Here’s why: The advertising business is split, roughly, into two. On one side are direct-response ads meant to induce an immediate purchase: Think classifieds, the Yellow Pages or catalogs.

In 2000, Google began running text-based ads alongside its search results. These ads quickly became one of the world’s most successful forms of direct-response advertising. In 2014, Google sold about $45 billion in search ads.

But Google’s enormous search haul is only a slice of the $550 billion global advertising market, according to the research firm eMarketer. As Mr. Thompson pointed out, most of that money is not in direct response ads like Google’s.

Instead, the bulk of the ad industry is devoted to something called brand ads. These are the ads you see on television and print magazines. They work on your emotions in the belief that, in time, your dollars will follow.

Google is great at information but it is still learning emotion.

This gets to the crux of Mr. Thompson’s argument that Google has peaked. The future of online advertising looks increasingly like the business of television. It is likely to be dominated by services like Facebook, Snapchat or Pinterest that keep people engaged for long periods of time.

“Google doesn’t create immersive experiences that you get lost in,” Mr. Thompson said. “Google creates transactional services. You go to Google to search, or for maps, or with something else in mind. And those are the types of ads they have. But brand advertising isn’t about that kind of destination. It’s about an experience.”