不做數學，用π理解人生

You probably first met pi—the number used to calculate the circumference of a circle—when you were in school. If you aren"t mathematically inclined， you probably haven"t thought about it since then. But pi has practical applications for everyone as a real tool to better understand the universe and life itself. Without doing a lick of math.

In Visions of Infinity， mathematician Ian Stewart explains that it took about 2，000 years of great minds working at the problem of pi—moving from Euclidian geometry to algebraic calculations—to understand it as an irrational and transcendental number. In math terms， this means that pi cannot be represented by a fraction or an algebraic expression.

Numerically， pi is 3.14159， plus some. That added bit—the plus some—continues infinitely， a series of digits that never stop in a number sequence that doesn"t repeat， ever. In that infinite repetition lies pi"s greatest lesson.

Computers have calculated pi to the trillions of digits. But pi isn"t really solved and doesn"t appear to be solvable. That makes it a fantastic philosophical tool， a reminder to both the mathematically and mystically inclined of all that cannot be finally understood despite great effort.

Pi is wonderful precisely because it can only ever be understood theoretically，never actually grasped in its entirety. The lack of solution can be liberating， a demonstration of a classic axiom: The wisest among us know only how little we know.

The greatest mathematical minds of the centuries made advances. Yet every step forward in comprehension and calculation also reveals the limitations of human knowledge. Pi shows that knowing，wholly， is an impossibility.

The more we know， the more apparent it is that there is much more to know. For each individual， and for humanity as a whole， there is always that added bit that simply can"t be figured out， no matter how much information or education we possess.

Mysteries remain， always， and that can be a good thing. Like the digits of pi that have yet to be calculated and stretch on endlessly—「the plus some」 that can"t be figured out—serves us. It is proof that calculations are necessarily imperfect and theoretical. Things we can"t imagine could still happen，for better and for worse.

Life and the universe， like pi， don"t make perfect sense. We may have a very good idea of what is likely to occur under a certain set of circumstances， applying all the information we have at a given time， and we may attempt to insure against all unknowns.

But mystery is a constant， a sliver containing infinite possibilities， in our math and in our lives. That is what pi demonstrates so certainly. Math is our guide. But not our master. It cannot provide all the answers.

你初次認識π大概是在上學的時候，這個數字用來計算圓周。如果沒有數學愛好，你恐怕以後就沒想過它。但是，π對每個人都有實際用處，是一個實用的工具，幫助我們更好地認識天地萬物和生活本身。而你根本不用碰數學。

數學家伊恩·斯圖爾特在《放眼無限》中解釋說，偉大的思想者花了大約2000年研究π的問題，從歐幾里得幾何學到代數計算，才認識到π是一個無理數和超越數。從數學角度，這意味著π不能由分數或代數式表示。

π的數值為3.14159，後面還有一些東西。附加的一點點——後面那些東西——是無限不循環數字。正是在這種無限無盡中蘊含著π的最大教訓。

計算機算出π的萬億位數字。但是，π這個問題沒有解決，似乎也無法解決。這使它成為絕妙的哲學工具，提醒數學愛好者和難解之謎愛好者，有很多東西就算你使出九牛二虎之力也無法最終理解。

π之所以絕妙，恰恰因為它只能在理論上理解，而無法真正被全部領會。這種無解的局面可能令人釋然，證明一條經典的格言：我們當中最有智慧的人知道我們是多麼無知。

幾千年來，偉大的數學家取得了種種進步。但是，理解和計算上每前進一步都揭示出人類知識的局限。π表明，徹底地知道是不可能的。

我們知道得越多，就越明白我們不知道的東西要多得多。對每一個體乃至全人類而言，永遠存在「後面的一些」，無論我們掌握多少信息或受過多高的教育都弄不明白。

謎存在，永遠都存在，這可能是好事。像π的那些還沒有計算出來並且無窮無盡的數字——也就是弄不清楚的「後面的一些」——一樣，這對我們有益。它證明，計算一定不完美，一定只是理論上的。想像之外的情況總會發生，無論好壞。

就像π一樣，生命和宇宙有時候沒有百分之百的道理。對於在某些條件下可能發生什麼，我們或許抱有相當肯定的看法，利用給定時間內手頭的所有信息，並且可能試圖防備一切未知。

但是，謎是恆量，是含有無儘可能的存儲條，在數學和生活中都是如此。這就是π明確無誤揭示出的道理。數學是我們的指導，卻不是我們的主人。它不能給你所有的答案。（趙菲菲譯自美國石英財經網站3月14日文章）

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