Speaker：Roger Antonsen

视频

原视频

摘要

• My claim is that understanding has to do with the ability to change your perspective.
  我认为理解是一种能力，转变(固有)观点的能力。

• My claim is that mathematics has to do with patterns.
  我的观点是，数学跟模式有关。

• My definition of mathematics is the following: First of all, it's about finding patterns. Second of all, I think it is about representing these patterns with a language. It's also about making assumptions and playing around with these assumptions and just seeing what happens. And finally, it's about doing cool stuff. Mathematics enables us to do so many things.
  我对数学有一个的定义： 首先，数学的关键是寻找模式。其次，我认为数学是一种语言， 用来描述各种模式。同时数学也需要进行假设，对假设进行多方验证看看结果如何。最后，数学可以用来做很酷的事情。 能帮我们完成很多事。

• When you change your perspective, and if you take another point of view, you learn something new about what you are watching or looking at or hearing.
  当你换一种角度来看问题，当你接受另一种观点，你就能在所见所闻中，学到新的东西。

• Every mathematical equation where you use that equality sign is actually a metaphor. It's an analogy between two things. You're just viewing something and taking two different points of view, and you're expressing that in a language.
  每一个使用等号连接的数学方程 实际上都是隐喻。是两种事物间的类比。你观察一件事情，产生两种观点，然后用一种语言来表达。

• My claim is that you understand something if you have the ability to view it from different perspectives.
  我认为只有当我们 从多个角度去审视同一事物时，才能说我们理解了它。

• If you're able to view a structure from the inside, then you really learn something about it. That's somehow the essence of something.
  如果你能从一个结构的内部去进行观察，那你就能够真正认识它。认识到它的本质。

• So my conclusion is the following: understanding something really deeply has to do with the ability to change your perspective.
  所以我的结论是：深入的理解一件事 与转换角度的能力密切相关。