Upper bounds

Sometimes, our environment limits us. Sometimes our physical capabilities limit us. It's good to know which, because a limit in one can reduce the usefulness of plentitude in the other.

For example, our visual system limits our ability to channel surf on a cable network. These limits create an upper bound on the number of channels that we can use on a cable network.

Why? Because we can surf only so fast, and therefore surf a finite number of stations in a given period of time. Let's assume that I can surf from channel to channel, spending one half second on each channel. If I start at channel 2 and work my way upwards, it will take me some amount of time to reach the end and "wrap" back to channel 2. With twenty channels, it takes ten seconds. With two hundred channels, almost two minutes. With a thousand channels, about twenty minutes.

If we had ten thousand channels, it would take the better part of a day to surf them. By the time we decided on a channel, the program would be long over.

Here's the interesting observation: With a thousand channels, by the time one surfs the entire collection, the original program (if a thirty-minute show) is more than half over. We have spent too much time surfing and not enough time watching. ur physical capabilities (the ability to process a video signal and decide to stay or go) creates an upper limit to the number of channels.

That limit holds for the strategy of surfing. If we use a different strategy (perhaps looking for specific programs or types of programs, or using an index, or relying on a TIVO-like prediction system) then we can use a larger cable network.

This effect comes in to play with a lot of things, not just cable television. The web is a large collection of channels. The applications on the Apple iTunes store is a large collection. Books in a bookstore. Videos on Youtube (or Hulu).

Books and web videos don't have the time-limit of television programs, yet we all have finite time, finite resources to spend on viewing, listening, processing, or reading. We are all constrained to make choices in finite time.

The trick is knowing our limits.