### "Less Than 1.5 Tons"

Computers in the future may weigh no more than 1.5 tons.- Popular Mechanics, 1949

The above is one of my favorite old wrong predictions. The history of computer science is full of such howlers, and I often use them in my classroom. For instance, when I explain to my students just why the IPv6 address space is so gosh darned big, I explain that since history is littered with predictions that underestimated both the capacity and demand for computing, it makes sense to err on the side of abundance. I share a few of these predictions, and the Popular Mechanics quote usually makes the cut.

Of course the prediction is, strictly speaking, true. It's funny because it ended up being way too cautious.

I've discovered that I can use that aspect of the prediction in explaining other concepts. For instance, today in my algorithms class I talked about Big-O notation. I'll spare my lay readers a formal definition of Big-O. It suffices here to say that a function f(n) is O(g(n)) if, for all practical purposes f(n) is no bigger than g(n).

For example, it's true that

n+100 is O(n).

This is provable using the mathematical definition, but common sense can tell you it's true. If n is say, 100000, the difference between n+100 and n is negligible.

Big-O has it's limitations. To illustrate these limitations, I point out to the class that

n is O(2^{n})

No one would argue against the assertion that for all practical purposes, and lots of impractical ones, n is no bigger than 2^{n}.

Of course this assertion, while true, is not very meaningful. Kind of like asserting that modern computers weigh less than 1.5 tons. And that's when I share the Popular Mechanics quote. Then I segue into an introduction of Theta notation, which I'll resist doing here. I don't want any more eyes to glaze over.

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