Now lastly, second-order thinking and exponential thinking.

最后，二阶思维和指数型思维。

And finally guys, we have exponential thinking.

最后，朋友们，我们来看指数型思维。

Judging by the exponential speed of technological improvements, probably not.

技术进步的指数速度来看，应该还没有。

Talk about exponential progress in science and research, absolutely amazing.

这些指数性增长的科研进展真是令人震惊。

We see an exponential curve for wind installations now.

我们现在看到的是风力发电装置的曲线。

The exponential curve on solar is even steeper and more dramatic.

太阳能的曲线甚至更陡，更令人瞩目。

Population growth was exponential but how much food we grow was not.

人口增长呈指数增长，但我们种植的食物数量却不是。

So let's see now how exponential technologies are taking health care.

现在让我们看看指数技术怎样进行。

What I'd like to talk about today is understanding these exponential technologies.

我今天想谈的是理解这些指数增长的技术。

Major pitfalls has been the exponential rise in dementia, cognitive impairment and Alzheimer's.

主要的不足是痴呆症认知障碍和阿尔茨海默氏症的指数上升了。

This is the nature of an exponential function. So smiles and laughters are contagious.

这是指数函数的本质 笑和笑声是传染的。

Over the last three years, we've seen an exponential increase in maritime smuggling.

在过去三年，海上偷渡呈指数增长。

And you can see here that there's an exponential Great Divergence.

大家可以看到大分流的走势。

We have seen a revolutionary breakthrough in the emergence of these exponential curves.

我们这些指数曲线的变化中看到了革命性的突破。

For most people, it seems extraordinary because people don' understand the nature of exponential function.

很多人会觉得不可思议 因为他们不懂指数函数的本质。

Well, an exponential curve is a curve that doubles every certain amount of time, Vespignani says.

维斯皮纳尼表示，指数曲线是在特定时间增倍的曲线图。

And then after that, you know, you're in very tough shape because of that exponential growth.

在那之后，因为感染人数指数增长，政府很难采取有效措施。

We've seen an exponential increase in greenhouse gases in the atmosphere over the past twenty years.

在过去的二十年中，我们见证了大气中温室气体越来越快的增长。

When something is growing or it's increasing really, really quickly, we describe this growth as exponential.

当某件物在增长，或者是增长得非常非常快的时候，我们就会以‘越来越快的’来描述。

It's a chart of exponential growth, and it shows that some things change faster over time.

它是一个指数增长图，，它表明有些情随着时间的推移变化得越来越快。