此地無科學證明。
作者／Geraint Lewis (雪黎大學天文學教授)
譯者／吳京
As an astrophysicist, I live and breathe science. Much of what I read and hear is couched in the language of science which to outsiders can seem little more than jargon and gibberish. But one word is rarely spoken or printed in science and that word is “proof”. In fact, science has little to do with “proving” anything.
These words may have caused a worried expression to creep across your face, especially as the media continually tells us that science proves things, serious things with potential consequences, such as turmeric can apparently replace 14 drugs, and more frivolous things like science has proved that mozzarella is the optimal cheese for pizza.
Surely science has proved these, and many other things. Not so!
身為一個天文學家，我的生活與科學息息相關。我所讀所聞的皆為科學的語言，對圈外人而言，這似乎代表行話、術語加上胡言亂語。而其中有個字眼在科學圈中甚少出現，乃「證明 (proof) 」也。事實上，科學家幾乎也沒證明過任何事。
這些言論可能會讓你眉頭一皺，尤其是媒體常告訴我們科學家在證明事情，一些嚴肅而意義深遠的事情。比如說「薑黃可以取代14種藥物」，又好比說「科學證明馬蘇里拉 (mozzarella) 起司是做披薩的最佳選擇」之類的冷知識。
當然啦，科學家已證明了這些東西，還有其他種種.........才怪！
The way of the mathematician
數學家之道
Mathematicians prove things, and this means something quite specific. Mathematicians lay out a particular set of ground rules, known as axioms, and determine which statements are true within the framework.
One of best known of these is the ancient geometry of Euclid. With only a handful of rules that define a perfect, flat space, countless children over the last few millenia have sweated to prove Pythagoras’s relation for right-angled triangles, or that a straight line will cross a circle at most at two locations, or a myriad of other statements that are true within Euclid’s rules.
數學家之道
Mathematicians prove things, and this means something quite specific. Mathematicians lay out a particular set of ground rules, known as axioms, and determine which statements are true within the framework.
One of best known of these is the ancient geometry of Euclid. With only a handful of rules that define a perfect, flat space, countless children over the last few millenia have sweated to prove Pythagoras’s relation for right-angled triangles, or that a straight line will cross a circle at most at two locations, or a myriad of other statements that are true within Euclid’s rules.
Whereas the world of Euclid is perfect, defined by its straight lines and circles, the universe we inhabit is not. Geometrical figures drawn with paper and pencil are only an approximation of the world of Euclid where statements of truth are absolute.
數學家們做證明，證明某些特殊的事。數學家們會擺出一套特定的基本規則，稱之為公理 (axioms) ，並在這個架構下決定各種命題的真偽。
最著名的例子要屬幾何學的始祖歐幾里得，他藉由少數幾條規則定義出完美的平面，幾千年來讓無以數計的孩子依循這些規則揮汗如雨地證明畢式定理、證明一條直線最多與圓交於兩點和其他各式各樣的證明題。
無論歐幾里得用直線和圓所定義出的世界有多完美，真實的宇宙並非如此。紙筆繪出的幾何圖形也只能近似於那個命題和真理都不容置疑的歐幾里得世界。
Over the last few centuries we’ve come to realise that geometry is more complicated than Euclid’s, with mathematical greats such as Gauss, Lobachevsky and Riemann giving us the geometry of curved and warped surfaces.
In this non-Euclidean geometry, we have a new set of axioms and ground-rules, and a new set of statements of absolute truth we can prove.
These rules are extremely useful for navigating around this (almost-)round planet. One of Einstein’s (many) great achievements was to show that curving and warping spacetime itself could explain gravity.
Yet, the mathematical world of non-Euclidean geometry is pure and perfect, and so only an approximation to our messy world.
