Order Of Magnitude Improvement: 3.16x

Disclaimer: Largely waffle.

A common principle in tech is that changes are only adopted on a grand scale when there is an order-of-magnitude improvement. That is, it’s not good enough to add a couple of new features to make the product 10% better; that will only bring a niche audience. You have to make it radically, qualitatively, better.

It’s easy to see examples of this: Google’s search was blatantly more useful to anyone acquainted with Alta Vista and friends; windowed UIs were blatantly more friendly to casual users than a text terminal, etc.

An interesting thing I wanted to mention is “how much is an order of magnitude improvement”? Well, the real answer is, it doesn’t really matter. It’s a principle, and it’s more about a disruptive, qualitatively different change, than something you can measure.

But that said, it’s often equated with a 10x improvement. That’s what English thinks anyway.

But actually, I always think of it as a 3.16x improvement. That is, the square root of 10. The reason I say that is that “orders of magnitude” implies a discrete scale, and jumping to the “next” order of magnitude means going 1 up. So you might say it’s anything more than 5x. But order of magnitude changes happen exponentially by definition, so if you can improve something by 3.16, you’re halfway there. (It would be halfway on a log-log chart.)

This is all very silly calculation, because like I say, the whole concept is wishy-washy. What are we even measuring anyway? Utility? Something else? And if someone came up with a 3.16x innovation as soon as the last one happened, then by this definition we’ve jumped only 10x but two orders of magnitude. Just thought I’d mention it anyway.

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