IN the 1960s, mainframe computers posed a significant technological challenge to common notions of privacy. That’s when the federal government started putting tax returns into those giant machines, and consumer credit bureaus began building databases containing the personal financial information of millions of Americans. Many people feared that the new computerized databanks would be put in the service of an intrusive corporate or government Big Brother.

“It really freaked people out,” says Daniel J. Weitzner, a former senior Internet policy official in the Obama administration. “The people who cared about privacy were every bit as worried as we are now.”

Along with fueling privacy concerns, of course, the mainframes helped prompt the growth and innovation that we have come to associate with the computer age. Today, many experts predict that the next wave will be driven by technologies that fly under the banner of Big Data — data including Web pages, browsing habits, sensor signals, smartphone location trails and genomic information, combined with clever software to make sense of it all.

Proponents of this new technology say it is allowing us to see and measure things as never before — much as the microscope allowed scientists to examine the mysteries of life at the cellular level. Big Data, they say, will open the door to making smarter decisions in every field from business and biology to public health and energy conservation.