Orders of magnitude

Orders of magnitude(gabrielweinberg.com)

72 points by gwil 13 years ago | 13 comments

georgemcbay 13 years ago |

"When people say they're looking to grow by an order of magnitude they usually mean ten times."

I think this gives "people" too much credit.

In my experience when people say they're looking to grow by an order of magnitude, they don't know that has a very specific meaning and they're just talking about getting bigger by some vague undefined number that could be anything from about two times on up.

vegashacker 13 years ago | |

Not saying you're wrong, but in my experience I only hear this phrase from technical people, and my understanding is they always mean base 10. Which was surprising to me cause in my CS education I was basically taught to forget base 10 and only think in 2s).

ISL 13 years ago | | |

In physics and astronomy, 10 is the dominant logarithmic base. It's my impression that it's also the case in engineering circles.

An important upshot of the article is really the idea that you should think logarithmically about scaling. It's a scale-independent way to think. It's an easy way to get a website that gets 10 hits/day on the same plot as one that gets 10^9 hits/day.

An example is here: http://measuredmass.wordpress.com/2012/10/20/more-hn-numbers...

georgemcbay 13 years ago | | |

I've heard it quite a bit from people who are exposed to technology regularly but not explicitly technical. For example, product managers that didn't come from the engineering side.

I don't even really blame them, because I'm sure they simply hear the phrase a few times from technical people without explicit explanation of meaning and then adopt it themselves to mean "any big growth" which is a fairly reasonable assumption contextually, prior to someone pointing out to them that it means something more specific.

FWIW, in my CS education (both at school and self-directed via books, system manuals and such) I was taught to worry about whatever base is relevant to my current data and level of abstraction to the machine. 2, 10, 16 and even 8 were the usual culprits, but certainly nobody tried to teach me to forget about the ones other than 2. I worry about base 2 far less than base 10 in my day to day code despite the fact that I'm old and know assembly (6502, 68k, x86, MIPS, ARM) and still do a lot of bit-twiddling.

shalmanese 13 years ago | | |

That's because we already have a word for a base two growth: doublings. Being engineers and having two words, it's best to be maximally precise by assigning each a distinct, unambiguous meaning.

ChuckMcM 13 years ago | |

Well for marketing people it can mean '2' and for technical people it does often mean '10'. But it gets also lumped into people who use the term "exponential" growth.

As Gabe points out, decimal orders of magnitude are good sign posts because they often separate the space into meaningful chunks, what ever it is.

Think about your own earning potential, the differences between earning $100/month, $1000/month, $10,000/month and $100,000 a month. Those are very different places to be.

foz 13 years ago |

Growing infrastructure by orders of magnitude makes more sense to me, and is often how I hear the term used. I was at a conference in Berlin a few years ago and Joyent gave a talk about scaling which touched on this very topic.

The argument given was that you should plan infrastructure expansion with orders of magnitude. For example, increasing disk space from 10tb to 100tb. Or replacing a network switch with one that has 10x traffic capacity. The reasoning goes that the time spent engineering the expansion is a better investment at 10x, rather than having to increase infrastructure incrementally.

zmitri 13 years ago |

My company recently grew by 1000% in less than 24 hours with regards to user base (and even higher with regards to content created and user interactions). Same product, same team, but perception of our company to outsiders has changed entirely. On the inside the only difference has been stepping up our support game, and having the opportunity to try things out on a much large scale -- plus server expenses...

bialecki 13 years ago |

Tangent: One of my favorite classes in college was one that taught physics only at the level of order of magnitudes. It'd tackle questions like: Why is nuclear power more efficient than coal? How much more efficient? and then sought to answer those questions in terms of simple math and fundamental constants.

Considering problems/situations from an orders of magnitude point of view is an under appreciated approach IMO.

Of course the orders of magnitude argument get abused by marketing people (but what doesn't?). That aside, they're extremely valuable for personal or team understanding of the problems and goals.

fatalerrorx3 13 years ago |

I liked the commenter on the article that suggested using fold as a unit of measure. Grow 2 fold, etc. That's how I think of things. Sometimes if you think about growing in orders of magnitude you end up with too high of an expectation. If you're just simply looking to double or triple, you're more likely to reach the mark, and even exceed it, which is probably better for morale.

martinced 13 years ago |

I've heard "10x" (pronounced "ten ex") very often and I think it's less confusing than "one order of magnitude".

mcherm 13 years ago | |

But it fails if you are talking about any changes greater than 1 order of magnitude. For instance, from the article: "we're still about one order of magnitude from making a measurable dent in the search market and two from a major one". The terminology of "orders of magnitude" lets you talk in terms of the logarithm of the value rather than the value itself, and for certain kinds of thinking this is useful. The terminology "10x" does not help do this (or at least I have never seen it used that way).

bigiain 13 years ago | | |

This is exactly the same "trick" as plotting graphs on a logarithmic scale - it gives you a different point of view on the data which sometimes (but certainly not always) reveals useful insights.

I wonder if there are interesting scaling/growth/startup point of view changes that are equivalent to other data visualization transformations? Is there a growth-data version of changing from cartesian to polar coordinates perhaps?