Mike Homer, a hard-charging executive at Netscape Communications in the 1990s, and his friends certainly subscribed to that belief. It is what led them two years ago to donate hundreds of thousands of dollars, along with powerful new computers, to the University of California, San Francisco, where some of the nation’s top researchers are trying to solve intractable medical mysteries.

However, the group is getting a sober lesson in the limits of technology and money. Last May, Homer, 50, learned he had Creutzfeldt-Jakob disease, a rare brain-wasting disorder sometimes likened to mad cow disease. A cure has not been found.

Similar lessons, under different circumstances, were learned last year when technological search-and-rescue operations, using the power of distributed computing, came up empty in the hunt for a computer scientist lost at sea and for an adventurer whose plane had disappeared in the desert.

Yet instead of discouraging the people involved, these failures have nourished an even stronger belief that if the person in front of them cannot be cured or helped, then the technology developed or refined in the effort will at least help a much broader section of society.

Silicon Valley has a long history of optimism -- a belief that its technology can defy the laws of nature. The inventor Ray Kurzweil has said that people will be able to reverse the effects of disease and aging, leading to a promise of immortality.

"This shows the strengths and weaknesses of Silicon Valley," Keen said. "The optimism, the can-do, the vitality are the classic American qualities that have helped Silicon Valley achieve so much. But there’s also an absurd side. People there are indulgent, they lack perspective, and they have a belief that they can do anything. There are some things you can’t do."

"We live in Silicon Valley," she said. "The impossible happens all the time, and in the grand scheme of things, usually doesn’t take very long."

Keeping an eye on a brighter future, even as the bubbles burst or hope fades, was certainly true in two other instances when Silicon Valley rallied to use technology to search for the missing. James Gray, a researcher with Microsoft and renowned computer scientist, disappeared in January 2007 when he sailed from San Francisco to scatter his mother’s ashes at sea. In September, the adventurer Steve Fossett was piloting a small plane over a Nevada desert when he vanished.

While both events led to full-scale search-and-rescue operations, they also provided showcases for Microsoft and Google, as well as for Amazon’s "Mechanical Turk" technology. The idea behind the Mechanical Turk program is that human beings perform some tasks better than computers, like identifying objects in photographs.