An anonymous source claims Twitter has just 200,000 "total active users" per week, according to TechCrunch's Michael Arrington. Or, about the population of Shreveport, Louisiana. That compares with 100,000 active weekly users in January, and 50,000 last April.

Impressive math, isn't it? Kind of like the old Breck shampoo commercials. If you get two friends to start using it, and then they each get two more friends on board, and so on, and so on, and so on, pretty soon the entire country will be happily using it!

Unfortunately for Twitter and its deep-pocketed investors, there are a few problems with this scenario. First, this is a rumor. Second, exponential growth projections -- especially those associated with Internet startups -- have a way of leveling off. Just ask the folks at Linden Lab, whose Second Life service has faltered in terms of growth in hours spent in-world and peak concurrency.

There is also a problem with definitions: What does "active users" mean? And why does Arrington's source claim there are more than one million "total users," while another user claims more than six million Twitter sign-ups?

Whatever the truth is, it's still very apparent that Twitter has a long way to go before it achieves mainstream penetration. Even if that happens, it's not clear how the service will generate serious revenue. Until these issues are addressed, the sky-high valuations of Twitter should be treated with extreme skepticism.

More news, commentary, and predictions from The Industry Standard:

• Opinion: 10 'Net services that will succeed (and 10 that will probably fail)
• Bill Snyder: Twitter: Fanatical users help build the brand, but not revenue