評論
打印
Renee was in her mid-twenties, with long black hair and round glasses.
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，黑色長發，帶一個銀邊眼鏡。
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教學的代數軟件程序。
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.
屏幕上出現了Y軸和X軸，教學程序要求使用者劃一條線穿過座標軸，舉個例子，如果我們在Y軸上標出5，在X軸上也標出5，那么計算機就會作出反應。
At this point, I'm sure, some vague memory of your middle-school algebra is coming back to you.
我相信，這時候，很多有關高中時的代數知識就會模糊地浮現在腦海中。
But rest assured, you don't need to remember any of it to understand the significance of Renee's example.
但是請放心，你不需要記住任何相關的知識，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.
實際上，在文中的下面幾段里，當你聽到雷妮的談話時，請不要關注她所說的內容，而是注意她談話的方式和為什么她會談到這些。
The point of the computer program, which Shoenfeld had created, was to teach students about how they can calculate the slope of a line.
肖恩菲爾德設計的計算程序是想教授學生如何計算直線的傾斜程度。
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），就是橫坐標與縱坐標上兩點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.
這個案例中要求畫出的斜線只要一條，橫軸和縱軸的數字都是5。
She's sitting at the keyboard, and she's trying to figure out what numbers to enter
現在雷妮坐在鍵盤前，試圖計算出，輸入哪些數字可以讓計算機劃出一條垂線，
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.
現在，高中時的數學知識會幫助你得出答案。實際上，這是不可能實現的，
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窮大：縱軸上的數字是無窮大的，Y軸上的數都以零開始且無窮大。
It's run, on the x axis, meanwhile, is zero. Infinity divided by zero is not a number.
當它穿過X軸的時候，數值為零，無窮大除以零，還是無窮大。
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.
但是雷妮沒有意識到她在嘗試做一件沒有答案的數學題，她正陷入被肖恩菲爾德稱為“美麗的理解誤區”中。
