Except, instead of rock and roll music, my concert was a lecture on black hole topology.

除了我排队不是摇滚乐，我演唱会是黑洞拓扑学讲座。

So that's the concept of retinotopy or the map in visual cortex.

这就是视网膜拓扑学或视觉皮层中地图概念。

First of all, topology is a branch of mathematics that focuses on fundamental properties of objects.

首先，拓扑学是数学一个分支，专注于研究物体基础性质。

You know, these concepts like topology and geometry, complicated, how do you do?

你知道，诸如拓扑学和几何学这概念，复杂难懂，该如何理解呢？

A donut and a coffee cup look the same to a topologist because they both have one hole.

对于拓扑学来说，甜甜圈和咖啡杯看起来是一，为它们都有一个洞。

Now, scientists are trying to transform slums with a mathematical approach to urban design called " topology" .

现在，科学们正试图通过一种称为“拓扑学”数学方法来改窟。

I'm not sure exactly what you might have had in mind there, maybe like topology or analysis or something.

我不确定你当时具体想到了什么，可能是拓扑学或分析学之类。

So it's like the number theory, geometry, So like differential geometry, topology.

所以就像数论、几何，就像微分几何、拓扑学。

The more I talk to topologists, the more they seem to not operate at all in the visual space.

我越与拓扑学交谈，越发现他们似乎完全不在视觉空间中操作。

For a long time, it wasn't clear whether topology was useful for describing the behaviors of subatomic particles.

长期以来，人们并不清楚拓扑学是否适用于描述亚原子粒子行为。

Gauge theory, the kind of very advanced geometry topology that he's interested in.

规范理论，即他感兴趣那种高度复杂几何拓扑学。

This involved lots of weird quantum phenomena, plus a branch of math called topology, which looks at how objects can be arranged and manipulated.

这包括许多奇特量子现象与数学中一个称为拓扑学分支，拓扑学关注是物体可如何被排列与操纵。

Thouless and the final winner, Duncan Haldane, are both also using topology to pave the way for a new kind of material: topological insulators.

索利斯及最后一位获奖者邓肯·霍尔丹都用拓扑学为一种新物质——拓扑绝缘体开辟了道路。

So that's the puzzle, remember it, and now let's take a seemingly unrelated sidestep to the total opposite side of the math universe: Topology.

所以这就是谜题， 记住它， 现在让我们来一个看似无关转折， 转向数学宇宙另一端：拓扑学。

It also underlies the video on the Borsuk-Ulam theorem being used to solve What was basically a counting puzzle by using topological facts about spheres?

它还支撑了一个关于使用博苏克-乌拉姆定理来解决基本上是一个计数谜题视频，这个谜题是通过球体拓扑学事实来解答。

They really trust the mathematics, which is really annoying to me because topology, and differential geometry feels like it has a lot of potential for beautiful pictures?

他们真非常信任数学， 这让我很烦恼，为拓扑学和微分几何似乎有很大潜力去生成美丽图像？

Topologists do this when the count the holes in a surface, physicists do this in defining the ideas of energy and momentum, or in special relativity when they define proper time.

拓扑学在计算表面孔洞数量时会这做，物理学在定义能量和动量概念时也会这做，或者在狭义相对论中定义固有时间时也是如此。

For me, so what I'm saying is, I get a little bit of the joy of kind of learning something purely as a scientist, something completely outside of what I do, mathematics.

对我来说，我意思是，我能感受到一种纯粹作为科学去学习某些完全超出我专业领域——数学之外东西乐趣。比如他感兴趣规范理论，那种非常高级几何拓扑学。

But when the topology gods close a door, they open a window, because the Borsuk-Ulam theorem guarantees that no matter what, there must be some other antipodal pair that now land on each other.

但当拓扑学神关闭一扇门时，他们会打开一扇窗， 为博苏克-乌拉姆定理保证无论怎，总会有一对其他对跖点现在会重合。

In topology since one block of buildings surrounded by roads is considered equivalent, settlements with a wide range of shapes and sizes, from the suburbs of Las Vegas to the slums of Mumbai, can be analyzed in the same way.

在拓扑学中，由于被道路包围一栋建筑物被认为是等效，从拉斯维加斯郊区到孟买窟各种形状和大小定居点，可以以相同方式进行分析。