Imagine if we were shooting on a football field, and we have a room, which is maybe 10 meters by 5; we can scale that room up to fit the football field.
想像一下，我们要拍摄一个在足球场上的片段，而我们只有一个10*5的房间，但我们可以通过调整房间大小来满足足球场的尺寸。
How do we have a huge impact on the research field in general, as well as with product groups to influence the future of Microsoft products?
我们怎么才能影响整个研究领域，并和产品小组一起对微软公司产品的未来产生影响？
The main thing I want to talk about is this, that we have this remarkable experience in this field of fundamental physics, that beauty is a very successful criterion for choosing the right theory.
我最想说的就是在基础物理领域我们有这个显著的经验，那种美是我们选择正确理论的标准。
We have said if we have a gradient field then we have this.
如果有一个梯度场，那就能得到这个。
OK, so let's assume that we have a vector field whose curl is zero.
假设有一个旋度为零的向量场。
There is another thing that we know because if a force derives from a potential 0 then that means its curl is zero Thats the criterion we have seen for a vector field to derive from a potential.
我们还知道,如果力是由势产生的,那么其旋度是,这就是我们得到的,关于从势产生的向量场的准则。
When we throw up an object in a gravitational field, you have the trajectory in a plane.
当我们把一个物体，放到引力场中，我们会得到在一个平面上的轨迹。
I don't want to manualize it, but we haven't articulated it as clearly as we should so that people in the field have a good idea of what works and what doesn't.
我并不想把它写成手册，但是我们并没有像我们应该做到的那样清楚地表达它。因此这个领域的工作者对哪些有效、哪些无效各有想法。
Actually, they have a vector field is still pointing perpendicular to the level curves that we have seen, just to remind you.
实际上，向量场，还是垂直于水平线，就像之前看到的那样，我只是想提醒一下大家。
We have a vector field that gives us a vector at every point.
有一个向量场来描述每一个点上的向量。
We have all heard of nanotechnology, but so far few of us can point to a particular field where its application has radically changed our lives.
我们都听说过纳米技术，但是很少有人能够说出该技术的应用到底在哪个领域从根本上改变了我们的生活。
In the wireless age, we should be able to have a level playing field in which an idea - an entrepreneur - will be judged by the content of its concept rather than by the color of its maker.
在无线网络时代，我们应该拥有一个公平的竞争环境，企业家们能够以自己的理念来判断问题，而不是其制造者的颜色来判断。
We have always maintained that cooperation in the field should be a highlight of cooperation for the international community instead of confrontational point for conflict.
我们一直主张，人权领域的合作应是国际社会合作的一个亮点，而不应该成为对抗的冲突点。
We could all have guessed that money is a great leveler for men, but would you have thought that a great education would level the playing field for women too?
我们所能猜到的是，金钱能拉平男性的地位，但尼恩能够想到好的教育背景也能让女性在游戏场中拉平地位吗？
I asked my mother why we lived with such modest means, unaware of how painful it must have been for a single parent with two young boys to field such questions.
我问妈妈，为什么我们生活得那么简朴，当时完全没有意识到，对于一个带着两个儿子的单身母亲而言回答这个问题是多么痛苦。
More about curl.If we have a velocity field, then we have seen that the curl measures the rotation affects.
关于旋度的更多介绍，设有一速度场，我们知道旋度是测量旋转影响的。
I want to remind you that if we have a solid in a force field, we can measure the torque exerted by the force on the solid.
提醒你们，假设力场中有一固体，可以由力对固体的作用测量出其扭转力矩。
Once we get a couple of hundred entrepreneurs, people who have bet their lives are gonna cause major structural change in this field. From all over the world, it's not us.
一旦我们拥有几百个企业家，这些孤注一掷的人将带来主要,结构改变，从整个世界来看，不是我们。
OK, so, we've seen that if we have a vector field defined in a simply connected region, and its curl is zero, then it's a gradient field, and the line integral is path independent.
一个向量场,如果定义在单连通区域并且旋度为零，那么它就是一个梯度场，并且其上的线积分与路径无关。
If we have a vector field that cannot possibly be a gradient then we shouldn't try to look for a potential.
如果一个向量场不可能是梯度场，那我们就不应该尝试去找势函数。
The question is how are we going to have a level playing field so that new energy companies can compete fairly and kick some ass?
问题是，我们如何才能获得公平的环境，使新能源公司能够公平竞争，并且有所作为？
Many times, the problems we see in the field could have been avoided by just following even a hint of a reasonable test plan.
通常，只要遵循合理的测试计划的提示，就可以避免看到这方面的问题。
We have come to dedicated a portion of that field, as a final resting place for those who here gave their lives that that [Delete doubled word.] nation might live.
把这战场之一角奉献给那些为国家生存而捐躯的人们，作为他们的最后安息之地。
We talked about the sense that, I think, young people have a sort of prejudice against the field and they think that finance is a field that you go into if you really value money rather than people.
我们谈论了，年轻人对这一行业的偏见，他们认为进入金融业的人，金钱至上，而不尊重他人。
So, to understand the explanation, and given what we've been doing, we should have a vector field in there.
为了理解这个解释，我们在这里设一个向量场。
And the reason for that is, again, we have seen for a velocity field that divergence measures how much things are expanding or how much stuff is being created.
原因是…，我们看过一个向量场，散度意味着多少东西膨胀，多少东西被创造。
Our main concern so far has been to say if we have a conservative force field it means that the work of a force is the change in the energy.
目前为止，我们主要关心的是，如果在保守力场中，力所做的功是，能量的改变。
Today we have the possibility to build a new field.
今天，我们将有可能开创一个新的领域。
Today we have the possibility to build a new field.
今天，我们将有可能开创一个新的领域。
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