Yet at the same time, you probably thought "Oh, yeah, well, I did come out pretty much in the place I expected to come out in despite the roundabout way of having gotten there."
但同时,你可能会想“哦,也是,尽管比较曲折,但是我也比预想的收获了更多“
we're probably more cohesive than all the other majors around campus and everything else.
我们可能比其他任何专业的凝聚力更强,其它方面也是。
And that makes sense, too, because the positive three pulling on minus one has a tighter binding energy than positive one pulling on minus one.
而这也是有意义的,因为+3和-1的相互吸引,产生了比+1和-1的吸引,更强的能量。
The fact of the proliferation of possible perspectives is just as important, and I would think it's actually even more important, as any single seemingly proper perspective.
这里关于可能的观点的扩展,也是非常重要的,我个人认为甚至比任何独立的合理观点更为重要。
And they're higher than perfect competition, which of course, has zero profits in this case.
并且它比完全竞争条件下的利润高,这也是必然的,因为完全竞争下的利润为零
There's the base case. If it's longer than one, what do I want to do? Well I'd like to check the two end points to see are they the same character? And if they are, then oh, I just need to know is everything else in the middle a palindrome?
如果只有一个元素也是回文,这是基本事件,如果比一个长的话那么我应该怎么做?,我将会查看两头是否相同?,如果是的,我只要知道中间剩下的部分是不是回文即可?
So that's why Yale is much more generous with financial aid than other universities and why we have beautiful -of course, this room was built,I believe, in the 30s.
这就是为什么耶鲁在助学金方面,比其他高校要慷慨的原因,也是为什么我们有美丽的...,当然,这间教室应该是建于30年代
I think they probably also invented a few things, but it was very,very characteristic of the Greeks to borrow from the cultures they encountered and to adapt them, to make them more useful for their own purposes and nothing could be clearer than the alphabet as an example of that.
我认为他们或许也发明过一些事物,但从他们所遇到的文明中进行借鉴,将之应用到自己的生活中去,并使它们更适于希腊人自己的目的,这样的方式也是非常希腊风格的,也没有什么,能比字母表这个例子更能清晰地说明这点了
But he believed that it was important to take the tools of science, to take the tools of rational thought and apply them to the good of the state, even if you saw that good of the state as in ships that could lob cannonballs even further against hostile ships, and that kind of thing.
但他同时还认为,借助利用科学和理性的工具,来为国家利益服务也是非常重要的,即使你所看到的所谓"国家利益",只是军舰上的炮弹能比敌舰射得更远,或者其他诸如此类的东西
It is certainly possible, for example, that a quadratic algorithm could run faster than a linear algorithm. It depends on what the input is, it depends on, you know, what the particular cases are. So it is not the case that, on every input, a linear algorithm is always going to be better than a quadratic algorithm.
一个二次平方级复杂度的算法,当然也是可能跑的比线性复杂度算法快的,这取决于,你知道的,输入以及特定的案例,因此并不是对于每个输入,线性复杂度就一定会,比二次平方级复杂度的算法的表现要好,只是通常来说是这样的。
You will always get a higher payoff from choosing 67, at least as high and sometimes higher, than the payoff you would have got, had you chosen 80, no matter what else happened in the room.
选择67的话你总会获得较好的收益,至少也是跟选80的收益一样高,有时候比选80的收益更高,不管别人选择的是什么样的策略
Again, leaving aside the science, about which I'm sure some of you know more than me here, the issue of carbon emissions is a Prisoners' Dilemma.
抛开科学层面来说,我相信在座的一些同学比我知道的还多,碳排放问题也是个囚徒困境
This is in a pretty small it's bigger than Belgium, but this is a pretty small territory.
这是仍然是一个相当小的数字,只比比利时稍大一点,不过比利时的领土也是很小的
So you have trade with the Mediterranean and most especially the eastern Mediterranean, because that's where the older, more sophisticated, more civilized cultures were and that's where wealth was too, compared to what was out in the west.
由此你知道了他们与地中海,特别是地中海东部地区有贸易往来,因为在那里有比西方更古老,更先进,更教化的文明,同时相比西方而言,那里也是富裕之地
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