過去的幾個世紀中，幾位數學大師，如高斯 (Gauss) 、羅巴切夫斯基 ( Lobachevsky) 和黎曼 (Riemann) ，又發展了彎曲纏繞表面上之幾何學，讓我們認識到比歐幾里德更複雜的東西。
在非歐式幾何學中，我們有另一套新的公理及基本規則，也有全新的命題要去證明。
這些規則對於解決繞著地球跑的導航問題十分有幫助。愛因斯坦的偉大成就之一，更展示了彎曲纏繞的表面可以解釋重力現象。
可惜，非歐式幾合的數學世界如此地純粹而完美，因而只是我們這個亂糟糟的世界的一個近似而已。
Yet, the mathematical world of non-Euclidean geometry is pure and perfect, and so only an approximation to our messy world.
過去的幾個世紀中，幾位數學大師，如高斯 (Gauss) 、羅巴切夫斯基 ( Lobachevsky) 和黎曼 (Riemann) ，又發展了彎曲纏繞表面上之幾何學，讓我們認識到比歐幾里德更複雜的東西。
在非歐式幾何學中，我們有另一套新的公理及基本規則，也有全新的命題要去證明。
這些規則對於解決繞著地球跑的導航問題十分有幫助。愛因斯坦的偉大成就之一，更展示了彎曲纏繞的表面可以解釋重力現象。
可惜，非歐式幾合的數學世界如此地純粹而完美，因而只是我們這個亂糟糟的世界的一個近似而已。
Just what is science?
問世間科學為何物？
But there is mathematics in science, you cry. I just lectured on magnetic fields, line integrals and vector calculus, and I am sure my students would readily agree that there is plenty of maths in science.
And the approach is same as other mathematics: define the axioms, examine the consequences.
Einstein’s famous E=mc^2, drawn from the postulates of how the laws of electromagnetism are seen by differing observers, his special theory of relativity, is a prime example of this.
「可是
不僅如此，連方法脈絡都和數學很像：定義公理，檢驗結果。最好的例子是著名的公式E=mc^2，係愛因斯坦以他的狹義相對論推導而來，其基本假設是去搞清楚由不同的觀測者來看，電磁波遵行的定律為何。
But such mathematical proofs are only a part of the story of science.
The important bit, the bit that defines science, is whether such mathematical laws are an accurate description of the universe we see around us.
To do this we must collect data, through observations and experiments of natural phenomena, and then compare them to the mathematical predictions and laws. The word central to this endeavour is “evidence”.
但這樣的數學證明只是科學的一部份。
很重要的小小一部份，定義科學的小小部份，期能用這些數學定律精準地描述出我們所見、所處的宇宙。
為此我們必須對自然現象進行觀測與實驗，搜整數據拿來和數學定律及預測做比對。關於這些努力，我們賦予的名稱是找「證據(evidence)」。
The scientific detective
名偵探「科學」
But such mathematical proofs are only a part of the story of science.
The important bit, the bit that defines science, is whether such mathematical laws are an accurate description of the universe we see around us.
To do this we must collect data, through observations and experiments of natural phenomena, and then compare them to the mathematical predictions and laws. The word central to this endeavour is “evidence”.
但這樣的數學證明只是科學的一部份。
很重要的小小一部份，定義科學的小小部份，期能用這些數學定律精準地描述出我們所見、所處的宇宙。
為此我們必須對自然現象進行觀測與實驗，搜整數據拿來和數學定律及預測做比對。關於這些努力，我們賦予的名稱是找「證據(evidence)」。
The scientific detective
名偵探「科學」
The mathematical side is pure and clean, whereas the observations and experiments are limited by technologies and uncertainties. Comparing the two is wrapped up in the mathematical fields of statistics and inference.
Many, but not all, rely on a particular approach to this known as Bayesian reasoning to incorporate observational and experimental evidence into what we know and to update our belief in a particular description of the universe.
Here, belief means how confident you are in a particular model being an accurate description of nature, based upon what you know. Think of it a little like the betting odds on a particular outcome.
數學的描述純粹而清爽，反之觀測和實驗會受到技術及不準確性質的限制。比較這兩個面相則是統計及推理的工作。
許多 (但並非所有) 這類的工作會利用一種稱之為「貝斯推論( Bayesian reasoning)」的方法，將觀測和實驗所得的證據套入已知模型，讓我們評估這個對宇宙的說明可以「相信」幾分。
這邊說的「相信」意指基於已知訊息，我們對特定模型能否精確描述自然法則有多少的信心，可以把它想成是壓在特定結論上的賭注。
Our description of gravity appears to be pretty good, so it might be odds-on favourite that an apple will fall from a branch to the ground.
