Wired article gets basic probability wrong
It may seem like a small thing, but if you write for one of America’s premier tech magazines, you have a responsibility to understand how probability works.
Earlier today Wired published an article on how a new Quantum theory could explain the flow of time. Great stuff, and really interesting. Definitely give it a read.
But in the course of the article the writer makes a mistake that I see more often than I’d like. Here’s the graf, and I have boldfaced the problem section.
Consequently, a tepid cup of coffee does not spontaneously warm up. In principle, as the pure state of the room evolves, the coffee could suddenly become unmixed from the air and enter a pure state of its own. But there are so many more mixed states than pure states available to the coffee that this practically never happens — one would have to outlive the universe to witness it.
While one might theoretically live to the age of several universes without seeing this phenomenon, the writer is technically wrong, and badly.
Let’s say the lifetime of the universe is x and the probability of event y happening – in this case, the overly rambunctious cuppa joe – is once every 2x. This does not mean that “one would have to outlive the universe to witness it.” The odds of y occurring are equal at every moment along that 2x timeline – that is, roughly stated, the odds are one in x right now and they’re one in x exactly a billion years from now.
The writer seems to think that if y happens once every billion years, that must mean it has to happen in a billion years. Well, it might, but the chances of it doing so are no different than the chances of it happening next Thursday.
This is how probability works and it isn’t complicated – we learned this in grade school, and basic probability doesn’t change just because the numbers get really big. While this little error isn’t a huge deal in the grand scheme of things – the article is right in asserting that your coffee is probably going to stay in the cup until you drink it – I don’t think I’m out of line in wanting places like Wired to be getting the fundamentals right.