Of course, we could perhaps deal with that problem by making us more rat-like in terms of our thinking processes.
当然也许可以解决那个问题,只要我们像老鼠一样思维。
I started thinking, you know what, the reason why in the United States we have such a problem,
你知道我开始想什么了吗,我在想为什么在美国我们会出现如此的问题,
I'm thinking about a problem, I'm going to show you an example in a second, first thing I'm going to do is say, what is the thing that's going to change every time I run through the same set of code?
我要解决一个问题,我马上会让大家看一个例子,第一件我要做的事情就是,弄明白每次运行同样的指令集时,每次都会改变的东西是什么?
That little semi-religious speech about modeling, I think economists, those of you who are Economics majors you're thinking, yeah, what's the problem?
有一条关于建模的准教训,对于经济学者,你们那些主修经济学的,应该经常问自己,出现什么问题了
So, we have a problem here if we're thinking about keeping things at the lowest energy, so there's a lot of ring strain in the system.
现在有个问题,我们考虑要把能量降到最低,所以环上有许多应力。
One could have an entire semester devoted to thinking about the philosophical problem of consciousness.
一个人可能得花上整整一个学期,全身心地思考,关于意识的哲学问题
I'm thinking of the general problem of the abstraction of virtue, an abstract notion of virtue. Think of all the questions that all of us at some point or other tend to associate with virtue.
我在思考贞操这个抽象概念,贞操这一抽象的概念,想想所有那些,我们时不时的会由贞操想到的问题。
So this is very similar, this is a kind of recursive thinking we talked about earlier, where we take our problem and we make it smaller we solve a smaller problem, et cetera.
我们则跳过比猜想数小的那个区间,然后我们重复这一过程,跟之前我们讲过的,递归思想非常类似,我们解决问题的时候,先把问题一步步变小,然后解决小问题。
Not so easy to see. All right, but this is actually a great one of those educational moments. This is a great example to think recursively. If I wanted to think about this problem recursively- what do I mean by thinking recursively?
看不太出来,好,但实际上是一个有教育意义的时刻,这是一个很好的关于递归的例子,如果我用递归的思想,去考虑这个问题-,我该怎么用递归去解决这个问题呢?
That's the problem we've been thinking about for the last minute.
那是我们刚才在思考的问题
And in terms of using these equations in solving problems on the exam, and also using these constants, make sure if you think there might be any chance you're going to get any little part of a problem wrong or do a calculation inaccurately, you need to write out every single step of your thinking as you write out these problems.
而当你在考试过程中用这些公式,来解题时,加上运用这些常数,如果你觉得有可能,在某一小问上出错,或者出现计算错误,请务必把你的思路一步一步地都写出来,当你在答题的时候。
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