But I have less confidence that electrons are tiny loops of rotating and gyrating string that is proposed by super-string theory, and it might be a thousand to one long-shot that it will provide accurate descriptions of future phenomena.
我們對重力的描述看起來滿好的，所以壓注在「蘋果會從樹枝上掉到地上」的勝率很高。
但我對「基於超弦理論，電子是旋轉又自旋弦的微小迴圈」就沒那麼多信心了，壓這一注的賠率高達一千比一，但勝算微乎其微，除非有天這個理論能準確地說明某些現象。
So, science is like an ongoing courtroom drama, with a continual stream of evidence being presented to the jury. But there is no single suspect and new suspects regularly wheeled in. In light of the growing evidence, the jury is constantly updating its view of who is responsible for the data.
But no verdict of absolute guilt or innocence is ever returned, as evidence is continually gathered and more suspects are paraded in front of the court. All the jury can do is decide that one suspect is more guilty than another.
因此，科學就像一齣比「鳥來伯與十三姨」還長壽的法庭劇，證據不斷地被提交給陪審團。然而這個法庭上沒有單一的嫌犯，新冒出的嫌疑人輪番前來受審，而鑑於越來越多的證據，陪審團經常改變判決，宣告哪位嫌犯該為哪些數據負責。
但這些判決的內容中，不會裁定誰是絕對有罪或無罪，當法庭上陳列著不停被搜整的證據及成行成伍的嫌犯時，陪審團只會說誰比誰更有嫌疑。
What has science proved?
科學證明過什麼？
In the mathematical sense, despite all the years of researching the way the universe works, science has proved nothing.
Every theoretical model is a good description of the universe around us, at least within some range of scales that it is useful.
But exploring into new territories reveals deficiencies that lower our belief in whether a particular description continues to accurately represent our experiments, while our belief in alternatives can grown.
以數學的意義來說，儘管人類研究宇宙如何運行已那麼久了，科學根本沒證明過什麼。
每一個理論模型對我們周圍的宇宙都能提出好的描述，至少在某個誤差範圍內，這些描述是說得通的。
但是，新領域的探索每每揭示某些描述的不足，即便這種說法曾經圓融地解釋可重覆的實驗，我們對他的信心還是會轉投到下一種說法。
Will we ultimately know the truth and hold the laws that truly govern the workings of the cosmos within our hands?
While our degree of belief in some mathematical models may get stronger and stronger, without an infinite amount of testing, how can we ever be sure they are reality?
I think it is best to leave the last word to one of the greatest physicists, Richard Feynman, on what being a scientist is all about:
我們最終會知道真理，並掌握宇宙運作真正依循的法則嗎？
我們對一些數學模型的信心程度也許會越來越強，但沒有無限的測試，我們怎麼能肯定他就是事實？
我想，偉大的物理學家理查德·費曼(Richard Feynman)對於身為一個科學家的自述，是本文最佳的結語：
譯按：現在網路那麼發達，大家搜尋一下就可以查到什麼事情有經過科學證明囉~
資料來源(Source of the materials)：
https://theconversation.com/wheres-the-proof-in-science-there-is-none-30570
原文於The Conversation網站公開授權轉載
譯文為屬館主自我練習，同意任何形式轉載，不成熟處敬請多加撻伐。
Many, but not all, rely on a particular approach to this known as Bayesian reasoning to incorporate observational and experimental evidence into what we know and to update our belief in a particular description of the universe.
Here, belief means how confident you are in a particular model being an accurate description of nature, based upon what you know. Think of it a little like the betting odds on a particular outcome.
