And it's what's called a topological invariant.

是一种拓扑不变量。

There were a bunch of these types of invariants.

这些类型的不变量有很多。

And yet, collected together, they have a single total amount that they spin about their center of mass.

但聚一起时，它们有一个单一的总的不变量，他们总是围绕着它们的质心旋转。

We're finding what's called an " invariant" .

我们正寻找所谓的“不变量”。

A lorentz invariant or field theory approach.

洛伦兹不变量和场论步骤。

Well, economics is not a traditional science because it is nearly impossible to control all the different variables.

经学不是一门传统科学，因为要控制所有不同变量几乎不可能。

There is no relationship between the two variables.

两个变量之间不存关系。

But there’s a key variable in this cycle that wasn’t always so carefully considered: you.

但这个周期中有一个关键变量并不总是被仔细考虑：你。

We already know what can happen to a bridge if you don't consider all the variables before you build one.

我们知道一座桥会发生什么 如果我们构它之前不处理所有变量。

We already know what can happen to a bridge if you don’t consider all the variables before you build one.

我们已经知道， 如果造桥梁之前不考虑所有变量， 桥梁会发生什么情况。

Those 500 axes represent variables that humans wouldn't even recognize or have names for, but the result is that the space has meaningful clusters.

这500个坐标轴代表了人类甚至不认识或不知道名字的变量，但结果是空间有了有意义的群。

So why place your confidence on something that's a variable that's not guaranteed, that can be a moving target, that may not even be fully defined yet?

那么，为什么要把信心放一个不确定的变量上呢，可能是一个移动的目标，甚至可能完全没有定义是什么？

But some of you watching this will one day face a problem where finding an invariant reveals a slick solution, and you might even look like a genius for doing so.

但你们中的一些人有一天会面临这样一个问题：找到一个不变量会揭示一个巧妙的解决方案，而这样做的甚至可能看起来像个天才。

And there's losing variables that are just not that practical, and this matters because in a world of limited resources, you don't want to waste it on people that actually have the same needs.

并且失去的变量并不那么实用，这很重要，因为一个资源有限的世界里， 你不想把它浪费实际上有相同需求的人身上。

As a student, it's easy to take for granted the definitions handed down to us, but the more puzzles you solve where the insight involves an invariant, the more you appreciate that each of these definitions was once a clever discovery.

作为一名学生， 我们很容易将传授给我们的定义视为理所当然，但是解决的洞察力涉及不变量的难题越多，就越会欣赏这些定义中的每一个都曾经是一个聪明的发现。