There are many reasons why companies go thumbs-down on good ideas. Some of those reasons seem reasonable: The idea doesn't align with the current mission, or it requires too much capital or manpower or too much of management's focus. Then there are the cases when the big bosses were perhaps not paying enough attention.

Consider Thomas Edison, who briefly employed in his lab a fellow named Nikola Tesla. Tesla had come up with an induction motor for alternating current and suggested to Edison that it was a better source of electricity than Edison's own direct-current dynamos. "Spare me that nonsense," Edison is said to have told the underling, in one of the most luminous miscalculations in business history. Let's revel in a few more.

Apple Tunes In

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In the late 1990s, as mp3 players were beginning to bloom, an engineer named Tony Fadell had an idea for a line of digital music players. Fadell had worked for big consumer electronics firms, but had been kicking around Silicon Valley for a decade trying to develop his own devices, with limited success. He took his player to one of the digital music leaders at the time, RealNetworks, which was selling music over a network and balked at creating a separate personal music device. Nor were consumer electronics firms like Philips and Sony all that interested.

Finally, he found some guy named Steve Jobs, whose computer company was desperate to get mp3 players hooked up to its iTunes app. Fadell figured he'd do some consulting to keep his own firm alive. He figured wrong. Jobs informed him: You're joining Apple and building this in a year. Fadell, like many others, apparently found Jobs as irresistible as he was irritating. Five years later, Apple sold its 100 millionth iPod. Alas, after a 20-year run the iPod will join the Walkman in the tech museum--Apple recently announced it will stop making the device.

DuPont Lets One Slip Away

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In the late 1950s, a chemical engineer named Wilbert "Bill" Gore was getting the warm fuzzies about a compound he was working with called poly­tetrafluoroethylene. This probably didn't make him popular at cocktail parties; it would, however, make him a whole lot of money.

Gore thought the compound, which DuPont called Teflon, had potential beyond what his employer had in mind--a nonstick coating. So he and his wife, Vieve, struck out on their own and founded W.L. Gore & Associates in 1958, in their basement in Newark, Delaware. PTFE was highly resistant to heat, making it perfect for electrical insulation--and just in time for the emerging space age and com­puter age, which craved electrical effi­ciency; it was applicable to medical implants as well.

But that's not why you know their surname today. In 1969, after their son Bob created a stretched version, called expanded PTFE, the company found a market for a breathable, waterproof fabric they called Gore-Tex--which would make winter weather much more bearable for all of us.

Ford Versus Lincoln

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This is a tale of two Henrys. Henry Leland was a genius machinist, a gunsmith, and a supplier to early auto companies who could make parts consistently within tolerances (0.001 inch) unheard of at the time. He envisioned a high-end auto that would run like a dream. Henry Ford, on the other hand, was a design innovator but, at the time, lousy at manufacturing. And at the turn of the past cen­tury, in his second company, Ford couldn't produce the low-end, roughly $1,000 models he was hired to make--and had no interest in fancy, $3,000 cars.

So, in 1902, Leland was brought in by the investors who controlled the Henry Ford Company to fix things. Ford, no longer running Ford, walked. Leland began focusing on high-end models and renamed the company Cadillac. Leland later sold Cadillac to GM, regretted it, and revived the idea for a standalone luxury car brand in 1917. Being an admirer of a certain U.S. president, his new luxe car was named Lincoln. Ford would have the last laugh, though, buying Lincoln out of bankruptcy in 1922. This year, Lincoln celebrates its 100th anniversary, the legacy of two great entrepreneurs who didn't always get everything right.

IBM Opens the Window for Microsoft

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The question was: "Do you want to buy it or do you want me to buy it?" The answer would change computing. The speaker was IBM exec Jack Sams, who needed an operating system for the IBM Personal Computer 5150. The machine was being built with open architecture--unheard of at IBM--when introduced in 1981. The question was posed to 24-year-old Bill Gates, whose startup, Microsoft, didn't actually have an OS, but had located one called QDOS (for Quick and Dirty Operating System) from a local firm. Given the opportunity to buy QDOS or rent it, IBM did the latter.

Gates shrewdly negotiated the right to license QDOS--which became MS-DOS, and later part of Windows--to all comers. And they came. The rush of third-party computer makers that followed the PC's introduction in 1981-- including Dell, Compaq, and HP--would turn Microsoft into the biggest software maker on the planet and eventually force IBM out of the PC market. Sams's question seems stupid now, but would have seemed less so for a company racing for a market that was getting away. Maybe IBM should have asked one of its mainframes first.