數學的描述純粹而清爽，反之觀測和實驗會受到技術及不準確性質的限制。比較這兩個面相則是統計及推理的工作。
許多 (但並非所有) 這類的工作會利用一種稱之為「貝斯推論( Bayesian reasoning)」的方法，將觀測和實驗所得的證據套入已知模型，讓我們評估這個對宇宙的說明可以「相信」幾分。
這邊說的「相信」意指基於已知訊息，我們對特定模型能否精確描述自然法則有多少的信心，可以把它想成是壓在特定結論上的賭注。
Our description of gravity appears to be pretty good, so it might be odds-on favourite that an apple will fall from a branch to the ground.
But I have less confidence that electrons are tiny loops of rotating and gyrating string that is proposed by super-string theory, and it might be a thousand to one long-shot that it will provide accurate descriptions of future phenomena.
我們對重力的描述看起來滿好的，所以壓注在「蘋果會從樹枝上掉到地上」的勝率很高。
但我對「基於超弦理論，電子是旋轉又自旋弦的微小迴圈」就沒那麼多信心了，壓這一注的賠率高達一千比一，但勝算微乎其微，除非有天這個理論能準確地說明某些現象。
 |
| 弦理論 |
So, science is like an ongoing courtroom drama, with a continual stream of evidence being presented to the jury. But there is no single suspect and new suspects regularly wheeled in. In light of the growing evidence, the jury is constantly updating its view of who is responsible for the data.
But no verdict of absolute guilt or innocence is ever returned, as evidence is continually gathered and more suspects are paraded in front of the court. All the jury can do is decide that one suspect is more guilty than another.
因此，科學就像一齣比「鳥來伯與十三姨」還長壽的法庭劇，證據不斷地被提交給陪審團。然而這個法庭上沒有單一的嫌犯，新冒出的嫌疑人輪番前來受審，而鑑於越來越多的證據，陪審團經常改變判決，宣告哪位嫌犯該為哪些數據負責。
但這些判決的內容中，不會裁定誰是絕對有罪或無罪，當法庭上陳列著不停被搜整的證據及成行成伍的嫌犯時，陪審團只會說誰比誰更有嫌疑。
 |
| 嫌犯都長這個樣子啊~ |
What has science proved?
科學證明過什麼？
In the mathematical sense, despite all the years of researching the way the universe works, science has proved nothing.
Every theoretical model is a good description of the universe around us, at least within some range of scales that it is useful.
But exploring into new territories reveals deficiencies that lower our belief in whether a particular description continues to accurately represent our experiments, while our belief in alternatives can grown.
以數學的意義來說，儘管人類研究宇宙如何運行已那麼久了，科學根本沒證明過什麼。
每一個理論模型對我們周圍的宇宙都能提出好的描述，至少在某個誤差範圍內，這些描述是說得通的。
但是，新領域的探索每每揭示某些描述的不足，即便這種說法曾經圓融地解釋可重覆的實驗，我們對他的信心還是會轉投到下一種說法。
Will we ultimately know the truth and hold the laws that truly govern the workings of the cosmos within our hands?
While our degree of belief in some mathematical models may get stronger and stronger, without an infinite amount of testing, how can we ever be sure they are reality?
I think it is best to leave the last word to one of the greatest physicists, Richard Feynman, on what being a scientist is all about:
我們最終會知道真理，並掌握宇宙運作真正依循的法則嗎？
我們對一些數學模型的信心程度也許會越來越強，但沒有無限的測試，我們怎麼能肯定他就是事實？
我想，偉大的物理學家理查德·費曼(Richard Feynman)對於身為一個科學家的自述，是本文最佳的結語：
I have approximate answers and possible beliefs in different degrees of certainty about different things, but I’m not absolutely sure of anything.
對於不同的事，我會有些近似的答案及可能的看法，我對這些看法會有不同程度的信心，但我對任何事情都沒有絕對的把握。
譯按：現在網路那麼發達，大家搜尋一下就可以查到什麼事情有經過科學證明囉~
資料來源(Source of the materials)：
https://theconversation.com/wheres-the-proof-in-science-there-is-none-30570
原文於The Conversation網站公開授權轉載
譯文為屬館主自我練習，同意任何形式轉載，不成熟處敬請多加撻伐。
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