身那樣真實, 無論我們是否意識到。

  • Euclid, the father of geometry, believed nature itself

    幾何之父-歐幾里得相信自然本身

  • was the physical manifestation of mathematical laws.

    是數學定律的物理表現。

  • Others argue that while numbers may or may not exist physically,

    其他人則認為不管數字是否存在實體,

  • mathematical statements definitely don't.

    數學的命題完全不是真實存在的。

  • Their truth values are based on rules that humans created.

    它們的真實價值急於人類所創立的原則。

  • Mathematics is thus an invented logic exercise,

    因此數學是一種被發明的邏輯練習,

  • with no existence outside mankind's conscious thought,

    在人類理性的想法之外並不存在,

  • a language of abstract relationships based on patterns discerned by brains,

    它只是一種被大腦識別、 用特殊格式所書寫的抽象語言,

  • built to use those patterns to invent useful but artificial order from chaos.

    用來避免發生混亂的。

  • One proponent of this sort of idea was Leopold Kronecker,

    這種理論的支持者之一 是利奧波德·克羅內克,

  • a professor of mathematics in 19th century Germany.

    他是十九世紀德國數學教授。

  • His belief is summed up in his famous statement:

    他的信仰可以總結如下:

  • "God created the natural numbers, all else is the work of man."

    “上帝創造了自然界的數字, 除此之外都是人類的工作。“

  • During mathematician David Hilbert's lifetime,

    在數學家大衛·希爾伯特的一生中,

  • there was a push to establish mathematics as a logical construct.

    他曾急著把數學作為邏輯來構建。

  • Hilbert attempted to axiomatize all of mathematics,

    希爾伯特曾嘗試 把所有數學的概念都變成公理,

  • as Euclid had done with geometry.

    就像歐幾里德在幾何上的成就一樣。

  • He and others who attempted this saw mathematics as a deeply philosophical game

    他和其他嘗試這樣做的人 將數學視作一種深層次的哲學遊戲,

  • but a game nonetheless.

    但仍然是一個遊戲。

  • Henri Poincaré, one of the father's of non-Euclidean geometry,

    非歐幾里得幾何之父 亨利·龐加萊

  • believed that the existence of non-Euclidean geometry,

    認為非歐幾里得幾何地存在

  • dealing with the non-flat surfaces of hyperbolic and elliptical curvatures,

    處理非水平的雙曲線表面, 以及橢圓曲度,

  • proved that Euclidean geometry, the long standing geometry of flat surfaces,

    證明歐幾里德幾何學,非水平表面的幾何學

  • was not a universal truth,

    並不是一個普遍的事實,

  • but rather one outcome of using one particular set of game rules.

    還不如用以一套特定遊戲規則所得出的結果。

  • But in 1960, Nobel Physics laureate Eugene Wigner

    但在1960年,後來的諾貝爾物理獎 獲得者尤金·維格納

  • coined the phrase, "the unreasonable effectiveness of mathematics,"

    套用了一句老話,“數學離譜得有效率,“

  • pushing strongly for the idea that mathematics is real

    把“數學證實存在”的想法硬推出來,

  • and discovered by people.

    並被人們所發現。

  • Wigner pointed out that many purely mathematical theories

    維格納指出,許多僅僅是憑空想出的數學理論,

  • developed in a vacuum, often with no view towards describing any physical phenomena,

    大多沒有任何觀點描述任何物理現象,

  • have proven decades or even centuries later,

    並在幾十年,甚至幾世紀後被證明,

  • to be the framework necessary to explain

    成為有必要解釋宇宙是如何

  • how the universe has been working all along.

    獨立運作的結構。

  • For instance, the number theory of British mathematician Gottfried Hardy,

    比如,英國數學家戈弗雷·哈代的數論。

  • who had boasted that none of his work would ever be found useful

    戈弗雷自誇稱自己描述任何在真實世界的現象

  • in describing any phenomena in the real world,

    都不會對建立

  • helped establish cryptography.

    密碼學有幫助。

  • Another piece of his purely theoretical work

    他的另一個理論性的成果,

  • became known as the Hardy-Weinberg law in genetics,

    戈弗雷·哈代遺傳定律, 為大家所知,

  • and won a Nobel prize.

    並獲得了諾貝爾獎。

  • And Fibonacci stumbled upon his famous sequence

    斐波那契在看一組被理想化的兔子總數時,

  • while looking at the growth of an idealized rabbit population.

    磕磕絆絆得出了他的著名的數列。

  • Mankind later found the sequence everywhere in nature,

    人類後來發現那個數列砸大自然中到處都是,

  • from sunflower seeds and flower petal arrangements,

    從向日葵的種子和花瓣排列規律,

  • to the structure of a pineapple,

    到菠蘿的結構,

  • even the branching of bronchi in the lungs.

    甚至是肺上的支氣管分支, 無處不在。

  • Or there's the non-Euclidean work of Bernhard Riemann in the 1850s,

    還有十九世紀50年代的 波恩哈德·黎曼的非歐裡機得研究成果,

  • which Einstein used in the model for general relativity a century later.

    愛因斯坦一世紀後才在研究遺傳關聯性的時候 才在模型中使用到它。

  • Here's an even bigger jump:

    這兒甚至有一個更大的跳躍:

  • mathematical knot theory, first developed around 1771

    紐結理論。 它在1771年左右形成,

  • to describe the geometry of position,

    用來描述位置的幾何學,

  • was used in the late 20th century to explain how DNA unravels itself

    在20世紀晚期被用來解釋 DNA在自我複製過程中

  • during the replication process.

    是如何解開自己的。

  • It may even provide key explanations for string theory.

    它甚至會為弦理論提供關鍵性的證明。

  • Some of the most influential mathematicians and scientists

    人類歷史上 最有影響力的機位數學家和科學家

  • of all of human history have chimed in on the issue as well,

    也已經就這個問題發表了自己的看法,

  • often in surprising ways.

    而且經常還是以令人驚訝的方式。

  • So, is mathematics an invention or a discovery?

    那麼,數學是一個發明還是一個發現呢?

  • Artificial construct or universal truth?

    是人工構建物還是普遍的真理?

  • Human product or natural, possibly divine, creation?

    是人類產物,還是自然 (或者是上帝)的創造物?

  • These questions are so deep the debate often becomes spiritual in nature.

    這些問題十分深奧, 辯論常常會變成自然的靈歌。

  • The answer might depend on the specific concept being looked at,

    答案也許隨著研究的特定概念的變化而變化,

  • but it can all feel like a distorted zen koan.

    但它可以像是一個扭曲的禪宗公案。

  • If there's a number of trees in a forest, but no one's there to count them,

    如果森林里有很多樹,但沒人去數,

  • does that number exist?

    那麼數字到底存在嗎?

Would mathematics exist if people didn't?

如果沒有人類,那麼數學還會存在嗎?

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B2 中高級 中文 美國腔 TED-Ed 數學 幾何 人類 數字 理論

TED-Ed】數學是發現還是發明?- Jeff Dekofsky (【TED-Ed】Is math discovered or invented? - Jeff Dekofsky)

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    稲葉白兎 發佈於 2021 年 01 月 14 日
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