-
So it's a complex issue, and I should leave it having said this much, at least for the moment.
因此它是一个很复杂的问题，而我就讲到这里，至少暂时这样。
-
We'll get into some spots where it gets a little trickier, a little bit more complicated later in class.
我们接下来在课堂上,会做一些更棘手，更复杂的问题。
-
So as you can see, as we escalate the problem difficulty, the difference between the good method and the not quite as good method gets bigger and bigger and bigger.
如你所见，当我们处理更复杂的,问题的时候，优良的算法,和并不那么好的算法之间的,差异会变的越来越大，这一点很重要。
-
Here's where three great figures there are others but these are considered the seminal figures begin to raise questions which complicate the whole issue of consciousness.
看一下这三个伟大的人物,当然了还有其他的人物，但这三位影响最为深远,这三个人物开始提出了一些问题,这些问题使整个意识的问题复杂化了。
-
That's really a complex systems problem, the kind of problems that engineers are very good at dealing with.
这真是复杂的系统性问题,解决这类问题,恰恰是生物医学工程的拿手好戏
-
I'm going to start with the simplest example and slowly add on bells and whistles and make it more and more complicated.
我会从最简单的例子开始,逐渐增加难度,让问题越来越复杂
-
Now let's take just one somewhat more complicated case.
现在考虑一个,更加复杂的问题。
-
Oh, completely. One of the things is that the intersection of religion and rights really complicates.
哦，完全可能，其中一点就是,宗教和权利的问题真是错综复杂。
-
In fact, linguists often argue about this subject, and it's a complicated one.
实际上，语言学家经常在这个问题上有争议，这是很复杂的一个东西。
-
And like all the other topics we've talked about in this class, it's a complicated subject, about which one could spend a great deal of time.
和课堂中涉及的所有话题一样，这是个复杂的问题，需要很长时间才能搞清楚。
-
So before we leave coordination games, I want to look at another one, a little bit more complicated one perhaps, that we mentioned briefly last time.
在我们结束讲解协调博弈前,我们再来看一个,稍微复杂点的问题,上一讲我简单提到过的
-
People who decide on dividends are facing a complicated issue.
决定分红的人们面临的是个复杂的问题
-
So, stereotypes are complicated and morally fraught things.
所以刻板印象是复杂的，会引起道德问题。
-
And in this quest for what is best, positive psychology does not rely on wishful thinking, self-deception,or hand waving; instead,it tries to adapt what is best in the scientific method to the unique problems that human behavior presents " in all its complexity."
在追求理想状态时，积极心理学不会盲目主观，或自欺欺人;,相反，它尝试用最科学的方法来探究,极其复杂的人类行为所表现出来的,特殊问题“
-
So in fact, over the next thirty or forty minutes we're going to show you a set of examples of sort of canonical algorithms, and the different classes of complexity.
在接下来的三四十分钟里面,我们将要讲一系列的,权威算法，以及不同种类的复杂度问题。
-
Linear algorithms tend to be things where, at one pass-through, you reduce the problem by a constant amount by one. If you reduce it by two, 1 it's going to be the same thing.
有问题么？,线性复杂度的算法，当进行了一个,常量级步数的操作的时候，将问题的规模缩小了一个。
-
Then next week we'll do more complicated problems that involve motion in higher dimensions, how to go to two dimensions or three dimensions.
下周我们将会处理更复杂的问题,包括更高维数的物体运动,如何处理二维以及三维运动
-
And you can imagine this gets complex and there's lots of interesting things to do to look to the real form, but those are the things that you should see.
可以想象下这样下去问题会变的复杂起来,而且当面对真实情况的时候,会有很多有趣的事情发生，但是这些东西你都应该明白的。
-
That's a really complicated question that we have gotten very confused about.
这也依然是一个复杂的问题,人们现在对此十分困惑
-
But then also a little bit about your history, where you come from, some of your experiences which have helped you or informed your opinions on this very difficult issue that the entire world really is spending a lot of time trying to work on.
然后再谈谈你们各自的经历，你们从何而来，谈一些你们自己的经历,一些帮助过你们，或形成了你们,就这个复杂问题的观点,这个全世界都在投入大量时间试图解决的问题。
-
That's a complicated thing that accountants figure out and accountants find it difficult to define the earnings of a company, but they do something and they come up with a number.
会计们会计算这个复杂的问题,他们还会发现公司收益很难定义,但是他们会想办法,得出一个数字
-
Let's talk about something a whole lot more complicated.
现在谈谈别的,更复杂的问题。
-
You might not want to know all of it and that's a really complicated question for an individual to figure out and a complicated question for society to figure out, what you want to make of available in the regard.
你不想什么都知道,这是个十分复杂的问题,无论是对个人,还是对社会都是如此,我们应该怎样控制它的使用范围
-
The problems are complex because we're trying to make a system in which people are able to make their own decisions as much as possible and to make them in a way that--in an environment that they trust.
问题总是复杂的,我们试图创造一个,人人都可在其中,尽情决策的系统,创建一个,人人彼此信任的环境
-
But helping you understand things that really are a conceptual difficulty is what they're here for and what we're here for, so please come and talk to us.
不过他们在这儿,是为了帮助你们,了解概念非常复杂的问题，所以请过来请教他们。
-
This case, I reduced the size of the problem in half.
这很好的表明了这是，对数级复杂度的问题，我马上就要解释。
-
On Thursday we'll do a more careful analysis and try and understand how I could have accomplished this seemingly magical task of solving an exponential problem so really quickly.
在周四的时候,我们会做进一步的分析,并且尝试理解我为什么,能如此快速的解决这种,看上去超复杂的指数型问题。
-
Then, of course, you can do more complicated things.
接下来我们就能解决一些更复杂的问题
-
That's the question we're going to try and address. If we can do this, this is good, because first of all, it removes any questions about what machine I'm running on, it's talking about fundamentally, how hard is this problem, and the second thing is, it is going to do it specifically in terms of the input. Which is one of the things that I was worried about.
这是一个我们接下来要去,尝试和解决的问题，如果我们能做到的话会很不错，因为首先，它解决了结果可能和我,运行的计算机有关系的问题，因为这从根本了告诉了，我们这个问题的复杂度，第二件事情,就是这种方法可以依据输入的大小来计算,而这正是我最担心的地方。
应用推荐