異類之不一樣的成功啟示錄 第166期:美麗的理解誤區(qū)
其中一名叫雷妮的女生給他留下了深刻的印象，雷妮大概20多歲，黑色長(zhǎng)發(fā)，帶一個(gè)銀邊眼鏡。
In the tape, she is playing with a software program designed to teach algebra.
在錄影帶中，她正在操作一套用來(lái)教學(xué)的代數(shù)軟件程序。
On the screen is an x and a y axis.The program asks you to punch in the set of coordinates and then draws a line view on the screen.
屏幕上出現(xiàn)了Y軸和X軸，教學(xué)程序要求使用者劃一條線穿過座標(biāo)軸，舉個(gè)例子，如果我們?cè)赮軸上標(biāo)出5，在X軸上也標(biāo)出5，那么計(jì)算機(jī)就會(huì)作出反應(yīng)。
At this point, I'm sure, some vague memory of your middle-school algebra is coming back to you.
我相信，這時(shí)候，很多有關(guān)高中時(shí)的代數(shù)知識(shí)就會(huì)模糊地浮現(xiàn)在腦海中。
But rest assured, you don't need to remember any of it to understand the significance of Renee's example.
但是請(qǐng)放心，你不需要記住任何相關(guān)的知識(shí)，就可以理解雷妮案例的重要性。
In fact, as you listen to Renee talking, don't focus on what she's saying, but rather on why and how she's talking the way she is.
實(shí)際上，在文中的下面幾段里，當(dāng)你聽到雷妮的談話時(shí)，請(qǐng)不要關(guān)注她所說的內(nèi)容，而是注意她談話的方式和為什么她會(huì)談到這些。
The point of the computer program, which Shoenfeld had created, was to teach students about how they can calculate the slope of a line.
肖恩菲爾德設(shè)計(jì)的計(jì)算程序是想教授學(xué)生如何計(jì)算直線的傾斜程度。
Slope, as I'm sure you remember (or, more accurately, as I'll bet you don't remember; I certainly didn't), is rise over run.
斜線，我相信，你一定記得（或者說，你記不得了，我就忘記了），就是橫坐標(biāo)與縱坐標(biāo)上兩點(diǎn)相連所形成的一條直線。
So that if you type in 5 on the y axis, and 5 on the x axis, the slope would be 1, 5 over 5. So there is Renee.
這個(gè)案例中要求畫出的斜線只要一條，橫軸和縱軸的數(shù)字都是5。
She's sitting at the keyboard, and she's trying to figure out what numbers to enter
現(xiàn)在雷妮坐在鍵盤前，試圖計(jì)算出，輸入哪些數(shù)字可以讓計(jì)算機(jī)劃出一條垂線，
in order to get the computer to draw a line that is absolutely vertical, that is directly superimposed over the y axis.
直接同Y軸垂直相交。
No, those of you who remember your high school math will know that this is, in fact, impossible. A vertical line has an undefined slope.
現(xiàn)在，高中時(shí)的數(shù)學(xué)知識(shí)會(huì)幫助你得出答案。實(shí)際上，這是不可能實(shí)現(xiàn)的，
It's rise is infinite: any number on the y axis starting at zero and going on forever.
垂線是一種特殊的斜線它的斜率無(wú)窮大：縱軸上的數(shù)字是無(wú)窮大的，Y軸上的數(shù)都以零開始且無(wú)窮大。
It's run, on the x axis, meanwhile, is zero. Infinity pided by zero is not a number.
當(dāng)它穿過X軸的時(shí)候，數(shù)值為零，無(wú)窮大除以零，還是無(wú)窮大。
And the reason why Schoenfeld likes to show this particular tape is that it is a perfect demonstration of how Renee came to resolve this misconception.
但是雷妮沒有意識(shí)到她在嘗試做一件沒有答案的數(shù)學(xué)題，她正陷入被肖恩菲爾德稱為“美麗的理解誤區(qū)”中。
