(FORTUNE Magazine) – Niels Bohr, Denmark's father of quantum physics, once confided that the problem he had with a proposed theorem wasn't that it sounded crazy, but that it didn't sound crazy enough. He was right. Back then physics required truly outrageous and counterintuitive insights to make quantum theory work. But it does. And we have the nuclear weaponry and silicon chips to prove it.

Fast-forward from Copenhagen to California: If someone you genuinely respected had told you way back in 1994 that high-tech startups founded by 25-year-olds who gave their products and services away--for free!--would soon attain market caps making them even more valuable than General Motors, would you have thought him "outrageous" and "counterintuitive"? Or would you have thought that he'd lost his mind? Now, perhaps we're all living through "tulip-bulbs.com" turbulence, but an equally probable scenario is that we've entered an era in which weirdness gets richly rewarded--if you can just package it right. Just ask Jerry Springer or the World Wrestling Federation.

Value-added outrageousness isn't easy in today's economy. Just as pop culture becomes more outrageous in its relentless bid to arouse a blase audience--Tonight!!! When Animals Attack America's Dumbest Criminals During High-Speed Police Chases!!!--business culture, too, is grasping for outrageousness as a mechanism to motivate and innovate. To get GE accelerating into cyberspace faster, Jack Welch now insists that each division create its own "destroyyourbusiness.com" e-commerce officer. In other words, GE's boss is asking his brightest Netheads to figure out how to use the Web to annihilate the company's mainstream businesses. Welch is globally celebrated for this "boldness." Yes, I think that's terrific, but it's still weird. Next thing you know, McKinsey will seek competitive advantage by paying its clients.

Ideas that initially seem radical and provocative aren't. A column I wrote predicting that online competency testing would eventually converge with online job hunting drew criticism from within FORTUNE as unduly speculative. Not seven weeks later, online job-search firms were trumpeting online testing in their marketing campaigns. I was embarrassed; a clever innovation I thought might be a year away was, in fact, barely two months away. I wasn't being nearly outrageous enough. Being outrageous--thinking weird--is becoming the conventional management wisdom.

But why not? In today's competitive environments, the urge to merge is outstripped only by the desire to differentiate. Where marketplaces become too crowded, weirdness and outrageousness become tools for cutting through the clutter. Who notices--or cares about--incremental innovations? You want the kind of differentiation that commands attention. You want to, if you'll excuse the expression, dramatically differentiate how you differentiate.

What's so different, thanks in part to the Web, is that the marginal costs of differentiation have shrunk. The economic barriers to business weirdness are collapsing. Much as cheap camcorders enable new genres of video weirdness, the Web enables weird new discount genres of business interaction. With the click of a mouse, companies can instantly charge a premium for what they once gave away, and give away what they once charged a premium for.

So where Peter Drucker got yesterday's mainstream managers asking themselves, "What business are we in?" today's outrageousness-intensive organizations now constantly ask themselves, "What business model are we in?" Technology has made business models as versatile and flexible as Silly Putty. Alas, that same technology makes it ever easier for competitors to become "fast followers" and imitate and emulate their way to success. The mean-time-to-innovation commoditization can be measured in days and weeks rather than months and years. Differentiation itself is becoming a commodity, and that's what makes outrageousness so alluring. E-business Balkanization becomes the rule. So this conspiracy of market forces is now driving entrepreneurs and established firms alike to opt for weirdness.

The catch is that leading or managing a firm in which people conform by thinking weird is going to prove quite the challenge. Neither Harvard nor Stanford MBAs are trained to manage outrageousness as a core competence. We'll see what the attrition rate looks like at GE in a couple of years. Remember, being conventionally weird won't be enough; there will be an ever-rising spiral of weirdness and outrageousness as ambitious individuals in the enterprise battle to own the soul of a new business model.

A decade ago people's ideas were rejected by FORTUNE 1,000 firms because they seemed too crazy; tomorrow there will be unhappy people whose ideas were rejected by FORTUNE 1,000 firms because their innovative ideas weren't crazy enough. Is that progress? Manage well, and insanity will bubble up from within. Manage poorly, and some crazy startup will Amazon you alive.

MICHAEL SCHRAGE is a research associate with the MIT Media Lab and author of Serious Play: How the World's Best Companies Simulate to Innovate (HBS Press). He may be reached at michael_schrage@fortunemail.com.