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So for example I defined p, remember back over here, as a Cartesian point, but I can actually ask for its polar form.
我可以要求返回它的极坐标形式，这里对我是可访问的，好，这很棒，请再记另外一个为什么。
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If its in Cartesian form I'll pass in an x and y and compute what a radius and angle is.
来得到的这个点,我都可以得到这个点的,全部的这种信息。
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What it looks like up here, the simple Cartesian model of it is these things smear this way.
它看起来像什么，它的简单的笛卡尔模型,就是这样重叠的。
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The idea of The Matrix is explicitly built upon Cartesian— Descartes' worries about an evil demon.
黑客帝国》的创意,完全基于笛卡尔的哲学,笛卡尔对于恶灵的忧虑
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And so, Descartes' attempt to establish the distinctness of the mind, the immateriality of the mind, on the basis of this Cartesian thought experiment, I think that's unsuccessful.
所以,笛卡尔试图,用他的卡式思想实验来证明,心灵的独立存在性,和非物质性,我认为这种尝试是失败的
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So p dot Cartesian is a kind of accessor, it's getting access to the data.
这就是为什么，我想要使用访问器的原因。
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If I look at the Cartesian, oh, I did have the Cartesian form, don't mind me while I mutter to myself here quietly.
如果我来看看这个笛卡尔，哦，我还没有笛卡尔形式，当我自言自语的时候,请大家别介意。
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I've got a definition of Cartesian point, I've got a definition of polar point.
让我们运行这个程序，来把应用这些定义。
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So I've got now things that are Cartesian points.
我想要创建很多个点,现在我已经创建了。
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So this Cartesian argument seems to show us that the mind is something separate from, distinct from, not reducible to, not just a way of talking about, my body.
所以这个卡氏论证似乎给我们表明了,心灵是独立于身体,不同于身体,不能称作身体,不是"我身体"的另一种说法
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I could imagine writing another function for same point, and I have to give it a name like same point polar, and same point Cartesian.
程序不知道怎么来做了,它没有对应的处理方法，所以它要抱怨了,那么我这里的问题就是，这也是我一直想要说的。
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Let's let p be Cartesian point, and we'll give it a couple of values. OK?
然后我们给它赋值，好不好？,发生了什么？
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A good, hygienic way of doing this is, not only do I not go in and change things except through a pre-defined method, I shouldn't read it other Cartesian than through a pre-defined method.
做这个的方式是，我不仅仅要通过提前定义好的方法,来改变数值,我还应该通过提前定义好的方法，来读这个值,我应该用。
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How do you know whether it's in Cartesian form or in polar form?
这没什么了不起的,但是现在出现问题了？
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If I now say, I'm going to go ahead and change the radius of this, something, my polar form did it right, but what happened to the Cartesian form?
如果我现在说，我要去改变这里的半径,一些这样的操作，我的极坐标形式，进行了正确的改动？
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I think the Cartesian argument does fail.
我认为笛卡尔论证的确是不成立
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At the end of last class, we started sketching an argument that comes from Descartes, the Cartesian argument, that says merely by the process of thinking, on the basis of thought alone, it tends to show that the mind-- We all agree that there are minds.
在上次课的最后,我们开始简述一个,来自笛卡尔的论证,或称为卡氏论证,这个论证说仅仅通过思考,仅仅在思想的基础上,它就能证明心灵,我们都承认有心灵
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That was Cartesian space. When I plot r as a distance out from the nucleus that is sort of our simple-minded planetary model. Now let's look at energy.
笛卡尔坐标系，当我用r表示,离原子核的距离时，那只是我们头脑中简单的,类似行星的模型，现在我们看一下能量问题。
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You know when you add 2 polar forms, you add the radii together, you don't add the angles together, you need to do it in Cartesian form.
表示形式的不同理解，返回给你了不同的值，这也就带来了一系列的问题，第二个问题是。
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same point Cartesian to have 1 representation for a point that supports different ways of getting information out, but has gathered within it, a method or a function for dealing with things like how do I know if it's the same point or not.
还有,这是一个比较极坐标的点,是否相同的不同的方法，但是这开始成了一个麻烦事儿了，我真正想要做的事情是,创建一个能支持不同的方式,输出已经收集的信息的点的表示。
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Having created this thing called Cartesian point, I'm going to create two instances of it.
这里面是控的,好，我们一会就会来完善它，但是类的概念就是。
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And that's a wonderful thing to have because it gives you that modularity, that encapsulation that basically says, when I create a point, the only way I can get at the values, is by using one of the defined methods, in this case it could be Cartesian, Cartesian and get all the pieces of that.
这是很棒的一件事情,因为它让你有了，模块性以及封装性，这基本上也就是说，当我创建了一个点，我能够得到它的值的唯一的方式，就是用一个定义好的方法，在这个例子中也就是。
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You see that little thing says dot Cartesian point in there.
当我要使用这些东西的时候,这些信息是很有价值的，对不对？
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I've got Cartesian points, I could create a polar points.
我已经有了一些笛卡尔坐标点了，我可以创建一个极坐标点。
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Oh, but what happened to the Cartesian form.
发生了什么呢？
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If that's right, then maybe the conclusion should be "Well, you know, yeah, the Cartesian thought experiment shows that there could be a world in which there are minds that are not identical to bodies.
如果事实如此,那么结论该是,怎么说呢,笛卡尔的思想实验表明,可能存在某个世界,其中存在着,不同于身体的心灵
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I take it that we all agree that when we attempt to run the Cartesian argument in terms of the Morning Star and the Evening Star, it fails. But it's harder to say what went wrong?
我想大家都同意,当我们试图把卡氏论证,用到晨星和昏星的例子上来时,它行不通了,但是很难说我们哪里错了
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If that argument, if the argument-- If trying to run the Cartesian argument for astronomy fails, yet it seems to be an exactly analogous argument, we ought to conclude that the argument for the distinctness of the mind and the body must fail as well.
如果这个论证,如果把卡氏论证运用到天文学,是失败的,看来我们也不得不承认,类似的那个证明心灵,和身体不同的那个论证,必然也是失败的
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It says, if I want to print out something I built in Cartesian form up here, says, again, I'm going to pass it in a pointer to the instance, that self thing, and then I'm going to return a string that I combine together with an open self and close paren, a comma in the middle, and getting the x-value and the y-value and converting them into strings before I put the whole thing together.
这不仅仅是个列表,它是怎么来做的？,流程是：如果我想要返回,一些已经在笛卡尔模式下建好的值，好，再说一遍，我首先要传入一个,指向实例的指针,也就是，然后我会返回一个,由开括号，闭括号,中间的一个逗号,以及提前转换为字符串格式的。
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I should have done this earlier by typing the Cartesian form earlier, so let me go back to where I was, sorry for that, let me go make this a 1 again.
我应该早点通过输入笛卡尔形式,来说明这个的，那么让我回到刚才说到的地方，很抱歉，让我去把，这个a，1再做一遍。
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