Net bottlenecks: an element of truth behind a game-show door

Net bottlenecks: an element of truth behind a game-show door

I don't want to turn this into IDG's "Puzzle Corner", but I hereby suspend my campaign to break the Internet's local bandwidth bottleneck. Instead, let's return to the now infamous Monty Hall Paradox.

Last week, while touting some Internet search software, I passed along the paradox. Since then, I've been inundated by readers - not about, not about Microsoft's brazen attempt to acquire Firefly, not about bandwidth bottlenecks, but about the Monty Hall Paradox.

Many of you wrote to upbraid me about the paradox being old hat. The fact that I received hundreds of e-mails proposing solutions is proof the paradox has many miles left on it.

Many readers were, and some still are, certain that their incorrect solutions to the paradox are correct. About half had solutions to paradoxes other than the one I posed, which is fair enough, and the other half were simply wrong. It's fun trying to convince the wrong ones - way more fun than convincing Windows users that Mac-intosh is better, or token ring users that Ethernet is better.

Again, imagine I'm Monty Hall, a game-show host with three doors behind which are two goats and a car - my irresistible all-wheel-drive Volvo station wagon.

So, I ask you to choose a door but not to open it yet. Knowing what's behind the doors and trying to boost your chances, I open one of the two unchosen doors and show you a goat. Then, I offer you what's behind the door you've chosen, or what's behind the unchosen unopened door.

So, do you take what's behind your chosen door, switch to the unchosen unopened door, or doesn't it matter?

Pause here to think about it.

Answer: by showing you the goat, Monty has doubled your chances of winning the car to two-thirds, but only if you switch to the unchosen unopened door.

Dozens of readers have written that it cannot matter if you switch, that your chances of winning the car are 50-50 either way. They seem prepared to cancel their subscriptions unless I capitulate. They are . . . sorry . . . wrong.

The car is behind the chosen door with a probability of one-third. Because Monty can open a door with a goat every time, this adds no new information about the chosen door, so the chances of it having the car are still one out of three. But, because the car has to be behind one of the two unopened doors, the chance of the unchosen unopened door hiding the car is now two-thirds, because one minus one-third equals two-thirds.

If you disagree, take three playing cards and play the game. Don't write to disagree unless you have done this. It won't take long to see that switching doubles your chances. And you'll see the most difficult concept in statistical decision theory: good decisions with bad outcomes.

Measuring the cost vs value of information in making decisions under uncertainty is an important tool in life. For example, the invention of Ethernet almost 25 years ago on May 22, 1973, was built upon the Alohanet's idea of using randomness to save the wasted time and complexity of knowing exactly whose turn it is to transmit in a shared communication medium.

Which brings me to an even better puzzle. It's about the communication media among our homes, offices and the Internet.

Again, how are we going to break the local bandwidth bottleneck?

Imagine the 100-year-old Soviet-style system of reg-ulated telecommunication monopolies is an empty wine bottle. Imagine the Internet is its cork. And imagine that someone has pushed the cork inside the bottle.

How do you get it out?

Turns out that pushing the cork into the bottle - be careful - is more difficult than getting it out.

I've been getting the cork out of the bottle in front of amazed audiences for almost a decade. If you haven't seen this, have fun racking your brain. This is a better puzzle than the Monty Hall Paradox.

The solution does not require such extraordinary efforts as heating the bottle or dissolving the cork with sulfuric acid.

Nor is it a trick. The solution is a straightforward application of physics.

All you need is what's on the table after dinner at (hint) a fine restaurant. Getting the cork out of the bottle will give you confidence that we can get the Internet out of the telopolies. Freeing the Internet from the telopolies may seem like an impossible task. But we shouldn't have to break the telopolies to get the Internet out of the bottle.

Technology pundit Bob Metcalfe invented Ethernet in 1973 and founded 3Com in 1979, and today he specialises in the Internet. E-mail:

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