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It's a simple problem, but I just want to do it so you get used to working with vectors.
这是个简单的问题,但我还是想做一下好让你们习惯矢量运算
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In there, I want to make this distinction, this nuance: the evaluator is still going to be taking those expressions and using its rules to get a value, but it's not going to print them back out.
在这里，我想要做这么一个，细微差别：运算器依然会,对表达式,进行求值，但是不会,显示结果值。
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All I did was, I did a little bit of calculus, a little bit of algebra, and then I drew the thing.
我只不过是稍微用了点微积分,做了点代数运算,然后就画出来了
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You might very well have done some very accurate math but it doesn't matter, because you did the math in the wrong place.
你可能很好地做完了一些很精确地数学运算,但是没有关系，因为你没有做错,数学运算。
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Do what you normally do with ordinary numbers.
就按照通常处理数的运算的方法去做
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We'll, later in the term when we get to more detailed numerical things, look at what's wrong.
这个学期的晚些时候我们,会做一些更具体的数值运算。
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Just as in grade school when you're doing division and multiplication, you do it from left to right in terms of order of operations.
正像是在小学你做除法和乘法的时候,你毫不含糊地从左到右,按顺序做运算。
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STUDENT: Standard order of operations, I guess take the multiplication first, and add the three.
学生：标准运算符的顺序，我猜是先做乘法，然后再去加3。
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So each time through the loop, I'm doing three steps. Three basic operations.
因此每次运行这个循环，我做了三次基本运算。
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And that's what they would do: they would do that specific computation.
那就是它们能做的事儿：,它们能做那个特定的运算。
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Doing incrementation, pretty useless; right?
做增量运算，相当无用的，对不？
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And now I have to do the mathematics.
现在我需要做一个数学运算。
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Because in doing that, Python would then have a value that it could pass on into some other part of a computation, and if it wasn't what I wanted, I might be a long ways downstream in the computation before I actually hit some result that makes no sense.
因为如果这样做的话，Python会将,输入的值传递到下面的,一些运算中去，如果这个值的类型不是我想要的，我可能会在得到,一个毫无意义的结果之前,经历一个很长时间的,计算过程。
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Now, the nanosecond is what, 10 to the minus 9 seconds.
一纳秒就是10的9次方分之一秒，而这个电脑一秒可以做2G次运算。
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