Investors will get a good look at the scope of those ambitions on Feb. 1, when the company, in its fourth-quarter earnings report, will disclose for the first time the costs and income of the collection of projects outside of Google’s core business.

As chief executive of Alphabet, Mr. Page is tasked with figuring how to spin Google’s billions in advertising profits into new companies and industries. When he announced the reorganization last summer, he said that he and Sergey Brin, Google’s other founder, would do this by finding new people and technologies to invest in, while at the same time slimming down Google — now called Google Inc., a subsidiary of Alphabet — so their leaders would have more autonomy.

Image Sundar Pichai, chief of Google Inc. Credit... Justin Sullivan/Getty Images

“In general, our model is to have a strong C.E.O. who runs each business, with Sergey and me in service to them as needed,” Mr. Page wrote in a letter to investors. He said that he and Mr. Brin would be responsible for picking those chief executives, monitoring their progress and determining their pay.

Google’s day-to-day management was left to Sundar Pichai, the company’s new chief executive. His job will not be about preventing cancer or launching rocket ships, but to keep Google’s advertising machine humming, to keep innovating in emerging areas like machine learning and virtual reality — all while steering the company through a thicket of regulatory troubles that could drag on for years.

Mr. Page’s new role is part talent scout and part technology visionary. He still has to find the chief executives of many of the other Alphabet businesses.

And he has said on several occasions that he spends a good deal of time researching new technologies, focusing on what kind of financial or logistic hurdles stand in the way of them being invented or carried out.