But the mathematicians told Dirac, "You cannot ignore the negative energy solution because it tells you there's a second solution and you cannot throw them out."
但数学家们告诉狄拉克,你不能忽略负的能量,因为数学告诉我有两个根,你不能随便丢掉
And one solution might be to pay tuition for people.
也许解决办法之一就是给人们付学费。
Proteins have three dimensional structures in solution and their structure determines what they do.
在溶液中,蛋白质以三维结构存在,它的结构决定功能
And the solution to this equation looks like this where it is written in terms of a quantity called a wavefunction.
这个方程的解法是,看起来像是写成数学符号就是,波函数。
What's the complexity of this decision tree solution? Well, in the worst case, we're enumerating every possibility of in and out.
决策树解决方法的复杂度是多少?,在最糟的例子中得列举,所有可能的输入和输出。
So sometimes the extra solution is very interesting and you should always listen to the mathematics when you get extra solutions.
所以有时候这些增根的意义很耐人寻味,当你解出增根的时候,别忘了想一想它的数学含义
The solution is so simple, give us $2, we'll give you a ticket and yet it takes nine steps to do that.
解决方案也简单,给我们2美元,我们将给你一张票,但是你需要9个步骤来处理。
And on Monday what we were discussing was the solution to the Schrodinger equation for the wave function.
周一我们讨论了,薛定谔方程解的波函数。
And then the magic is really finding the right solution in the middle that combines all these needs and desires and wishes the customer has with all the technology ingredients.
关键在于,找出,中和二者方法,使其既合乎顾客需求,又在技术上可行。
There are also related reading materials quizzes exams problem sites, solution sites and so on.
还有相关阅读材料,小测,考试,提出问题网站,答案网站等。
And the only solution that I can see, at least the best solution that I can see, is to accept the no branching rule.
且我看唯一的解决方法,至少是最合适的解决方法,就是接受无分支理论。
So skepticism, just throwing up your hands and giving up on moral reflection is no solution.
因此怀疑论让你们举起双手,放弃道德反思,这绝非可行之策。
Well, there's what I like to call the Eastern solution that you find in many an Eastern religion and philosophy that says that man is, in fact, nothing. He is dust.
有一种看法被我称之为,东方式解答,你们会发现许多东方的宗教,和哲学认为,事实上人类,什么都不是,人只不过是尘埃
This is where the solution, by the way, to bringing together--and you could write this down-- to bringing together all the warring countries and religions of this planet is an alien attack.
顺便告诉大家,这个办法,是让…你们可以写下来-,让敌对国家合作的方法,让地球上的宗教合作的方法就是外星人袭击。
Because if anything worked, there would be a solution that would have some value over time and people wouldn't have to be seeking out the newest miracle, getting every little thing they see on TV and the like, and I'll show you some amusing examples of those in the next class.
如果真有用,那就找到了长期有效的解决方法,人们就不会再三地寻找方法了,只要看到电视上有什么小妙招就要尝试,下堂课我会举几个有趣的例子
Suppose f of x, y, z equals k1, that is my equation, s1 and it gives me a solution s1.
假设我的方程是这样,然后给出了一个解。
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