My startup, Socialize, is a part of a great media accelerator sponsored byTurner Broadcasting called MediaCamp.

Turner has created MediaCamp specifically because it believes that it needs to be proactive in thinking about what disruptive technologies could affect its legacy line of businesses. It's definitely forward thinking of Turner to dedicate the resources necessary to fund an accelerator program, especially when its parent company, TimeWarner, made $29 billion in revenue and almost $3 billion in net income last year.

In fact, media companies face the classic Innovator's Dilemma: It's hard (impossible?) to dedicate meaningful resources and focus to technologies that aren't generating billions of dollars in revenue and income when the current business is a cash cow. Obviously, startups don't have this problem.

We've been having a spirited debate about the Innovator's Dilemma at Media Camp, and how Turner has been addressing it. But here's the thing I can't quite rationalize and understand: What's a meaningful disruption timeframe for a media company to plan around? And specifically, how does any company predict that timeframe to take meaningful action on it when they don't know what disruptive adoption curves might look like?

The reason I'm asking this question is because of graphs like this, of world population:

If, around 1,000 AD, you were to try to predict the world's population in the year 2000 by looking at historical growth, would you have really thought that it could reach 6 billion just 1,000 years later? Any reasonable person might've said that it could double, from 400 million to 800 million. But in fact, while it took humans 50,000 years to get to 1 billion (by 1830), we doubled to 2 billion in just 100 years (1930) and doubled again to 4 billion just 45 years after that, by 1975.

So what kind of trend is the adoption of technology on? Is it an exponential (or maybe logarithmic) curve, or a more linear curve? Do large media companies like Turner have anything to be worried about in the next six months? Twelve months? Five years? Do they have to invest heavily in new distribution channels (like mobile-first) right now at the expense of their cash cow? Or can they take their time figuring out what their business might look like in the future?

One of the MediaCamp startups ran across this GigaOm article about the Olympics recently, which said that the Xfinity customers who viewed the games online authenticated on an average of 2.4 devices. That's one data point about the adoption of new distribution channels. Here's another: Traditional newspaper media's advertising revenue, adjusted for inflation:

That graph is from Professor Mark Perry's blog. Here's a great quote from that post, "It took 50 years to go from about $20 billion in annual newspaper ad revenue in 1950 (adjusted for inflation) to $63.5 billion in 2000, and then only 11 years to go from $63.5 billion back to about $20 billion in 2011."

And to hear a futurist like Ray Kurzweil talk about technology (is he crazy, or a genius?), the pace of technology will only quicken. Here's his graph:

In fact, Kurzweil has written a lot about the law of accelerating returns. This Forbes article interviewed Kurzweil and wrote:

"Technology progresses at an exponential rate. Humans, having evolved to hunt game and avoid predators, are designed to think linearly.

School of Tech: Kurzweil addresses the Singularity University Executive Program fall 2011 class via telepresence. If business leaders are to stay ahead of the curve, they need to internalize the confounding power of exponential progressions.

“It took the printing press 400 years to reach a large audience,” he says. “It took the telephone 50 years, the mobile phone seven years, and social networks only three.” The pace of innovation will only continue to accelerate, he says, because exponential evolution is built into the very nature of technology."

And so that's what I'm really wondering: If we as humans are designed to think linearly, but technology is progressing exponentially, then how much time do companies that are dependent on technology have to re-work their business models?

I don't know the answer, but I'd love to hear your opinions. I'm mostly looking for really pragmatic points of view: Are we talking 6 months or 10 years in terms of timeframe? And whichever you believe it is, how are you so sure?