Peter Norvig is wrong. He claims that "Any technology that surpasses 50% penetration will never double again (in any number of months)," but the raw foodism reached 100% penetration millions of years ago, fell off sharply after the discovery of fire, and has doubled several times in the past couple of decades.

It depends on the unit that is doubling. From how I read the claim, Peter Norvig is using penetration percentage as such unit. Once you reach 50%, doubling means 100%, which is very unlikely since it is almost certain that somewhere in the world there is someone that does not use certain technology (meaning writing, clothing, radio, cellphones or whatever...). In short: the claim is just a clever joke :)

Yes, we got the joke. But suppose in 50 years we come up with a cool technology that is so good it drives cell phone penetration down to 1% (ie young people growing up then never buy cell phones). Then cell phones can make a comeback and double to 2%. And double again to 4%, etc.

But then, as far as business is concerned, hasn't it already been shown that the cool new technology was a replacement for cell phones? Assuming CoolTech isn't subsequently found to cause the sudden onset of rickets in its users (or whatever), the market for [stuff that stuff that satisfies the need for cell phones] is still saturated. The market won't start roaring again the way it was; cell phones can only cannibalize CoolTech's portion of the market.

The latent Apple analogy is making me uncomfortable now, so I'll stop here.

If my_var=current_penetration(Time.now) is at 55%, you'll never double my_var. You'll only be able to double something else. You're trying to use the term "current penetration" at two different times to get different results to change what was supposed to double.

One could argue, that "raw foodism" isn't really technology. In your example the technology would be "fire" or "cooking".

But isn't it the population that's 100%, not how much food each gets?

You missed cperciva's point.

Any technology that passes 50% penetration can indeed double again if in the future it goes below 50%.

Any technology that surpasses 33.3333% penetration will never tripple again (in any number of months).

I know a few people that carry two cell phones... It's a technicality but you can have more than 100% market penetration. Does that count?

"Luxembourg racked up 158 mobile subscriptions per 100 people, closely followed by Lithuania (127) and Italy (122)." Source: http://news.bbc.co.uk/1/hi/technology/7116599.stm

The article's not that long! Here's the second half:

To be clear, it all depends on what you count. If you're counting units sold, you can double your count by selling everyone 1 unit, then 2, then 4, etc. (In Finland I understand that cell phone usage is above 1 per capita, but still growing.) If you're counting the total number of households that own the product, you can double your count by doubling the population, or by convincing everyone to divorce and become two households. But if you're counting percentage of people (or households), there's just no more doubling after you pass 50%.

Right, I actually did read that far. I'm just trying to illustrate unless he defines it in a way the excludes cases like that, I'm not sure you can call it a law...a generalization with exceptions, maybe. As his law is written, the cell phone example kinda disproves it. I think the problem is that paragraph you quoted can't easily be reduced to language that fits in that blue box. Just playing devil's advocate...

A worthy aim, but the whole idea of the "law" is Norvig's implied definition of what market penetration means. If 75% of the people in the world have never owned a smartphone, then doubling the number of smartphone owners is a big accomplishment, and doubling it again means you've introduced 100% of the world to smartphones. The number of phones you've sold is not the concern, it's the proportion of people whose needs have been satisfied. (At least, that's what Norvig cares about.)

Without going down the route of identifying a new market, once more than 50% of the population in question has had its needs met, that market is mature -- its growth has reached a point of inflection, and no amount of pushing on the part of the existing industry will make the product continue to change lives at the rate it used to. The opportunity that was there has already been identified and seized.

Now, if everyone in Finland has a personal cell phone, and another 25% also keep a separate cell phone for business use, it's suddenly worth redefining what the market is. Should the industry try to double market penetration of business-only cell phones, now? Why isn't one phone enough, and could a new product meet these separate needs better? Or alternately, some people keep two phones with different plans, and switch between them to keep the total bill down -- breaking that confusopoly is another business opportunity worth identifying, but tracking units/plans sold instead of actual market penetration by population will mask it.

This law only holds true for very broad catagories of technologies e.g. use of fire, hydraulics, electricity, radio, genetics, atomic power, nanotech, etc.

If you try to apply the it to something more narrow you run into the problem that many specific technologies come in and out of favor depending on market conditions.